# PSP$/$IS$\odot$IS Observation of a Solar Energetic Particle Event Associated
With a Streamer Blowout Coronal Mass Ejection During Encounter 6

T. Getachew Department of Astrophysical Sciences, Princeton University,
Princeton, NJ 08544, USA  Heliophysics Science Division, NASA Goddard Space
Flight Center, Greenbelt, MD 20771, USA  Physics Department, The Catholic
University of America, Washington, DC 20064, USA  D. J. McComas Department of
Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA  C. J.
Joyce University of New Hampshire, Durham, NH 03824, USA  E. Palmerio Space
Sciences Laboratory, University of California–Berkeley, Berkeley, CA 94720,
USA  CPAESS, University Corporation for Atmospheric Research, Boulder, CO
80301, USA  E. R. Christian Heliophysics Science Division, NASA Goddard Space
Flight Center, Greenbelt, MD 20771, USA  C. M. S. Cohen California Institute
of Technology, Pasadena, CA 91125, USA  M. I. Desai Southwest Research
Institute, San Antonio, TX 78228, USA  University of Texas at San Antonio, San
Antonio, TX 78249, USA  J. Giacalone Lunar & Planetary Laboratory, University
of Arizona, Tucson, AZ 85721, USA  M. E. Hill Johns Hopkins University Applied
Physics Laboratory, Laurel, MD 20723, USA  W. H. Matthaeus University of
Delaware, Newark, DE 19716, USA  R. L. McNutt Heliophysics Science Division,
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  D. G. Mitchell
Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA  J.
G. Mitchell Heliophysics Science Division, NASA Goddard Space Flight Center,
Greenbelt, MD 20771, USA  Department of Physics, George Washington University,
Washington, DC 20052, USA  J. S. Rankin Department of Astrophysical Sciences,
Princeton University, Princeton, NJ 08544, USA  E. C. Roelof Johns Hopkins
University Applied Physics Laboratory, Laurel, MD 20723, USA  N. A. Schwadron
Department of Astrophysical Sciences, Princeton University, Princeton, NJ
08544, USA  University of New Hampshire, Durham, NH 03824, USA  J. R. Szalay
Department of Astrophysical Sciences, Princeton University, Princeton, NJ
08544, USA  G. P. Zank Department of Space Science, The University of Alabama
in Huntsville, Huntsville, AL 35899, USA  L.-L. Zhao Department of Space
Science, The University of Alabama in Huntsville, Huntsville, AL 35899, USA
B. J. Lynch Space Sciences Laboratory, University of California–Berkeley,
Berkeley, CA 94720, USA  T. D. Phan Space Sciences Laboratory, University of
California–Berkeley, Berkeley, CA 94720, USA  S. D. Bale Space Sciences
Laboratory, University of California–Berkeley, Berkeley, CA 94720, USA
Physics Department, University of California–Berkeley, Berkeley, CA 94720, USA
The Blackett Laboratory, Imperial College London, SW7 2AZ London, UK  P. L.
Whittlesey Space Sciences Laboratory, University of California–Berkeley,
Berkeley, CA 94720, USA  J. C. Kasper BWX Technologies Inc., Washington, DC
20002, USA  Department of Climate and Space Sciences and Engineering,
University of Michigan, Ann Arbor, MI 48109, USA

###### Abstract

In this paper we examine a low-energy SEP event observed by IS$\odot$IS’s
Energetic Particle Instrument-Low (EPI-Lo) inside 0.18 AU on September 30,
2020. This small SEP event has a very interesting time profile and ion
composition. Our results show that the maximum energy and peak in intensity is
observed mainly along the open radial magnetic field. The event shows velocity
dispersion, and strong particle anisotropies are observed throughout the event
showing that more particles are streaming outward from the Sun. We do not see
a shock in the in-situ plasma or magnetic field data throughout the event.
Heavy ions, such as O and Fe were detected in addition to protons and 4He, but
without significant enhancements in 3He or energetic electrons. Our analysis
shows that this event is associated with a slow streamer-blowout coronal mass
ejection (SBO-CME) and the signatures of this small CME event are consistent
with those typical of larger CME events. The time–intensity profile of this
event shows that PSP encountered the western flank of the SBO-CME. The
anisotropic and dispersive nature of this event in a shockless local plasma
give indications that these particles are most likely accelerated remotely
near the Sun by a weak shock or compression wave ahead of the SBO-CME. This
event may represent direct observations of the source of low-energy SEP seed
particle population.

##  1 Introduction

Solar energetic particles (SEPs) in the heliosphere are accelerated from a few
keV up to GeV energies by at least two mechanisms, namely reconnection (e.g.,
associated with solar flares) and coronal mass ejection (CME)-driven shocks.
Particle populations associated with flares are known as impulsive SEP events,
while particle populations accelerated by near-Sun CME-shocks are termed as
gradual SEP events, and those associated with local CME-shocks are known as
energetic storm particle (ESP) events (for reviews, see e.g., Desai &
Giacalone, 2016; Vainio & Afanasiev, 2018). The characteristics of impulsive
and gradual SEP events at $\sim$1 AU can be found elsewhere (for reviews, see
e.g., Reames, 1999; Desai & Giacalone, 2016; Vainio & Afanasiev, 2018) but, to
summarize, impulsive events are usually less intense, more prompt and shorter-
lived SEP fluxes than gradual events. Impulsive SEP events are typically
electron rich, show enhancements in 3He/4He up to about 1000 times greater
than coronal values, are associated with type III radio bursts, and have high
charge states of heavy ions (for reviews, see e.g., Reames, 1999; Mason, 2007;
Desai & Giacalone, 2016; Vainio & Afanasiev, 2018; Bučík, 2020). Gradual SEP
events are associated with CMEs and CME-driven shocks and are often
accompanied by type II radio bursts. They are more intense than impulsive
events and last longer, and their composition is similar to that of the solar
corona.

The most extensive and detailed observations of SEPs have been made from
spacecraft near 1 AU. Because of their low intensities and large observation
distances (1 AU and beyond), the energetic particle environment of the quiet
Sun, which is crucial for our understanding of the solar corona and solar
wind, is not well understood. The quiet Sun is a solar region without sunspot-
bearing active regions (Bellot Rubio & Orozco Suárez, 2019) and includes solar
features at granular (smallest so far resolvable magnetic features by current
instruments, Ishikawa et al., 2008) and supergranular scales, which includes
internetwork (Livingston & Harvey, 1975), network field structures (Sheeley,
1967), and other small-scale active regions, such as coronal bright points
(CBPs; Harvey et al., 1975).

The connection between small-scale (quiet-Sun) and large-scale (active-region)
magnetic structures as well as their generation mechanisms are topics of
active research. Quiet-Sun magnetic field elements make a dominant
contribution to the total magnetic field on the solar surface (Getachew et
al., 2019a, b; Mursula et al., 2021), and may store and transfer huge amounts
of energy to the upper atmosphere through different mechanisms. A CME can
erupt from the quiet Sun, where the field is weak and no large filament or
active region needs to be present in the pre-CME corona to initiate an
eruption (e.g., Robbrecht et al., 2009; Podladchikova et al., 2010; Vourlidas
& Webb, 2018).

Streamer-blowout coronal mass ejections (SBO-CMEs) are one of the
manifestations of the quiet-Sun magnetic field. SBO-CMEs are usually slow
(with an average speed of about 390 km/s) and originate in the solar streamer
belt. They are commonly characterized by a gradual swelling of the overlying
streamer over a period of a few hours to a few days, followed by emergence of
a bright and well-structured flux rope, and a generally slow CME from the
streamer that leaves behind a depleted corona (Illing & Hundhausen, 1986;
Sheeley et al., 1982). Although SBO-CMEs show some variation with solar cycle,
they do not follow the sunspot cycle, implying that they are not associated
with active regions but originate in the quiet Sun. Their average duration,
from the start of the streamer swelling to the release of the CME, is about 40
hours (Vourlidas & Webb, 2018). SBO-CMEs are observed only in streamer belts,
and their locations follow the global dipolar field (the tilt of the global
heliospheric current sheet). SBO-CMEs are typically stealth CMEs (see
Robbrecht et al., 2009, who first reported the eruption of a CME that left “no
trace behind”), but in-situ signatures during their passage over a spacecraft
do not differ significantly from those typical of interplanetary CMEs (see
Möstl et al., 2009; Lynch et al., 2010; Nieves-Chinchilla et al., 2011, who
analyzed the Robbrecht et al. event at 1 AU). Lynch et al. (2016) suggested
that SBO-CMEs are formed along the polarity inversion line below the streamer
belt when magnetic energy accumulated by solar differential rotation is
released via reconnection.

As the perihelion of the orbit of the Parker Solar Probe (PSP; Fox et al.,
2016) spacecraft approaches closer and closer to the Sun (perihelion from 35
solar radii ($R_{\odot}$) for the first orbit to $<$10 $R_{\odot}$ for the
final three orbits), we are able to obtain in-situ measurements of solar
output of plasma, energetic particles, and electromagnetic fields of the near-
Sun environment that had not been previously explored (Bale et al., 2019;
Kasper et al., 2019; McComas et al., 2019; Howard et al., 2019). The
Integrated Science Investigation of the Sun (IS$\odot$IS; McComas et al.,
2016) instrument suite, as part of the PSP mission, has observed several
medium-sized SEP events, as well as weak, low-energy SEP events that are
likely not detectable at 1 AU (McComas et al., 2019). We now have growing
evidence that the existence of weak SEP events near the quiet Sun will enable
a new way of interpreting SEP events associated with quiet-Sun magnetic
structures (e.g., McComas et al., 2019; Desai et al., 2020; Giacalone et al.,
2020; Hill et al., 2020; Schwadron et al., 2020; Joyce et al., 2021a, b;
Mitchell et al., 2020a, b). Recently, Joyce et al. (2021b) studied the radial
evolution of energetic particles using PSP/IS$\odot$IS and Solar Terrestrial
Relations Observatory Ahead (STEREO-A; Kaiser et al., 2008) spacecraft data,
and showed that the properties of energetic particles observed at PSP’s orbit
and 1 AU are quite different, indicating that transport effects acted on the
energetic particle populations and affected their properties in transit
between the two spacecraft.

In this paper, we study the weak, low-energy SEP event of September 30, 2020
using PSP data from its sixth solar encounter around perihelion, and
investigate the possible sources associated with this event. Our results show
that the September 30, 2020 SEP event is weak, dispersive, and anisotropic and
is associated with a slow SBO-CME observed by the coronagraph onboard STEREO-A
off the solar east limb. The paper is organized as follows: Section 2 presents
observations based on remote solar data. Section 3 focuses on the
PSP$/$IS$\odot$IS in-situ observations. Finally, we discuss the results and
present our conclusions in Section 4.

##  2 Remote Solar Observations

STEREO-A observed a slow and narrow CME on September 29, 2020 ejected from the
eastern limb of the Sun, i.e., in close proximity to PSP’s longitudinal
location. Figure 1 shows the position of the planets and spacecraft within
${\sim}$1 AU from the Sun together with the weak CME as it passes PSP on
September 30, 2020 at 16:00 UT. The figure is generated using simulation
results from the WSA–ENLIL+Cone model (Odstrcil, 2003; Arge et al., 2004). The
different panels in the figure show results for the solar wind density in the
ecliptic (out to 1 AU and zoomed-in to 0.3 AU), meridional, and radial planes.
CME input parameters for the simulation were obtained via application of the
Graduated Cylindrical Shell (GCS; Thernisien, 2011) model to simultaneous
observations of the eruption in coronagraph data from the COR2 camera part of
the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI;
Howard et al., 2008) on board STEREO-A and the C3 camera part of the Large
Angle Spectroscopic Coronagraph (LASCO; Brueckner et al., 1995) on board the
Solar and Heliospheric Observatory (SOHO; Domingo et al., 1995, located near
Earth). Figure 1 shows that PSP is magnetically connected to the CME, which
grazes the spacecraft from its western flank.

Figure 1: WSA–Enlil+Cone simulation results for the solar wind density on
September 30, 2020 at 16:00 UT.(a) Ecliptic plane, with the outer boundary set
at (left) 1 AU and (right) 0.3 AU. (b) Meridional and (c) radial planes
containing PSP. The radial location of PSP (magenta square) is shown as a
thick black orbit and the CME (black contour) is indicated with a yellow arrow
in panel (a). STEREO-A is marked by a red square. The simulation can be also
found at NASA’s Community Coordinated Modeling Center (CCMC), run id:
Erika_Palmerio_072721_SH_1.

Figure 2 shows STEREO-A COR2 (upper panels) and the corresponding running-
difference (COR2/RD, bottom panels) images taken on September 29, 2020 at
05:06, 10:06, 15:06, and 20:06 UT (from left to right). As can be seen from
Figure 2, at the start of the event, a streamer off the solar eastern limb is
seen to brighten and swell prior to the CME eruption (better seen in the
associated movie). Subsequently, the CME is released slowly into the outer
corona, followed by plasma outflows that also last for many hours. The CME
leaves behind a depleted streamer, which is consistent with the properties of
a typical streamer-blowout type CME (Vourlidas & Webb, 2018; Korreck et al.,
2020; Liewer et al., 2021).

Figure 2: STEREO-A COR2 (upper panels) and COR2/RD (bottom panels) observation
of the SBO-CME focused on the eastern limb on 29 September at 05:06, 10:06,
15:06 and 20:06 UT (from left to right). The animated version of this figure
runs from September 28, 2020 at 12:00 UT to September 30, 2020 at 12:00 UT.
(An animation of this figure is available.)

Figure 3 shows remote-sensing observations in extreme ultra-violet (EUV) of
the September 29, 2020 SBO-CME taken by the SECCHI Extreme UltraViolet Imager
(EUVI) instrument on board the STEREO-A spacecraft in the 171 Å (upper panels)
and 195 Å (bottom panels) channels. As can be seen from Figure 3, a flux rope-
like structure (marked by the white arrows) slowly lifts off the northeastern
limb (better seen in 171 Å) starting on September 27, 2020 around 18:00 UT,
and is seen to deflect gradually towards the equator and the heliospheric
current sheet. This structure moves in a “rolling” fashion (most evident in
the associated movie), which is a common characteristics for slow, quiet-Sun
eruptions during solar minimum (e.g., Panasenco et al., 2013). The CME started
leaving the Sun already on late September 27, 2020, and completely left the
EUVI field of view about 2 days later, which is a typical time-frame for SBO-
CMEs (e.g., Vourlidas & Webb, 2018; Liewer et al., 2021; Palmerio et al.,
2021). We note that the strong southward deflection observed in EUVI imagery
is not reflected in COR2 data (Figure 2), where the CME is seen to propagate
almost radially along the direction of the overlying coronal streamer. This is
consistent with previous findings, which showed that the most dramatic CME
deflections and rotations tend to occur below ${\sim}5\,R_{\odot}$ due to
magnetic forces in the low corona (e.g., Kay & Opher, 2015).

Figure 3: Remote-sensing observations of the September 29, 2020 SBO-CME by the
EUVI telescope on board the STEREO-A spacecraft in the 171 Å (upper panels)
and 195 Å (bottom panels) channels. The off-limb emission has been enhanced
with a radial filter. The white arrows mark the core of the SBO-CME in the
successive panels, showing its southward deflection. A flux rope-like
structure (better seen in the animation) is observed on the northeastern limb
on September 27, 2020 at about 18:00. The structure is channeled towards the
solar equator through time. The animated version of this figure runs from
September 27, 2020 at 12:00 UT to September 30, 2020 at 00:00 UT.
(An animation of this figure is available.)

##  3 PSP/IS$\odot$IS In-situ Observations

###  3.1 Orbit 6 Overview

IS$\odot$IS has been measuring solar energetic particles using the Energetic
Particle Instrument-Low (EPI-Lo, Hill et al., 2017, 2020) and the Energetic
Particle Instrument-High (EPI-Hi, Wiedenbeck et al., 2017). EPI-Lo consists of
eight wedges (W) with 10 time-of-flight apertures in each wedge (80 apertures
in total) and provides observations of particles from 20 keV/nuc to 1.5
MeV/nuc over 2$\pi$ steradians. EPI-Hi consists of three telescopes of stacked
solid-state detectors, including double and single-ended low-energy telescopes
(LETs) and a double-ended high-energy telescope (HET). Collectively, EPI-Lo
and EPI-Hi measure energetic particles of energies ranging from $\sim$0.2 to
200 MeV/nuc and species from protons to nickel, providing a comprehensive set
of observations.

Figure 4: Overview of the geometry and the energetic particle measurements
during orbit 6 of PSP following the plot format of McComas et al. (2019). The
EPI-Lo ion count rate summed over all apertures and energy ranges between
30–200 keV are shown inside the orbit, and the EPI-Hi count rate of LETA range
1 protons corresponding to about 1–2 MeV particles are shown outside the
orbit. The SEP event analyzed in this paper (highlighted with an orange
circle) is observed during PSP’s encounter 6 in the outbound portion of the
orbit inside 0.18 AU. The Sun is shown as a small orange sphere (not to
scale). The count rate levels are indicated by both the height and color of
the bars. This event was detected by EPI-Lo on September 30, 2020 (DOY
274-2020) but not detected by EPI-Hi.

PSP’s orbit 6 spanned from August 2, 2020 (DOY 215-2020) through November 22,
2020 (DOY 327-2020). Encounter 6 (when PSP was inside 0.25 AU) started on
September 21, 2020 and ended on October 2, 2020. Perihelion occurred on
September 29, 2020 at a distance of 0.09 AU (19.35 $R_{\odot}$) from the
center of the Sun. Figure 4 shows an overview of PSP’s orbit 6 geometry and
the corresponding energetic particle measurements. The EPI-Hi LET1 A count
rates (counts/sec) of protons and EPI-Lo count rates (counts/sec) of ions are
shown on the outside and inside of the orbit, respectively. Color
intensifications and taller bars indicate the occurrence of energetic particle
events. The event analyzed in this paper is highlighted with an orange circle.
As can be seen in Figure 4, this event is detected by the EPI-Lo instrument,
but is too small to extend into the EPI-Hi energy range $(\gtrsim
1{\rm\;MeV})$. The orbit 6 period is within the solar minimum phase and
therefore populated with rather quiet energetic particle conditions. This
gives a good opportunity to study the near-quiet-Sun energetic particle
populations.

###  3.2 The September 30, 2020 Event

Figure 5 shows an overview plot of the in-situ data for the September 30, 2020
SEP event as measured by PSP. Panel (a) shows the 315 eV heat flux strahl
electron pitch angle distribution (PAD) from the Solar Probe Analyzer–Electron
(SPAN-E; Whittlesey et al., 2020) instrument part of the Solar Wind Electrons
Alphas and Protons (SWEAP; Kasper et al., 2016) investigation. Panel (b) shows
the spectrogram for time-of-flight (TOF) only ions from IS$\odot$IS$/$EPI-Lo.
The spectrogram is obtained by averaging over all the apertures except for 25,
31, 34, 35, and 44, which have a high rate of photon-induced accidentals due
to punctures in its foil window from dust particle collisions (Hill et al.,
2020; Szalay et al., 2020). We also calculated the intensity of the energetic
particles moving away from and toward the Sun. The intensity of particles
moving away from the Sun is obtained from the Ion-ToF particle intensities
measured through the apertures of the EPI-Lo wedges looking in the sunward
direction (W2, W3, and W4), while the intensity of particles moving toward the
Sun is obtained from the Ion-ToF particle intensities measured through the
apertures of the wedges looking in the anti-sunward direction (W0, W7, and
W6). Panel (c) depicts the intensity of energetic particles moving from and
toward the Sun obtained from IS$\odot$IS$/$EPI-Lo, demonstrating that this
event was anisotropic. Panels (d) and (e) show the solar wind density and
radial speed, respectivly, at PSP from the Solar Probe Cup (SPC; Case et al.,
2020) part of SWEAP. Panel (f) shows the magnetic field vectors from the
FIELDS instrument (Bale et al., 2016) in the radial–tangential–normal (RTN)
coordinate system. The position of PSP (in au) relative to the solar center is
shown at the top of Figure 5. Figure 6 is a zoomed-in version of Figure 5, for
better visibility of the event.

Figure 5: Overview plot of the CME Event that began on September 30, 2020. The
top axis shows the spacecraft’s solar radial distance in AU. Panels from top
to bottom are (a) 315 eV heat flux electron PADs from SPAN-E, (b) EPI-Lo
spectrogram, (c) EPI-Lo intensities of ions (red and blue lines depict from
and toward the Sun, respectively), (d) radial solar wind speed and (e) solar
wind density measured by SPC and (f) magnetic field vector components (R-blue
line, T-green line, and N-red line) and magnetic field strength (black line)
as measured by FIELDS. All the data are averaged over 5-minute intervals. The
SEP event onset is marked with a vertical purple line. The two vertical green
lines represent the start and end time of the plateau (peak in intensity). The
two vertical red lines bound the SBO-CME passage at PSP, and the dashed red
line indicates the CME ejecta arrival time estimated by the WSA–Enlil
simulation shown in Figure 1.

As can be seen from the ion spectrogram (panel (b) of Figure 5), the SEP event
onsets at about 19:40 UT on September 29, 2020 (vertical purple line) and
shows clear velocity dispersion signatures, with the fastest particles
arriving first. Similar dispersive events for low-energy ions associated with
slow CMEs have been observed by the EPI-Lo instrument. The events observed on
November 5, 2018 (Hill et al., 2020), November 11, 2018 (Giacalone et al.,
2020; Mitchell et al., 2020a), and January 20, 2020 (Joyce et al., 2021b) are
some examples of weak SEP events that show clear velocity dispersion. A
dispersive event indicates that the source of the energetic particles is
remote, instead of being local.

Figure 5 shows that the energy of ions starts to increase up to a couple
hundred keV at about 02:00 on September 30, 2020 (DOY 274-2020) when solar
wind speed, density, and magnetic field (particularly in the T-component)
properties start to change, indicating the passage of a new field structure.
The strongest intensity for this event is observed in the time interval
between 02:00 and 08:50 UT on September 30 (bounded by two green vertical
lines) and shows a flat (constant) intensity–time profile throughout the
interval, which is slightly different from the rest of the event. The flat
intensity–time profile that persisted for about 8 hours suggests a constant
acceleration of particles of that energy (Reames, 1999) and prolonged magnetic
connectivity. The plasma and magnetic field data show that this enhancement
(peak) in energetic particles seem to be associated with extremely slow solar
wind speed and open magnetic field structure (indicated by the unidirectional
strahl electron flow) and that the enhancement is observed before the
predicted arrival time of the CME (dashed vertical red line). As shown in
panel (a) of Figure 5, the strahl electron flow is unidirectional throughout
the event except in the time interval between 10:00 and 16:00 UT on September
30, 2020 (DOY 274-2020), during which the flow is bidirectional. A
unidirectional electron flow implies the magnetic field lines are open or
attached to the Sun only from one end, whereas a bidirectional electron flow
represents a closed magnetic field structure in which the field lines are
attached to the Sun at both ends (Gosling et al., 1987).

A dropout in energetic particles is observed in the time interval between
11:00 and 16:00 UT. The dropout is clearly seen in both the spectrogram and
intensity plots shown in panels (b) and (c) of Figure 5. This dropout
coincides with the CME arrival time as predicted by WSA–Enlil (vertical dashed
red line), a bidirectional flow of strahl electrons, and a somewhat smooth
rotation of the magnetic field vectors. The solar wind speed features an
increasing profile and the plasma density is rather high, indicating a
structure that is being compressed from behind by a faster solar wind flow
(Pizzo, 1978; Gosling, 1996). Note that a bidirectional flow of strahl
electrons (Gosling et al., 1987) and a smooth rotation of the magnetic field
components (Burlaga et al., 1981) are commonly used as indicators of a CME
magnetic structure, which we identify to encounter PSP between ${\sim}$11 and
16 UT on September 30, 2020 (solid vertical red lines in Figure 5). We note
that the magnetic field strength (panel (f)) of the identified CME is not
significantly higher than its surroundings, as is common in CME ejecta (e.g.,
Kilpua et al., 2017). However, we consider that (1) the weak, slow CME
observed in remote-sensing imagery likely featured no strong, intrinsic
magnetic fields, and (2) the trend of the magnetic field components ($B_{T}$
and $B_{N}$ rotate in the first half of the ejecta and stay around zero during
the second half, while $B_{R}$ rotates from negative to positive) are
suggestive of a flank/leg encounter, in agreement with the WSA–Enlil
simulation results (Figure 1). The ion dropout during the CME arrival time is
not surprising since energetic particles are often suppressed within CME
magnetic clouds (Forbush, 1937; Cane, 2000).

Figure 6: Zoomed-in version of Figure 5.

We do not find signatures of a local shock in the plasma or magnetic field
data shown in Figures 5 and 6. The absence of a local shock may indicate that
these particles were remotely accelerated somewhere near the Sun. 150 kev/nuc
protons can travel the spiral-distance between the solar low corona and PSP
($\sim$0.14 AU) in shortly over a hour, hence they would have departed around
18:30 UT on September 30, 2020, when the CME was already well into the outer
corona (see its location in the corona a day earlier in Figure 2). As
discussed in Section 2, PSP was well connected to the CME since it encountered
the eruption in situ, but such encounter was determined to be a flank one
through both WAS–Enlil simulation results (Figure 1) and in-situ observations
(Figure 6). Hence, it is possible that particles traveled toward PSP once the
western flank of the CME became magnetically connected to it as a consequence
of expansion. Hence, it is possible that the CME initially drove a (weak)
shock near the Sun. The profile of the SEP event studied here is consistent
with that of magnetic connectivity achieved from the west of the observer (see
Figure 3.4 in Reames, 1999), in agreement with our interpretation mentioned
above. In this case, the strongest acceleration is assumed to occur near the
central region of the shock, where the shock is presumably strongest and the
speed is likely to be highest, and tends to decline around on the flanks (see,
e.g., Reames, 1999). It is worth noting that the strongest acceleration
typically reflects the geometry of the shock and magnetic field, which can
also make the flanks important for accelerating particles (see, e.g., Tylka et
al., 2005; Zank et al., 2006; Hu et al., 2017, 2018). As can be seen from
panel (c) of Figure 5, there is a clear anisotropy of energetic particles,
indicating that the energetic particles of this event are propagating
predominantly outward from the Sun, which gives additional evidence that the
energetic particles are likely accelerated remotely.

Figure 7: The event-averaged spectra of the the September 30, 2020 event
(black line) and the November 11, 2018 event (blue line) plotted together for
comparison. The November 11, 2018 spectrum is the same as Figure 2 (averaged
over the entire day) of Giacalone et al. (2020).

Figure 7 shows the event-averaged spectrum of this event (black line). For
comparison the event averaged spectrum of the November 11, 2018 event (same as
black symbols of Figure 2 of Giacalone et al. (2020)) is reproduced and shown
in blue line. As can be seen in Figure 7, the shape of the spectrum of this
event and the November 11, 2018 event are somewhat similar except that the
spectrum of this event is softer than the November 11, 2018 event. Note that
the November 11, 2018 event is a CME-related event observed by
PSP$/$IS$\odot$IS during its first orbit when it was about 0.25 AU from the
Sun, where PSP encountered the central region of the CME.

###  3.3 Ion Composition

SEP ion composition has been used as a good indicator of the origin,
acceleration, and transport of SEPs (Reames, 2021). Figure 8 shows the ion
composition of the September 30, 2020 event. For reference, panels (a) and (b)
reproduce panels (a) and (b) of Figure 5, respectively. Panels (c), (d), (e),
and (f) show the spectrograms for protons, helium (4He), oxygen (O), and iron
(Fe), respectively, and panel (g) reproduces panel (f) of Figure 5. As can be
seen from Figure 8, heavy ions are observed in this event. It is populated
with protons, helium, oxygen, and iron. Heavy ions are observed especially in
the leading edge of the event (well before the arrival of the SBO-CME). The
dispersive characteristic during the onset of this event (vertical purple
line) is also clearly seen in Figure 8. This event has similar ion composition
as the CME event of November 11, 2018 studied by Giacalone et al. (2020) and
Mitchell et al. (2020a), which was associated with an SBO-CME (Korreck et al.,
2020) with no shock–sheath system identified during the eruption of the CME or
in the in-situ plasma data at PSP. We note that during the September 30, 2020
event, 3He and energetic electrons are not observed to be significantly above
the EPI-Lo detector background, and also the FIELDS instrument did not detect
radio bursts above the FIELDS instrument background.

Figure 8: Ion composition of the September 30, 2020 event. The top axis shows
the spacecraft’s solar radial distance in AU, same as Figure 5. Panel (a) and
(b) are reproduced from Figure 6 for reference (context). Panels (c), (d),
(e), and (f) show spectrograms for proton (H), helium (4He), oxygen (O), and
iron (Fe). Panel (g) is the same as panel (f) of Figure 5. All the data are
averaged over 5-minute intervals. Vertical lines are described in Figures 5
and 6.

##  4 Discussion and Conclusions

In this paper we have studied in detail a low-energy SEP event observed by
IS$\odot$IS$/$EPI-Lo on September 30, 2020 during the encounter 6 period
inside 0.18 AU. The September 30, 2020 event is interesting in that there was
no sunspot-bearing active region (at least around the longitudinal position of
PSP), which gives an excellent opportunity to study the energetic particle
environment of the near-quiet Sun. The event onset occurs at approximately
19:40 UT on September 29, 2020. The event shows clear velocity dispersion
during its onset, with the fastest particles arriving first. The STEREO/COR2-A
coronagraph observed a CME being ejected from the solar eastern limb on
September 29, 2020 around 07:00 UT, 12 hrs before the onset of the SEP event
at PSP. The CME arrived at PSP (0.17 AU) about a day after the onset of the
SEP event and and PSP encountered the CME’s western flank. Throughout this SEP
event, strong particle anisotropies were observed, showing that more particles
are streaming outward from the Sun.

This small SEP event has a very interesting time profile. The energetic
particle intensity rises gradually from a few to several hours and reaches a
plateau later on. The strongest intensity for this event is observed in the
time interval between 02:00 and 08:50 UT on September 30, 2020, which is well
before the CME passage. It is quite interesting that at the start of the
plateau (first green vertical line in Figures 5), the magnetic field and
plasma properties start to change, indicating that PSP crossed a new field
structure. It is possible that this new field structure is channeling
energetic particles from a remote acceleration site, which most likely
happened at the front of the CME. The in-situ magnetic field and strahl
electron PAD indicate that these strongest energetic particle intensities are
observed in the open magnetic field structure prior to the CME arrival, and
there is a dropout both in intensity and number of relatively high-energy
particles inside the CME structure as shown in Figures 5 and 6. As noted
earlier, PSP crosses the western flank of the CME during its passage, and the
time profile of this event is consistent with a western flank encounter (see
Figure 3.4 in Reames, 1999).

The ion composition plot shown in Figure 8 depicts that some heavy ions such
as oxygen and iron are observed, in addition to protons and helium-4, but no
significant enhancement of helium-3 and energetic electrons, giving evidence
that the source of this event is unlikely to be a solar flare. Therefore, this
small SEP event is not a typical small impulsive event, rather, it seems to be
a small gradual SEP event. In fact, both remote-sensing (as discussed in
Section 2) and in-situ (as discussed in Section 3.2) data show that this event
is associated with a slow CME. Remote solar data observed using STEREO/COR2-A
show that the source of this event is most likely an SBO-CME on September 29,
2020. The in-situ magnetic field and strahl electron PAD data show that the
magnetic field is open and mostly radial prior to the arrival of the SBO-CME
but closed upon arrival. As shown in Figures 5 and 6, throughout the event,
the strahl electron flow is unidirectional except in the time interval between
11:00 and 16:00 on 274-2020 (DOY-year), where the flow is bidirectional
indicating a closed magnetic field structure. This closed structure observed
during the period of bidirectional electrons coincides with the SBO-CME
arrival time. During its earlier orbits, PSP encountered SBO-CMEs (Korreck et
al., 2020; Lario et al., 2020; Nieves-Chinchilla et al., 2020) and SEP
enhancements associated with SBO-CMEs were also observed (Giacalone et al.,
2020; Lario et al., 2020; Mitchell et al., 2020a), consistent with our
observation.

We do not see a local shock in the in-situ plasma or magnetic field data
throughout the event. An anisotropic and dispersive SEP event in a shockless
local plasma give evidence that the dominant sources of particles were remote
rather than local, consistent with earlier observations (see, e.g., Giacalone
et al., 2020; Mitchell et al., 2020a; Joyce et al., 2021b). There are several
candidates as a possible source of remote acceleration mechanism of these
energetic particles. One possible mechanism may be that particle acceleration
occurring either at plasma compressions formed in front of the propagating CME
or at a weak shock initially driven by the CME that was not detected at its
arrival at PSP (Giacalone et al., 2020). Another candidate as a possible
source of remote acceleration mechanism of these energetic particles is the
one proposed by Mitchell et al. (2020a), which is associated with strong
field-aligned current system that run in the solar atmosphere (Janvier et al.,
2014). These energetic particles could be also accelerated due to magnetic-
island reconnection-related processes (Zank et al., 2014, 2015; Zhao et al.,
2018, 2019a, 2019b). In this scenario, the magnetic islands will be located
closer to the Sun than the location where the energetic particles are
observed. However, the intensity–time profile of this event gives indications
that the particles are likely accelerated by a weak shock or compression
driven by the CME near the Sun in agreement with earlier observations
(Giacalone et al., 2020). However, it should be noted here that the SEP
profile of this event is consistent with a western flank connectivity, as
noted above, and the event-averaged spectrum is an indicative of a weaker
event, while the event studied by (Giacalone et al., 2020) was consistent with
central connectivity. During this event, PSP was not radially aligned with
other spacecraft and thus we could not compare this event with other energetic
particle observations.

It is quite interesting to see that the in-situ signatures of this small
gradual SEP event (associated with a weak CME) show similar properties to the
well-established signatures of larger CME events, which are often associated
with active regions containing sunspots, giving evidence that small SEP events
may be generated by similar mechanisms as in large SEP events regardless of
the size and strength of the CME. Small gradual SEP events are not totally
absent at 1 AU ( see, e.g., Reames, 2020; Joyce et al., 2021b), but they are
rare (particularly, those with energies below 1 MeV) due to a variety of
reasons. One reason may be that they are just too small and spread out.
Another possible reason may be that these are a feature of SBO-CMEs in
agreement with our analysis. This event may represent direct observations of
the source of low-energy SEP seed particle populations and provides a unique
opportunity to show how particles evolve in the near quiet-Sun environment and
also to further investigate the connection between small gradual SEP events
and SBO-CMEs. This work highlights the importance of small SEP events in
understanding the solar activity of the near-Sun environment that had not been
previously explored.

Acknowledgements. This work was supported as a part of the Integrated Science
Investigations of the Sun on NASA’s Parker Solar Probe mission, under contract
no. NNN06AA01C. The IS$\odot$IS data and visualization tools are available to
the community at: https://spacephysics.princeton.edu/missions-
instruments/isois; data are also available via the NASA Space Physics Data
Facility (https://spdf.gsfc.nasa.gov/). Parker Solar Probe was designed,
built, and is now operated by the Johns Hopkins Applied Physics Laboratory as
part of NASA’s Living with a Star (LWS) program (contract no. NNN06AA01C).
Simulation results have been provided by the Community Coordinated Modeling
Center at Goddard Space Flight Center through their public Runs on Request
system (http://ccmc.gsfc.nasa.gov). The WSA model was developed by C. N. Arge
(currently at NASA/GSFC), and the ENLIL model was developed by D. Odstrcil
(currently at GMU). We thank the STEREO team for making the SECCHI data used
in this study publicly available. E.P.’s research was supported by the NASA
LWS Jack Eddy Postdoctoral Fellowship Program, administered by UCAR’s
Cooperative Programs for the Advancement of Earth System Science (CPAESS)
under award no. NNX16AK22G. B.J.L. acknowledges NASA HGI 80NSSC21K0731, NASA
LWS 80NSSC21K1325, and NSF AGS 1851945.

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# In-situ Raman gain between hyperfine ground states
in a potassium magneto-optical trap

Graeme Harvie  Adam Butcher  Jon Goldwin<EMAIL_ADDRESS>School of
Physics and Astronomy, University of Birmingham,
Edgbaston, Birmingham B15 2TT, United Kingdom

###### Abstract

We study optical gain in a gas of cold 39K atoms. The gain is observed during
operation of a conventional magneto-optical trap without the need for
additional fields. Measurements of transmission spectra from a weak probe show
that the gain is due to stimulated Raman scattering between hyperfine ground
states. The experimental results are reproduced by a simplified six-level
model, which also helps explain why such gain is not observed in similar
experiments with rubidium or cesium.

††preprint: APS/123-QED

##  I  Introduction

It was realized early in the development of laser cooling with alkali atoms
that the typical conditions in a magneto-optical trap (MOT) support steady-
state optical gain Tabosa1991 ; Grison1991 . Multiple mechanisms have been
observed in both cesium and rubidium MOTs. For probe frequencies near the
cooling laser frequency, a narrow dispersively shaped spectral feature arises
due to Raman scattering between $m_{F}$ states of a single hyperfine level
$F$, the degeneracy of which is lifted by polarization-dependent light shifts
Grison1991 ; Hilico1992 ; Guerin2008 . Under certain conditions, in-situ four-
wave mixing and recoil-induced resonances can also be observed Guo1992 ;
Brzozowski2005 ; Guerin2008 . At a probe frequency near twice the detuning of
the cooling laser from the cycling transition, a broader feature is observed.
This feature is due to Mollow gain between dressed states Mollow1972 ; Yu1977
; Mitsunaga1996 ; Guerin2008 ; Sawant2017 . It is particularly notable that
these gain mechanisms do not require additional lasers beyond those used for
cooling and trapping, suggesting a relatively simple setup for continuous-wave
amplification or lasing with cold atoms.

Recently we observed steady-state lasing with cold 39K atoms in a ring cavity
Megyeri2018 . To our knowledge this was the first demonstration of gain in an
operating potassium MOT. Compared to cesium or rubidium, 39K has relatively
small excited-state hyperfine splittings, being on the order of the natural
linewidth; a simplified energy level schematic is shown in Fig. 1. This means
a potassium MOT operates in a significantly different way, in that light
scattering is dominated by a non-cycling transition — the primary cooling
laser in our experiment preferentially drives the
$\ket{F=2}\to\ket{F^{\prime}=2^{\prime}}$ transition (primes denote excited
states), which decays by spontaneous emission to the $\ket{1}$ ground state
with $50\%$ probability. Because of this, 39K MOTs require more repump light
than their rubidium or cesium counterparts, and the fractional population in
the lower ground state can be much larger.

Figure 1: Energy level diagram for the D2 lines of 39K at 767 nm (the excited-
and ground-state manifolds and their separation are not to scale with each
other). The MOT cooling light is represented in red and the repump in blue.
Frequencies are given in units of MHz, and the indicated detunings are the
default values for making a MOT with a large atom number in our experiment.
The natural linewidth is $6.0$ MHz full-width at half-maximum (FWHM), denoted
by the grey bar around the $F^{\prime}=3^{\prime}$ level.

In our experiment, we observe no evidence of the Raman gain or recoil-induced
resonances between nearly-degenerate Zeeman states which are familiar from
cesium and rubidium. We do observe a broader gain feature which we previously
associated with Mollow gain on the $\ket{2}\to\ket{2^{\prime}}$ transition.
However, subsequent measurements, presented in detail here, suggest that the
gain is in fact due to Raman scattering between the $\ket{1}$ and $\ket{2}$
ground states. The rest of this paper is organized as follows. In Section II
we describe the experimental apparatus, and present measurements of
transmission spectra for varying detunings of the MOT cooling and repump
light. In Section III we present a six-level model for hyperfine Raman gain
which is in good agreement with the measured spectra. Motivated by this model,
we investigate the role of the ground state populations in Section IV. Finally
in Section V we return to a comparison with rubidium and cesium and give an
outlook for future work.

##  II  Transmission Spectra

Our experiment is described in detail in Culver2016 ; rob_thesis ;
andreas_thesis ; Megyeri2018 , so we only give a brief overview here.
Potassium atoms released from a heated ampule are cooled in a 2D-MOT, and
continuously loaded into a 3D-MOT with a quasi-resonant pushing laser. The
cooling and repump lasers are near resonance with the groups of
$\ket{2}\to\ket{F^{\prime}}$ and $\ket{1}\to\ket{F^{\prime}}$ transitions,
respectively (recall Fig. 1). As mentioned above, the designations of cooling
and repump light do not accurately apply to a 39K MOT, but we use them here
for consistency with other work. The repump light is derived from the same
laser as the cooling light using an acousto-optic modulator (AOM), and both
beams are amplified with a single tapered amplifier. The amplified light is
coupled into polarization-maintaining single-mode optical fibers for spatial
mode cleaning and delivered to the atoms in a conventional three-beam, retro-
reflected geometry; the cooling and repump beams have similar peak intensities
of $\approx 14$ mW/cm2 at the position of the atoms. A quadrupole magnetic
field with a gradient of 11 G/cm is on during all experiments. Under typical
conditions the temperature of the cloud is around 1 mK.

A linearly polarized probe beam derived from an independent laser is used to
measure the transmission spectrum of the running MOT. The probe passes through
the center of the MOT, and is focused such that the beam waist of $\approx
100~{}\mu$m is much smaller than the MOT radius (typically $800~{}\mu$m),
ensuring the probe traverses the maximum column density of atoms. The probe
power is $\approx 1\mu$W, which does not noticeably perturb the running MOT.
The corresponding probe intensity at the atoms is $\approx 1$ mW/cm2, which is
just below the saturation intensity of $1.75$ mW/cm2 calculated for the
$\ket{2}\to\ket{3^{\prime}}$ cycling transition. The probe propagates nearly
parallel to one pair of MOT beams, then passes through a $4.1$ mm aperture to
filter out stray MOT light, before being detected on an avalanche photodiode
(Thorlabs APD110A/M). The probe laser is free running, with its frequency
scanned over a range of at least 1 GHz, allowing all of the D2 features to be
observed in a single scan. To calibrate the frequency sweep rate, a fraction
of the probe light is incident on a high finesse optical cavity. Sidebands can
be added to the probe at $17.3$ MHz by modulating the laser current, and the
resulting sidebands in the cavity transmission spectrum can then be used as a
frequency reference for the probe scan. The modulation sidebands are turned
off during MOT transmission measurements.

Figure 2: Fractional probe transmission spectrum obtained using the default
MOT beam detunings shown in Fig. 2. The cooling laser frequency and the
expected hyperfine Raman gain frequency are indicated by the red and blue
lines, respectively.

An example spectrum obtained using our default MOT detunings is shown in Fig.
2. To obtain a normalized transmission spectrum, the photodiode signal is
first averaged 32 times on a digital storage oscilloscope; a linear fit to the
wings of the spectrum accounts for the intensity change of the laser during
the frequency scan, and the probe beam is then blocked in order to make a
measurement of the background. We observe two large absorption features
corresponding to the $\ket{2}\to\ket{3^{\prime}}$ and
$\ket{2}\to\ket{2^{\prime}}$ transitions, a smaller
$\ket{2}\to\ket{1^{\prime}}$ absorption feature, and a single gain feature to
the red. The gain feature is qualitatively similar to what one would expect
for Mollow gain on the $\ket{2}\to\ket{2^{\prime}}$ transition, in the sense
that the linewidth is on the order of the natural linewidth, and the center
frequency is approximately double the detuning of the cooling beam from the
$\ket{2}\to\ket{2^{\prime}}$ absorption resonance (indicated by the red line).
However the gain feature is also close to the two-photon Raman transition
between the ground states (blue line). This suggests an alternative
explanation — the gain could be caused by a stimulated Raman transition from
$\ket{1}\to\ket{2}$, with the MOT repump light acting as the Raman pump. The
small offset between the expected Raman transition frequency and the gain
feature is comparable to the calculated Stark shifts of the ground states from
the MOT beams.

In order to differentiate between Mollow and hyperfine Raman gain, further
measurements were taken with varying detunings for the MOT cooling and repump
beams. The two mechanisms are expected to exhibit complementary behavior with
respect to the laser frequencies — neglecting relatively small light shifts,
the frequency of the Raman gain peak should depend only on the MOT repump
laser frequency, while Mollow gain should depend only on the frequency of the
cooling light.

(a)  (b)

Figure 3: Absorption and gain for varying MOT beam frequencies. (a) Measured
probe transmission as the cooling frequency is changed. Absorption is shown in
blue and gain is shown in red. Note the difference in scale between red and
blue in the colorbars. The green curve shows the expected resonance frequency
for Mollow gain on $\ket{2}\to\ket{2^{\prime}}$ and the blue line the
$\ket{1}\to\ket{2}$ Raman resonance frequency in the absence of AC Stark
shifts. (b) Measured probe transmission as the repump laser frequency is
changed.

Figure 3 shows that the gain resonance frequency is primarily determined by
the repump laser frequency, implying Raman gain. This is most evident in Fig.
3(a), which shows no observable dependence on the cooling laser frequency,
even when the cooling frequency crosses the
$\ket{2}\rightarrow\ket{2^{\prime}}$ resonance. This is in sharp contrast to
the avoided crossing one would expect from Mollow gain (green curve)
Mitsunaga1996 . For comparison, Fig. 3(b) shows that the gain frequency
closely follows the two-photon Raman resonance as the repump detuning is
varied; Mollow gain would lead to a similar resonance frequency for these
parameters, but one which would not depend on the repump detuning. Note that
the cooling detuning was increased to $-31$ MHz for this measurement. This
reduces the rate of optical pumping into the $\ket{1}$ state, which allows a
wider range of repump detunings to be explored while maintaining a reasonable
number of atoms in the MOT.

The amplitudes of the gain and absorption features also depend on the cooling
and repump frequencies. This is due in part to changes in the total number of
atoms in the MOT. Interestingly, we observe that the gain amplitude is higher
when the absorption amplitude is lower, and vice versa. The theoretical model
presented in the next section shows that this is expected for Raman gain
between hyperfine ground states. This is because the amount of absorption is
proportional to the population in the $\ket{2}$ state, whereas the gain
amplitude is proportional to the population difference between the $\ket{1}$
and $\ket{2}$ states Vrijsen2011 .

It is worth noting that Fig. 3(a) appears to contradict our previous
measurements, where the gain resonance moved with the cooling laser frequency
(denoted as ‘pump’ detuning in Fig. S1(a) of the supporting material for
Megyeri2018 ). In that work the repump frequency was also changing, with a
fixed frequency offset relative to the cooling beam, set by the AOM used to
derive the repump light. Based on previous work with cesium and rubidium MOTs,
we did not foresee that the repump light itself could act as the gain pump. In
the work presented here we have been careful to vary the frequency of only one
field at a time — when the cooling laser frequency is changed in Fig. 3(a),
the AOM frequency is counter-tuned to maintain a fixed repump frequency; in
Fig. 3(b), only the repump frequency is varied, by keeping the cooling laser
frequency fixed and tuning the AOM. These new measurements show unambiguously
that the gain resonance frequency is determined by the repump frequency in our
experiment.

##  III  Theoretical Model

In order to better understand the observed spectra, we reduce the system to a
six-level model consisting of the hyperfine levels $F=1,2$ and
$F^{\prime}=0^{\prime}$–$3^{\prime}$, but neglecting the nearly degenerate
Zeeman sub-states. A Lindblad-type master equation is used to solve for the
density matrix $\rho$,

$\dot{\rho}=\frac{1}{i\hbar}[H,\rho]+\sum_{n}\frac{\gamma_{n}}{2}(2a_{n}\rho
a_{n}^{{\dagger}}-a_{n}^{{\dagger}}a_{n}\rho-\rho a_{n}^{{\dagger}}a_{n})\;,$
(1)

where $H$ is the Hamiltonian. Each $n$ represents a channel for incoherent
evolution of the system; $a_{n}$ is the corresponding collapse operator, and
$\gamma_{n}$ the associated rate constant. The steady state of the system is
found by solving for $\dot{\rho}=0$.

In the dipole approximation and interaction picture,

$\displaystyle H$
$\displaystyle=\hbar\delta\ket{2}\\!\\!\bra{2}-\sum_{F^{\prime}}\hbar\Delta_{F^{\prime}}\ket{F^{\prime}}\\!\\!\bra{F^{\prime}}$
$\displaystyle-\sum_{F^{\prime}}\frac{\hbar\Omega_{1F^{\prime}}}{2}\Big{(}\ket{1}\\!\\!\bra{F^{\prime}}+\ket{F^{\prime}}\\!\\!\bra{1}\Big{)}$
(2)
$\displaystyle-\sum_{F^{\prime}}\frac{\hbar\Omega_{2F^{\prime}}}{2}\Big{(}\ket{2}\\!\\!\bra{F^{\prime}}+\ket{F^{\prime}}\\!\\!\bra{2}\Big{)}\quad.$

Here $\delta$ is the two-photon Raman detuning between the probe and the
repump, and $\Delta_{F^{\prime}}$ is the repump detuning from the unperturbed
$\ket{1}\to\ket{F^{\prime}}$ transition. The Rabi frequency
$\Omega_{1F^{\prime}}$ describes the repump light driving the
$\ket{1}\to\ket{F^{\prime}}$ transition, while $\Omega_{2F^{\prime}}$
describes the weak probe acting on $\ket{2}\to\ket{F^{\prime}}$. In
calculating the Rabi frequencies, we use effective Clebsch-Gordan coefficients
$C_{FF^{\prime}}$ for $\pi$ transitions averaged over all possible Zeeman
states as in Megyeri2018 .

The cooling light is included in Eq.(1) as an incoherent pumping term from the
$\ket{2}$ state to the $\ket{1}$ state with effective collapse operator
$\ket{1}\\!\\!\bra{2}$ and rate $w$. This replicates the effect of the cooling
beam in repopulating the $\ket{1}$ state, without giving rise to additional
features due to coherent scattering within the numerous $\Lambda$ systems
involved Birnbaum2006 . A similar approach was adopted in Refs. Meiser2009 ;
Vrijsen2011 . An added benefit of this is that it allows a straightforward
calculation of the transmission spectrum by including a weak probe term in the
Hamiltonian, without causing beating with the cooling light. Spontaneous
emission is represented by collapse operators $\ket{F}\\!\\!\bra{F^{\prime}}$
with rates $\Gamma\,b_{FF^{\prime}}$, where $\Gamma=2\pi\times 6.0$ MHz is the
natural linewidth (FWHM) and $b_{FF^{\prime}}$ are branching ratios. Dephasing
between ground states is described by a collapse operator for the population
difference $(\,\ket{1}\\!\\!\bra{1}-\ket{2}\\!\\!\bra{2}\,)$ with rate
$\gamma_{12}\,$. The steady-state solution for $\rho$ is solved numerically
using the QuTiP software package JOHANSSON2013 .

The linear probe susceptibility for the $\ket{2}\to\ket{F^{\prime}}$
transition is proportional to $\rho_{2F^{\prime}}$, with the imaginary part
giving the absorption or gain. The probe transmission for an optically thin
MOT is finally given by,

$T=1-A\sum_{F^{\prime}}C_{2F^{\prime}}\imaginary\\{\rho_{2F^{\prime}}\\}\quad,$
(3)

where $A$ is an overall scaling factor used to match the peak absorption to
the measured value. This is ultimately determined by the column density of the
MOT.

Figure 4: Calculated transmission spectrum, with the repump detuning shown in
Fig. 1. The phenomenological parameters used were $w=2\pi\times 1.0$ MHz and
$\gamma_{12}=2\pi\times 1.5$ MHz. The rest of the parameters matched the
experimental conditions.

A calculated probe spectrum is shown in Fig. 4. The parameters $A$, $w$, and
$\gamma_{12}$ were set to match the measured spectrum in Fig. 2. Increasing
$A$ increases the amplitude of all features by a common factor; the amplitude
of the gain peak increases with $w$ and decreases with $\gamma_{12}$, while
the width of the gain peak increases with both. We obtain a good match to the
data for $w=2\pi\times 1.0$ MHz and $\gamma_{12}=2\pi\times 1.5$ MHz. The
optical pumping rate $w$ can be estimated from the optical Bloch equations,
which predict $w=2\pi\times 0.6\,$-$0.8$ MHz for our conditions, depending on
the fraction of the total MOT light intensity on the cooling transitions,
which can vary due to competition for gain in the tapered amplifier. Dephasing
at a rate $\gamma_{12}$ leads to broadening of the simulated lines, such that
the half-widths at half-maximum increase from approximately
$\tfrac{1}{2}(\Gamma+w)\to\tfrac{1}{2}(\Gamma+w+\gamma_{12})$ for absorption
and $\tfrac{1}{2}w\to\tfrac{1}{2}w+2\gamma_{12}$ for gain. To compare the
simulations to the data, we assume Voigt lineshapes for the measured features,
with Lorentzian widths corresponding to the left-hand sides of these
expressions, broadened by a common Gaussian width $\eta$ (HWHM). For the data
presented here, $\eta$ is dominated by relative frequency fluctuations between
the MOT laser and the free-running probe laser. We measure a Gaussian beat
note with a half-width of $2\pi\times 1.8$ MHz. To estimate the effects of
Zeeman shifts in the spatially varying magnetic field, we first calculate the
root-mean-squared value of $(g_{2}m_{2}-g_{1}m_{1})$ over the 40 possible
Raman transitions between $\ket{1}$ and $\ket{2}$, weighted by the appropriate
transition strengths (here the $g_{F}$ are Landé $g$-factors and the $m_{F}$
are magnetic quantum numbers). This gives an effective scale factor of
$(25/24)^{1/2}\mu_{B}/\hbar$. Then averaging the quadrupole gradient magnetic
field over the Gaussian density of atoms along the probe beam direction, we
obtain a half-width of $2\pi\times 0.6$ MHz. Finally, we expect a contribution
due to Doppler broadening. In the case of Raman scattering, this depends on
the angle between pump and probe beams, which is approximately 0, 90, or 180
degrees for each of the six MOT beams. The resulting Doppler widths are in the
range of 0 to 2 times the single-photon value of $2\pi\times 0.7$ MHz.
Combining all of these effects, we estimate $\eta\approx 2\pi\times 2.1$ MHz.
Together with the known value of $\Gamma$ and the simulated value of $w$, the
corresponding Voigt linewidths for absorption and gain imply
$\gamma_{12}=2\pi\times 0.8\,$-$2.3$ MHz.

To further compare the theoretical model to the experiment, a contour plot
similar to Fig. 3(b) was made. This is shown in Fig. 5, with all parameters,
including the total atom number, fixed. This can also be seen to match the
experimental results well. In particular, the increase in peak gain and
reduction in absorption with increasing repump detuning is replicated in the
numerical model. Note that the value of $w$ used in this simulation is lower
than in Fig. 4, reflecting the fact that the cooling beam was further detuned
in the corresponding measurement.

Figure 5: Calculated probe transmission for varying repump detuning.
Parameters were chosen to match the experimental conditions of Fig. 3(b), but
with fixed atom number. The optical pumping rate was $w=2\pi\times 0.5$ MHz
and the dephasing rate was $\gamma_{12}=2\pi\times 1.5$ MHz.

Despite some apparent similarities, the model presented here is qualitatively
different than the four-level model used in Megyeri2018  under the assumption
of Mollow gain on the $\ket{2}\to\ket{2^{\prime}}$ transition. Specifically,
the present model only describes Raman gain pumped by the repump light,
whereas the four-level model only describes Mollow gain pumped by the cooling
light. The fact that both models predict gain for our experiment suggests
that, in principle, both gain mechanisms could coexist in our experiment.
However the four-level Mollow model does not include the $\ket{1}$ ground
state, and therefore cannot account for optical pumping out of $\ket{2}$. This
pumping suppresses Mollow gain and increases Raman gain, as described in more
detail in the next section. We have found that all of our experimental results
are well described by pure Raman gain induced by the repump light for the
parameter regimes we have studied.

##  IV Ground state populations

Hyperfine Raman gain is proportional to the population difference between the
$\ket{1}$ and $\ket{2}$ ground states Vrijsen2011 . These populations should
therefore be measured, in order to ensure they are consistent with the
theoretical model. The populations can be determined from transmission spectra
spanning all of the D2 transitions. Example spectra are shown in Fig. 6 for
the default cooling frequency and two different values of the repump
frequency.

Figure 6: Measured transmission spectra used to obtain the ground state
populations. The red and blue curves correspond to repump detunings of $-34.7$
and $-30.7$ MHz, respectively. The features around zero detuning are the gain
and $\ket{2}\to\ket{F^{\prime}}$ absorption resonances, and the feature around
460 MHz comprises the overlapping $\ket{1}\to\ket{F^{\prime}}$ transitions.
The inset shows a detail of the region between the gain and
$\ket{2}\to\ket{3^{\prime}}$ absorption resonances.

The dominant $\ket{2}\to\ket{3^{\prime}}$ and combined
$\ket{1}\to\ket{F^{\prime}}$ absorption features have similar optical depths
when the populations are equal (relatively $0.47$ and $0.45$, respectively).
These features are therefore used for estimating the populations by
normalizing the measured optical depth to the square of the relevant Clebsch-
Gordan coefficient. The populations determined in this way are shown in Fig.
7(a) for varying detuning of the repump light. The data show that the
population difference goes to zero at small repump detunings, which is the
reason for the reduction in peak gain observed in Fig. 5. For increasing
repump detuning, the population difference reaches a maximum and then drops
off due to the reduction in total atom number in the MOT. The theoretical
model does not include the variation in the total column density of the MOT as
the repump detuning changes, but a direct comparison between the experimental
and theoretical populations can be made by looking at the fractional
population difference. Figure 7(b) shows that the normalized difference
continues to increase with repump detuning. The theoretical populations
obtained from the master equation reproduce this behavior.

Figure 7: Ground state populations versus repump detuning. (a) The
experimentally determined population difference $n_{\rm diff}=n_{1}-n_{2}$
(red circles) and sum $n_{\rm sum}=n_{1}+n_{2}$ (blue triangles), where
$n_{i}$ is the column density of atoms in ground state $\ket{i}$. (b) The
normalized population difference $n_{\rm diff}/n_{\rm sum}$, from experiment
(points) and theory (line).

##  V  Conclusion

We have studied optical gain in an operating magneto-optical trap of 39K
atoms. The gain was shown to arise from Raman transitions between the
hyperfine ground states, which has not been observed in-situ with more
commonly used species such as rubidium or cesium. The conditions for such gain
are set by the relatively small excited-state hyperfine splittings. First, the
cooling light is closer to resonance with an open transition than the cycling
transition, leading to rapid optical pumping into the lower ground state. This
in turn necessitates a relatively large intensity for the repump light, which
must also be red-detuned to reduce heating. Even with these adjustments, we
typically have a larger population in the lower ground state, creating the
effective inversion needed for gain. For completeness, we note that hyperfine
Raman gain also has been exploited to impressive effect in a wide range of
more complex experiments with cold rubidium or cesium McKeever2003 ;
Schneble2004 ; Yoshikawa2004 ; Yoshikawa2005 ; Vrijsen2011 ; Bohnet2012 ;
Baudouin2013 . Our demonstration of in-situ Raman gain in a potassium MOT
suggests a comparatively simple and robust experimental platform for studying
steady-state gain and lasing with cold atoms.

Our measurements of the potassium ring laser have shown that the gain is
effectively homogeneously broadened, despite the presence of inhomogeneous
magnetic fields and Doppler shifts Megyeri2018 . This prevents simultaneous
bidirectional lasing into the counter-propagating modes of the ring cavity in
favor of random switching between modes. By intermittently shutting off the
MOT fields and applying a separate far-detuned Raman pump, it should be
possible to realize homogeneous gain linewidths on the order of only a few Hz
Bohnet2012 . In this case inhomogeneous Doppler broadening should enable
simultaneous lasing SargentMurray1974 .

###### Acknowledgements.

This work was funded by the UK Engineering and Physical Sciences Research
Council (EP/J016985/1). We are grateful to the members of the Quantum Matter
research group at the University of Birmingham for useful discussions and the
loan of equipment.

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