# Perspectives on high-frequency nanomechanics, nanoacoustics, and
nanophononics

Priya  Université Paris-Saclay, CNRS, Centre de Nanosciences et de
Nanotechnologies, 91120 Palaiseau, France  E. R. Cardozo de Oliveira
Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies,
91120 Palaiseau, France  N. D. Lanzillotti-
<EMAIL_ADDRESS>Université Paris-Saclay, CNRS, Centre
de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France

###### Abstract

Nanomechanics, nanoacoustics, and nanophononics refer to the engineering of
acoustic phonons and elastic waves at the nanoscale and their interactions
with other excitations such as magnons, electrons, and photons. This
engineering enables the manipulation and control of solid-state properties
that depend on the relative positions of atoms in a lattice. The access to
advanced nanofabrication and novel characterization techniques enabled a fast
development of the fields over the last decade. The applications of
nanophononics include thermal management, ultrafast data processing,
simulation, sensing, and the development of quantum technologies. In this
review, we cover some of the milestones and breakthroughs, and identify
promising pathways of these emerging fields.

##  1 Introduction

Usually seen as a major source of decoherence, acoustic phonons recently
became an asset for optoelectronics [1, 2, 3], quantum technologies [4], and
the simulation of solid-state systems [5]. Indeed, all the properties of a
solid-state structure that are determined by the position of the atoms are
subject to be modified or modulated by the presence of acoustic phonons.
Moreover, acoustic phonons can be used to interface platforms based on
different excitations (electrons, excitons, photons, or magnons) through the
engineering of their interactions.

The engineering of acoustic waves at the nanoscale covers a broad range of
frequencies from MHz (ultrasound) to GHz (hypersound) and THz (heat).
Depending on the scientific community, it is refereed as nanomechanics [6]
(i.e., when referring to NEMS and MEMS, acronyms for nano- and
microelectromechanical systems, respectively), nanoacoustics [7] (i.e., in
cavity optomechanics), or nanophononics [8, 9] (i.e., in spectroscopy,
hypersound engineering, and thermal transport). The focus of this review is to
highlight the latest advances and trends and present some of the open
challenges and future perspectives in the field.

By engineering nanostructures it is possible to control the confinement and
propagation of acoustic vibrations, unlocking a plethora of applications. The
short wavelength (in the 1-100 nm range) associated with acoustic phonons of
GHz-THz frequencies opens the possibility of both developing novel acoustic
nanoscopies based on acoustic nanowaves, and reaching ultrasmall interaction
mode volumes necessary for the future on-chip integrated phononic devices.
Acoustic phonons constitute an efficient and versatile simulation platform.
The long mean free path combined with the short wavelength enables the
simulation of complex solid-state systems. In addition, one can have access to
the full phonon wavefunction, which is difficult or impossible using platforms
based on electrons and photons. The characteristic high frequencies in
nanophononics have associated low occupation numbers, reaching the quantum
regime using standard cryogenic techniques, paving the way for quantum
applications where phonons play a central role to manipulate information.

Despite all these promising perspectives, nanophononics still faces some open
challenges. The lack of standard transducers, in opposition to classical
acoustics, motivates the development of novel strategies and experimental
techniques to control the interactions with other excitations. A stringent
requirement of nanophononic devices is the materials and the superior
interface quality. With required roughness down to atomic scales for the
higher frequency bands, it is the most limiting property for raising the
working frequency. By overcoming these challenges, one will be able to address
the full control of interaction mechanisms in order to efficiently generate,
manipulate the dynamics, and detect acoustic phonons.

Figure 1:  The acoustic quality factor (symbols) plotted as function of
designed acoustic frequency for an assembly of acoustic systems operating at
cryogenic (blue) and room (red) temperatures [10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,
37, 38, 39, 40, 41, 42, 43, 44, 7, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55,
56, 57, 58, 59, 60, 61, 62]. The gray-shaded region represents the
intersection of the fields of optomechanics (on the left) and nanophononics
(orange-shaded region,on the right)

Figure 1 highlights the diversity of acoustic structures developed over the
past two decades for the confinement of phonons in a cavity at different
frequencies [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,
26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 7,
45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62]. This
limited selection of structures is characterized by the acoustic quality
factor Q. Q (symbols) are presented in Fig. 1 as a function of operating
acoustic frequency. It is worth noting that acoustic structures with higher Q
values at lower frequencies (MHz range) work at room temperature, while at
higher frequencies (GHz range), cryogenic temperatures of a few mK are
required. There is a demand for raising the Q-factor for room environment
conditions. Even though this figure is not a detailed picture of the field, it
is worth noting the proportion of works studying structures designed for the
range of frequencies between tens to hundreds of gigahertz (highlighted in
orange) is considerably smaller than at lower frequencies. Clearly, the
development of high-Q resonators operating at high-frequencies, and able to
work at room temperature, remains an open challenge in nanophononics.

The recent advances in material science, experimental techniques,
nanofabrication methods, and the understanding of solid-state systems set the
perfect framework and timing to explore the flourishing field of nanophononics
[63, 64]. The physics associated with acoustic phonons has implications in
research fields, such as optomechanics, thermal nanophononics, bulk acoustic
waves (BAWs), and surface acoustic waves (SAWs), which are closely connected
to the topic of research discussed in this review. However, the operating
frequency range, experimental techniques, and fabrication methods are
different. The reader interested in thermal phonons, BAWs or SAWs is invited
to refer to the respective review articles [65, 66, 67, 68, 69, 70]. In this
article we will highlight some recent results in the fields of nanoacoustics
and nanophononics, and then we will present what we believe are promising and
exciting new avenues for the following years.

##  2 Recent developments in nanophononics and nanoacoustics

###  2.1 Confinement of light and acoustic phonons

The control of the acoustic nanowave dynamics is usually performed using
acoustic resonators at the nano- and microscale. At the intersection between
optomechanics and nanophononics, the state of the art is based on microdisks
[30, 33, 71], microcavities [72, 5], nanobeams [7, 73], and membrane-based
resonators [12, 74]. Recent applications include sensing [75], phonon lasing
[4], and the generation of non-classical phononic states [45].

The fabrication of these devices relies on a top-down approach, thereby
limiting the smallest achievable feature, and hence the working frequency
range, generally to less than 10 GHz (See Fig. 1 and references therein). To
reach even higher bands, bottom-up techniques warranting atomic-flat
interfaces and nm-thick layers, such as molecular beam epitaxy and high-
quality sputtering, are needed. Using thin films, multilayers, distributed
Bragg reflectors, and Fabry-Perot resonators working up to 1 THz unlocked the
domain of ultrahigh frequency nanophononics [76, 77]. Fabry-Perot GaAs/AlAs-
based nanocavities can be designed for the simultaneous confinement and
colocalization of light and hypersound due to the equal ratios of speeds and
impedances for light and sound in these materials [5, 72, 78]. These
resonators constitute an innovative platform for accessing phonon dynamics
[79] and cavity optomechanics applications.

These multilayered cavities can be laterally etched to create optophononic
micropillar cavities, as shown in Fig. 2(a). This results in the 3D
confinement of phonons and photons, thus tailoring the acoustic dispersion and
local acoustic density of states [74], as well as the optophononic
interactions [72, 5]. Semiconductor-based micropillar cavities are widely used
in applications involving quantum dots [80], quantum wells [81], and
optoelectronic devices, which makes them the perfect scenario for studying
phononic interactions.

###  2.2 Simulation of solid-state systems

Analogous to band structures for photons and electrons in solid-state physics,
one can engineer the acoustic band structure using multilayered periodic
systems, such as superlattices (SLs) or coupled cavity systems. In these
systems, it is possible to slow down a wavepacket, change the sign of
propagation, and manipulate different mode symmetries [82]. Extending the
electronic and acoustic bands analogy, it is possible to mimic any arbitrary
potential. For instance, the Bloch oscillations of acoustic phonons [83] and
topological interface states [5] were implemented in both SLs-based and
coupled-cavity systems [82, 84]. The acoustic-phonon band engineering in SLs
[82] and coupled cavity structures [84] enable a versatile implementation of
1D tight binding and nearly free electron models using high-frequency phonons.

Figure 2:  (a) SEM images of GaAs/AlAs micropillar cavities. Top panel: Array
of etched micropillars of different sizes and shapes. Bottom left panel:
Zoomed image of a single micropillar. Bottom right panel: Colormap of the
displacement field highlighting the confinement of acoustic phonons in the
cavity, superposed on the enlarged microscopy image. (b) Photo of a
micropillar glued and mode-matched to a single-mode fiber. (c) Left panel:
Reflectivity timetrace of a pump-probe experiment. An enlargement of the
timetrace is shown on the inset, unveiling the presence of coherent
oscillations. Right panel: FFT spectra of the displayed timetrace. (d)
Interferometric-based filtering of acoustic modes of a 3D micropillar. (e)
Angular filtering technique to access 20 GHz acoustic modes in Brillouin
scattering for planar cavities.

###  2.3 Experimental techniques to access acoustic phonons

The absence of standard characterization techniques for high-frequency
acoustic phonons motivated the development of optical techniques both in the
frequency and temporal domains. Picosecond ultrasonics based on pump-probe
schemes using ultrafast lasers unveils the coherent phonon dynamics [85],
while high-resolution Raman and Brillouin scattering spectroscopy techniques
unveil the incoherent phonon characteristics.

The pump-probe technique allows the investigation of the reflectivity
timetrace after a perturbation induced by an ultrashort pulsed laser (Fig.
2c). In the picosecond ultrasonics framework, the coherent acoustic phonons,
generated via photoinduced stress by the pump pulse [86], modulate the
refractive index and shape of the material. The coherently generated phononic
signal is then imprinted on the transient optical reflectivity or transmission
sensed by the probe pulse, and can be reconstructed by scanning the relative
time delay between pump and probe pulses [85]. Depending on the lifetime of
the acoustic phonons, the use of long optomechanical delay lines ($\sim 4$ m)
is needed, which affects the stability of the spatiotemporal overlap of the
pump and probe laser. This issue can be addressed by employing the
asynchronous optical sampling (ASOPS) technique based on the traditional
pump–probe experiment, using two mode-locked lasers pulsing at slightly
different repetition rates [87]. This technique eliminates the need for a
mechanical delay line, thus increasing the stability of the setup. On the
other hand, ASOPS requires two oscillators and the precise control on the
repetition rates, which might be challenging. To deal with the mechanical
stability issue differently, as well as the reproducibility of focalization,
and optical mode matching, we recently developed fiber-integrated planar and
micropillar optophonic cavities (Fig. 2(b)) for pump-probe experiments [88].
In this approach, a single-mode fiber is aligned and glued onto an
optophononic microcavity (planar or micropillar) with sufficient optical mode
overlap and requires no further alignment steps in real-time experiments. This
monolithic sample structure is potentially transportable to perform
reproducible plug-and-play pump-probe experiments in individual
microstructures at any laboratory.

Non-invasive Raman and Brillouin spectroscopy experiments based on the
inelastic scattering of light from excited incoherent phonons are routinely
performed to analyze the phononic modes of nanostructures [89]. In Raman
scattering, the scattered signal from optical phonons (in THz range) is
separated by a large frequency shift from the excitation laser, while reading
out the small frequency shift of Brillouin scattered signal from acoustic
phonons (GHz range) is a non-trivial task. Brillouin spectroscopy experiments
usually incorporate multiple passage tandem interferometers or single-pass
Fabry-Pérot spectrometers to record the Brillouin spectra of high-frequency
acoustic phonons ranging from hundreds of MHz to GHz [90, 91, 92, 93]. More
recently, in order to probe the Brillouin scattering spectra from phononic
nanostructures and devices working at broad acoustic and optical wavelength
ranges, we developed custom-built versatile experimental techniques as
sketched in Figs. 2(d) and 2(e). Figure 2(d) displays the diffraction-based
spatial filtering method to assess the Brillouin scattering at 300 GHz in a 3D
micropillar resonator [59]. In this scheme, mismatched spatial patterns of the
diffracted laser excitation (shown in red) and the Gaussian-shaped Brillouin
signal (shown in blue) are exploited to selectively collect the Brillouin
signal transmitted through the node of the pattern. A fiber-based angular
filtering technique is shown in Fig. 2(e) to measure the confined acoustic
mode in the range of 20-300 GHz in multilayered optophononic planar cavities
[94]. This scheme is based on the excitation (laser indicated in green) and
collection of the enhanced Brillouin scattering signals (shown in yellow)
through the optical cavity satisfying the double optical resonance condition
[95]. The technique permits for better angular filtering of the signal using a
single-mode fiber and employs etalon-filtering to further achieve high-
spectral resolution at low-frequency phonons.

Noise spectroscopy, a conventional experimental technique in optomechanics,
finds its limits in frequency, wavelength, or required sensitivity, motivating
new developments in the fields at the intersection between cavity
optomechanics and Brillouin spectroscopy. Electrical and magnetic generation
of coherent acoustic phonons [96, 55] are challenging but promising research
perspectives. Even the use of phase-changing materials (VO2) as innovative
transducers has been reported [97].

###  2.4 Novel nanoacoustic materials and structures

Traditionally, acoustic phonon engineering is performed in highly crystalline
and ordered systems, based on semiconductors, metals, and oxides systems.
However, recent works demonstrate, on one hand, the feasibility and potential
of nonperiodic systems such as disordered superlattices [78]. On the other
hand, the use of easily available materials has been demonstrated in
nanophononics that are based on reliable fabrication methods such as
mesoporous [98, 99, 100, 101] medium, and polymer-based colloidal crystals
[102, 103]. Acoustic frequencies in resonators based on mesoporous materials
range between 5 and 40 GHz, with Q-factors in the order of $\sim$5-20 [101].
The chemical functionalization of resonators upon fluid adsorption finds its
interest in sensing applications. [104] These functionalities and inexpensive
fabrication processes are ideal for practical applications.

###  2.5 Resonators for ultrahigh frequency phonons and light

The confinement of photons, phonons, and excitons in the same hybrid resonator
provides a gateway to allow phononic control on the strong light-matter
coupling regime [105, 58, 4].

An optomechanical resonator facilitates the strong coherent coupling of
photons to phonons resulting in the so-called dynamical back-action, which
allows both the laser cooling [40] down to the ground state of mechanical
motion as well as the amplification of mechanical oscillations [106]. A hybrid
polariton-based optomechanical system was theoretically proposed to evince the
cooling of mechanical motion at a single polariton level [107] and to reveal
the unconventional dissipative coupling to mechanical mode [108]. These hybrid
systems are experimentally investigated to yield ultrastrong photoelastic
coupling up to $10^{5}$ at exciton-polariton resonance in GaAs/AlAs multiple
quantum wells [105]. This strong coupling of cavity polaritons to the high-
frequency acoustic phonons in GaAs superlattices emanates as a prospective
approach beneficial to experimentally achieve the cooling down of the
mechanical vibrations to the quantum level. A recent study has introduced a
new platform for the electrically driven longitudinal acoustic phonon-induced
modulation of the polariton energies with amplitudes larger than the Rabi-
splitting [109]. The electrically generated and detected coherent super high-
frequency longitudinal bulk acoustic waves (LBAWs) have emerged as a powerful
tool for governing different excitations in semiconductors [110, 111] and
provide an access to explore nonlinear acoustic processes such as second
harmonic generation [112], parametric oscillations and amplification featuring
phonon lasing phenomenon.

A sound laser is characterized by the stimulated coherent emission of acoustic
phonons and is also commonly referred to as a ‘phonon laser’ [4, 113, 114,
96]. The phonon lasing action has been theoretically advised and
experimentally reported in several optomechanical systems at different
acoustic frequencies ranging from MHz to hundreds of GHz [4, 114, 96, 115,
116, 117, 118]. At ultrahigh frequencies, the experimental observation of
phonon amplification has been reported in hybrid systems coupling BEC with
acoustic phonons [4], and in semiconductor superlattices exploiting electron-
phonon interactions [96].

###  2.6 Nanoacoustics using optical nanoantennas

Optical nanoantennas and, more recently, metasurfaces, revolutionized the
field of optics. Their use in nanophononics came up as an original strategy to
overcome one of the main roadblocks in the field, the lack of tailored and
efficient transducers. Gigahertz mechanical modes are strongly dependent on
the shape and materials of nanoantenna structures, and the interactions with
light can be polarization-dependent, which enables a new playground for
nanoacoustics. Indeed, single nanoantennas [119], or extended metasurfaces
[120, 121, 122] can be used as selective phonon generators, detectors and also
for the demonstration of directional transport of phonons at the nanoscale
[123, 124]. Furthermore, plasmonic nanoparticles scaled down to 1 nm size
range present acoustic resonances up to a few THz, which makes them potential
acoustic terahertz generators [125, 126]. An advanced engineering of the
interaction of optical and GHz-acoustic fields in nanoantenna arrays is a
promising arena for the development of optical, optoelectronic, and data
communication applications.

##  3 What are the perspectives on acoustic phonon engineering?

###  3.1 Tunable, responsive, and active optophononic devices

The development and integration of ultrahigh frequency optomechanical
functionalities in Si-based platforms appear as a natural step in the
evolution of the field. [127] The functionalization and dynamical tuning of
artificial acoustic materials, particularly at the nanoscale, would be a
breakthrough in the engineering of intelligent and programmable materials. In
nanoacoustics, despite the potential impact on data communications, sensing,
optoelectronics, non-destructive testing, and in general on fundamental
physics, with counted exceptions [103], no tunable nanophononic devices have
been reported up to now. A reversible, and potentially ultrafast, change in
the elastic properties (speed of sound, density, absorption, shape) of a
nanostructure under external environment control (Fig. 3(a)) would enable such
dynamical behavior. Mesoporous thin films [101], susceptible of being
functionalized and sensitive to environmental conditions, VO2 showing a phase
change associated with the emission of shock waves [97], graphene and other 2D
heterostructures having tunable electronic properties [128], and
magnetoelastic materials [129, 130, 131, 132] are possible ways towards the
implementation of dynamical structures.

Figure 3:  Schematics of perspectives on high-frequency acoustic phonons. (a)
Tunable acoustic resonators: Under external environment control – such as
relative humidity (RH), temperature (T), strain ($\sigma$), energy ($h\nu$),
electric field ($\vec{E}$) or magnetic field ($\vec{B}$)–, the acoustic
resonator $\Omega$, that depends on the structural parameters mass density
($\rho$), index of refraction ($n$), speed of sound ($v$) and acoustic
impedance ($Z$), undergoes changes on its resonance mode
$\Omega^{\prime}=\Omega+\Delta\Omega$ due to variation on the structure
constants ($\rho^{\prime}$, $n^{\prime}$, $v^{\prime}$,$Z^{\prime}$). (b) Top
panel: the principle of dynamical back action[106] applied to an
optomechanical system operating in the resolved sideband regime where the
frequency of the mechanical mode ($\omega_{m}$) is higher than the cavity
line-width of optical mode ($\omega_{c}$). Upon interaction with the blue-
detuned incident laser, there is an amplification of the mechanical mode, on
the other hand, the red-detuned laser leads to the cooling of the mechanical
mode. Bottom panel: Raman protocol for the creation (I. Write) and the
annihilation (II. Read) of single phonon Fock state [62] (c) Left panel:
Interfacing different solid-state platforms via coherent acoustic phonons. The
physical system $\ket{\psi}$ with engineered properties to couple with
acoustic phonons, after excitation, transfers information to another system
$\ket{\psi^{\prime}}$ via coherent acoustic phonons, that can be sensed, e.g.,
optically. Right panel: Coupled acoustic resonators establishing a phonon
network.

###  3.2 Quantum nanoacoustics

The core competencies for scalable quantum information processing are high
bandwidth and long coherence times, which are fulfilled by coherent acoustic
phonons. During the past few decades, the quantum nature of optomechanical
systems has been investigated under two different experimental configurations
as sketched in Fig. 3(b): by creating a quantum ground state of mechanical
motion under dynamical back-action (top panel) [106] at cryogenic temperatures
or using Raman scattering for creation and annihilation of a single phonon
(bottom panel) in an ultrafast laser detection method [45]. In recent
experiments, optical phonons (40 THz) in bulk diamond lattices are exploited
to observe non-classical correlations [133] and phonon entanglement [134], and
further to perform a Bell non-locality test [62]. Contrary to optical phonons,
acoustic phonons are able to couple with various excitations (photons,
electrons, etc) over a broad frequency range, and their interaction can be
controlled at will in engineered structures for stronger interactions. For
instance, the band structure engineering of acoustic phonons constitutes a
unique asset. In this context, the emergent quantum technologies demand a
quantum acoustical platform [135, 136, 137] operating at gigahertz frequencies
providing single phonons for their use as quantum transducers, quantum sensors
for displacement, and also as a probe in quantum thermodynamics.

###  3.3 Phonon transport and interfacing

Owing to the strong coupling of acoustic phonons with other excitations, such
as electrons, photons, excitons, plasmons, polaritons, and magnons, the
interfacing of platforms based on different excitations is possible by
engineering their interactions. Recently, the coupling of qubits with surface
acoustic waves has been achieved [29]. Furthermore, acoustic phonons can be
employed as information carriers due to their long mean free path, which leads
to potential application on signal processing and phononic networks (Fig.
3(c)). However, previous works are frequency-limited up to a few GHz [123,
124, 2, 137, 138, 139, 140]. By bringing these concepts to nanoacoustics and
nanophononics it is possible to raise the frequency of the systems, thus
reaching the quantum acoustic regime, and guide the quantum information as
desired in complex acoustic networks. Inspired by developments in optics and
electronics, topology appears as a promising tool towards the achievement of
loose-less transport of nanophononic information and energy. In this sense, it
is essential to develop and unlock 2D and 3D structures (resonators,
waveguides, generators, and detectors) working in the GHz-THz regime where
topological engineering can be defined.

##  4 Conclusions

We have shown our vision of the state of the art in phononic engineering at
the tens to hundreds of GHz frequency range, highlighting exciting phenomena,
such as the strong coupling with other excitations, and prospects in quantum
applications. The nanoacoustics and nanophononics landscape is vast and
difficult to cover in a short review. For instance, we did not cover the full
field of bulk acoustic waves, high-impact applications like thermal transport
management [141], nanoimaging and non-destructive testing, the study of
biological tissues [142, 143, 144, 145], or the potential of new research
fields such as ultrahigh frequency sonochemistry [146]. Combining these
concepts with the ones presented in this article, incorporating novel
materials, or bringing the acoustic resonators towards low occupation numbers
will lead to a new generation of tunable and responsive nanophononic devices,
quantum nanoacoustics, and the interfacing of different solid-state platforms
via coherent acoustic phonons. The fast-growing fields of nanoacoustics and
nanophononics will perhaps become the striking element for future quantum
communication, sensing applications, and data communication technologies.

##  5 Acknowledgements

The authors acknowledge funding by the European Research Council Starting
Grant No. 715939, Nanophennec, the French RENATECH network, and through a
public grant overseen by the ANR as part of the “Investissements d’Avenir”
program (Labex NanoSaclay Grant No. ANR-10-LABX-0035).

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