Qubit dynamics driven by smooth pulses of finite duration
We present a study of the dynamics of a qubit driven by a pulsed field of
finite duration. The pulse shape starts and ends linearly in time. The most
typical example of such a shape is the sine function between two of its nodes,
but several other pulse shapes are also studied. All of them present smooth
alternatives to the commonly used rectangular pulse shape, resulting in much
weaker power broadening, much faster vanishing wings in the excitation line
profile and hence much reduced sidebands. In the same time, such shapes with a
well-defined finite duration do not suffer from the spurious effects arising
when truncating a pulse of infinite duration, e.g. Gaussian. We derive two
approximate analytic solutions which describe the ensuing quantum dynamics.
Both approximations assume that the field changes linearly at the beginning and
the end of the driving pulse, and adiabatically in between. The first
approximation matches the linear and adiabatic parts at an appropriate instant
of time and is expressed in terms of Weber's parabolic cylinder functions. The
second, much simpler, approximation uses the asymptotics of the Weber function
in order to replace it by simpler functions, and some additional
transformations. Both approximations prove highly accurate when compared to
experimental data obtained with two of the IBM Quantum processors. Both the
greatly reduced power broadening and the greatly suppressed sidebands are
observed for all pulse shapes, in a nearly complete agreement between theory
and experiment.
Ivo S. Mihov Nikolay V. Vitanov