The correspondence limit is illustrated for the periodically kicked pendulum. The classical dynamics of this system can be represented by a discrete map. A corresponding quantum map is derived and then rendered in the Ehrenfest formulation for expectation values. The Ehrenfest representation is studied for a minimum uncertainty Gaussian wave packet. It is shown that as \ensuremath{\Elzxh} gets very small, followed by a decrease in the variance of the wave packet, the quantum map shadows the classical map with an error approaching zero for a length of time approaching infinity. The Gaussian form of the wave packet is preserved by the time evolution provided ${\mathrm{\ensuremath{\omega}}}_{0}$T\ensuremath{\ll}1. This constraint implies that the classical map is predominantly not chaotic with very small regions of very weak chaos. As ${\mathrm{\ensuremath{\omega}}}_{0}$T approaches 1, where the classical map becomes strongly chaotic, the propagation in time of the Gaussian wave packet completely breaks down. The possible significance of this breakdown is discussed.The correspondence limit is illustrated for the periodically kicked pendulum. The classical dynamics of this system can be represented by a discrete map. A corresponding quantum map is derived and then rendered in the Ehrenfest formulation for expectation values. The Ehrenfest representation is studied for a minimum uncertainty Gaussian wave packet. It is shown that as \ensuremath{\Elzxh} gets very small, followed by a decrease in the variance of the wave packet, the quantum map shadows the classical map with an error approaching zero for a length of time approaching infinity. The Gaussian form of the wave packet is preserved by the time evolution provided ${\mathrm{\ensuremath{\omega}}}_{0}$T\ensuremath{\ll}1. This constraint implies that the classical map is predominantly not chaotic with very small regions of very weak chaos. As ${\mathrm{\ensuremath{\omega}}}_{0}$T approaches 1, where the classical map becomes strongly chaotic, the propagation in time of the Gaussian wave packet completely breaks down. The possible significance of this breakdown is discussed.

Physical Review AMar 1, 199021 citations

Time-dependent wave packet propagation using quantum hydrodynamics

Brian K. Kendrick

Springer eBooksJan 1, 20122 citations

Time-dependent wave packet propagation using quantum hydrodynamics

Brian K. Kendrick

Theoretical Chemistry AccountsJan 1, 201219 citations

Matter-wave analog of a fiber-optic gyroscope

Katarzyna A. Krzyzanowska, Jorge Ferreras, Changhyun Ryu +2 more

Confining the propagating wave packets of an atom interferometer inside a waveguide can substantially reduce the size of the device while preserving high sensitivity. We have realized a two-dimensional Sagnac atom interferometer in which Bose-condensed $^{87}\mathrm{Rb}$ atoms propagate within a tight waveguide formed by a collimated laser beam, a matter wave analog of the fiber optic gyro. The condensate is split, reflected, and recombined with a series of Bragg pulses while the waveguide moves transversely so that the wave-packet trajectories enclose an area. Delta-kick cooling is used to prepare low-density atomic wave packets with a temperature of $3\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{K}$ . The low density reduces the impact of interatomic interactions, while the low temperature limits the expansion of the wave packet during the interferometer cycle. The effective enclosed area is $0.8\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{m}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}$ with an average fringe contrast of 20% and underlying contrast up to 60%. The main source of the reduced average contrast is phase noise caused by mechanical vibrations of the optical components. We present a measurement of Allan deviation for such an atom rotation sensor, showing that the interferometer phase noise falls with averaging time $\ensuremath{\tau}$ as ${\ensuremath{\tau}}^{\ensuremath{-}1/2}$ for $\ensuremath{\tau}$ up to 10 000 seconds. The statistical noise falls below the Earth rotation rate after 30 minutes of averaging.Confining the propagating wave packets of an atom interferometer inside a waveguide can substantially reduce the size of the device while preserving high sensitivity. We have realized a two-dimensional Sagnac atom interferometer in which Bose-condensed $^{87}\mathrm{Rb}$ atoms propagate within a tight waveguide formed by a collimated laser beam, a matter wave analog of the fiber optic gyro. The condensate is split, reflected, and recombined with a series of Bragg pulses while the waveguide moves transversely so that the wave-packet trajectories enclose an area. Delta-kick cooling is used to prepare low-density atomic wave packets with a temperature of $3\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{K}$. The low density reduces the impact of interatomic interactions, while the low temperature limits the expansion of the wave packet during the interferometer cycle. The effective enclosed area is $0.8\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{m}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}$ with an average fringe contrast of 20% and underlying contrast up to 60%. The main source of the reduced average contrast is phase noise caused by mechanical vibrations of the optical components. We present a measurement of Allan deviation for such an atom rotation sensor, showing that the interferometer phase noise falls with averaging time $\ensuremath{\tau}$ as ${\ensuremath{\tau}}^{\ensuremath{-}1/2}$ for $\ensuremath{\tau}$ up to 10 000 seconds. The statistical noise falls below the Earth rotation rate after 30 minutes of averaging.

arXiv:2201.12461Physical Review AOct 10, 202340 citations

Evolution of quantum wave packets in the presence of time-dependent absorption

Maximilien Barbier, Mathieu Beau, Arseni Goussev

Bulletin of the American Physical SocietyMar 5, 20150 citations

^{87}\mathrm{Rb}

atoms propagate within a tight waveguide formed by a collimated laser beam, a matter wave analog of the fiber optic gyro. The condensate is split, reflected, and recombined with a series of Bragg pulses while the waveguide moves transversely so that the wave-packet trajectories enclose an area. Delta-kick cooling is used to prepare low-density atomic wave packets with a temperature of

3\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{K}

. The low density reduces the impact of interatomic interactions, while the low temperature limits the expansion of the wave packet during the interferometer cycle. The effective enclosed area is

0.8\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{m}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}

with an average fringe contrast of 20% and underlying contrast up to 60%. The main source of the reduced average contrast is phase noise caused by mechanical vibrations of the optical components. We present a measurement of Allan deviation for such an atom rotation sensor, showing that the interferometer phase noise falls with averaging time $\ensuremath{\tau}$ as ${\ensuremath{\tau}}^{\ensuremath{-}1/2}$ for $\ensuremath{\tau}$ up to 10 000 seconds. The statistical noise falls below the Earth rotation rate after 30 minutes of averaging.