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The Off-Resonant Ratchet: A Study of the Crossover Between Classical and Quantum Dynamics

Rajendra K. Shrestha, Wa Kun Lam, Jiating Ni, G. S. Summy

Published Oct 20, 2012• 0 citations
OpenAlex

Abstract

We study the crossover between classical and quantum dynamics by observing the behavior of a quantum ratchet created by exposing a Bose-Einstein condensate to short pulses of a potential which is periodic in both space and time. Such a ratchet is manifested by a directed current of particles, even though there is an absence of a net bias force. We confirm that the ratchet behavior can under certain circumstances be the same in both regimes. We demonstrate that this behavior can be understood using a single variable containing many of the experimental parameters and thus the ratchet current is describable using a single universal scaling law.

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Quantum-resonance ratchets associated with the kicked particle are experimentally realized for arbitrary quasimomentum using a Bose-Einstein condensate (BEC) exposed to a pulsed standing light wave. The ratchet effect for general quasimomentum arises even though both the standing-wave potential and the initial state of the BEC have a point symmetry. The experimental results agree well with theoretical ones which take into account the finite quasimomentum width of the BEC. In particular, this width is shown to cause a suppression of the ratchet acceleration for exactly resonant quasimomentum, leading to a saturation of the directed current.

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We study the crossover between classical and quantum dynamics by observing the behavior of a quantum ratchet created by exposing a Bose-Einstein condensate to short pulses of a potential which is periodic in both space and time. Such a ratchet is manifested by a directed current of particles, even though there is an absence of a net bias force. We confirm that the ratchet behavior can under certain circumstances be the same in both regimes. We demonstrate that this behavior can be understood using a single variable containing many of the experimental parameters and thus the ratchet current is describable using a single universal scaling law.
We experimentally investigate the phenomenon of a quantum ratchet created by exposing a Bose-Einstein condensate to short pulses of a potential which is periodic in both space and time. Such a ratchet is manifested by a directed current of particles, even though there is an absence of a net bias force. We confirm a recent theoretical prediction [M. Sadgrove and S. Wimberger, New J. Phys. 11, 083027 (2009)] that the current direction can be controlled by experimental parameters which leave the underlying symmetries of the system unchanged. We demonstrate that this behavior can be understood using a single variable containing many of the experimental parameters and thus the ratchet current is describable using a single universal scaling law.
We use an atomic ratchet realized by applying short pulses of an optical standing-wave to a Bose–Einstein condensate to study the crossover between classical and quantum dynamics. The signature of the ratchet is the existence of a directed current of atoms, even though there is an absence of a net bias force. Provided that the pulse period is close to one of the resonances of the system, the ratchet behavior can be understood using a classical like theory which depends on a single variable containing many of the experimental parameters. Here we show that this theory is valid in both the true classical limit, when the pulse period is close to zero, as well as regimes when this period is close to other resonances where the usual scaled Planck's constant is nonzero. By smoothly changing the pulse period between these resonances we demonstrate how it is possible to tune the ratchet between quantum and classical types of behavior.
Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential.
A theory of quantum ratchets for a particle periodically kicked by a general periodic potential under quantum-resonance conditions is developed for arbitrary values of the conserved quasimomentum β. A special case of this theory is experimentally realized using a Bose–Einstein condensate (BEC) exposed to a pulsed standing light wave. While this case corresponds to completely symmetric potential and initial wave-packet, a purely quantum ratchet effect still arises from the generic noncoincidence of the symmetry centers of these two entities. The experimental results agree well with the theory after taking properly into account the finite quasimomentum width of the BEC. This width causes a suppression of the ratchet acceleration occurring for "resonant" β, so that the mean momentum saturates to a finite ratchet velocity, strongly pronounced relative to that for nonresonant β.
We study the response of a Bose-Einstein condensate to an unbiased periodic driving potential. By controlling the space and time symmetries of the driving we show how a directed current can be induced, producing a coherent quantum ratchet. Weak driving induces a regular behavior, and space and time symmetries must both be broken to produce a current. For strong driving, the behavior becomes chaotic and the resulting effective irreversibility means that it is unnecessary to explicitly break time symmetry. Spatial asymmetry alone is then sufficient to produce the ratchet effect, even in the absence of interactions, and although the system remains completely coherent.
Quantum-resonance ratchets associated with the kicked particle are experimentally realized for arbitrary quasimomentum using a Bose-Einstein condensate (BEC) exposed to a pulsed standing light wave. The ratchet effect for general quasimomentum arises even though both the standing-wave potential and the initial state of the BEC have a point symmetry. The experimental results agree well with theoretical ones which take into account the finite quasimomentum width of the BEC. In particular, this width is shown to cause a suppression of the ratchet acceleration for exactly resonant quasimomentum, leading to a saturation of the directed current.