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arXiv:1712.09890 · Annalen der Physik

Hamiltonian Ratchets with Ultra‐Cold Atoms

Jiating Ni, Siamak Dadras, Wa Kun Lam, Rajendra K. Shrestha, Mark Sadgrove, Sandro Wimberger, Gil S. Summy

Published Jul 7, 2017• 26 citations
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Abstract

Quantum‐resonance ratchets have been realized over the last ten years for the production of directed currents of atoms. These non‐dissipative systems are based on the interaction of a Bose‐Einstein condensate with an optical standing wave potential to produce a current of atoms in momentum space. In this paper we provide a review of the important features of these ratchets with a particular emphasis on their optimization using more complex initial states. We also examine their stability close to resonance conditions of the kicking. Finally we discuss the way in which these ratchets may pave the way for applications in quantum (random) walks and matter‐wave interferometry.

DOI
10.1002/andp.201600335

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Quantum‐resonance ratchets have been realized over the last ten years for the production of directed currents of atoms. These non‐dissipative systems are based on the interaction of a Bose‐Einstein condensate with an optical standing wave potential to produce a current of atoms in momentum space. In this paper we provide a review of the important features of these ratchets with a particular emphasis on their optimization using more complex initial states. We also examine their stability close to resonance conditions of the kicking. Finally we discuss the way in which these ratchets may pave the way for applications in quantum (random) walks and matter‐wave interferometry.
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.
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.
We demonstrate quantum resonance ratchets created with Bose-Einstein condensates exposed to pulses of an off-resonant standing light wave. We show how some of the basic properties of the ratchets are controllable through the creation of different initial states of the system. In particular, our results prove that through an appropriate choice of initial state it is possible to reduce the extent to which the ratchet state changes with respect to time. We develop a simple theory to explain our results and indicate how ratchets might be used as part of a matter-wave interferometer or quantum random walk experiment.
We investigate the effect of the nonlinear interaction on the quantum resonance ratchet for the periodically kicked Bose-Einstein condensate that is realized on a ring. In the noninteracting case, the wave packet spreads asymmetrically in momentum space, leading to a directed current. We show that for the weak nonlinear interaction, the probability density distribution in momentum space has two peaks which linearly shift to ward positive and negative momentum, respectively. The force periodically acting on each peak is a constant with time evolution. The competition between the motions of the two parts of cold atoms leads to the reduce or the revival of the momentum current. For the strong nonlinearity, the momentum distribution has only one peak which does not shift with time. The force on this peak is almost zero with time evolution, thus the directed current varnishes.
The dynamical evolution of a periodically kicked Bose-Einstein condensate was investigated by simulation. Emphasis was placed on the influence of the nonlinear interaction between atoms on the quantum-resonance ratchet effect. It was found that weak nonlinear interaction reduces the ratchet effect while the strong nonlinear interaction causes the ratchet current to disappear or even reversed. The ratchet effect under high-order quantum resonance conditions was further studied. The ratchet effect is not obvious in this case and can be easily destroyed by the noise of the kicking potential period.
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.