Directed Transport of Atoms in a Hamiltonian Quantum Ratchet

Abstract

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.

Quantum ratchet transport with minimal dispersion rate

“…1(a)]. In contrast to its classical counterpart, however, where the chaotic dynamics erases the memory about the initial conditions of the system preparation exponentially fast [18,19], a fully coherent quantum ratchet maintains this information, which is encoded in the coefficients C(t 0 ) forever. All the symmetries from Table I, except the first oneŜ 1 , involve time transformations-time inversion inŜ 2 , time shift inŜ 3 , and a combined transformation inŜ 4 -so that the contributions from the eigenstates with opposite quasimomenta might be different for a given, fixed t 0 , C α,−κ (t 0 ) = C α,κ (t 0 ), even when one (or all) of the symmetriesŜ 2 ,Ŝ 3 ,Ŝ 4 are obeyed.…”

“…The system given by Eqs. (2)-(4) could describe the dynamics of a diluted cloud of ultracold atoms placed into optical potential formed by counterpropagating laser beams with periodically modulated intensities [19]. The Hamiltonian (2) is periodic both in time and space.…”

“…The Hilbert space of the system can be imagined as a set of "conveyer belt" eigenstates, each one of which is moving with its own velocity, and the overall ratchet current depends on how the initial wave packet |ψ(t = t 0 ) was distributed among the various belts [18,19].…”

“…An interesting class of ratchet systems are dissipation-free Hamiltonian ratchets, classical [1,6,12] and, even more intriguingly, quantum ones [1,[7][8][9][13][14][15][16][17][18]. For example, a bi-harmonic flashing potential with periodically and uniformly modulated potential height [18], could be turned into a conveyer belt for a Bose-Einstein condensate (BEC) of rubidium atoms [19].…”

Controlling the momentum current of an off-resonant ratchet

“…It has revealed a wide variety of interesting effects including: dynamical localization [2], quantum resonances (QR) [2][3][4], quantum accelerator modes [5,6], and quantum ratchets [7][8][9][10][11][12][13][14][15]. The latter are quantum mechanical systems that display directed motion of particles in the absence of unbalanced forces.…”