Initial-state dependence of a quantum resonance ratchet

Abstract

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.

Experimental realization of a momentum-space quantum walk

“…We also draw attention to the fact that, regardless of the ratchet strength, all three walks have some diffusion between the diverging momentum peaks. However, since our shift operator works based on the quantum ratchet, we should be able to achieve walks with less diffusion through the manipulation of the initial state; by increasing the number of components contributing to the initial momentum state, we can achieve narrower spatial wave functions that result in "cleaner" ratchets [44,59] and hence "purer" walk distributions.…”

“…The quantum resonant ratchet effect requires breaking the spatial-temporal symmetry of the problem [44,45,57,58] to direct the dynamics of the AOKR in momentum space accordingly. Experimentally, this is achieved by the choice of an initial state 1/ √ 2(|n = 0 + e iφ |n = 1 ) created by a long pulse of the off-resonant standing wave (Bragg pulse) on the original BEC (|n = 0 ) [44,59]. Applying the AOKR to this state, results in a change in the average momentum by an amount ∆ p = −k sin (φ)/2 after each pulse [45].…”

Spontaneous emission in quantum walks of a kicked Bose-Einstein condensate

“…This is in accord with our earlier statement that the dominating effect is the loss of the resonance condition by the random change of the quasimomentum. Once an atom loses the resonance condition is stops to follow the ratchet-like directed motion [24,25] and hence to follow the designed walk dynamics [14]. Therefore a steering of the walk by induced SE is not directly possible.…”

Hamiltonian Ratchets with Ultra‐Cold Atoms

“…This asymmetry can be enhanced by optimizing the initial state of the ratchets, as shown in Ref. [] and elaborated below. Our experimental results highlight that in general a strong directed current and minimal spread go hand‐in‐hand with each other.…”