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arXiv:2402.13218 · Physical Review A

Spontaneous-emission-induced ratchet in atom-optics kicked-rotor quantum walks

Nikolai Bolik, Sandro Wimberger

Published Jun 4, 2024• 2 citations
arXivHTMLPDF

Abstract

Quantum walks have gained significant attention over the past decades, mainly because of their variety of implementations and applications. Atomic quantum walks are typically subject to spontaneous emissions arising from the control fields. We investigate spontaneous emission in an atom-optics kicked-rotor quantum walk. Here, spontaneous emission occurs naturally due to the driving by the kicks, and it is generally viewed as a nuisance in the experiment. We find, however, that spontaneous emission may induce asymmetries in an otherwise symmetric quantum walk. Our results underscore the utility of spontaneous emission and the application of the asymmetric evolution in the walker's space, i.e., for the construction of a quantum walk ratchet or for Parrondo-like quantum games. This highlights the potential for reinterpreting seemingly adverse effects as beneficial under certain conditions, thus broadening the scope of quantum walks and their applications.

DOI
10.1103/physreva.109.063307

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Quantum walks have gained significant attention over the past decades, mainly because of their variety of implementations and applications. Atomic quantum walks are typically subject to spontaneous emissions arising from the control fields. We investigate spontaneous emission in an atom-optics kicked-rotor quantum walk. Here, spontaneous emission occurs naturally due to the driving by the kicks, and it is generally viewed as a nuisance in the experiment. We find, however, that spontaneous emission may induce asymmetries in an otherwise symmetric quantum walk. Our results underscore the utility of spontaneous emission and the application of the asymmetric evolution in the walker's space, i.e., for the construction of a quantum walk ratchet or for Parrondo-like quantum games. This highlights the potential for reinterpreting seemingly adverse effects as beneficial under certain conditions, thus broadening the scope of quantum walks and their applications.
We analytically investigate the analogy between a standard continuous-time quantum walk in one dimension and the evolution of the quantum kicked rotor at quantum resonance conditions. We verify that the obtained probability distributions are equal for a suitable choice of the kick strength of the rotor. We further discuss how to engineer the evolution of the walk for dynamically preparing experimentally relevant states. These states are important for future applications of the atom-optics kicked rotor for the realization of ratchets and quantum search.
Randomness is the essence of many processes in nature and human society. It can provide important insights into phenomena as diverse as disease transmission, financial markets, and signal processing. Quantum randomness is intrinsically different from classical stochasticity since it is affected by interference and entanglement. Quantum walks profit from the entanglement that is built up between a walker's position and the "coin" degree of freedom that determines the direction of a walker's motion. This entanglement makes quantum walks promising candidates for the implementation of quantum computational algorithms and as a detector of quantum behavior. While several proof-of-principle quantum walk experiments have recently been implemented, the walk scheme we demonstrate here involves the synthesis of the atom-optics kicked rotor with the dynamics of a state selective ratchet realized with a Bose-Einstein condensate. Here we present a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. To implement each step of the walk, i.e. a coin toss followed by a unitary shift operator, we use a microwave pulse, which produces a superposition of two internal states, and a resonant quantum ratchet, which entangles the internal and external degrees of freedom. Our quantum ratchet, whose direction at each step depends on the result of the coin toss, is realized by the atom-optics kicked rotor. We demonstrate the principle features of a standard quantum walk, contrasting them to the behavior of a classical walk. In addition, by manipulating either the walk or coin operator we show how the walk dynamics can be biased or reversed. Furthermore, we show the quantum-to-classical transition in our walk, via randomizing the mixing between the two internal states during each coin toss. Our walk offers distinct advantages arising from the robustness of its dynamics in momentum space, extendability to higher dimensions, and possible dependence on many-body correlations.
This thesis reports on the experimental investigation of several applications of the atom-optical quantum kicked rotor (AOQKR) using a Bose-Einstein condensate (BEC) of 87Rb atoms. The AOQKR was achieved by exposing a BEC to short periodic pulses from a horizontal optical standing wave formed from the interference of two off-resonant laser beams. In the first set of experiments the fidelity or overlap between the kicked rotor states with a reference state was studied. The fidelity resonance widths in pulse period and in acceleration were found to scale as the inverse cube of the kick numbers, a sub-Fourier behavior with possible application in precision measurement experiments. The sensitivity of the fidelity to acceleration was experimentally and theoretically investigated and found to depend on the magnitude and direction of the applied acceleration. The asymmetry between positive and negative acceleration was found to be related to the temperature of the atomic sample. In the second set of experiments, the phenomenon of a quantum ratchet (which is manifested by a directed current of particles in the absence of a net bias force) both at resonance and away from resonance was studied. It was confirmed that the current direction can be controlled by changing experimental parameters which leave the underlying symmetries of the system unchanged. It was demonstrated that this behavior can be understood using a single variable containing many of the experimental parameters. These experiments confirmed that such a ratchet behavior can under certain circumstances be the same in both the true classical and quantum regimes. The final application of the AOQKR discussed in this thesis is the quantum accelerator mode. Both the formation and decay mechanism of these modes were studied.