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Results in Physics

Quantum transport and control of a classically chaotic open system

Mingliang Zou, Gengbiao Lu, Yunrong Luo, Wenhua Hai

Published May 11, 2020• 10 citations
Publisher

Abstract

We report on the first direct investigation of quantum transport and control of a classically chaotic open system which means a single atom held in an open and depth-tilt-modulated one-dimensional (1D) optical lattice. The area of chaotic region is demonstrated to decrease with the increase of damping of the classical open system. The corresponding non-Hermitian Hamiltonian is constructed, where the quantum decay rate positively correlating to the classical damping is qualitatively revealed. Under high-frequency approximation of the tilt modulation, we obtain a set of analytical solutions with the effective coupling being strengthened by the adjustable decay rate. The analytical and numerical results mean accordantly that we can enhance the tunneling rate to suppress the decoherence by increasing the decay rate to leave the chaotic region. These results could be useful for qubit transport and control based on the classically chaotic open systems.

DOI
10.1016/j.rinp.2020.103157

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We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.
We investigate the coherent control of quantum tunneling for a single particle held in a driven double-well potential. For a moderate-frequency region, we demonstrate that the irregular quantum tunneling is associated with classically chaotic dynamics. A set of lower resonance-like frequencies is found, for which the coherent destruction of tunneling in the sense of the time average is illustrated numerically. For a high-frequency region, it is shown that the particle is located at the bottom of each well alternately for a long time and the time located in one well can be modulated by adjusting the driving field. The results could be useful for the experiments of controlling single-particle tunneling [see, e.g., E. Kierig, U. Schnorrberger, A. Schietinger, J. Tomkovic, and M. K. Oberthaler, Phys. Rev. Lett. 100, 190405 (2008).].
Atomic quantum systems such as atomic clocks or qubits with cold atoms in tweezer arrays have attracted enormous interests both in academia and industry. In this work, we report a theoretical study and experimental demonstration of quantum tunneling of atoms in 1D optical lattices with decoherence. In such decoherence process, the expansion of atomic wave packet is suppressed and resonance spectrum is broadened. In this regime, as the decoherence rate L or the modulation time t increases, the evolution of atomic wave packets transitions from coherent tunneling to classical diffusion. We propose a detection method to fast evaluate the degree of decoherence in such systems. Our work benefits the study of decoherence properties of precision measurements based on optical lattice.
Summary form only given. Since optical lattices can be used to investigate both classical energy band transport and the corresponding quantized states, they are ideal for studying the classical-quantum correspondence. Here, we investigate this correspondence for cold sodium atoms in a one-dimensional optical lattice along the x-direction and a three-dimensional harmonic trap. The energy versus crystal momentum dispersion relation for the lowest energy band of the optical lattice, together with the harmonic potential, define an effective Hamiltonian that we use to calculate classical atom paths. When a symmetry axis of the harmonic trap is aligned with the optical lattice, the atoms follow stable trajectories similar to Bloch oscillations But tilting this symmetry axis away from the optical lattice direction induces a transition to strongly chaotic dynamics.
We investigate coherent control of a single atom interacting with an optical bipartite lattice via a combined high-frequency modulation. Our analytical results show that the quantum tunneling and dynamical localization can depend on phase difference between the modulation components, which leads to a different route for the coherent destruction of tunneling and a convenient phase-control method for stabilizing the system to implement the directed transport of atom. The similar directed transport and the phase-controlled quantum transition are revealed for the corresponding many-particle system. The results can be referable for experimentally manipulating quantum transport and transition of cold atoms in the tilted and shaken optical bipartite lattice or of analogical optical two-mode quantum beam splitter, and also can be extended to other optical and solid-state systems.
We study dissipative transport of spontaneously emitting atoms in a one-dimensional (1D) standing-wave laser field in the regimes where the underlying deterministic Hamiltonian dynamics is regular and chaotic. A Monte Carlo stochastic wave-function method is applied to simulate semiclassically the atomic dynamics with coupled internal and translational degrees of freedom. It is shown in numerical experiments and confirmed analytically that chaotic atomic transport can take the form either of ballistic motion or a random walking with specific statistical properties. The character of spatial and momentum diffusion in the ballistic atomic transport is shown to change abruptly in the atom-laser detuning regime where the Hamiltonian dynamics is irregular in the sense of dynamical chaos. We find a clear correlation between the behavior of the momentum diffusion coefficient and Hamiltonian chaos probability which is a manifestation of chaoticity of the fundamental atom-light interaction in the diffusivelike dissipative atomic transport. We propose to measure a linear extent of atomic clouds in a 1D optical lattice and predict that, beginning with those values of the mean cloud's momentum for which the probability of Hamiltonian chaos is close to 1, the linear extent of the corresponding clouds should increase sharply. A sensitive dependence of statistical characteristics of dissipative transport on the values of the detuning allows us to manipulate the atomic transport by changing the laser frequency.