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arXiv:1003.3074 · Physical Review A

Driven Dirac-like equation via mirror oscillation: Controlled cold-atom Zitterbewegung

Qi Zhang, Jiangbin Gong, C. H. Oh

Published Feb 12, 2010• 27 citations
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Abstract

By considering mirror oscillation in a ``tripod-scheme'' laser-atom system, we advocate explorative studies of driven Dirac-like equations. Both analytical and numerical studies show that mirror oscillation can be used to drive an effective spin-orbit interaction and hence control the amplitude, the frequency, and the damping of the cold-atom Zitterbewegung oscillation. Our results demonstrate an interesting coupling between the mirror mechanical motion and a fundamental quantum coherent oscillation, opening up new means of matter-wave manipulation.

DOI
10.1103/physreva.81.023608

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By considering mirror oscillation in a ``tripod-scheme'' laser-atom system, we advocate explorative studies of driven Dirac-like equations. Both analytical and numerical studies show that mirror oscillation can be used to drive an effective spin-orbit interaction and hence control the amplitude, the frequency, and the damping of the cold-atom Zitterbewegung oscillation. Our results demonstrate an interesting coupling between the mirror mechanical motion and a fundamental quantum coherent oscillation, opening up new means of matter-wave manipulation.
The Zitterbewegung effect in spin-orbit-coupled spin-1 cold atoms is investigated in the presence of the Zeeman field and a harmonic trap. It is shown that the Zeeman field and the harmonic trap have significant effect on the Zitterbewegung oscillatory behaviors. The external Zeeman field could suppress or enhance the Zitterbewegung amplitude and change the frequencies of oscillation. A much slowly damping Zitterbewegung oscillation can be achieved by adjusting both the linear and the quadratic Zeeman fields. Multifrequency Zitterbewegung oscillation can be induced by the applied Zeeman field. In the presence of the harmonic trap, the subpackets corresponding to different eigenenergies would always keep coherent, resulting in the persistent Zitterbewegung oscillations. The Zitterbewegung oscillation would display very complicated and irregular oscillation characteristics due to the coexistence of different frequencies of the Zitterbewegung oscillation. Furthermore, numerical results show that the Zitterbewegung effect is robust even in the presence of interaction between atoms.
We theoretically and computationally show the simplest realization of SOC using two-level cold atoms interacting with only one laser beam. The underlying mechanism is based on the non-adiabatic nature of laser-atom interaction, with the Rabi frequency being not much larger than the kinetic energy of the atom. We use Zitterbewegung oscillation to further illustrate the effects of the synthesized SOC on the quantum dynamics of the two-level cold atoms. We expect our proposal to be of experimental interest in the quantum simulation of SOC-related physics.
Based on the spin-orbit coupling recently implemented in a neutral cold-atom gas, we propose a scheme to realize spin-dependent scattering of cold atoms. In particular we consider a matter wave packet of cold-atom gas impinging upon a step potential created by the optical light field, inside of which the atoms are subject to spin-orbit interaction. We show that the proposed system can act as a spin polarizer or spin-selective atom mirror for the incident atomic beam. The principle and the operating parameter regime of the system are carefully discussed.
Spin-orbit-coupled ultracold atoms provide an intriguing new avenue for the study of rich spin dynamics in superfluids. In this Rapid Communication, we observe Zitterbewegung, the simultaneous velocity (thus position) and spin oscillations, of neutral atoms between two spin-orbit-coupled bands in a Bose-Einstein condensate (BEC) through sudden quantum quenches of the Hamiltonian. The observed Zitterbewegung oscillations are perfect on a short time scale but gradually damp out on a long time scale, followed by sudden and strong heating of the BEC. As an application, we also demonstrate how Zitterbewegung oscillations can be exploited to populate the upper spin-orbit band and observe a subsequent dipole motion. Our experimental results are corroborated by a theoretical and numerical analysis and showcase the great flexibility that ultracold atoms provide for investigating rich spin dynamics in superfluids.
We propose a scheme for the realization of a quantum walker and a quantum simulator for the Dirac equation with ultracold spinor atoms in driven optical lattices. A precise control of the dynamics of the atomic matter wave can be realized using time-dependent external forces. If the force depends on the spin state of the atoms, the dynamics will entangle the inner and outer degrees of freedom, which offers unique opportunities for quantum information and quantum simulation. Here we introduce a method to realize a quantum walker based on the state-dependent transport of spinor atoms and a coherent driving of the internal state. In the limit of weak driving the dynamics are equivalent to that of a Dirac particle in 1+11+11+1 dimensions. Thus it becomes possible to simulate relativistic effects such as Zitterbewegung and Klein tunneling.
Spin-orbit coupling (SOC), the interaction between the spin and momentum of a quantum particle, is crucial for many important condensed matter phenomena. The recent experimental realization of SOC in neutral bosonic cold atoms provides a new and ideal platform for investigating spin-orbit coupled quantum many-body physics. In this Letter, we derive a generic Gross-Pitaevskii equation as the starting point for the study of many-body dynamics in spin-orbit coupled Bose-Einstein condensates. We show that different laser setups for realizing the same SOC may lead to different mean-field dynamics. Various ground state phases (stripe, phase separation, etc.) of the condensate are found in different parameter regions. A new oscillation period induced by the SOC, similar to the Zitterbewegung oscillation, is found in the center-of-mass motion of the condensate.