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arXiv:1207.5585

Sequential Landau-Zener transitions in spin-orbit coupled systems

Xiaolong Zhang, Jiahao Huang, Yuexia Zhang, Kelin Gao, Chaohong Lee

Published Jul 24, 2012• 0 citations
arXivHTMLPDF

Abstract

We investigate the Landau-Zener (LZ) process in spin-orbit coupled systems of single or multiple two-level (spin-$\frac{1}{2}$) particles. The coupling between internal spin states and external vibrational states, a simple spin-orbit coupling (SOC), is induced by applying a spin-dependent harmonic trap. Because of the SOC, the single-particle energy-level structures are modified by the Franck-Condon (FC) effects, in which some avoided energy-level-crossings (ELCs) are almost closed and some ELCs are opened. The close of avoided ELCs and the open of ELCs result in the FC blockade and the vibrational transitions, respectively. For a given low sweeping rate, the sequential LZ transitions of ladder-like population transition can be induced by strong SOC. We derive an analytical formula for the final population which is well consistent with the numerical results. For a given strong SOC, the sequential LZ transitions are submerged in the non-adiabatic transitions if the sweeping rate is sufficiently high. Further, we study LZ transitions of multiple interacting two-level Bose particles in a spin-dependent harmonic trap. The interplay between the SOC effects and the interaction effects is explored.

DOI
10.48550/arxiv.1207.5585

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We analytically study the effect of gravitational and harmonic forces on ultracold atoms with synthetic spin-orbit coupling (SOC). In particular, we focus on the recently observed transitions between internal states induced by acceleration of the external modes. Our description corresponds to a generalized version of the Landau-Zener (LZ) model: the dimensionality is enlarged to combine the quantum treatment of the external variables with the internal-state characterization; additionally, atomic-interaction effects are considered. The emergence of the basic model is analytically traced. Namely, by using a sequence of unitary transformations and a subsequent reduction to the spin space, the SOC Hamiltonian, with the gravitational potential incorporated, is exactly converted into the primary LZ scenario. Moreover, the transitions induced by harmonic acceleration are approximately cast into the framework of the basic LZ model through a complete analytical procedure. We evaluate how the validity of our picture depends on the system preparation and on the magnitude of atomic-interaction effects. The identification of the regime of applicability and the rigorous characterization of the parameters of the effective model provide elements to control the transitions.
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The Landau-Zener (LZ) transition is one of the most fundamental phenomena in quantum dynamics. It describes nonadiabatic transitions between quantum states near an avoided crossing that can occur in diverse physical systems. Here we report experimental measurements and tuning of LZ transitions between the dressed eigenlevels of a Bose-Einstein condensate (BEC) that is synthetically spin-orbit (SO) coupled. We measure the transition probability as the BEC is accelerated through the SO avoided crossing and study its dependence on the coupling between the diabatic (bare) states, eigenlevel slope, and eigenstate velocity---the three parameters of the LZ model that are independently controlled in our experiments. Furthermore, we performed time-resolved measurements to demonstrate the breaking down of the spin-momentum locking of the spin-orbit-coupled BEC in the nonadiabatic regime, and we determined the diabatic switching time of the LZ transitions. Our observations show quantitative agreement with the LZ model and numerical simulations of the quantum dynamics in the quasimomentum space. The tunable LZ transition may be exploited to enable a spin-dependent atomtronic transistor.
Abstract The effects of modulating spin-orbit coupled Bose–Einstein condensates are analytically studied. A sinusoidal driving of the coupling amplitude is shown to induce significant changes in the energy bands and in the associated spin-momentum locking. Moreover, in agreement with recent experimental results, gravitational acceleration of the modulated system is found to generate transitions between the modified energy bands. The applicability of the Landau–Zener (LZ) model to the understanding of the experimental findings is rigorously traced. Through a sequence of unitary transformations and the reduction to the spin space, the modulated Hamiltonian, with the gravitational potential incorporated, is shown to correspond to an extended version of the LZ scenario. The generalization of the basic LZ model takes place along two lines. First, the dimensionality is enlarged to combine the description of the external dynamics with the internal-state characterization. Second, the model is extended to incorporate two avoided crossings emerging from the changes induced in the energy bands by the modulation. Our approach allows a first-principle derivation of the effective model-system parameters. The obtained analytical results provide elements to control the transitions.
We explore the asymmetric sequential Landau-Zener (LZ) dynamics in an ensemble of interacting Bose-condensed two-level atoms coupled with a cavity field. Assuming the couplings between all atoms and the cavity field are identical, the interplay between atom-atom interaction and detuning may lead to a series of LZ transitions. Unlike the conventional sequential LZ transitions, which are symmetric to the zero detuning, the LZ transitions of Bose-condensed atoms in a cavity field are asymmetric and sensitively depend on the photon number distribution of the cavity. In LZ processes involving single excitation numbers, both the variance of the relative atom number and the step slope of the sequential population ladder are asymmetric, and the asymmetry becomes more significant for smaller excitation numbers. Furthermore, in LZ processes involving multiple excitation numbers, there may appear asymmetric population ladders with decreasing step heights. During a dynamical LZ process, due to the atom-cavity coupling, the cavity field shows dynamical collapses and revivals. In comparison with the symmetric LZ transitions in a classical field, the asymmetric LZ transitions in a cavity field originate from the photon-number-dependent Rabi frequency. The asymmetric sequential LZ dynamics of Bose-condensed atoms in a cavity field may open up a way to explore the fundamental many-body physics in coupled atom-photon systems.
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