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.
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.
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.
We report the observation of synthesized spin-orbit coupling (SOC) for ultracold spin-1 (87)Rb atoms. Different from earlier experiments where a one dimensional (1D) atomic SOC of pseudo-spin-1/2 is synthesized with Raman laser fields, the scheme we demonstrate employs a gradient magnetic field (GMF) and ground-state atoms, thus is immune to atomic spontaneous emission. The strength of SOC we realize can be tuned by changing the modulation amplitude of the GMF, and the effect of the SOC is confirmed through the studies of: 1) the collective dipole oscillation of an atomic condensate in a harmonic trap after the synthesized SOC is abruptly turned on; and 2) the minimum energy state at a finite adiabatically adjusted momentum when SOC strength is slowly ramped up. The condensate coherence is found to remain very good after driven by modulating GMFs. Our scheme presents an alternative means for studying interacting many-body systems with synthesized SOC.
Spin-orbit coupling (SOC) can give rise to interesting physics, from spin Hall to topological insulators, in condensed matter systems. Recently, this topical area has extended into atomic quantum gases in searching for artificial or synthetic gauge potentials. The prospects of tunable interaction and quantum state control promote neutral atoms as nature's quantum emulators for SOC. Lin et al. recently demonstrated a special form of the SOC ${k}_{x}{\ensuremath{\sigma}}_{y}$, which they interpret as an equal superposition of Rashba and Dresselhaus couplings in Bose-condensed atoms [Lin, Jim\'enez-Garc\'{\i}a, and Spielman, Nature (London) 471, 83 (2011)]. This work reports a method of implementing arbitrary forms of SOC by switching between two pairs of Raman laser pulses like the method used by Lin et al. While one pair affects ${k}_{x}{\ensuremath{\sigma}}_{y}$ for some time, a second pair creates ${k}_{y}{\ensuremath{\sigma}}_{y}$ at other times with Raman pulses from different directions and a subsequent spin rotation into $\ifmmode\pm\else\textpm\fi{}{k}_{y}{\ensuremath{\sigma}}_{x}$. With a sufficient number of pulses, the effective actions from different durations are small and accumulate in the same exponent despite the fact that ${k}_{x}{\ensuremath{\sigma}}_{y}$ and $\ifmmode\pm\else\textpm\fi{}{k}_{y}{\ensuremath{\sigma}}_{x}$ do not commute. Our scheme involves no added complication and can be demonstrated within current experiments. It applies equally to bosonic or fermionic atoms.
Ultra-cold quantum gases subjected to light-induced synthetic gauge potentials have become an emergent field of theoretical and experimental studies. Because of the novel application of two-photon Raman transitions, ultra-cold neutral atoms behave like charged particles in magnetic field. The Raman coupling naturally gives rise to an effective spin-orbit interaction which couples the atom’s center-of-mass motion to its selected pseudo-spin degrees of freedom. Combined with unprecedented controllability of interactions, geometry, disorder strength, spectroscopy, and high resolution measurement of momentum distribution, etc., we are truly in an exciting era of ful- filling and going beyond Richard Feynman’s vision of realizing quantum simulators to better understand the quantum mechanical nature of the universe, manifested immensely in the ultra-cold regimes. In this dissertation, we present a collection of theoretical progresses made by the doctoral candidate and his colleagues and collaborators. From the past few years of work, we mainly address three aspects of the synthetic spin-orbit and light field induced coupling in ultracold quantum gases: a) The ground-state physics of single- particle system, two-body bound states, and many-body systems, all of which are subjected to spin-orbit coupling originated from synthetic gauge potentials; b) The symmetry breaking, topological phase transition and quench dynamics, which are conveniently offered by the realized experimental setup; c) The proposal and impli- cations of light field induced dynamical spin-orbit coupling for atoms inside optical cavity. Our work represents an important advancement of theoretical understanding to the active research frontier of ultra-cold atom physics with spin-orbit coupling.
The dissertation explores the effects of synthetic spin-orbit coupling on the behaviour of quantum gases in several different contexts. We first study realistic methods to create vortices in spin-orbit-coupled (SOC) Bose-Einstein condensates (BEC). We propose two different methods to induce thermodynamically stable static vortex configurations: (1) to rotate both the Raman lasers and the anisotropic trap; and (2) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. We solve the Gross-Pitaevskii equation for several experimentally relevant regimes and find new interesting effects such as spatial separation of left- and right-moving spin-orbit-coupled condensates, and the appearance of unusual vortex arrangements. Next we consider cold atoms in an optical lattice with synthetic SOC in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model and derive the low-energy spin Hamiltonian which is a combination of Heisenberg model, quantum compass model and Dzyaloshinskii-Moriya interaction. We find that the Hamiltonian supports a rich classical phase diagram with collinear, spiral and vortex phases. Next we study the time evolution of the magnetization in a Rashba spin-orbit-coupled Fermi gas, starting from a fully-polarized initial state. We model the dynamics using a Boltzmann equation, which we solve in the Hartree-Fock approximation. The resulting non-linear system of equations gives rise to three distinct dynamical regimes controlled by the ratio of interaction and spin-orbit-coupling strength λ: for small λ, the magnetization decays to zero. For intermediate λ, it displays undamped oscillations about zero and for large λ, a partially magnetized state is dynamically stabilized. Motivated by an interesting stripe phase which appears in BEC with SOC [Li et al., Phys. Rev. Lett. 108, 225301 (2011)], we study the finite-temperature phase diagram of a pseudospin-1/2 Bose gas with contact interactions. We show that strong inter-spin interactions can lead to the appearance of magnetically ordered phases at temperatures above the superfluid transition. For the case of inter-spin attraction, we also discuss the possibility of a bosonic analogue of the Cooper-paired phase, however this state is not energetically favourable. We extend our calculations to a spin-orbit-coupled Bose gas to investigate the possibility of stripe ordering in the normal phase. However, within our approximations, we do not find an instability towards stripe formation. Finally, we consider a two-dimensional Bose gas at zero temperature with an underlying quartic single-particle dispersion in one spatial direction. This Hamiltonian can be realized using the NIST scheme of spin-orbit coupling [Y.-J. Lin, K. Jimenez-Garcia, and I. B. Spielman, Nature 471, 83 (2011)], or using the shaken lattice scheme of Parker et al. [C. V. Parker, L.-C. Ha and C. Chin, Nature Physics 9, 769 (2013)]. By numerically comparing energies of various trial wave-functions, we show that, at low densities, the ground state is strongly correlated, in contrast to a typical mean-field BEC. The trial wave-function with the lowest energy is of Jastrow-type and it describes a state with finite, but strongly reduced, condensate fraction.
Rabi model is a popular model in quantum optics and describes a two-level system coupling to a quantum resonator. The fruitful physics appears when the coupling strength is comparable to the frequency of the resonator. We investigate the Bose gases of Raman induced spin-orbit coupling with an external harmonic trapping. Using the displacement Fock state in quantum optics we seek for an approximate ground state. We find the superposition state of left and right displaced oscillator state with odd parity has lower energy than the displaced state itself. Besides, we study the time evolution of both the momentum and the position of the system at single particle level to demonstrate the Zitterbewegung oscillating characteristics, which present an intuitive physical picture and are in qualitative agreement with the relevant experimental results. The results are useful to study the Rabi model in deep-strong coupling regime, the model that is difficult to realize in today’s experiment based on the high controllability property of laser, and these results are also instructive for the cold atom physics field.