Abstract We consider a macroscopic spin qubit based on spin–orbit coupled Bose–Einstein condensates, where, in addition to the spin–orbit coupling (SOC), spin dynamics strongly depends on the interaction between particles. The evolution of the spin for freely expanding, trapped, and externally driven condensates is investigated. For condensates oscillating at the frequency corresponding to the Zeeman splitting in the synthetic magnetic field, the spin Rabi frequency does not depend on the interaction between the atoms since it produces only internal forces and does not change the total momentum. However, interactions and SOC bring the system into a mixed spin state, where the total spin is inside rather than on the Bloch sphere. This greatly extends the available spin space making it three-dimensional, but imposes limitations on the reliable spin manipulation of such a macroscopic qubit. The spin dynamics can be modified by introducing suitable spin-dependent initial phases, determined by the SOC, in the spinor wave function.
Abstract We consider a macroscopic spin qubit based on spin–orbit coupled Bose–Einstein condensates, where, in addition to the spin–orbit coupling (SOC), spin dynamics strongly depends on the interaction between particles. The evolution of the spin for freely expanding, trapped, and externally driven condensates is investigated. For condensates oscillating at the frequency corresponding to the Zeeman splitting in the synthetic magnetic field, the spin Rabi frequency does not depend on the interaction between the atoms since it produces only internal forces and does not change the total momentum. However, interactions and SOC bring the system into a mixed spin state, where the total spin is inside rather than on the Bloch sphere. This greatly extends the available spin space making it three-dimensional, but imposes limitations on the reliable spin manipulation of such a macroscopic qubit. The spin dynamics can be modified by introducing suitable spin-dependent initial phases, determined by the SOC, in the spinor wave function.
We study the spin mixing dynamics of a spin-orbit coupled spin-1 Bose–Einstein condensate. Using mean-field theory and adopting plane wave solutions, the spin mixing dynamics can be well described by an internal Josephson equation. In order to establish the role of the different terms in spin mixing dynamics clearly, we consider the equilibrium state firstly, which shows that the spin-orbit coupling can significantly modify the dispersion relation and change the property of ground state of the condensate. For the non-equilibrium state, the spin-orbit coupling plays an important role in the spin mixing dynamics. Moreover, the oscillation period of spin mixing dynamics is determined by the coupled effects of momentum, magnetization, spin-dependent atomic interaction and spin-orbit coupling. When spin-orbit coupling is less than a critical value, it can prolong the oscillation period of spin mixing dynamics. Conversely, when the spin-orbit coupling is larger than the critical value, it can shorten the oscillation period of spin mixing dynamics. Particularly, when spin-orbit coupling is equal to the critical value, the period tends to infinity. Our study provides a complete spin mixing dynamics of spin-orbit coupled spin-1 BEC, which can be used to explore the spin mixing dynamics experimentally.
We study the collective dynamics of the spin-orbit coupled two pseudospin components of a Bose-Einstein condensate trapped in a quasi-one-dimensional harmonic potential, by using variational and directly numerical approach of binary mean-field Gross-Pitaevskii equations. The results show that, because of strong coupling of spin-orbit coupling (SOC), Rabi coupling, and atomic interaction, the collective dynamics of the system behave as complex characters. When the Rabi coupling is absent, the density profiles of the system preserve the Gauss type and the wave packets do harmonic oscillations. The amplitude of the collective oscillations increases with SOC. Furthermore, when the SOC strength increases, the dipole oscillations of the two pseudospin components undergo a transition from in-phase to out-of-phase oscillations. When the Rabi coupling present, there will exist a critical value of SOC strength (which depends on the Rabi coupling and atomic interaction). If the SOC strength is less than this critical value, the density profiles of the system can preserve the Gauss type and the wave packets do anharmonic (the frequency of dipole oscillations depends on SOC) oscillations synchronously (i.e., in-phase oscillations). However, if the SOC strength is larger than this critical value, the wave packets are dynamically fragmented and the stable dipole oscillations of the system can not exist. The collective dynamics of the system can be controlled by adjusting the atomic interaction, SOC, and Rabi-coupling strength.
Dynamical characteristics of internal and external states of a Bose-Einstein condensate are generally different and independent, thus requiring different experimental manipulation techniques. The spin-orbit coupling recently achieved in Bose-Einstein condensates essentially connects spin and motion degree of freedom, endowing spin states with the ability to respond to orbital manipulation, and vice versa. In this work, a dynamical response effect, induced by simultaneously manipulating the internal and external states of a spin-orbit-coupled Bose-Einstein condensate, is predicted. Here, the “simultaneously manipulating the internal and external states” means that the driving field combines the Zeeman field applied to the internal state of the atom and the orbital potential affecting the external states of the atom. Specifically, the Bose-Einstein condensate is assumed to be activated by an abruptly applied Zeeman field and a sudden shake of the trapping potential. After some reasonable simplification and approximation of the model (i.e. neglecting the inter-atomic interactions and modelling the shake of the trapping potential by a short time-dependent pulse), an analytical relationship connecting spin frequency spectrum and the parameters of the driving fields is derived. The numerical calculations based on directly integrating the Gross-Pitaevskii equation are in good agreement with the results from the analytical relationship. The physical origin of the predicted spin dynamical response can be traced back to the quantum interference among different spin-orbit states. Due to the fact that a series of characteristic parameters of the condensate can be manifested in the spin frequency spectrum, the dynamical response effect predicted here provides a candidate method for determining and calibrating various system parameters by measuring the spin frequency spectrum.
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.
Solitons play a fundamental role in the dynamics of nonlinear excitations. Here we explore the motion of solitons in one-dimensional Bose-Einstein condensates subjected to a spin-orbit coupling (SOC). We demonstrate that the spin dynamics of solitons is governed by a nonlinear Bloch equation. The spin dynamics affects the orbital motion of solitons leading to spin-orbit effects in the dynamics of macroscopic quantum objects (mean-field solitons). The latter perform oscillations with a frequency determined by the SOC, Raman coupling, and intrinsic nonlinearity. These findings reveal unique features of solitons affected by the SOC, which are confirmed by analytical considerations and numerical simulations of the underlying Gross-Pitaevskii equations.
In this paper, we study the dynamic properties of spin–orbit coupling (SOC) spin-1 antiferromagnetic Bose–Einstein condensates with inhomogeneous external magnetic field by numerical simulations of the multicomponent Gross–Pitaevskii equation. Our results show that the spin dynamics process is greatly affected by SOC when the system is in the absence of magnetic field. The periodicity of spin exchange dynamics disappears and the population of thermal clouds for [Formula: see text] and [Formula: see text] gradually increases and decreases and then reaches a steady value. In this case, a stable stripe phase emerges for three-component wavefunction. Nevertheless, the spin dynamics process becomes complex in the presence of magnetic field, depending on the competition between magnetic field and SOC. The influences of SOC are masked by the relatively strong magnetic field and the density structures are similar to the case of without or weak magnetic field.