Abstract We study the ground state and the Bloch oscillations of the spin-orbit coupled Bose-Einstein condensates in one-dimensional deep optical lattices. The phase transition between the zero-momentum phase and the plane-wave phase in untilted deep optical lattices is studied analytically. The Bloch oscillations in tilted lattices started in different ground state phases are analyzed. It is found that the Bloch dynamics is harmonic (anharmonic) in the zero-momentum phase (plane-wave phase). Furthermore, the modification of the Bloch oscillations induced by spin-orbit coupling, tunnelling coefficient and the external force (the inclination of the tilt) is revealed. In addition, the analytical condition for emerging the long-lived Bloch oscillations is obtained and the corresponding diagram in parameter space is provided. Particularly, we find that the spin-orbit coupling can extend the duration of the Bloch oscillations in the plane-wave phase. We provide an effective method to manipulate the Bloch dynamics in the deep optical lattices.
Abstract We study the ground state and the Bloch oscillations of the spin-orbit coupled Bose-Einstein condensates in one-dimensional deep optical lattices. The phase transition between the zero-momentum phase and the plane-wave phase in untilted deep optical lattices is studied analytically. The Bloch oscillations in tilted lattices started in different ground state phases are analyzed. It is found that the Bloch dynamics is harmonic (anharmonic) in the zero-momentum phase (plane-wave phase). Furthermore, the modification of the Bloch oscillations induced by spin-orbit coupling, tunnelling coefficient and the external force (the inclination of the tilt) is revealed. In addition, the analytical condition for emerging the long-lived Bloch oscillations is obtained and the corresponding diagram in parameter space is provided. Particularly, we find that the spin-orbit coupling can extend the duration of the Bloch oscillations in the plane-wave phase. We provide an effective method to manipulate the Bloch dynamics in the deep optical lattices.
We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.
Bloch oscillations appear for a particle in a weakly tilted periodic potential. The intrinsic spin Hall effect is an outcome of a spin-orbit coupling. We demonstrate that both of these phenomena can be realized simultaneously in a gas of weakly interacting ultracold atoms exposed to a tilted optical lattice and to a set of spatially dependent light fields inducing an effective spin-orbit coupling. It is found that both the spin Hall and the Bloch oscillation effects may coexist, showing, however, a strong correlation between the two. These correlations are manifested as a transverse spin current oscillating in-phase with the Bloch oscillations. On top of the oscillations originating from the periodicity of the model, a trembling motion is found which is believed to be atomic Zitterbewegung. It is argued that the damping of these Zitterbewegung oscillations may to a large extent be prevented in the present setup considering a periodic optical lattice potential.
Atomic interaction leads to dephasing and damping of Bloch oscillations (BOs) in optical lattices, which limits observation and applications of BOs. How to obtain persistent BOs is particularly important. Here, the nonlinear Bloch dynamics of the Bose–Einstein condensate with two-body and three-body interactions in deep optical lattices is studied. The damping rate induced by interactions is obtained. The damping induced by two-body interaction plays a dominant role, while the damping induced by three-body interaction is weak. However, when the two-body and three-body interactions satisfy a threshold, long-lived coherent BOs are observed. Furthermore, the Bloch dynamics with periodical modulation of linear force is studied. The frequencies of linear force corresponding to resonance and pseudoresonance are obtained, and rich dynamical phenomena, i.e., stable and strong BOs, drifting and dispersion of wave packet, are predicted. The controllable Bloch dynamics is provided with the periodic modulation of the linear force.
Abstract We study the Bloch oscillation (BO) dynamics of spin–orbit coupled cold atoms in a one-dimensional Su–Schrieffer–Heeger optical lattice. The Hamiltonian of our system can be mapped into a tilted SSH ladder pierced by an effective magnetic flux. Based on the calculation of Wannier–Stark states, we investigate dynamical properties of BOs with the chiral character of spin-momentum locking. Importantly, the chiral Bloch–Zener oscillations can be induced by adjusting system parameters. The corresponding Landau–Zener (LZ) tunneling probability is analytically derived by the LZ model and we found a good agreement with the numerical simulation.
We study the phonon mode excitation of spin–orbit (SO) coupled Bose–Einstein condensates trapped in a one-dimensional optical lattice. The sound speed of the system is obtained analytically. Softening of the phonon mode, i.e., the vanishing of sound speed, in the optical lattice is revealed. When the lattice is absent, the softening of phonon mode occurs only at the phase transition point, which is not influenced by the atomic interaction and Raman coupling when the SO coupling is strong. However, when the lattice is present, the softening of phonon modes can take place in a regime near the phase transition point. Particularly, the regime is widened as lattice strength and SO coupling increase or atomic interaction decreases. The suppression of sound speed by the lattice strongly depends on atomic interaction, Raman coupling, and SO coupling. Furthermore, we find that the sound speed in plane wave phase regime and zero-momentum phase regime behaves with very different characteristics as Raman coupling and SO coupling change. In zero-momentum phase regime, sound speed monotonically increases/decreases with Raman coupling/SO coupling, while in plane wave phase regime, sound speed can either increase or decrease with Raman coupling and SO coupling, which depends on atomic interaction.
The collective excitations of a spin-orbit–coupled Bose-Einstein condensate are investigated by using a variational method and numerical simulation. The collective modes are depicted in zero-momentum and plane-wave phases, while the mechanism for inducing the anharmonic collective oscillations is revealed analytically. The coupling among spin-orbit coupling, Raman coupling, and atomic interaction results in multiple external collective modes, which can lead to the collective dynamics being the superposition of the multiple harmonic oscillations. When one of the external frequencies is close to the inherent frequency of the conventional condensate and the amplitudes of other external frequencies vanish, the collective oscillations are harmonic, otherwise the collective oscillations are anharmonic. Thus the collective dynamics can undergo a harmonicity-anharmonicity transition. This can provide a possible way for elaborating distinct collective oscillation modes. Moreover, the collective excitations exhibit distinct properties in different phases, while the softening of collective modes is detected at the phase transition point, which can be used to map out the phase boundaries in experiment.