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Register a new userAcceleration of spin-orbit coupled Bose-Einstein condensates: analytical description of the emergence of Landau-Zener transitions
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We analytically study the effect of gravitational and harmonic forces on ultra-cold 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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In this paper, we show that for sufficiently strong atomic interactions, there exist analytical solutions of current-carrying nonlinear Bloch states at the Brillouin zone edge to the model of spin-orbit-coupled Bose-Einstein condensates (BECs) with symmetric spin interaction loaded into optical lattices. These simple but generic exact solutions provide an analytical demonstration of some intriguing properties which have neither an analog in the regular BEC lattice systems nor in the uniform spin-orbit-coupled BEC systems. It is an analytical example for understanding the superfluid and other related properties of the spin-orbit-coupled BEC lattice systems.
We explore a new way of producing the Rashba spin-orbit coupling (SOC) for ultracold atoms by using a two-component (spinor) atomic Bose-Einstein condensate (BEC) confined in a bilayer geometry. The SOC of the Rashba type is created if the atoms pick up a {pi} phase after completing a cyclic transition between four combined spin-layer states composed of two spin and two layer states. The cyclic coupling of the spin-layer states is carried out by combining an intralayer Raman coupling and an interlayer laser assisted tunneling. We theoretically determine the ground-state phases of the spin-orbit-coupled BEC for various strengths of the atom-atom interaction and the laser-assisted coupling. It is shown that the bilayer scheme provides a diverse ground-state phase diagram. In an intermediate range of the atom-light coupling two interlacing lattices of half- skyrmions and half-antiskyrmions are spontaneously created. In the strong-coupling regime, where the SOC of the Rashba-type is formed, the ground state represents plane-wave or standing-wave phases depending on the interaction between the atoms. A variational analysis is shown to be in a good agreement with the numerical results.
The fragmentation of spin-orbit coupled spin-1 Bose gas with a weak interaction in external harmonic trap is explored by both exact diagonalization and mean-field theory. This fragmentation tendency, which originates from the total angular momentum conservation, is affected obviously by the spin-orbit coupling strength and the spin-dependent interaction. Strong spin-orbit interaction raises the inverse participation ratio, which describes the number of significantly occupied single-particle states. As the spin-dependent interaction changes from anti-ferromagnetic to ferromagnetic, the peak values in the inverse participation ratio become lower. Without the confinement of the appointed total angular momentum, the condensate chooses a zero or finite total angular momentum ground state, which is determined by both the interaction and the spin-orbit coupling strength.
We numerically investigate low-energy stationary states of pseudospin-1 Bose-Einstein condensates in the presence of Rashba-Dresselhaus-type spin-orbit coupling. We show that for experimentally feasible parameters and strong spin-orbit coupling, the ground state is a square vortex lattice irrespective of the nature of the spin-dependent interactions. For weak spin-orbit coupling, the lowest-energy state may host a single vortex. Furthermore, we analytically derive constraints that explain why certain stationary states do not emerge as ground states. Importantly, we show that the distinct stationary states can be observed experimentally by standard time-of-flight spinindependent absorption imaging.
We consider an ultracold bosonic binary mixture confined in a one-dimensional double-well trap. The two bosonic components are assumed to be two hyperfine internal states of the same atom. We suppose that these two components are spin-orbit coupled between each other. We employ the two-mode approximation starting from two coupled Gross-Pitaevskii equations and derive a system of ordinary differential equations governing the temporal evolution of the inter-well population imbalance of each component and that between the two bosonic species. We study the Josephson oscillations of these spin-orbit coupled Bose-Einstein condensates by analyzing the interplay between the interatomic interactions and the spin-orbit coupling and the self-trapped dynamics of the inter-species imbalance. We show that the dynamics of this latter variable is crucially determined by the relationship between the spin-orbit coupling, the tunneling energy, and the interactions.
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