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AIP conference proceedings

On the ground state phases in spin-orbit coupled Bose-Einstein condensates with weak repulsive interactions

Rajamanickam Ravisankar, Thangarasu Sriraman, Paulsamy Muruganandam

Published Jan 1, 2020• 1 citation
Publisher

Abstract

We study the ground-state phases of spin-orbit coupled Bose-Einstein condensates with an equal combination of Rashba and Dresselhaus and with Rabi mixing in a quasi-one-dimension setting. We analyze the role of the parameters, namely, spin-orbit and Rabi couplings, and inter- and intra-species interactions in a weak harmonic trap.
DOI
10.1063/5.0017155

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We study the role of coupling parameters on the ground state phases of spin-orbit coupled Bose-Einstein condensates with an equal combination of Rashba and Dresselhaus coupling strength with Rabi mixing using quasi-one-dimensional coupled Gross-Pitaevskii equations. By considering weak repulsive inter- and intra-species interactions between the condensate atoms, we investigate the contribution of spin-orbit and Rabi coupling parameters on the phases. We find that for a finite Rabi coupling strength, the system undergoes a phase transition from double plane-wave phase to stripe wave phase at a critical spin-orbit coupling strength.
Abstract We study the miscibility properties and ground state phases of two-component spin–orbit (SO) coupled Bose–Einstein condensates (BECs) in a harmonic trap with strong axial confinement. By numerically solving the coupled Gross–Pitaevskii equations in the two-dimensional setting, we analyze the SO-coupled BECs for two possible permutations of the intra- and interspecies interactions, namely (i) weak intra- and weak interspecies interactions (W–W) and (ii) weak intra- and strong interspecies interactions (W–S). Considering the density overlap integral as a miscibility order parameter, we investigate the miscible–immiscible transition by varying the coupling parameters. We obtain various ground state phases, including plane wave, half quantum vortex, elongated plane wave, and different stripe wave patterns for W–W interactions. For finite Rabi coupling, an increase in SO coupling strength leads to the transition from the fully miscible to the partially miscible state. We also characterize different ground states in the coupling parameter space using the root mean square sizes of the condensate. The spin density vector for the ground state phases exhibits density, quadrupole and dipole like spin polarizations. For the W–S interaction, in addition to that observed in the W–W case, we witness semi vortex, mixed mode, and shell-like immiscible phases. We notice a wide variety of spin polarizations, such as density, dipole, quadrupole, symbiotic, necklace, and stripe-like patterns for the W–S case. A detailed investigation in the coupling parameter space indicates immiscible to miscible state phase transition upon varying the Rabi coupling for a fixed Rashba SO coupling. The critical Rabi coupling for the immiscible–miscible phase transition decreases upon increasing the SO coupling strength.
We study the system of spin-orbit (SO) coupled Bose–Einstein condensates (BEC) with Rabi coupling in quasi-two dimensions characterized by unequal Rashba and Dresselhaus couplings. The ground state properties and the phase diagram of the system are studied within the mean-field approximation at T = 0. The energy-momentum dispersion relation corresponding to the single-particle ground state exhibits an infinitely degenerate Rashba ring, whose degeneracy is destroyed by the Rabi coupling, leading to a single-point lowest energy. The effect of Rabi coupling and interaction in the system show up three different phases, namely stripe, plane wave and zero momentum phase. At a particular parametric condition, the system admits a critical point separating all three different phases, known as the tri-critical point. For further insight, the momentum distribution, the energy and the longitudinal/transverse spin polarization corresponding to the quantum phases are comprehensively discussed.
We consider a spin-orbit coupled configuration of spin-1/2 interacting bosons with equal Rashba and Dresselhaus couplings. The phase diagram of the system at T=0 is discussed with special emphasis on the role of the interaction treated in the mean-field approximation. For a critical value of the density and of the Raman coupling we predict the occurrence of a characteristic tricritical point separating the spin mixed, the phase separated, and the zero momentum states of the Bose gas. The corresponding quantum phases are investigated analyzing the momentum distribution, the longitudinal and transverse spin polarization, and the emergence of density fringes. The effect of harmonic trapping as well as the role of the breaking of spin symmetry in the interaction Hamiltonian are also discussed.
Recently, strong spin-orbit coupling with equal Rashba and Dresselhaus strength has been realized in neutral atomic Bose-Einstein condensates via a pair of Raman lasers. In this report, we investigate spin and field squeezing of the ground state in spin-orbit coupled Bose-Einstein condensate. By mapping the spin-orbit coupled BEC to the well-known quantum Dicke model, the Dicke type quantum phase transition is presented with the order parameters quantified by the spin polarization and occupation number of harmonic trap mode. This Dicke type quantum phase transition may be captured by the spin and field squeezing arising from the spin-orbit coupling. We further consider the effect of a finite detuning on the ground state and show the spin polarization and the quasi-momentum exhibit a step jump at zero detuning. Meanwhile, we also find that the presence of the detuning enhances the occupation number of harmonic trap mode, while it suppresses the spin and the field squeezing.
We present the collective excitation spectrum analysis of binary Bose-Einstein condensates (BECs) with spin-orbit (SO) and Rabi couplings in a quasi-two-dimensional system. In particular, we investigate the role of SO and Rabi coupling strengths in determining the dynamical stability of the coupled BECs using Bogoliubov--de Gennes (BdG) theory. Using the eigenenergy of the BdG spectrum, we confirm the existence of phonon, roton, and maxon modes with weak repulsive intra- and interspecies contact interactions. The depth of the minimum corresponding to the roton mode strongly depends on the coupling strength. We find that the increase of the SO coupling leads to instability, while the increase in the Rabi coupling stabilizes the system. Also, the eigenvectors of the BdG spectrum indicate the presence of a densitylike mode in the stable regime and spinlike modes in the unstable regimes. A phase diagram demonstrating the stability regime in the plane of SO and Rabi coupling strengths is obtained. Finally, we complement the observation of the excitation spectrum with the direct numerical simulation results of coupled Gross-Pitaevskii equations.