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arXiv:1702.04714 · Physical Review A

Bosons with incommensurate potential and spin-orbit coupling

Sayak Ray, Bhaskar Mukherjee, Subhasis Sinha, K. Sengupta

Published Aug 4, 2017• 11 citations
arXivHTMLPDF

Abstract

We chart out the phases of ultracold ``spin-half'' bosons in a one-dimensional optical lattice in the presence of Aubry-Andr\'e (AA) potential and with spin-orbit (SO) and Raman couplings. We investigate the superfluid (SF) and localized phases and demonstrate the existence of density wave phase for nearest-neighbor interaction (NNI) between the bosons. We show that the presence of SO coupling and AA potential leads to a spin-split momentum distribution of the bosons in the localized phase near the boundary with the SF phase, which can act as a signature of the SF-localized phase transition. We also obtain the level statistics of the bosons in the superfluid phase with finite NNI and demonstrate its change from Gaussian unitary ensemble (GUE) to Gaussian orthogonal ensemble (GOE) as a function of the Raman coupling. We discuss experiments which can test our theory.

DOI
10.1103/physreva.96.023607

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We chart out the phases of ultracold ``spin-half'' bosons in a one-dimensional optical lattice in the presence of Aubry-Andr'e (AA) potential and with spin-orbit (SO) and Raman couplings. We investigate the superfluid (SF) and localized phases and demonstrate the existence of density wave phase for nearest-neighbor interaction (NNI) between the bosons. We show that the presence of SO coupling and AA potential leads to a spin-split momentum distribution of the bosons in the localized phase near the boundary with the SF phase, which can act as a signature of the SF-localized phase transition. We also obtain the level statistics of the bosons in the superfluid phase with finite NNI and demonstrate its change from Gaussian unitary ensemble (GUE) to Gaussian orthogonal ensemble (GOE) as a function of the Raman coupling. We discuss experiments which can test our theory.
Motivated by recent experiments [Y. J. Lin et al., Nature (London) 471, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional square optical lattice with nearest-neighbor hopping amplitude ttt and in the presence of a spin-orbit coupling characterized by a tunable strength $\ensuremath{\gamma}$. Using both strong-coupling expansion and Gutzwiller mean-field theory, we chart out the phase diagrams of the bosons in the presence of such spin-orbit interaction. We compute the momentum distribution of the bosons in the Mott phase near the SI transition point and show that it displays precursor peaks whose position in the Brillouin zone can be varied by tuning $\ensuremath{\gamma}$. Our analysis of the critical theory of the transition unravels the presence of unconventional quantum critical points at $t/\ensuremath{\gamma}=0$, which are accompanied by emergence of an additional gapless mode in the critical region. We also study the superfluid phases of the bosons near the SI transition using a Gutzwiller mean-field theory that reveals the existence of a twisted superfluid phase with an anisotropic twist angle which depends on $\ensuremath{\gamma}$. Finally, we compute the collective modes of the bosons and point out the presence of reentrant SI transitions as a function of $\ensuremath{\gamma}$ for nonzero ttt. We propose experiments to test our theory.
Interacting bosons with two ``spin'' states in a lattice show superfluid-insulator phase transitions in the presence of spin-orbit coupling. Depending on the parameter regime, bosons in the superfluid phase can condense to either a zero-momentum state or to one or multiple states with finite momentum, leading to an unconventional superfluid phase. We study the response of such a system to modulation of the optical lattice potential. We show that the change in momentum distribution after lattice modulation shows distinct patterns in the Mott and the superfluid phase and these patterns can be used to detect these phases and the quantum phase transition between them. Further, the momentum-resolved optical modulation spectroscopy can identify both the gapless (Goldstone) and gapped amplitude (Higgs) mode of the superfluid phase and clearly distinguish between the superfluid phases with a zero-momentum condensate and a twisted superfluid phase by looking at the location of these modes in the Brillouin zone. We discuss experiments which can test our theory.
The superfluid-to-Anderson-insulator transition of a strongly repulsive Bose gas is studied in a one-dimensional incommensurate optical lattice. In the hard-core limit, the Bose-Fermi mapping allows us to deal with the system using the exact numerical method. Based on the Aubry-Andr\'e model, we exploit the phase transition of the hard-core boson system from the superfluid phase with all single-particle states extended to the Bose-glass phase with all the single-particle states being Anderson localized as the strength of the incommensurate potential increases relative to the hopping amplitude. We evaluate the superfluid fraction, one-particle density matrices, momentum distributions, the natural orbitals, and their occupations. All of these quantities show that there exists a superfluid-to-insulator phase transition in the system.
Synthetic spin-orbit coupling in ultracold atomic gases can be taken to extremes rarely found in solids. We study a two dimensional Hubbard model of bosons in an optical lattice in the presence of spin-orbit coupling strong enough to drive direct transitions from Mott insulators to superfluids. Here we find phase-modulated superfluids with finite momentum that are generated entirely by spin-orbit coupling. We investigate the rich phase patterns of the superfluids, which may be directly probed using time-of-flight imaging of the spin-dependent momentum distribution.
Synthetic spin-orbit coupling in ultracold atomic gases can be taken to extremes rarely found in solids. We study a two-dimensional Hubbard model of bosons in an optical lattice in the presence of spin-orbit coupling strong enough to drive direct transitions from Mott insulators to superfluids. Here we find phase-modulated superfluids with finite momentum that are generated entirely by spin-orbit coupling. We investigate the rich phase patterns of the superfluids, which may be directly probed using time-of-flight imaging of the spin-dependent momentum distribution.
Ultracold atoms have emerged as an indispensable setting to study quantum many-body systems. Recent experimental and theoretical work has explored the curious phases and novel properties of Bose-Einstein Condensate with optical lattices, and Bose-Einstein Condensate with light-induced artificial spin-orbit coupling. In this thesis, we report our research on these two types of boson systems. In the first topic, in contrast with calculations of bosons in optical lattices that focus on the tight-binding regime, we note that the single-particle states of bosons in a periodic potential generally satisfy the Mathieu equation, and have developed a formalism for studying bosons in an optical lattice using the Mathieu equation. Moreover, based on this formalism, we have proposed a self-consistent scheme for describing interacting bosons in an optical lattice using Hartree Fock approximation. We apply this scheme to quantify the effects of inter-atomic interactions on the properties of bosons in an optical lattice, as exhibited in the comparison between observables of non-interacting and interacting systems, such as the superfluid transition temperature and momentum distribution as probed in time-of-flight expansion. In the second topic, the phases of a Bose-Einstein condensate with light-induced spin-orbit coupling are studied within the mean-field approximation. We obtain the phase diagram at fixed chemical potential and at fixed density for bosons with spin-orbit coupling, finding a regime of phase separation and a regime in which the bosons condensed into a mixed phase. We determine how this phase diagram evolves as a function of the atom interaction parameters and as a function of the strength of light-atom coupling. The mixed phase is found to be stable for sufficiently small light-atom coupling. Specifically, we show that the structure of the phase diagram at fixed chemical potential suggests an unusual density dependence for the mixed phase in a harmonic trapping potential, in which the density of one spin increases with increasing radius, suggesting a unique experimental signature of this state. The collective Bogoliubov sound mode is shown to also provide a signature of the mixed phase, vanishing as the boundary to the regime of phase separation is approached. Together, in these two topics we address the need to enhance the understanding of the unconventional physical properties of Bose-Einstein Condensate in a controlled electromagnetic environment (optical lattices, Raman lasers, etc.), and provide predictions for possible experimental findings.