Striped states in weakly trapped ultracold Bose gases with Rashba spin-orbit coupling

Ozawa, Tomoki; Baym, Gordon

doi:10.1103/physreva.85.063623

Cited by 34 publications

(23 citation statements)

References 22 publications

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“…The simultaneous breaking of these symmetries is a typical feature of supersolids, a phase of matter not yet realized experimentally, despite systematic efforts made in solid 4 He [5]. The realization of supersolidity is presently the object of several theoretical proposals, focusing on atomic gases interacting with dipolar [6-8] or soft-core, finite-range forces [9][10][11][12][13][14][15].The occurrence of a striped phase in spin-orbit-coupled two-component Bose gases has been the object of several recent theoretical investigations [17][18][19][20][21][22][23][24][25][26][27]. The experiment of Ref.…”

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Approach for making visible and stable stripes in a spin-orbit-coupled Bose-Einstein superfluid

Martone

Stringari

2014

Phys. Rev. A

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The striped phase exhibited by a spin-1/2 Bose-Einstein condensate with spin-orbit coupling is characterized by the spontaneous breaking of two continuous symmetries: gauge and translational symmetry. This is a peculiar feature of supersolids and is the consequence of interaction effects. We propose an approach to produce striped configurations with high-contrast fringes, making their experimental detection in atomic gases a realistic perspective. Our approach, whose efficiency is directly confirmed by three-dimensional Gross-Pitaevskii simulations, is based on the space separation of the two spin components into a two-dimensional bilayer configuration, causing the reduction of the effective interspecies interaction and the increase of the stability of the striped phase. We also explore the effect of a π/2 Bragg pulse, causing the increase of the fringe wavelength, and of a π/2 rf pulse, revealing the coherent nature of the order parameter in the spin channel.The experimental realization of synthetic gauge fields and spin-orbit-coupled configurations in spinor Bose-Einstein condensates [1-4] has opened interesting perspectives for the realization of novel quantum phases. Among them the striped phase represents one of the most challenging configurations, being characterized by the spontaneous breaking of two continuous symmetries: gauge and translational symmetry. The simultaneous breaking of these symmetries is a typical feature of supersolids, a phase of matter not yet realized experimentally, despite systematic efforts made in solid 4 He [5]. The realization of supersolidity is presently the object of several theoretical proposals, focusing on atomic gases interacting with dipolar [6-8] or soft-core, finite-range forces [9][10][11][12][13][14][15].The occurrence of a striped phase in spin-orbit-coupled two-component Bose gases has been the object of several recent theoretical investigations [17][18][19][20][21][22][23][24][25][26][27]. The experiment of Ref.[4] was not, however, able to reveal the typical features of this phase, characterized by the occurrence of periodic modulations of the density profile. The main reason is that the contrast and the wavelength of the modulations in the experimental conditions of [4] are too small. When written in a locally spin-rotated frame [28], the single-particle spin-orbit Hamiltonian realized in [4] takes the following form:This Hamiltonian is the result of the application of two counterpropagating polarized lasers with wave vector difference k 0 , chosen along the x direction, providing Raman transitions between two different hyperfine states, in the presence of a nonlinear Zeeman field. The strength of the Raman coupling is fixed by the parameter . Equation (1) also includes the coupling with an effective magnetic field δ given by the sum of the true external magnetic field and of the frequency detuning between the two lasers (see, for example, [28]). The spin matrices entering the single-particle Hamiltonian are the usual 2 × 2 Pauli matrices. The operator p = −i ∇ i...

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confidence: 99%

“…The occurrence of a striped phase in spin-orbit-coupled two-component Bose gases has been the object of several recent theoretical investigations [17][18][19][20][21][22][23][24][25][26][27]. The experiment of Ref.…”

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confidence: 99%

Approach for making visible and stable stripes in a spin-orbit-coupled Bose-Einstein superfluid

Martone

Stringari

2014

Phys. Rev. A

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“…From the mean-field solution, we expect M α (r) to monotonically reach a constant value at large distances for PW states when α points in the direction of κ. In the stripe phase oscillating behavior occurs, since spins rotate in the plane orthogonal to the vector κ with a spatial frequency equal to 2κ [24].…”

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Finite-temperature phases of two-dimensional spin-orbit-coupled bosons

Kawasaki

Holzmann

2017

Phys. Rev. A

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We determine the finite temperature phase diagram of two dimensional bosons with two hyperfine (pseudo-spin) states coupled via Rashba-Dresselhaus spin-orbit interaction using classical field Monte Carlo calculations. For anisotropic spin-orbit coupling, we find a transition to a BerenzinskiiKosterlitz-Thouless superfluid phase with quasi-long range order. We show that the spin-order of the quasi-condensate is driven by the anisotropy of interparticle interaction, favoring either a homogeneous plane wave state or stripe phase with broken translational symmetry. Both phases show characteristic behavior in the algebraically decaying spin density correlation function. For fully isotropic interparticle interaction, our calculations indicate a fractionalized quasi-condensate where the mean-field degeneracy of plane wave and stripe phase remains robust against critical fluctuations. In the case of fully isotropic spin-orbit coupling, the circular degeneracy of the single particle ground state destroys the algebraic ordered phase in the thermodynamic limit, but a cross-over remains for finite size systems.Introduction. The coupling of artificial gauge fields to ultracold atomic gases [1] has opened the possibility of studying spin-orbit coupled Bose gases [2][3][4][5] where translational symmetry may be broken spontaneously in the superfluid ground state [6]. At the mean-field level, spin-orbit coupling (SOC) introduces degenerate ground states expected to enhance fluctuation effects and giving rise to new, exotic quantum phases. The occurrence and nature of finite temperature transitions in these systems have not yet been fully established [7][8][9][10][11][12].In the following we consider a two-dimensional homogeneous gas of Rashba-Dresselhaus spin-orbit coupled bosons. Mean-field calculations [10-14] indicate a Bose condensed ground state of a single plane wave with nonvanishing momentum or a linear superposition of two plane waves with opposite momenta, called plane wave state (PW) and stripe phase (SP), respectively. For spinindependent particle interaction, PW and SP remain degenerate at the mean-field level. In addition, in the case of isotropic SOC, ground states with momenta lying on a circle are connected by symmetry. These degeneracies may be broken by classical or quantum fluctuations.In this work we explore the phase diagram using classical field Monte Carlo calculations. We show that for anisotropic SOC, the systems undergoes a KosterlitzThouless phase transition from a normal to superfluid state. In the superfluid state, the single particle density matrix decays algebraically and directly reflects the PW/SP character of the mean-field ground state. In the limit of isotropic interparticle interaction, the PW/SP degeneracy is unaffected by the transition. Thus, at large but finite system sizes, fragmentation [15] of the condensate occurs. In the case of isotropic SOC, we show that the transition temperature decreases with increasing system size due to the increasing number of degenerate mean-field ground s...

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“…Motivated by the above experiments, we investigate the lowest-energy states that appear in a spin-orbitcoupled Bose-Einstein-condensed cloud of atoms that is trapped in an annular potential, using the mean-field approximation. A lot of work has been done in homogeneous [26,27,[55][56][57][58] and in harmonically-trapped systems [28,33,36,39,40,44,[59][60][61]. In the presence of an annular potential, however, this problem becomes surprisingly challenging.…”

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confidence: 99%

Spin–orbit-coupled Bose–Einstein-condensed atoms confined in annular potentials

et al. 2016

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A spin-orbit-coupled Bose-Einstein-condensed cloud of atoms confined in an annular trapping potential shows a variety of phases that we investigate in the present study. Starting with the noninteracting problem, the homogeneous phase that is present in an untrapped system is replaced by a sinusoidal density variation in the limit of a very narrow annulus. In the case of an untrapped system there is another phase with a striped-like density distribution, and its counterpart is also found in the limit of a very narrow annulus. As the width of the annulus increases, this picture persists qualitatively. Depending on the relative strength between the inter-and the intra-components, interactions either favor the striped phase, or suppress it, in which case either a homogeneous, or a sinusoidal-like phase appears. Interactions also give rise to novel solutions with a nonzero circulation.

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Striped states in weakly trapped ultracold Bose gases with Rashba spin-orbit coupling

Cited by 34 publications

References 22 publications

Approach for making visible and stable stripes in a spin-orbit-coupled Bose-Einstein superfluid

Approach for making visible and stable stripes in a spin-orbit-coupled Bose-Einstein superfluid

Finite-temperature phases of two-dimensional spin-orbit-coupled bosons

Spin–orbit-coupled Bose–Einstein-condensed atoms confined in annular potentials

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