Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2206.12053 · New Journal of Physics

Elementary excitations in a spin–orbit-coupled spin-1 Bose–Einstein condensate

Yuanyuan Chen, Hao Lyu, Yong Xu, Yongping Zhang

Published Jul 1, 2022• 25 citations
arXivHTMLPDF

Abstract

Abstract While a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC) has been experimentally observed, its elementary excitations remain unclear in the stripe phase. Here, we systematically study the elementary excitations in three distinct phases of a spin–orbit-coupled spin-1 BEC. We find that the excitation spectrum as well as the corresponding static response function and structure factor depend strongly on spin–orbit coupling parameters such as the quadratic Zeeman field and the Rabi frequency. In the stripe phase, besides two gapless Goldstone modes, we show the existence of roton excitations. Finally, we demonstrate that quantum phase transitions between these different phases including the zero-momentum, plane wave and stripe phases are characterized by the sound velocities and the quantum depletion.

DOI
10.1088/1367-2630/ac7fb1

Related papers

Elementary excitations in a spin–orbit-coupled Floquet spinor Bose–Einstein condensate

Anru Hou, Hao Lyu, Yuanyuan Chen +1 more

We study elementary excitations in a Floquet-engineered spin-1 BEC with spin–orbit coupling, which can be realized by periodically driving the quadratic Zeeman shift. We calculate the excitation spectrum of the plane-wave phase, the zero-momentum phase, and the stripe phase, as well as the corresponding response function and static structure factor. In special, we find that two roton modes appear in the lowest two excitation bands of the stripe phase, which are tunable by changing the driving parameters. The phase transition between different phases can be identified by the sound velocity of these phases. We also investigate spin dynamics in such a system, which strongly depend on the driving parameter.

Results in Physics•Jun 6, 2024•3 citations

SPIN-ORBIT-COUPLED BOSE-EINSTEIN CONDENSATES

Yun Li, Giovanni Italo Martone, S. Stringari

The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this review we explore the properties of a spin-orbit-coupled Bose-Einstein condensate with equal Rashba and Dresselhaus strengths. This system presents a rich phase diagram, which exhibits a tricritical point separating a zero-momentum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the system. In particular, the excitation spectrum exhibits intriguing features, including the suppression of the sound velocity, the emergence of a roton minimum in the plane-wave phase, and the appearance of a double gapless band structure in the stripe phase. Finally, we discuss a combined procedure to make the stripes visible and stable, thus allowing for a direct experimental detection.

arXiv:1410.5526•Annual review of cold atoms and molecules•Mar 24, 2015•42 citations

Plane- and stripe-wave phases of a spin-orbit-coupled Bose-Einstein condensate in an optical lattice with a Zeeman field

Kristian Mæland, Andreas T. G. Janssønn, Jonas H. Rygh +1 more

A weakly interacting, spin-orbit-coupled, ultracold, dilute Bose gas on a two-dimensional square lattice with an external Zeeman field is studied. We explore the plane- and stripe-wave phases of the system involving nonzero condensate momenta, which occur when the Zeeman field is below a critical value. Their excitation spectra are found using Bogoliubov theory and by two different routes. The validity of each method to obtain the excitation spectrum is discussed, and it is found that projection on the lowest single-particle band is an excellent approximation in the plane-wave phase, while it is a poor approximation in the stripe-wave phase. While the plane-wave phase has a phonon minimum at its single condensate momentum, revealing a nonzero sound velocity of the excitations, the stripe-wave phase has quadratic minima at its two condensate momenta showing zero sound velocity of the excitations. We discuss how the presence of more than one condensate momentum is essential for these differences between the two phases. Additionally, it is emphasized that the zero sound velocity in the stripe-wave phase is a lattice effect, since continuum studies of the same phase have shown nonzero sound velocity.

arXiv:2009.04538•Physical Review A•Nov 19, 2020•11 citations

Phase transitions and elementary excitations in spin-1 Bose gases with Raman-induced spin-orbit coupling

Zeng-Qiang Yu

We study the ground-state phase diagram and the quantum phase transitions in spin-1 Bose gases with Raman-induced spin-orbit coupling. In addition to the Bose-Einstein condensates with uniform density, three types of stripe condensation phases that simultaneously break the U(1) symmetry and the translation symmetry are identified. The transitions between these phases are investigated, and the occurrences of the various tricritical points are predicted. The excitation spectra in the plane-wave phase and the zero-momentum phase show rich roton-maxon structures, and their instabilities indicate the tendency to develop the crystalline order. We propose the atomic gas of $^{23}\mathrm{Na}$ could be a candidate for observing the stripe condensate with high contrast fringes.

arXiv:1512.04091•Physical Review A•Mar 29, 2016•54 citations

Anisotropic dynamics of a spin-orbit-coupled Bose-Einstein condensate

Giovanni Italo Martone, Yun Li, Лев П. Питаевский +1 more

By calculating the density response function we identify the excitation spectrum of a Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit coupling. We find that the velocity of sound along the direction of spin-orbit coupling is deeply quenched and vanishes when one approaches the second-order phase transition between the plane-wave and the zero momentum quantum phases. We also point out the emergence of a roton minimum in the excitation spectrum for small values of the Raman coupling, providing the onset of the transition to the stripe phase. Our findings point out the occurrence of a strong anisotropy in the dynamic behavior of the gas. A hydrodynamic description accounting for the collective oscillations in both uniform and harmonically trapped gases is also derived.

arXiv:1207.6804•Physical Review A•Dec 19, 2012•161 citations

Static and dynamic properties of spin-orbit-coupled Bose-Einstein condensates

Giovanni Italo Martone

The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this thesis we explore the properties of spin-orbit-coupled Bose-Einstein condensates with equal Rashba and Dresselhaus strengths. These systems present a rich phase diagram, which exhibits a tricritical point separating a single-minimum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the system. In particular, the excitation spectrum exhibits intriguing features, including the suppression of the sound velocity, the emergence of a roton minimum in the plane-wave phase, and the appearance of a double gapless band structure in the stripe phase. Finally, we discuss a combined procedure to make the stripes visible and stable, thus allowing for a direct experimental detection.

•Jan 1, 2014•1 citation
Abstract While a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC) has been experimentally observed, its elementary excitations remain unclear in the stripe phase. Here, we systematically study the elementary excitations in three distinct phases of a spin–orbit-coupled spin-1 BEC. We find that the excitation spectrum as well as the corresponding static response function and structure factor depend strongly on spin–orbit coupling parameters such as the quadratic Zeeman field and the Rabi frequency. In the stripe phase, besides two gapless Goldstone modes, we show the existence of roton excitations. Finally, we demonstrate that quantum phase transitions between these different phases including the zero-momentum, plane wave and stripe phases are characterized by the sound velocities and the quantum depletion.
We study elementary excitations in a Floquet-engineered spin-1 BEC with spin–orbit coupling, which can be realized by periodically driving the quadratic Zeeman shift. We calculate the excitation spectrum of the plane-wave phase, the zero-momentum phase, and the stripe phase, as well as the corresponding response function and static structure factor. In special, we find that two roton modes appear in the lowest two excitation bands of the stripe phase, which are tunable by changing the driving parameters. The phase transition between different phases can be identified by the sound velocity of these phases. We also investigate spin dynamics in such a system, which strongly depend on the driving parameter.
The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this review we explore the properties of a spin-orbit-coupled Bose-Einstein condensate with equal Rashba and Dresselhaus strengths. This system presents a rich phase diagram, which exhibits a tricritical point separating a zero-momentum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the system. In particular, the excitation spectrum exhibits intriguing features, including the suppression of the sound velocity, the emergence of a roton minimum in the plane-wave phase, and the appearance of a double gapless band structure in the stripe phase. Finally, we discuss a combined procedure to make the stripes visible and stable, thus allowing for a direct experimental detection.
A weakly interacting, spin-orbit-coupled, ultracold, dilute Bose gas on a two-dimensional square lattice with an external Zeeman field is studied. We explore the plane- and stripe-wave phases of the system involving nonzero condensate momenta, which occur when the Zeeman field is below a critical value. Their excitation spectra are found using Bogoliubov theory and by two different routes. The validity of each method to obtain the excitation spectrum is discussed, and it is found that projection on the lowest single-particle band is an excellent approximation in the plane-wave phase, while it is a poor approximation in the stripe-wave phase. While the plane-wave phase has a phonon minimum at its single condensate momentum, revealing a nonzero sound velocity of the excitations, the stripe-wave phase has quadratic minima at its two condensate momenta showing zero sound velocity of the excitations. We discuss how the presence of more than one condensate momentum is essential for these differences between the two phases. Additionally, it is emphasized that the zero sound velocity in the stripe-wave phase is a lattice effect, since continuum studies of the same phase have shown nonzero sound velocity.
We study the ground-state phase diagram and the quantum phase transitions in spin-1 Bose gases with Raman-induced spin-orbit coupling. In addition to the Bose-Einstein condensates with uniform density, three types of stripe condensation phases that simultaneously break the U(1) symmetry and the translation symmetry are identified. The transitions between these phases are investigated, and the occurrences of the various tricritical points are predicted. The excitation spectra in the plane-wave phase and the zero-momentum phase show rich roton-maxon structures, and their instabilities indicate the tendency to develop the crystalline order. We propose the atomic gas of 23Na^{23}\mathrm{Na}23Na could be a candidate for observing the stripe condensate with high contrast fringes.
By calculating the density response function we identify the excitation spectrum of a Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit coupling. We find that the velocity of sound along the direction of spin-orbit coupling is deeply quenched and vanishes when one approaches the second-order phase transition between the plane-wave and the zero momentum quantum phases. We also point out the emergence of a roton minimum in the excitation spectrum for small values of the Raman coupling, providing the onset of the transition to the stripe phase. Our findings point out the occurrence of a strong anisotropy in the dynamic behavior of the gas. A hydrodynamic description accounting for the collective oscillations in both uniform and harmonically trapped gases is also derived.
The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this thesis we explore the properties of spin-orbit-coupled Bose-Einstein condensates with equal Rashba and Dresselhaus strengths. These systems present a rich phase diagram, which exhibits a tricritical point separating a single-minimum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the system. In particular, the excitation spectrum exhibits intriguing features, including the suppression of the sound velocity, the emergence of a roton minimum in the plane-wave phase, and the appearance of a double gapless band structure in the stripe phase. Finally, we discuss a combined procedure to make the stripes visible and stable, thus allowing for a direct experimental detection.