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arXiv:2004.02063 · Annalen der Physik

Phase Diagrams of Periodically Driven Spin–Orbit Coupled 87Rb and 23Na Bose–Einstein Condensates

Zhi Lin

Published Nov 1, 2020• 2 citations
arXivHTMLPDF

Abstract

Abstract The phase boundaries of periodically driven spin–orbit coupled BECs with effective two‐body interactions are analytically calculated by using variational method. The phase diagrams of periodically driven and systems present distinguished features from undriven systems, respectively. For the BECs, the critical density (density at quantum tricritical point) will be dramatically reduced in some parameter regions, and the prospect of observing this intriguing quantum tricritical point is greatly enlarged. Moreover, a series of quantum tricritical points emerge quasi‐periodically when increasing the Raman coupling strength with fixed density. In the BECs, two hyperfine states of atoms can be miscible within the suitable regions of driving parameter space. As a result, systems will stay in the stripe phase with small Raman frequency at typical density, which expands the region of stripe phase in the phase diagram. In addition, an absence of quantum tricritical point in such system is observed, which is very unlike systems.

DOI
10.1002/andp.202000194

Related papers

Bose–Einstein Condensates: Phase Diagrams of Periodically Driven Spin–Orbit Coupled 87Rb and 23Na Bose–Einstein Condensates (Ann. Phys. 1/2021)

Zhi Lin

The phase diagrams of periodically driven spin–orbit coupled 87Rb and 23Na Bose–Einstein condensates (BECs) are visually distinct from undriven systems. In article number 2000194, Zhi Lin demonstrates two distinguishing features of these systems. A series of quantum tricritical points emerge quasi-periodically from 87Rb BECs, while the existence of stripe phase in a suitable parameter region is found in the driven driven 23Na BECs.

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We theoretically study the ground-state phases and superfluidity of tunable spin-orbit-coupled Bose-Einstein condensates (BECs) under the periodic driving of Raman coupling. An effective time-independent Floquet Hamiltonian is proposed by using a high-frequency approximation, and we find single-particle dispersion, spin-orbit-coupling, and asymmetrical nonlinear two-body interaction can be modulated effectively by the periodic driving. The critical Raman coupling characterizing the phase transition and relevant physical quantities in three different phases (the stripe phase, plane-wave phase, and zero momentum phase) are obtained analytically. Our results indicate that the boundary of ground-state phases can be controlled and the system will undergo three different phase transitions by adjusting the external driving. Interestingly, we find the contrast of the stripe density can be enhanced by the periodic driving in the stripe phase. We also study the superfluidity of tunable spin-orbit-coupled BECs and find the dynamical instability can be tuned by the periodic driving of Raman coupling. Furthermore, the sound velocity of the ground-state and superfluidity state can be controlled effectively by tuning the periodic driving strength. Our results indicate that the periodic driving of Raman coupling provides a powerful tool to manipulate the ground-state phase transition and dynamical instability of spin-orbit-coupled BECs.

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MAGNETIZED PLANE WAVE AND STRIPE-ORDERED PHASES IN SPIN-ORBIT-COUPLED BOSE GASES

Andika Putra

Quantum degenerate gases have provided rich systems to simulate engineered Hamiltonians and to explore quantum many-body problems in laboratory-scale experiments. In this work, I focus on spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) of Rubidium-87 atoms realized using two-photon Raman coupling in which various novel phases are predicted to exist due to competing energies from the atomic internal structure, coupling strength, and many-body collisions. BECs are observed primarily using the interaction between light and matter, where it is common to probe the atoms with near-resonant light and image their shadow on a camera. This absorption imaging technique measures the integrated column density of the atoms and it is crucial to focus the imaging system. I present a systematic method to bring the ultracold atom systems into an optimal focus using the power spectral density (PSD) of the atomic density-density correlation function. The spatial frequency at which the defocus-induced artifacts first appear in the PSD is maximized at the focus. The focusing process thus identifies the range of spatial frequencies over which the PSD is uncontaminated by finite-thickness effects. Next, I describe magnetic phases which exist in spin-1 spin-orbit-coupled condensates at a near-zero temperature. I observe ferromagnetic and unmagnetized phases which are stabilized by the locking between the spin and linear momentum of the system. Our measurements of both the first- and second-order transitions are in agreement with theory. Finally, I discuss the stripe-ordered phase that occurs in SOC Bose gases favoring the miscibility configuration. The stripe phase is theoretically predicted to have an excitation spectrum analogous to that of a supersolid and to exhibit spatial density modulation within specific regions of parameter space. I used optical Bragg scattering to probe the small density modulation present in the atomic spatial distribution. I present for the very first time observation of the stripe phase in a Raman SOC Bose gas and its phase diagram in various parameter space. Our observations of the phase boundaries are consistent with theory and previous work.

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We study the ground-state phases, the stability phase diagram and collapse dynamics of Bose—Einstein condensates (BECs) with tunable spin—orbit (SO) coupling in the two-dimensional harmonic potential by variational analysis and numerical simulation. Here we propose the theory that the collapse stability and collapse dynamics of BECs in the external trapping potential can be manipulated by the periodic driving of Raman coupling (RC), which can be realized experimentally. Through the high-frequency approximation, an effective time-independent Floquet Hamiltonian with two-body interaction in the harmonic potential is obtained, which results in a tunable SO coupling and a new effective two-body interaction that can be manipulated by the periodic driving strength. Using the variational method, the phase transition boundary and collapse boundary of the system are obtained analytically, where the phase transition between the spin-nonpolarized phase with zero momentum (zero momentum phase) and spin-polarized phase with non-zero momentum (plane wave phase) can be manipulated by the external driving and sensitive to the strong external trapping potential. Particularly, it is revealed that the collapsed BECs can be stabilized by periodic driving of RC, and the mechanism of collapse stability manipulated by periodic driving of RC is clearly revealed. In addition, we find that the collapse velocity and collapse time of the system can be manipulated by periodic driving strength, which also depends on the RC, SO coupling strength and external trapping potential. Finally, the variational approximation is confirmed by numerical simulation of Gross—Pitaevskii equation. Our results show that the periodic driving of RC provides a platform for manipulating the ground-state phases, collapse stability and collapse dynamics of the SO coupled BECs in an external harmonic potential, which can be realized easily in current experiments.

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Abstract We investigate the dynamics of a two-component Bose–Einstein condensate subject to spin–orbital-angular-momentum coupling and confined to a ring, via the variational approach. Adopting a single-mode approximation by assuming that the BEC carries a single angular momentum for SU(2)-symmetric spin interactions, the equations of motion for the variational parameters are derived. The phase diagram of the ground state in the plane of the Raman coupling and detuning contains three different phases which meet at a tricritical point, and the exact phase boundaries between the three phases are determined. Linear stability analysis shows that the stationary state is dynamically stable, and there exists an oscillation eigenmode with frequency determined by detuning, angular momentum, and Raman coupling. The time-evolution results indicate that the spin vector undergoes periodic rotation along a closed orbit on the Bloch sphere, which can be interpreted as a precession of the collective spin around an effective field determined by the Raman coupling strength, the detuning, and the angular momentum.

Chinese Physics B•Apr 3, 2026•0 citations
Abstract The phase boundaries of periodically driven spin–orbit coupled BECs with effective two‐body interactions are analytically calculated by using variational method. The phase diagrams of periodically driven and systems present distinguished features from undriven systems, respectively. For the BECs, the critical density (density at quantum tricritical point) will be dramatically reduced in some parameter regions, and the prospect of observing this intriguing quantum tricritical point is greatly enlarged. Moreover, a series of quantum tricritical points emerge quasi‐periodically when increasing the Raman coupling strength with fixed density. In the BECs, two hyperfine states of atoms can be miscible within the suitable regions of driving parameter space. As a result, systems will stay in the stripe phase with small Raman frequency at typical density, which expands the region of stripe phase in the phase diagram. In addition, an absence of quantum tricritical point in such system is observed, which is very unlike systems.
We theoretically study the ground-state phases and superfluidity of tunable spin-orbit-coupled Bose-Einstein condensates (BECs) under the periodic driving of Raman coupling. An effective time-independent Floquet Hamiltonian is proposed by using a high-frequency approximation, and we find single-particle dispersion, spin-orbit-coupling, and asymmetrical nonlinear two-body interaction can be modulated effectively by the periodic driving. The critical Raman coupling characterizing the phase transition and relevant physical quantities in three different phases (the stripe phase, plane-wave phase, and zero momentum phase) are obtained analytically. Our results indicate that the boundary of ground-state phases can be controlled and the system will undergo three different phase transitions by adjusting the external driving. Interestingly, we find the contrast of the stripe density can be enhanced by the periodic driving in the stripe phase. We also study the superfluidity of tunable spin-orbit-coupled BECs and find the dynamical instability can be tuned by the periodic driving of Raman coupling. Furthermore, the sound velocity of the ground-state and superfluidity state can be controlled effectively by tuning the periodic driving strength. Our results indicate that the periodic driving of Raman coupling provides a powerful tool to manipulate the ground-state phase transition and dynamical instability of spin-orbit-coupled BECs.
Quantum degenerate gases have provided rich systems to simulate engineered Hamiltonians and to explore quantum many-body problems in laboratory-scale experiments. In this work, I focus on spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) of Rubidium-87 atoms realized using two-photon Raman coupling in which various novel phases are predicted to exist due to competing energies from the atomic internal structure, coupling strength, and many-body collisions. BECs are observed primarily using the interaction between light and matter, where it is common to probe the atoms with near-resonant light and image their shadow on a camera. This absorption imaging technique measures the integrated column density of the atoms and it is crucial to focus the imaging system. I present a systematic method to bring the ultracold atom systems into an optimal focus using the power spectral density (PSD) of the atomic density-density correlation function. The spatial frequency at which the defocus-induced artifacts first appear in the PSD is maximized at the focus. The focusing process thus identifies the range of spatial frequencies over which the PSD is uncontaminated by finite-thickness effects. Next, I describe magnetic phases which exist in spin-1 spin-orbit-coupled condensates at a near-zero temperature. I observe ferromagnetic and unmagnetized phases which are stabilized by the locking between the spin and linear momentum of the system. Our measurements of both the first- and second-order transitions are in agreement with theory. Finally, I discuss the stripe-ordered phase that occurs in SOC Bose gases favoring the miscibility configuration. The stripe phase is theoretically predicted to have an excitation spectrum analogous to that of a supersolid and to exhibit spatial density modulation within specific regions of parameter space. I used optical Bragg scattering to probe the small density modulation present in the atomic spatial distribution. I present for the very first time observation of the stripe phase in a Raman SOC Bose gas and its phase diagram in various parameter space. Our observations of the phase boundaries are consistent with theory and previous work.
We study the ground-state phases, the stability phase diagram and collapse dynamics of Bose—Einstein condensates (BECs) with tunable spin—orbit (SO) coupling in the two-dimensional harmonic potential by variational analysis and numerical simulation. Here we propose the theory that the collapse stability and collapse dynamics of BECs in the external trapping potential can be manipulated by the periodic driving of Raman coupling (RC), which can be realized experimentally. Through the high-frequency approximation, an effective time-independent Floquet Hamiltonian with two-body interaction in the harmonic potential is obtained, which results in a tunable SO coupling and a new effective two-body interaction that can be manipulated by the periodic driving strength. Using the variational method, the phase transition boundary and collapse boundary of the system are obtained analytically, where the phase transition between the spin-nonpolarized phase with zero momentum (zero momentum phase) and spin-polarized phase with non-zero momentum (plane wave phase) can be manipulated by the external driving and sensitive to the strong external trapping potential. Particularly, it is revealed that the collapsed BECs can be stabilized by periodic driving of RC, and the mechanism of collapse stability manipulated by periodic driving of RC is clearly revealed. In addition, we find that the collapse velocity and collapse time of the system can be manipulated by periodic driving strength, which also depends on the RC, SO coupling strength and external trapping potential. Finally, the variational approximation is confirmed by numerical simulation of Gross—Pitaevskii equation. Our results show that the periodic driving of RC provides a platform for manipulating the ground-state phases, collapse stability and collapse dynamics of the SO coupled BECs in an external harmonic potential, which can be realized easily in current experiments.
We study the zero-temperature phase diagram of a spin-orbit-coupled Bose-Einstein condensate of spin 1, with equally weighted Rashba and Dresselhaus couplings. Depending on the antiferromagnetic or ferromagnetic nature of the interactions, we find three kinds of striped phases with qualitatively different behaviors in the modulations of the density profiles. Phase transitions to the zero-momentum and the plane-wave phases can be induced in experiments by independently varying the Raman coupling strength and the quadratic Zeeman field. The properties of these transitions are investigated in detail, and the emergence of tricritical points, which are the direct consequence of the spin-dependent interactions, is explicitly discussed.
Abstract We investigate the dynamics of a two-component Bose–Einstein condensate subject to spin–orbital-angular-momentum coupling and confined to a ring, via the variational approach. Adopting a single-mode approximation by assuming that the BEC carries a single angular momentum for SU(2)-symmetric spin interactions, the equations of motion for the variational parameters are derived. The phase diagram of the ground state in the plane of the Raman coupling and detuning contains three different phases which meet at a tricritical point, and the exact phase boundaries between the three phases are determined. Linear stability analysis shows that the stationary state is dynamically stable, and there exists an oscillation eigenmode with frequency determined by detuning, angular momentum, and Raman coupling. The time-evolution results indicate that the spin vector undergoes periodic rotation along a closed orbit on the Bloch sphere, which can be interpreted as a precession of the collective spin around an effective field determined by the Raman coupling strength, the detuning, and the angular momentum.