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arXiv:1709.01978 · Physical Review A

Oscillating Casimir potential between two impurities in a spin-orbit-coupled Bose-Einstein condensate

Pei-Song He, Qing Sun, An-Chun Ji

Published Oct 18, 2017• 3 citations
arXivHTMLPDF

Abstract

We study the Casimir potential between two impurities immersed in a spin-orbit-coupled Bose-Einstein condensate (BEC) with plane-wave order. We find that by exchanging the virtual excitations, a remarkable anisotropic oscillating potential with both positive and negative parts can be induced between the impurities, with the period of the oscillation depending on the spin-orbit-coupling strength. As a consequence, this would inevitably lead to a noncentral Casimir force, which can be tuned by varying the strength of the spin-orbit coupling (SOC). These results are elucidated for BECs with one-dimensional Raman-induced and two-dimensional Rashba-type SOCs.

DOI
10.1103/physreva.96.043617

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We study the Casimir potential between two impurities immersed in a spin-orbit-coupled Bose-Einstein condensate (BEC) with plane-wave order. We find that by exchanging the virtual excitations, a remarkable anisotropic oscillating potential with both positive and negative parts can be induced between the impurities, with the period of the oscillation depending on the spin-orbit-coupling strength. As a consequence, this would inevitably lead to a noncentral Casimir force, which can be tuned by varying the strength of the spin-orbit coupling (SOC). These results are elucidated for BECs with one-dimensional Raman-induced and two-dimensional Rashba-type SOCs.
We explore a way of producing the Rashba spin-orbit coupling (SOC) for ultracold atoms by using a two-component (spinor) atomic Bose-Einstein condensate (BEC) confined in a bilayer geometry. The SOC of the Rashba type is created if the atoms pick up a $\ensuremath{\pi}$ phase after completing a cyclic transition between four combined spin-layer states composed of two spin and two layer states. The cyclic coupling of the spin-layer states is carried out by combining an intralayer Raman coupling and an interlayer laser assisted tunneling. We theoretically determine the ground-state phases of the spin-orbit-coupled BEC for various strengths of the atom-atom interaction and the laser-assisted coupling. It is shown that the bilayer scheme provides a diverse ground-state phase diagram. In an intermediate range of the atom-light coupling two interlacing lattices of half-skyrmions and half-antiskyrmions are spontaneously created. In the strong-coupling regime, where the SOC of the Rashba type is formed, the ground state represents plane-wave or standing-wave phases depending on the interaction between the atoms. A variational analysis is shown to be in good agreement with the numerical results.
Abstract We study the thermal Casimir effect in ideal Bose gases with spin–orbit (S–O) coupling of Rashba type below the critical temperature for Bose–Einstein condensation. In contrast to the standard situation involving no S–O coupling, the system exhibits long-ranged Casimir forces in both two and three dimensions ( d = 2 and d = 3). We identify the relevant scaling variable involving the ratio D / ν of the separation between the confining walls D and the S–O coupling magnitude ν . We derive and discuss the corresponding scaling functions for the Casimir energy. In all the considered cases, the resulting Casimir force is attractive and the S–O coupling ν has impact on its magnitude. In d = 3 the exponent governing the decay of the Casimir force becomes modified by the presence of the S–O coupling, and its value depends on the orientation of the confining walls relative to the plane defined by the Rashba coupling. In d = 2 the obtained Casimir force displays a singular behavior in the limit of vanishing ν .
Abstract We investigate the modulation instability (MI) of plane-wave states in a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC). The MI of the system can be adjusted by the intensities of the spin–orbit coupling (SOC), Raman coupling and atom–atom interactions. Our analysis shows that the MI of a system without the SOC and Raman coupling mainly occurs for repulsive density–density and spin–exchange interactions due to the combined effects coming from both of them. But when considering the SOC, a multi-peak structure appears in the momentum distribution for the instability, which may be thought of as a precursor to the generation of the stripe-type nonlinear excitations in such systems. The MI becomes more remarkable with increasing intensity of Raman coupling. In addition, the SOC inevitably contributes to the instability for the ternary superfluid regardless of the nature of the density–density and spin–exchange interactions.
We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman-induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground states, using which we construct an effective two-mode model. The Hamiltonian of the two-mode model takes the form of the one-axis-twisting Hamiltonian, which is known to generate spin squeezing. More importantly, we show that the SOC provides a convenient control knob to adjust the spin nonlinearity responsible for spin squeezing. Specifically, the spin nonlinearity strength can be tuned to be comparable to the two-body density-density interaction, and hence is much larger than the intrinsic spin-dependent interaction strength in conventional two-component BEC systems such as 87Rb^{87}\mathrm{Rb}87Rb and 23Na^{23}\mathrm{Na}23Na in the absence of the SOC. We confirm the spin squeezing by carrying out a fully beyond-mean-field numerical calculation using the truncated Wigner method. Additionally, the experimental implementation is also discussed.
We study the collective dynamics of the spin-orbit coupled two pseudospin components of a Bose-Einstein condensate trapped in a quasi-one-dimensional harmonic potential, by using variational and directly numerical approach of binary mean-field Gross-Pitaevskii equations. The results show that, because of strong coupling of spin-orbit coupling (SOC), Rabi coupling, and atomic interaction, the collective dynamics of the system behave as complex characters. When the Rabi coupling is absent, the density profiles of the system preserve the Gauss type and the wave packets do harmonic oscillations. The amplitude of the collective oscillations increases with SOC. Furthermore, when the SOC strength increases, the dipole oscillations of the two pseudospin components undergo a transition from in-phase to out-of-phase oscillations. When the Rabi coupling present, there will exist a critical value of SOC strength (which depends on the Rabi coupling and atomic interaction). If the SOC strength is less than this critical value, the density profiles of the system can preserve the Gauss type and the wave packets do anharmonic (the frequency of dipole oscillations depends on SOC) oscillations synchronously (i.e., in-phase oscillations). However, if the SOC strength is larger than this critical value, the wave packets are dynamically fragmented and the stable dipole oscillations of the system can not exist. The collective dynamics of the system can be controlled by adjusting the atomic interaction, SOC, and Rabi-coupling strength.
Impurities immersed in a Bose-Einstein condensate (BEC) can interact indirectly through the exchange of Bogoliubov excitations. These impurities, which form dressed quasiparticles known as Bose polarons due to their interaction with the BEC, can pair up to form a bound state called a bipolaron, via an induced interaction. Previous studies on induced interactions have focused primarily on cases with an isotropic excitation spectrum. In this work, we investigate the properties of induced interactions and bipolarons mediated by anisotropic Bogoliubov excitations using field theory. Taking a BEC with spin-orbit coupling as an example, we show that the induced interaction becomes anisotropic. Notably, a double-minima feature appears in the induced interaction in momentum space due to the exchange of roton excitations. Additionally, we calculate the binding energy and wave functions of these bipolarons induced by anisotropic interactions. Unlike previously studied bipolarons formed through the exchange of isotropic phonon excitations, we identify an alternative type of bipolaron whose wave functions feature a double-peak structure under strong impurity-boson interactions. Our work extends the theory of induced interactions from isotropic to anisotropic systems, and it reveals the novel features in both the induced interactions and bipolarons arising from BEC with an unconventional excitation spectrum.