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arXiv:2010.10965 · Physical Review A

Symmetry breaking and phase transitions in Bose-Einstein condensates with spin–orbital-angular-momentum coupling

Yuxiong Duan, Y. M. Bidasyuk, A. Surzhykov

Published Dec 24, 2020• 20 citations
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Abstract

Theoretical study is presented for a spinor Bose-Einstein condensate, whose two components are coupled by copropagating Raman beams with different orbital angular momenta. The investigation is focused on the behavior of the ground state of this condensate, depending on the atom-light coupling strength. By analyzing the ground state, we have identified a number of quantum phases, which reflect the symmetries of the effective Hamiltonian and are characterized by the specific structure of the wave function. In addition to the well-known stripe, polarized, and zero-momentum phases, our results show that the system can support phases whose wave functions contain a complex vortex molecule. Such a molecule plays an important role in the continuous phase transitions of the system. The predicted behavior of vortex-molecule phases can be examined in cold-atom experiments using currently existing techniques.

DOI
10.1103/physreva.102.063328

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Theoretical study is presented for a spinor Bose-Einstein condensate, whose two components are coupled by copropagating Raman beams with different orbital angular momenta. The investigation is focused on the behavior of the ground state of this condensate, depending on the atom-light coupling strength. By analyzing the ground state, we have identified a number of quantum phases, which reflect the symmetries of the effective Hamiltonian and are characterized by the specific structure of the wave function. In addition to the well-known stripe, polarized, and zero-momentum phases, our results show that the system can support phases whose wave functions contain a complex vortex molecule. Such a molecule plays an important role in the continuous phase transitions of the system. The predicted behavior of vortex-molecule phases can be examined in cold-atom experiments using currently existing techniques.
We investigate the ground-state phase diagram and excitation spectrum of an interacting spinor Bose-Einstein condensate with spin-orbital-angular-momentum (SOAM) coupling realized in recent experiments by introducing atomic Raman transition with a pair of copropagating Laguerre-Gaussian laser beams that carry different orbital angular momenta (OAM) [Chen et al., Phys. Rev. Lett. 121, 113204 (2018) and Zhang et al., Phys. Rev. Lett. 122, 110402 (2019)]. Because of the ground-state degeneracy of the single-particle Hamiltonian at vanishing detuning, several angular-stripe phases, which are the superposition of states with different angular quantum numbers, appear in the phase diagram. However, these phases normally exist at small detuning, which makes them hard to be probed in experiments. We show that for a large OAM difference of the laser beams, an asymmetric kind of angular-stripe phase can exist even at large detuning. The excitation spectra in different phases exhibit distinct features: In the angular-stripe phase there exist two gapless bands corresponding to the broken U(1)\mathrm{U}(1)U(1) and rotational symmetries, while in the half-skyrmion phase the gapless band exhibits a rotonlike structure. Our predictions of the angular-stripe phases and the low-energy excitations can be examined in recently realized Bose-Einstein condensates with SOAM coupling.
An effective spin-orbit coupling can be generated in a cold atom system by engineering atom-light interactions. In this Letter we study spin-1/2 and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop nontrivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role of a domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave, and it forms a spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determine the transition point between the two phases.
We present a theoretical study of the collective excitations of the supersolid annular stripe phase of a spin-orbital-angular-momentum-coupled (SOAM-coupled) spin-1 Bose-Einstein condensate. The annular stripe phase simultaneously breaks two continuous symmetries, namely rotational and U(1)U(1)U(1) gauge symmetry, and is more probable in the condensates with a larger orbital angular momentum transfer imparted by a pair of Laguerre-Gaussian beams than what has been considered in the recent experiments. Accordingly, we consider a SOAM-coupled spin-1 condensate with a $4\ensuremath{\hbar}$ orbital angular momentum transferred by the lasers. Depending on the values of the Raman coupling strength and quadratic Zeeman term, the condensate with realistic antiferromagnetic interactions supports three ground-state phases: the annular stripe, the vortex necklace, and the zero angular momentum phase. We numerically calculate the collective excitations of the condensate as a function of coupling and quadratic Zeeman field strengths for a fixed ratio of spin-dependent and spin-independent interaction strengths. At low Raman coupling strengths, we observe a direct transition from the zero angular momentum to the annular stripe phase, characterized by the softening of a double symmetric roton mode, which serves as a precursor to supersolidity.
We investigate the ground-state structures and vortex configurations in a two-component Bose-Einstein condensate under the influence of spin-orbital-angular-momentum coupling (SOAMC) with a high spatial inhomogeneity and high characteristic orbital angular momentum. By modulating the coupling strength, we uncover two distinct quantum phases: a stripe phase at low coupling strengths and a new vortex-necklace phase at higher coupling intensities. The latter is characterized by vortices forming a ring-shaped structure that acts as a domain wall, a unique phase boundary between a central stripe phase and an outer single-momentum phase. For a better understanding of this new mixed phase of the system, we develop an analytical model to describe the domain-wall radius as a function of coupling strength, which aligns well with numerical simulations. Our findings contribute to the understanding of SOAMC-driven quantum phase transitions and domain-wall formation, offering new insights into topological phenomena in ultracold atomic systems.
We propose a simple model with spin and orbit angular momentum coupling in a spin-1 Bose-Einstein condensate, where three internal atomic states are Raman coupled by a pair of copropagating Laguerre-Gaussian beams. The resulting Raman transition imposes a transfer of orbital angular momentum between photons and the condensate in a spin-dependent way. Focusing on a regime where the single-particle ground state is nearly threefold degenerate, we show that the weak interatomic interaction in the condensate produces a rich phase diagram, and that a many-body Rabi oscillation between two quantum phases can be induced by a sudden quench of the quadratic Zeeman shift. We carried out our calculations using both a variational method and a full numerical method, and found excellent agreement.
By inducing a Raman transition using a pair of Gaussian and Laguerre-Gaussian laser beams, we realize a ^{87}Rb condensate whose orbital angular momentum (OAM) and its internal spin states are coupled. By varying the detuning and the coupling strength of the Raman transition, we experimentally map out the ground-state phase diagram of the system for the first time. The transitions between different phases feature a discontinuous jump of the OAM and the spin polarization, and hence are of first order. We demonstrate the hysteresis loop associated with such first-order phase transitions. The role of interatomic interaction is also elucidated. Our work paves the way to explore exotic quantum phases in the spin-orbital-angular-momentum coupled quantum gases.