Supersolid striped droplets in a Raman spin-orbit-coupled system

Abstract

We analyze the role played by quantum fluctuations on a Raman Spin-Orbit Coupled system in the stripe phase. We show that beyond mean-field effects stabilize the collapse predicted by meanfield theory and induce the emergence of two phases: a gas and a liquid, which also show spatial periodicity along a privileged direction. We show that the energetically favored phase is determined by the Raman coupling and the spin-dependent scattering lengths. We obtain the ground-state solution of the finite system by solving the extended Gross-Pitaevskii equation and find self-bound, droplet-like solutions that feature internal structure through a striped pattern. We estimate the critical number for binding associated to these droplets and show that their value is experimentally accessible. We report an approximate energy functional in order to ease the evaluation of the Lee-Huang-Yang correction in practical terms.

Self-Bound Quantum Droplet with Internal Stripe Structure in 1D Spin-Orbit-Coupled Bose Gas

“…The coefficient c 2 , as shown in Fig. 1, has a roughly quadratic dependence on RC strength while c 3 remains constant in the range of 0 < Ω < 3E r , in agreement with the preceding work [32]. Also, such a behavior occurs in the Rabi-coupled case [34] where the coefficient of usual n 3/2 term in LHY energy is free of Ω.…”

“…In previous studies, the stripe state has been investigated in the BEC-gas region with repulsive MF ground-state energy. Recently, theoretically stud-ies [31,32] reveal that the stripe state can also exist in the quantum droplet regime. In Ref.…”

“…In Ref. [32] the LHY energy of a three-dimensional system with SOC was calculated numerically, and its fitted form was used in the extended (GP) equation. The phase transition between a stripe gas and a stripe liquid was found by tuning coupling constants and RC.…”

Spinor Boson Droplets Stabilized By Spin Fluctuations

“…While some recent work claim that these modes can be stabilized due to exotic manybody effects like bosonic pairing [17] or beyond LHY contributions [19,20], other theories neglect them, claiming that the instability would be too slow to be observed in the experiment. Broadening the family of droplets [21][22][23][24][25] by adding a new stabilization mechanism may lead to novel phenomena and further enhance droplet theories.…”

Coherently Coupled Mixtures of Bose-Einstein Condensed Gases

“…For reasons of space we are unable to discuss here important results concerning coherently coupled mixtures where the mean-field description is not appropriate like, for example, the case of large enough attractive interspecies interaction, where beyond mean field Lee-Huang-Yang corrections become crucially important (8) and even yield self bound droplet states (9,10,11,12), and the case of cold gases trapped in deep optical lattice where the system is properly described by Bose-Hubbard-like Hamiltonians allowing for strongly correlated configurations (see, e.g., (13,14,15,16,17,18)).…”