Supersolid is a special state of matter with both superfluid properties and spontaneous modulation of particle density. In this paper we focus on the supersolid stripe phase realized in a spin-orbit-coupled Bose-Einstein condensate and explore the properties of a class of metastable supersolids. In particular, we study a one-dimensional supersolid whose characteristic wave number
k (magnitude of wave vector) deviates from
km, i.e., the one in the ground state. In other words, the period of density modulation is shorter or longer than the one in the ground state. We find that this class of supersolids can still be stable if their wave numbers fall in the range
kc1<k<kc2, with two thresholds
kc1 and
kc2. Stripes with
k outside this range suffer from dynamical instability with a complex Bogoliubov excitation spectrum at long wavelength. Experimentally, these stripes with
k different from
km are accessible by exciting the longitudinal spin dipole mode, resulting in temporal oscillation of the stripe period as well as
k. Within the mean-field Gross-Pitaevskii theory, we numerically confirm that for a large enough amplitude of spin dipole oscillation, the stripe states become unstable through breaking periodicity, in qualitative agreement with the existence of thresholds of
k for stable stripes. Our work extends the concept of supersolid and uncovers an unconventional class of metastable supersolids to explore.
Superstripe phases in Bose-Einstein condensates (BECs), possessing both crystalline structure and superfluidity, open a new avenue for exploring exotic quantum matters---supersolids. However, conclusive detection and further exploration of a superstripe is still challenging in experiments because of its short period, low visibility, fragility against magnetic-field fluctuation, or short lifetime. Here we propose a scheme in a spin-orbit coupled BEC which overcomes these obstacles and generates a robust magnetic superstripe phase, with only spin-density (no total density) modulation due to the magnetic translational symmetry, ready for direct real-space observation. In the scheme, two hyperfine spin states are individually Raman coupled with a largely detuned third state, which induce a momentum-space separation between two lower band dispersions, yielding an effective spin-1/2 system with tunable spin-orbit coupling and Zeeman fields. Without effective Zeeman fields, spin-dependent interaction dominates, yielding a magnetic superstripe phase with a long tunable period and high visibility. Our scheme provides a platform for observing and exploring exotic properties of superstripe phases as well as novel physics with tunable spin-orbit coupling.
The recent experimental realization of spin-orbit coupling for ultracold atomic gases provides a powerful platform for exploring many interesting quantum phenomena. In these studies, spin represents the spin vector (spin 1/2 or spin 1) and orbit represents the linear momentum. Here we propose a scheme to realize a new type of spin-tensor-momentum coupling (STMC) in spin-1 ultracold atomic gases. We study the ground state properties of interacting Bose-Einstein condensates with STMC and find interesting new types of stripe superfluid phases and multicritical points for phase transitions. Furthermore, STMC makes it possible to study quantum states with dynamical stripe orders that display density modulation with a long tunable period and high visibility, paving the way for the direct experimental observation of a new dynamical supersolidlike state. Our scheme for generating STMC can be generalized to other systems and may open the door for exploring novel quantum physics and device applications.
Significant experimental progress has been made recently for observing long-sought supersolidlike states in Bose-Einstein condensates, where spatial translational symmetry is spontaneously broken by anisotropic interactions to form a stripe order. Meanwhile, the superfluid stripe ground state was also observed by applying a weak optical lattice that forces the symmetry breaking. Despite the similarity of the ground states, here we show that these two symmetry breaking mechanisms can be distinguished by their collective excitation spectra. In contrast to gapless Goldstone modes of the spontaneous stripe state, we propose that the excitation spectra of the forced stripe phase can provide direct experimental evidence for the gapped pseudo-Goldstone modes. We characterize the pseudo-Goldstone mode of such lattice-induced stripe phase through its excitation spectrum and static structure factor. Our work may pave the way for exploring spontaneous and forced or approximate symmetry breaking mechanisms in different physical systems.
The coupled dynamics of the atom and photon fields in optical ring cavities with two counterpropagating modes give rise to both spin-orbit interactions as well as long-ranged interactions between atoms of a many-body system. At zero temperature, the interplay between the two-body and cavity-mediated interactions determines the ground state of a Bose-Einstein condensate. In this work, we find that cavity quantum electrodynamics in the weak-coupling regime favors a stripe-phase state over a plane-wave phase as the strength of cavity-mediated interactions increases. Indeed, the stripe phase is energetically stabilized even for condensates with attractive intraspecies and interspecies interactions for sufficiently large cavity interactions. The elementary excitation spectra in both phases correspond to linear dispersion relation at long wavelengths, indicating that both phases exhibit superfluidity, although the plane-wave phase also displays a characteristic roton-type feature. The results suggest that even in the weak-coupling regime, cavities can yield interesting new physics in ultracold quantum gases.
Recently spin-orbit (SO)-coupled superfluids in free space or harmonic traps have been extensively studied, motivated by the recent experimental realization of SO coupling for Bose-Einstein condensates (BEC). However, the rich physics of SO-coupled BEC in optical lattices has been largely unexplored. In this paper, we show that in a suitable parameter region the lowest Bloch state forms an isolated flat band in a one-dimensional SO-coupled optical lattice, which thus provides an experimentally feasible platform for exploring the recently celebrated topological flatband physics in lattice systems. We show that the flat band is preserved even with the mean-field interaction in BEC. We investigate the superfluidity of the BEC in SO-coupled lattices through dynamical and Landau stability analysis, and show that the BEC is stable on the whole flat band.