Spin-Tensor–Momentum-Coupled Bose-Einstein Condensates

Abstract

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 spin vector (spin-1/2 or spin-1) and orbit represents 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 (BECs) 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 direct experimental observation of a new dynamical supersolid-like 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.Introduction.-The coupling between matter and gauge field plays a crucial role for many fundamental quantum phenomena and practical device applications in condensed matter [1][2][3] and atomic physics [4]. A prominent example is the spin-orbit coupling, the coupling between a particle's spin and orbit (e.g., momentum) degrees of freedom, which is responsible for important physics such as topological insulators and superconductors [2,3]. In this context, recent experimental realization of spin-orbit coupling in ultracold atomic gases [5][6][7][8][9][10][11][12][13] opens a completely new avenue for investigating quantum many-body physics under gauge field [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].So far in most works on spin-orbit coupling in solid state and cold atomic systems, the spin degrees of freedom are taken as rank-1 spin vectors F i (i = x, y, z), such as electron spin-1/2 or pseudospins formed by atomic hyperfine states that can be large (e.g., spin-1 or 3/2). Experimentally, spin-orbit coupling for spin-1 Bose-Einstein condensates (BECs) has been realized recently [29,30] and interesting magnetism physics has been observed [31][32][33][34][35]. Mathematically, it is well known that there exist not only spin vectors, but also spin tensors [e.g., irreducible rank-2 spin-quadrupole tensorin a large spin (≥ 1) system. Therefore two natural questions are: i ) Can the coupling between spin tensors of particles and their linear momenta be realized in experiments? ii ) What new physics may emerge from such spin-tensor-momentum coupling (STMC)?In this Letter, we address these two questions by proposing a simple experimental scheme for realizing STMC for spin-1 ultracold atomic gases. Our scheme is based on slight modification of previous experimental setup [29] and is experimentally feasible. The STMC changes the band structure dramatically, leading to interesting new physics in the presence of many-body interactions between atoms. Although both bosons and fermions can be studied, here we only consider spi...

Experimental realization of a long-lived striped Bose-Einstein condensate induced by momentum-space hopping

“…Such simultaneous breaking of continuous translational symmetry and U(1) gauge symmetry was first predicted for solid helium [2,3], but convincing evidence of a supersolid state in this system has remained elusive [4]. In recent years, the experimental realization of spin-orbit coupling (SOC) in ultracold atomic gases [5][6][7][8][9][10][11][12][13][14][15][16][17] has opened a new pathway for demonstrating long-sought supersolidlike states [18][19][20][21][22][23][24][25][26][27][28][29][30].The lowest energy band in the SOC dispersion is characterized by two local minima at distinct momenta [5]. For a narrow range of system parameters, mean-field interactions within a Bose-Einstein condensate (BEC) favor a ground state which is composed of a coherent superposition of two plane-wave states at the dispersion minima [22].…”

Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings

“…Nowadays, various types of spin-vector-momentum coupling for both spin-1/2 and spin-1 have been proposed and realized [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. A scheme for realizing spin-tensor-momentum coupling of spin-1 atoms has also been proposed recently [55] with ongoing experimental efforts [56]. Our scheme is built on these experimentally available setups [50,53] and may even pave the way for identifying solid-state materials with our novel types of TDPs.…”

Momentum space Aharonov-Bohm interferometry in Rashba spin-orbit coupled Bose-Einstein condensates

“…Our analysis can be extended to different experimental conditions such as an anisotropic ring loop or a loop with several local minima. The interferometry approach may find wide applications on various nontrivial energy bands as well as on high-spin [57][58][59][60][61][62][63] systems. e ipη(rη−Aη)…”