Exotic superfluidity in spin-orbit coupled Bose-Einstein condensates

Abstract

We study the superfluidity of a spin-orbit coupled Bose-Einstein condensate (BEC) by computing its Bogoliubov excitations, which are found to consist of two branches: one is gapless and phonon-like at long wavelength; the other is typically gapped. These excitations imply a superfluidity that has two new features: (i) due to the absence of the Galilean invariance, one can no longer define the critical velocity of superfluidity independent of the reference frame; (ii) the superfluidity depends not only on whether the speed of the BEC exceeds a critical value, but also on cross helicity that is defined as the direction of the cross product of the spin and the kinetic momentum of the BEC.

Properties of spin–orbit-coupled Bose–Einstein condensates

“…Due to the Galilean invariance of a regular BEC, the physics of a moving optical lattice is equivalent to that of physically moving a BEC. However, for a SOC BEC, the Galilean invariance is broken, and these two schemes are no longer equivalent [44,169]. Moreover, the results are expected to be asymmetric for lattices moving in different directions.…”

“…Comparing the SOC terms with the original H soc , we find thatH M sp is non-trivially different from H soc due to the term δ + 2mγv/h, which can be interpreted as an effective detuning of the Raman beams. This term depends on the frame velocity v and signifies the broken Galilean invariance of the SOC BEC [44].…”

“…The most famous example of this is the existence of a stripe phase that is an equal superposition of two minima in momentum space [40]. The ground state and collective excitations of SOC BECs have been investigated for a large number of different settings, such as homogeneous [40][41][42][43][44][45][46][47][48][49], harmonic [50][51][52][53][54], in the presence of a periodic optical lattice [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72], a double-well [73][74][75], rotation [76][77][78][79][80][81], inside an optical cavity [82][83][84][85][86], and for particles with dipolar interaction …”

Bright solitons in a two-dimensional spin-orbit-coupled dipolar Bose-Einstein condensate

“…But this is only valid for a system respecting Galilean transform invariance. In fact, Galilean invariance is broken in a spin-orbit-coupled BEC [68], and this violation dictates that the shape of a soliton depends on its velocity strength [55]. Here, for a soliton in a spin-orbit-coupled dipolar BEC in 2D, we assume that a moving soliton can be written as…”

“…These solitons exhibit unique features that are absent without spin-orbit coupling, for instance, the plane wave profile with a spatially varying phase and the stripe profile with a spatially oscillating density for BECs, as well as the presence of Majorana fermions inside a soliton for Fermi superfluids. Also, the violation of Galilean invariance [55,68,69] by spin-orbit coupling dictates that the structure of solitons changes with their velocities.…”