Polar phase of one-dimensional bosons with large spin

Part of Focus on Strongly Correlated Quantum Fluids - from Ultracold Quantum Gases to QCD Plasmas

Spinor ultracold gases in one dimension (1D) represent an interesting example of strongly correlated quantum fluids. They have a rich phase diagram and exhibit a variety of quantum phase transitions. We consider a 1D spinor gas of bosons with a large spin S. A particular example is the gas of chromium atoms (S=3), where the dipolar collisions efficiently change the magnetization and make the system sensitive to the linear Zeeman effect. We argue that in 1D the most interesting effects come from the pairing interaction. If this interaction is negative, it gives rise to a (quasi)condensate of singlet bosonic pairs with an algebraic order at zero temperature, and for (2S+1)1 the saddle point approximation leads to physically transparent results. Since in 1D one needs a finite energy to destroy a pair, the spectrum of spin excitations has a gap. Hence, in the absence of a magnetic field, there is only one gapless mode corresponding to phase fluctuations of the pair quasicondensate. Once the magnetic field exceeds the gap, another condensate emerges, namely the quasicondensate of unpaired bosons with spins aligned along the magnetic field. The spectrum then contains two gapless modes corresponding to the singlet-paired and spin-aligned unpaired Bose condensed particles, respectively. At T=0, the corresponding phase transition is of the commensurate-incommensurate type.