Polar Phase of 1D Bosons with Large Spin

TL;DR

This paper explores the phase diagram of one-dimensional large-spin bosonic gases, revealing a polar phase with singlet pairing and multiple gapless modes influenced by magnetic fields and temperature.

Contribution

It introduces a theoretical analysis of the polar phase in 1D large-spin bosons, highlighting the role of pairing interactions and magnetic fields in shaping the quantum phases.

Findings

Existence of a singlet bosonic pair condensate with algebraic order at zero temperature.

Presence of a gap in spin excitations due to pairing interactions.

Emergence of a second condensate with aligned spins when magnetic field exceeds the gap.

Abstract

Spinor ultracold gases in one dimension 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 one-dimensional 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 one dimension 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 $(2S+1)\gg 1$ the saddle point approximation leads to physically transparent results. Since in one dimension one needs a finite energy to destroy a pair, the spectrum of spin excitations has a gap. Hence, in the absence of 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.