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arXiv:2401.14751

Fragmented Condensate in a Two-Component Bose Gas with $p$-wave Interactions

Mingyang Liu, Shizhong Zhang

Published Jan 26, 2024• 0 citations
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Abstract

In this Letter, we discuss the effects of $p$-wave attractive interaction in a spin-$1/2$ Bose gas. With a repulsive $s$-wave background interaction, we show that for weak $p$-wave attraction, one obtains a standard Bose-Einstein condensate at zero momentum with spins fully polarized. Upon increasing the $p$-wave attraction, a fragmented condensate state with singlet pair formation and $p$-wave correlation emerges. We determine the transition point and investigate the properties of the fragmented condensate using an ansatz wave function. We construct the relevant Gross-Pitaevskii equations for the fragmented condensate and show that the sound velocities are anisotropic and may vanish in specific directions. Based on the many-body wave function, we also discuss the low-energy spin excitations of the system.

DOI
10.48550/arxiv.2401.14751

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Fragmented Condensate in a Two-Component Bose Gas with ppp-wave Interactions
In this Letter, we discuss the effects of ppp-wave attractive interaction in a spin-1/21/21/2 Bose gas. With a repulsive sss-wave background interaction, we show that for weak ppp-wave attraction, one obtains a standard Bose-Einstein condensate at zero momentum with spins fully polarized. Upon increasing the ppp-wave attraction, a fragmented condensate state with singlet pair formation and ppp-wave correlation emerges. We determine the transition point and investigate the properties of the fragmented condensate using an ansatz wave function. We construct the relevant Gross-Pitaevskii equations for the fragmented condensate and show that the sound velocities are anisotropic and may vanish in specific directions. Based on the many-body wave function, we also discuss the low-energy spin excitations of the system.
Recently it has been predicted that if a gas of spin-1/2 bosonic atoms is cooled down while conserving its total spin, it can form a Bose-Einstein condensate in a new type of fragmented state. In that fragmented state two orbital wave functions are macroscopically occupied. We derive a set of Gross-Pitaevskii equations that describe the two occupied wave functions, taking into account the effects of interatomic interactions. We then analyze the solutions of those equations in some special cases. In particular, we find that if the fragmented state is realized in a toroidal trap, under certain conditions the system will spontaneously acquire macroscopic orbital angular momentum. Finally, we discuss the nature of the phase transition from an uncondensed gas to a fragmented-state condensate.
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The competition between particle and pair condensation in Bose liquids is studied using a mean field variational ground state that comprises both the Bogoliubov approximation for weakly interacting Bose gases and the Valatin-Butler pair state. We first consider structureless bosons, disregarding the fact that an attractive gas will necessarily collapse. We show that a pair state occurs only if the attraction is strong enough to bind two bosons together. The limit of low densities is treated exactly. At higher density, we use a separable interaction model and we show that the pairs dissociate at a critical density Nc (where their ionization gap vanishes). Past that threshold, ordinary particle condensation sets in. In order to cure collapse, we consider bosons with an internal spin structure : the interaction is binding in some states, repulsive on the average. Taking spin 1 particles as an example, we repeat the previous analysis, and we substantiate its conclusions while retaining a positive compressibility. In the pair regime the ground state is isotropic (singlet pairs). Past the dissociation threshold, an anisotropic one particle condensate appears. We show that it is linearly polarized (in an arbitrary direction), and non fragmented. We discuss briefly its physical properties, and we suggest that the transition from pair to particle condensation might be first order.
An attractive Bose-Einstein condensate in two spatial dimensions is expected to collapse for supercritical values of the interaction strength. Moreover, it is known that for nonzero quanta of angular momentum and infinitesimal attraction the gas prefers to fragment and distribute its angular momentum over different orbitals. In this work we examine the two-dimensional trapped Bose gas for finite values of attraction and describe the ground state in connection to its angular momentum by theoretical methods that go beyond the standard Gross-Pitaevskii theory. By applying the best-mean-field approach over a variational ansatz whose accuracy has been checked numerically, we derive analytical relations for the energy, the fragmentation of the ground states, and the critical (for collapse) value of the attraction strength as a function of the total angular momentum LLL.
The dynamics of a two-component dilute Bose-Einstein gas of atoms at zero temperature is described in the mean-field approximation by a two-component Gross-Pitaevskii equation. We solve this equation assuming a Gaussian shape for the wave function, where the free parameters of the trial wave function are determined using a moment method. We derive equilibrium states and the phase diagrams for the stability for positive and negative sss-wave scattering lengths, and obtain the low-energy excitation frequencies corresponding to the collective motion of the two Bose-Einstein condensates.
We investigate a weakly interacting two-component Bose--Einstein condensate in the miscible regime in the presence of \emph{altermagnetism}, i.e., a collinear and globally compensated magnetic order that breaks spin-rotation symmetry while maintaining zero net magnetization. Within Bogoliubov theory, we derive the quasiparticle spectrum and coherence factors and show that altermagnetic order generically induces an angular dependence of the low-energy excitations. As a result, the sound velocity, momentum-resolved magnetization in the quantum depletion, and density--spin response functions acquire anisotropic components. We show that these anisotropic contributions vanish after angular averaging, consistent with the defining feature of altermagnetism: nontrivial local spin polarization without a global magnetization. Finally, we evaluate the Lee--Huang--Yang correction to the ground-state energy in the altermagnetic phase. Our results should be testable with ultracold-atom experiments in the foreseeable future.