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arXiv:1802.02113 · Physical Review A

Dimer-dimer zero crossing and dilute dimerized liquid in a one-dimensional mixture

A. Pricoupenko, Dmitry S. Petrov

Published Jun 15, 2018• 25 citations
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Abstract

We consider the system of dimers formed in a one-dimensional mass-balanced Bose-Bose mixture of species $\ensuremath{\sigma}=\ensuremath{\uparrow},\ensuremath{\downarrow}$ with attractive interspecies and repulsive intraspecies contact interactions. In the plane parametrized by the ratios of the coupling constants ${g}_{\ensuremath{\uparrow}\ensuremath{\uparrow}}/|{g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}|$ and ${g}_{\ensuremath{\downarrow}\ensuremath{\downarrow}}/|{g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}|$ we trace out the curve where the dimer-dimer interaction switches from attractive to repulsive. We find this curve to be significantly (by more than a factor of 2) shifted towards larger ${g}_{\ensuremath{\sigma}\ensuremath{\sigma}}$ (or smaller $|{g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}|$) compared to the mean-field stability boundary ${g}_{\ensuremath{\uparrow}\ensuremath{\uparrow}}{g}_{\ensuremath{\downarrow}\ensuremath{\downarrow}}={g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}^{2}$. For a weak dimer-dimer attraction we predict a dilute dimerized liquid phase stabilized against collapse by a repulsive three-dimer force.

DOI
10.1103/physreva.97.063616

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In this thesis we investigate the properties of mixtures of Bose gases in one dimensions at zero temperature using quantum Monte-Carlo methods. First we investigate the limiting case of an impurity interacting with an atomic bath. We characterize the impurity, by calculating its effective mass, binding energy as well as the contact parameter between the impurity and the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. Then we describe uniform balanced mixtures with repulsive interactions. We investigate the miscibility phase diagram of the two components and find that correlations do not alter the phase diagram predicted by mean-field theories. We investigate the Andreev-Bashkin effect , a non-dissipative drag between the the two components of the gas and find that the drag becomes very large in the strongly interacting regime. In non-homogeneous systems we also investigate the frequency of the spin-dipole mode. Finally we describe mixtures with attractive inter-species interactions, where one can obtain a liquid ground state because of the competition between the inter-species attraction and intra-species repulsion. We characterize the the liquid and we find that the liquid state can be formed if the ratio of coupling strengths between inter-species attractive and intra-species repulsive interactions exceeds a critical value.
By using exact quantum Monte Carlo methods we calculate the ground-state properties of the liquid phase in one-dimensional Bose mixtures with contact interactions. We find that the liquid state can be formed if the ratio of coupling strengths between interspecies attractive and intraspecies repulsive interactions exceeds a critical value. As a function of this ratio we determine the density where the energy per particle has a minimum and the one where the compressibility diverges, thereby identifying the equilibrium density and the spinodal point in the phase diagram of the homogeneous liquid. Furthermore, in the stable liquid state, we calculate the chemical potential, the speed of sound, as well as structural and coherence properties, such as the pair correlation function, the static structure factor, and the one-body density matrix, thus providing a detailed description of the bulk region in self-bound droplets.
We solve the three-boson problem with contact two-and three-body interactions in one dimension and analytically calculate the ground and excited trimer-state energies.Then, by using the diffusion Monte Carlo technique we calculate the binding energy of three dimers formed in a one-dimensional Bose-Bose or Fermi-Bose mixture with attractive interspecies and repulsive intraspecies interactions.Combining these results with our three-body analytics, we extract the three-dimer scattering length close to the dimer-dimer zero crossing.In both considered cases the three-dimer interaction turns out to be repulsive.Our results constitute a concrete proposal for obtaining a one-dimensional gas with a pure three-body repulsion.
We discuss the mean-field theories obtained from the leading order in a large-NNN approximation for one- and two-component dilute Bose gases. For a one-component Bose gas, this approximation has the following properties: the Bose-Einstein condensation (BEC) phase transition is second order but the critical temperature Tc{T}_{c}Tc​ is not shifted from the noninteracting gas value T0{T}_{0}T0​. The spectrum of excitations in the BEC phase resembles the Bogoliubov dispersion with the usual coupling constant replaced by the running coupling constant which depends on both temperature and momentum. We then study two-component Bose gases with both inter- and intraspecies interactions and focus on the stability of the mixture state above Tc{T}_{c}Tc​. Our mean-field approximation predicts an instability from the mixture state to a phase-separated state when the ratio of the interspecies interaction strength to the intraspecies interaction strength (assuming equal strength for both species) exceeds a critical value. At high temperature this is a structural transition and the global translational symmetry is broken. Our work complements previous studies on the instability of the mixture phase in the presence of BEC.
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We study the ground states of one-dimensional Bose-Bose mixtures under harmonic confinement. As we vary the interspecies coupling strength up to the limit of infinite repulsion, we observe a generalized, composite-fermionization crossover. The initially coexisting phases demix as a whole for weak intraspecies interactions, whereas the atoms localize individually for strong intraspecies repulsion. By symmetry, the two components end up with strongly overlapping profiles, albeit sensitive to symmetry-breaking perturbations. Different pathways emerge if the two components have different atom numbers, different intraspecies interactions, or different masses and/or trap frequencies.