Polarization Suppression and Nonmonotonic Local Two-Body Correlations in the Two-Component Bose Gas in One Dimension

📝 Abstract

We study the interplay of quantum statistics, strong interactions and finite temperatures in the two-component (spinor) Bose gas with repulsive delta-function interactions in one dimension. Using the Thermodynamic Bethe Ansatz, we obtain the equation of state, population densities and local density correlation numerically as a function of all physical parameters (interaction, temperature and chemical potentials), quantifying the full crossover between low-temperature ferromagnetic and high-temperature unpolarized regimes. In contrast to the single-component, Lieb-Liniger gas, nonmonotonic behaviour of the local density correlation as a function of temperature is observed.

💡 Analysis

We study the interplay of quantum statistics, strong interactions and finite temperatures in the two-component (spinor) Bose gas with repulsive delta-function interactions in one dimension. Using the Thermodynamic Bethe Ansatz, we obtain the equation of state, population densities and local density correlation numerically as a function of all physical parameters (interaction, temperature and chemical potentials), quantifying the full crossover between low-temperature ferromagnetic and high-temperature unpolarized regimes. In contrast to the single-component, Lieb-Liniger gas, nonmonotonic behaviour of the local density correlation as a function of temperature is observed.

📄 Content

Polarization Suppression and Nonmonotonic Local Two-Body Correlations in the Two-Component Bose Gas in One Dimension Jean-S´ebastien Caux1, Antoine Klauser1,2 and Jeroen van den Brink2 1Institute for Theoretical Physics, Universiteit van Amsterdam, 1018 XE Amsterdam, The Netherlands and 2Instituut-Lorentz, Universiteit Leiden, P. O. Box 9506, 2300 RA Leiden, The Netherlands (Dated: October 22, 2021) We study the interplay of quantum statistics, strong interactions and finite temperatures in the two-component (spinor) Bose gas with repulsive delta-function interactions in one dimension. Using the Thermodynamic Bethe Ansatz, we obtain the equation of state, population densities and local density correlation numerically as a func- tion of all physical parameters (interaction, temperature and chemical potentials), quantifying the full crossover between low-temperature ferromagnetic and high-temperature unpolarized regimes. In contrast to the single- component, Lieb-Liniger gas, nonmonotonic behaviour of the local density correlation as a function of temper- ature is observed. The experimental realization of interacting quantum sys- tems using cold atoms has reignited interest in many-body physics of strongly-interacting quantum systems in and out of equilibrium [1]. Effectively one-dimensional realizations of bosonic 87Rb quantum gases with tunable local interac- tion strength [2, 3, 4, 5, 6] realize the single-component Lieb-Liniger model [7, 8], for which the crossover from weakly- to strongly-interacting physics is experimentally ac- cessible and well understood from first principles. Observed finite temperature thermodynamics [9] even fit predictions from the Thermodynamic Bethe Ansatz (TBA) [10]. For a single bosonic species in one dimension, statistics and interactions are intimately related: the limit of infinitely strong interactions (impenetrable bosons) causes a crossover from bosonic to effectively fermionic behaviour [11, 12] for density-dependent quantities. Density profiles and fluctua- tions accessible from exact thermodynamics allow to discrim- inate between these fermionized and quasicondensate regimes [13, 14, 15, 16]. Multicomponent (spinor) systems however provide a much larger number of different regimes than their single-component counterparts, and realize situations where important interaction and quantum statistics effects coexist and compete. Their thermodynamics has not been extensively studied using exact methods; in this work, we wish to high- light some unexpected features inherent to a system in this class. The experimentally realizable [17] case of two-component bosons in 1D with symmetric interactions, which we will fo- cus on here, contrasts with the Lieb-Liniger case in many ways. The ground state is (pseudo-spin) polarized [18, 19] (ferromagnetic), as expected from a general theorem valid when spin-dependent forces are absent [20], and thus coin- cides with the Lieb-Liniger ground state. On the other hand, excitations carry many additional branches, starting from the simplest spin-wave-like one. These excitations are difficult to describe in general, even in the strongly-interacting limit (there, no effective fermionization can be used, since the two pseudospin components remain strongly coupled), where spin-charge separation occurs [21, 22, 23, 24, 25]. The ther- modynamic properties are drastically different from those of the one-component Lieb-Liniger gas [26] and at large cou- pling and low temperature correspond to those in an isotropic XXX ferromagnetic chain [27]. Temperature suppresses the entropically disfavoured polarized state, and opens up the possibility of balancing entropy and quantum statistics gains (from the wavefunction symmetrization requirements) with interaction and kinetic energy costs in the free energy. Us- ing a method based on the integrability of the system, we find that this thermally-driven interplay leads to a correlated state with many interesting features, the most remarkable being a nonmonotonic dependence of the local density fluctuations of the system with respect to temperature or relative chemical potential. For definiteness, we consider a system of N particles on a ring of length L, subjected to the Hamiltonian HN = −ℏ2 2m N X i=1 ∂2 ∂x2 i

• g1D X 1≤i<j⩽N δ(xi −xj). (1) The effective one-dimensional coupling parameter g1D is re- lated to the effective 1D scattering length a1D [28] via the relation g1D = ℏ2a1D/2m, and to the effective interaction parameter γ = c/n (where n = N/L is the total linear density) via c = g1Dm/ℏ2. We set ℏ= 2m = 1 to sim- plify the notations. Yang and Sutherland [29, 30] showed that the repulsive delta-function interaction problem admits an exact solution irrespective of the symmetry imposed on the wavefunction, meaning that the wavefunctions of (1) are of Bethe Ansatz form whether the particles are distinguishable, or mixtures of various bosonic and fermionic species [31]. The ground state and excitations of multicomponent

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