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Register a new userMany-body properties of quasi-one dimensional Boson gas across a narrow CIR
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We study strong interaction effects in a one-dimensional (1D) Boson gas across a narrow confinement induced resonance (CIR). In contrast to the zero range potential, the 1D two-body interaction in the narrow CIR can be written as a polynomial of derivative $delta$-function interaction on many-body level. Using the asymptotic Bethe ansatz, we find that the low energy physics of this many-body problem is described by the Tomonaga-Luttinger liquid where the Luttinger parameters are essentially modified by an effective finite range parameter $v$. This parameter drastically alters quantum criticality and universal thermodynamics of the gas. In particular, it drives the Tonks-Girardeau (TG) gas from non-mutual Fermi statistics to mutual statistics or to a more exclusive super TG gas. This novel feature is further discussed in terms of the breathing mode which is experimentally measurable.
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We theoretically investigate quantum-mechanical dynamics of quasi-one-dimensional boson-fermion mixtures of atomic gases trapped in a toroidal potential, where effective inter-atomic interactions are tunable and affect the dynamics. We especially focus on effects of quantum statistics and many-body correlations beyond the Hartree-Fock (HF) mean-field approximation on the dynamics. In order to predict the dynamics, we utilize the numerical exact diagonalization method and also reproduce the calculation in the HF approximation for comparison. The toroidal gases originally have a rotational symmetry in the toroidal direction. We firstly prepare a deformed ground state as an initial state by adding a weak potential deformed in the toroidal direction, and then remove the potential to start the dynamics. In the dynamics, number densities of the deformed gases exhibit oscillations as demonstrated in the present paper. As a result, we find out that the bosons and fermions show quite different behaviors owing to quantum statistics. In particular, the bosons exhibit a low-frequency oscillation in the strong boson-boson attraction regime owing to the many-body correlations, and it can not be reproduced in the HF approximation. The oscillation of the fermions is strongly influenced by that of the bosons through the boson-fermion interaction as a forced oscillator. In addition, we also discuss a relationship between the low-frequency oscillation and restoration of the broken symmetry.
We study the viscous properties of a system of weakly interacting spin-$frac{1}{2}$ fermions in one dimension. Accounting for the effect of interactions on the quasiparticle energy spectrum, we obtain the bulk viscosity of this system at low temperatures. Our result is valid for frequencies that are small compared with the rate of fermion backscattering. For frequencies larger than this exponentially small rate, the excitations of the system become decoupled from the center of mass motion, and the fluid is described by two-fluid hydrodynamics. We calculate the three transport coefficients required to describe viscous dissipation in this regime.
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 study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled and compare with the Luttinger-liquid theory.
Solitons, or non-destructible local disturbances, are important features of many one-dimensional (1D) nonlinear wave phenomena, from water waves in narrow canals to light pulses in optical fibers. In ultra-cold gases, they have long been sought, and were first observed to be generated by phase-imprinting. More recently, their spontaneous formation in 1D gases was predicted as a result of the Kibble-Zurek mechanism, rapid evaporative cooling, and dynamical processes after a quantum quench. Here we show that they actually occur generically in the thermal equilibrium state of a weakly-interacting elongated Bose gas, without the need for external forcing or perturbations. This reveals a major new quality to the experimentally widespread quasicondensate state. It can be understood via thermal occupation of the famous and somewhat elusive Type II excitations in the Lieb-Liniger model of a uniform 1D gas.
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