Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactions

In this paper, we study the phase diagram of a homogeneous Bose gas with a repulsive interaction near a wide Feshbach resonance at zero temperature. The Bose-Einstein-condensation (BEC) state of atoms is a metastable state. When the scattering length $a$ exceeds a critical value depending on the atom density $n$, $na^3>0.035$, the molecular excitation energy is imaginary and the atomic BEC state is dynamically unstable against molecule formation. The BEC state of diatomic mol...

We present a study of the effects of temperature upon the excitation frequencies of a Bose-Einstein condensate formed within a dilute gas with a weak attractive effective interaction between the atoms. We use the self-consistent Hartree-Fock Bogoliubov treatment within the Popov approximation and compare our results to previous zero temperature and Hartree-Fock calculations The metastability of the condensate is monitored by means of the $l=0$ excitation frequency. As the num...

We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of ...

We consider a one dimensional system of $N$ bosons interacting via an attractive Dirac delta function potential. We place the bosonic quantum particles at thermal equilibrium in a box of length $L$ with periodic boundary conditions. At large $N$ and for $L$ much larger than the diameter of a two particle bound state, we predict by numerical and analytical studies of a simple model derived from first principles that the system exhibits a first order phase transition in a high ...

We propose the new exactly solvable model for bosons corresponding to the attractive pairing interaction. Using the electrostatic analogy, the solution of this model in thermodynamic limit is found. The transition from the superfluid phase with the Bose condensate and the Bogoliubov - type spectrum of excitations in the weak coupling regime to the incompressible phase with the gap in the excitation spectrum in the strong coupling regime is observed.

The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein condensates with attractive 1/r interaction is investigated with both a variational approach and numerically exact calculations. We show that these condensates exhibit signatures known from the nonlinear dynamics of autonomous Hamiltonian systems. The two stationary solutions created in a tangent bifurcation at a critical value of the scattering length are identified as elliptical and hyperbolical fixed p...

We systematically construct stationary soliton states in a one-component, two-dimensional, repulsive, Gross-Pitaevskii equation with a ring-shaped target-like trap similar to the potential used to confine a Bose-Einstein condensate in a recent experiment [Eckel, et al.\ {\em Nature} {\bf 506}, 200 (2014)]. In addition to the ground state configuration, we identify a wide variety of excited states involving phase jumps (and associated dark solitons) inside the ring. These conf...

We experimentally investigate the dynamical instability of a Bose Einstein condensate in an optical ring resonator for various cavity detuning and pump powers. The resulting phase diagram is asymmetric with respect to the cavity detuning and can be described by the coupling of two atomic modes with one optical mode. We compare the experimental data to a numerical simulation and to an analytic expression of the phase boundary. For positive and negative pump cavity detuning dif...

We study a quasi-one-dimensional attractive Bose gas confined in an optical lattice with a superimposed harmonic potential by analyzing the effective one-dimensional Bose-Hubbard Hamiltonian of the system. In order to have a reliable description of the ground-state, that we call quantum bright soliton, we use the Density-Matrix-Renormalization-Group (DMRG) technique. By comparing DMRG results with mean-field (MF) ones we find that beyond-mean-field effects become relevant by ...

We investigate the dynamics and modulation of ring dark soliton in 2D Bose-Einstein condensates with tunable interaction both analytically and numerically. The analytic solutions of ring dark soliton are derived by using a new transformation method. For shallow ring dark soliton, it is stable when the ring is slightly distorted, while for large deformation of the ring, vortex pairs appear and they demonstrate novel dynamical behaviors: the vortex pairs will transform into dar...