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

Considering an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a toroidal trap, we find that the system undergoes a phase transition from a uniform to a localized state, as the magnitude of the coupling constant increases. Both the mean-field approximation, as well as a diagonalization scheme are used to attack the problem.

Investigating the quantum phase transition in a ring from a uniform attractive Bose-Einstein condensate to a localized bright soliton we find that the soliton undergoes transverse collapse at a critical interaction strength, which depends on the ring dimensions. In addition, we predict the existence of other soliton configurations with many peaks, showing that they have a limited stability domain. Finally, we show that the phase diagram displays several new features when the ...

It is shown that the quasi-one-dimensional Bose-Einstein condensate is experimentally accessible and rich in intriguing phenomena. We demonstrate numerically and analytically the existence, stability, and perturbation-induced dynamics of all types of stationary states of the quasi-one-dimensional nonlinear Schrodinger equation for both repulsive and attractive cases. Among our results are: the connection between stationary states and solitons; creation of vortices from such s...

We consider the ground-state properties of an extended one-dimensional Bose gas with pointwise attractive interactions. We take the limit where the interaction strength goes to zero as the system size increases at fixed particle density. In this limit the gas exhibits a quantum phase transition. We compute local correlation functions at zero temperature, both at finite and infinite size. We provide analytic formulas for the experimentally relevant one-point functions $g_2$, $...

We employ mean-field, Bogoliubov, and many-body theories to study critical fluctuations in position and momentum of a Bose-Einstein condensate whose translation symmetry is spontaneously broken due to attractive interactions. In a homogeneous system, the many-body ground state of the symmetry-preserving Hamiltonian is very fragile against superposition of low-lying states, while mean-field theory predicts a stable bright soliton which spontaneously breaks translation symmetry...

When matter undergoes a continuous phase transition on a finite timescale, the Kibble-Zurek mechanism predicts universal scaling behavior with respect to structure formation. The scaling is dependent on the universality class and is irrelevant to the details of the system. Here, we examine this phenomenon by controlling the timescale of the phase transition to a Bose-Einstein condensate using sympathetic cooling of a ultracold Bose thermal could with tunable interactions in a...

We analyse the static solutions of attractive Bose-Einstein condensates under transverse confinement, both with and without axial confinement. By full numerical solution of the Gross-Pitaevskii equation and variational methods we map out the condensate solutions, their energetic properties, and their critical points for instability. With no axial confinement a bright solitary wave solution will tend to decay by dispersion unless the interaction energy is close to the critical...

We consider a homogeneous Bose gas of particles with an attractive interaction. Mean field theory predicts for this system a spontaneous symmetry breaking at a certain value of the interaction strength. We show that at this point a second-order quantum phase transition occurs. We investigate the system in the vicinity of the critical point using Bogoliubov theory and a continuous description, that allows us to analyze {\it quantum fluctuations} in the system even when the Bog...

We study the phase transitions in a one dimensional Bose-Einstein condensate on a ring whose atomic scattering length is modulated periodically along the ring. By using a modified Bogoliubov method to treat such a nonlinear lattice in the mean field approximation, we find that the phase transitions are of different orders when the modulation period is 2 and greater than 2. We further perform a full quantum mechanical treatment based on the time-evolving block decimation algor...

We investigate the many-body dynamics of an effectively attractive one-dimensional Bose system confined in a toroidal trap. The mean-field theory predicts that a bright-soliton state will be formed when increasing the interparticle interaction over a critical point. The study of quantum many-body dynamics in this paper reveals that there is a modulation instability in a finite Bose system correspondingly. We show that Shannon entropy becomes irregular near and above the criti...