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Physical Review A

Ground-state fragmentation phase transition for attractive bosons in anisotropic traps

N. C. Cizek, Mark A. Kasevich

Published Dec 26, 2013• 2 citations
Publisher

Abstract

We construct a two-state theoretical model describing attractively interacting bosons in a cylindrical harmonic potential of varied anisotropy. These systems exhibit true many-body ground-state energy minima stable against variations in single-particle state radial and axial widths and occupation number. The many-body ground state undergoes a phase transition from pure to fragmented as the aspect ratio increases above an anisotropy threshold dependent on the interaction energy per particle. This fragmentation is robust and does not require careful tuning of experimental parameters.

DOI
10.1103/physreva.88.063641

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Comment on “Ground-state fragmentation phase transition for attractive bosons in anisotropic traps”

Hiroki Saito

In a recent article [Phys. Rev. A 88, 063641 (2013)], Cizek and Kasevich claimed that quantum fragmentation occurs in the metastable state of a Bose-Einstein condensate with an attractive interaction confined in an elongated harmonic potential. This result was obtained using the two-state Gaussian variational method. However, modified methods show that no fragmentation occurs for the parameters used by Cizek and Kasevich.

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We construct a two-state theoretical model describing attractively interacting bosons in a cylindrical harmonic potential of varied anisotropy. These systems exhibit true many-body ground-state energy minima stable against variations in single-particle state radial and axial widths and occupation number. The many-body ground state undergoes a phase transition from pure to fragmented as the aspect ratio increases above an anisotropy threshold dependent on the interaction energy per particle. This fragmentation is robust and does not require careful tuning of experimental parameters.
We investigate whether the many-body ground states of bosons in a generalized two-mode model with localized inhomogeneous single-particle orbitals and anisotropic long-range interactions (e.g., dipole-dipole interactions) are coherent or fragmented. It is demonstrated that fragmentation can take place in a single trap for positive values of the interaction couplings, implying that the system is potentially stable. Furthermore, the degree of fragmentation is shown to be insensitive to small perturbations on the single-particle level.
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We investigate the transition of a quasi-one-dimensional few-boson system from a weakly correlated to a fragmented and finally a fermionized ground state. Our numerically exact analysis, based on a multiconfigurational method, explores the interplay between different shapes of external and interparticle forces. Specifically, we demonstrate that the addition of a central barrier to an otherwise harmonic trap may support the system's fragmentation, with a symmetry-induced distinction between even and odd atom numbers. Moreover, the impact of inhomogeneous interactions is studied, where the effective coupling strength is spatially modulated. It is laid out how the ground state can be displaced in a controlled way depending on the trap and the degree of modulation. We present the one- and two-body densities and, beyond that, highlight the role of correlations on the basis of the natural occupations.
We apply controlled perturbation theory to calculate the spectrum of the Gross-Pitaevskii equation for a system composed of attractive bosons confined in an anisotropic harmonic trap. The energy spectrum is calculated as a function of the coupling parameters for traps going from cigar to pancake shapes. The critical number of particles that ensures real values for the energy spectrum is obtained as a function of the potential anisotropic parameter, showing strong dependence of the critical number on the anisotropy of the trap. For a number of particles above the critical value the metastability of the system is characterized through the calculation of the condensate lifetime, using the imaginary part of the energy values. The obtained results are relevant for experiments where highly anisotropic traps are considered.