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Journal of Physics A Mathematical and Theoretical

Angular momentum mixing dynamics of attractive Bose–Einstein condensates on a deformed ring

Zhifeng Chen, Zhibing Li

Published Jan 21, 2009• 0 citations
Publisher

Abstract

The Hamiltonian of an attractive N -boson system confined on a ring is diagonalized. The particles have strong correlation as a result of a quantum phase transition in the strong-interaction phase, where the yrast states are quasi-degenerate. It is found that a small deformation of the ring will mix the quasi-degenerate yrast states to form cluster states which break the spatial symmetry explicitly. The time evolution of the average angular momentum in an elliptic ring exhibits strong oscillation.

DOI
10.1088/1751-8113/42/7/075305

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The Hamiltonian of an attractive N -boson system confined on a ring is diagonalized. The particles have strong correlation as a result of a quantum phase transition in the strong-interaction phase, where the yrast states are quasi-degenerate. It is found that a small deformation of the ring will mix the quasi-degenerate yrast states to form cluster states which break the spatial symmetry explicitly. The time evolution of the average angular momentum in an elliptic ring exhibits strong oscillation.
Abstract We investigate the dynamics of a two-component Bose–Einstein condensate subject to spin–orbital-angular-momentum coupling and confined to a ring, via the variational approach. Adopting a single-mode approximation by assuming that the BEC carries a single angular momentum for SU(2)-symmetric spin interactions, the equations of motion for the variational parameters are derived. The phase diagram of the ground state in the plane of the Raman coupling and detuning contains three different phases which meet at a tricritical point, and the exact phase boundaries between the three phases are determined. Linear stability analysis shows that the stationary state is dynamically stable, and there exists an oscillation eigenmode with frequency determined by detuning, angular momentum, and Raman coupling. The time-evolution results indicate that the spin vector undergoes periodic rotation along a closed orbit on the Bloch sphere, which can be interpreted as a precession of the collective spin around an effective field determined by the Raman coupling strength, the detuning, and the angular momentum.
Properties of the yrast states of a system of NNN bosons confined to a one-dimensional ring and interacting via contact forces is examined both variationally and by numerical diagonalizations. The latter allow for obtaining numerical correlated many-body wave functions explicitly. The study of correlation functions involving different yrast states indicates that a quantum phase transition previously detected in the properties of the ground state in the case of attractive two-body interactions is an yrast phenomenon involving the onset of `deformation', in the sense given to this term by Bohr and Mottelson in connection with the description of nuclear spectra, including enhanced transition operators and emergence of a shared intrinsic correlation structure. In this case the moment of inertia of the deformed state is essentially the rigid moment of inertia, `intrinsic' states being essentially degenerate.
We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for metastable states in finite-size systems. In particular, we treat the one-dimensional Bose gas on a ring in the presence of both interactions and rotation. To support our study, we bring to bear mean-field theory, i.e., the nonlinear Schr\"odinger equation, and linear perturbation or Bogoliubov--de Gennes theory. Both methods give a consistent result in the weakly interacting regime: there exist two topologically distinct quantum phases. The first is the typical picture of superfluidity in a Bose-Einstein condensate on a ring: average angular momentum is quantized and the superflow is uniform. The second is where one or more dark solitons appear as stationary states, breaking the symmetry, the average angular momentum becomes a continuous quantity. The phase of the condensate can therefore be continuously wound and unwound.
The Hamiltonian of an NNN-boson system confined on a ring with zero spin and repulsive interaction is diagonalized. The excitation of a pair of ppp-wave particles rotating reversely appears to be a basic mode. The fluctuation of many of these excited pairs provides a mechanism of oscillation; the states can be thereby classified as oscillation bands. The particle correlation is studied intuitively via the two-body densities. Bose clustering originating from the symmetrization of wave functions is found, which leads to the appearance of one-, two-, and three-cluster structures. The motion is divided into being collective and relative; this leads to the establishment of a relation between the very high vortex states and the low-lying states.
We investigate the stability and dynamics of the orbital angular momentum modes of a repulsive Bose-Einstein condensate trapped in two tunnel-coupled rings in a stack configuration. Within mean-field theory, we derive a two-state model for the system in the case in which we populate both rings equally with a single orbital angular momentum mode and include small perturbations in other modes. Analyzing the fixed-point solutions of the model and the associated classical Hamiltonian, we characterize the destabilization of the stationary states and the subsequent dynamics. By populating a single orbital angular momentum mode with an arbitrary population imbalance between the rings, we derive analytically the boundary between the regimes of Josephson oscillations and macroscopic quantum self-trapping and study numerically the stability of these solutions.