Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0812.4387 · Physical Review A

Generalized purity and quantum phase transition for Bose-Einstein condensates in a symmetric double well

Thiago F. Viscondi, K. Furuya, M. C. de Oliveira

Published Jul 16, 2009• 13 citations
arXivHTMLPDF

Abstract

The generalized purity is employed for investigating the process of coherence loss and delocalization of the $Q$ function in the Bloch sphere of a two-mode Bose-Einstein condensate in a symmetrical double well with cross collision. Quantum phase transition of the model is signaled by the generalized purity as a function of an appropriate parameter of the Hamiltonian and the number of particles $(N)$. A power-law dependence of the critical parameter with $N$ is derived.

DOI
10.1103/physreva.80.013610

Related papers

Phase transition, entanglement and squeezing in a triple-well condensate

Thiago F. Viscondi, K. Furuya, M. C. de Oliveira

We provide an in-depth characterization of a three-mode Bose-Einstein condensate trapped in a symmetric circular triple-well potential. We show how the purity related to the su (3) algebra scales for increasing number of atoms and signals the quantum phase transition between two dynamical regimes in a specific configuration. This measure, which is intrinsically related to particle entanglement, also depicts if some squeezing is occurring when we consider the system's ground state. Unlike the well-known double-well model, the triple-well model exhibits a first-order quantum phase transition, which could be investigated with the current trapping technology.

arXiv:1002.0557•Europhysics Letters (EPL)•Apr 1, 2010•23 citations

Binary mixture of Bose-Einstein condensates in a double-well potential: Berry phase and two-mode entanglement

Mehmet Günay

A binary mixture of Bose-Einstein condensate structures exhibits an incredible richness in terms of holding different kinds of phases. Depending on the ratio of the inter- and intra-atomic interactions, the transition from the mixed to separated phase, which is also known as the miscibility-immiscibility transition, has been reported in different setups. Here, we describe such a quantum phase transition (QPT) in an effective Hamiltonian approach by applying the Holstein-Primakoff transformation in the limit of a large number of particles. We demonstrate that a nontrivial geometric phase near the critical coupling is present, which confirms the connection between the Berry phase and QPT. We also show that, by using the spin form of the Hillery and Zubairy criterion, a two-mode entanglement accompanies this transition in the limit of a large, but not infinite, number of particles.

arXiv:1910.14433•Physical Review A•Apr 13, 2020•3 citations

Quantum Nonlinear Dynamics Of An Atomic Bose-einstein Condensate

Gerard J Milburn, Joel Frederick Corney, David Harris

The quantum nonlinear dynamics of an atomic Bose-Einstein condensate (BEC) in a double-well potential is studied. Using a double-well single-particle potential model system and a two-mode approximation, results showed that the coherent oscillations resulting from tunneling are suppressed when the number of atoms is greater than a critical value. The spectrum if nonresonant light scattered by the condensate to include an asymmetric double peak structure with peak separation and relative heights determined by the number of atoms in the condensate and the interaction strength for hard sphere collisions.

Quantum Electronics and Laser Science Conference•Jan 1, 1997•1 citation

Quantum entanglement manifestation of transition to nonlinear self-trapping for Bose-Einstein condensates in a symmetric double well

Liu Fu, Jie Liu

We investigate the nonlinear self-trapping phenomenon of a Bose-Einstein condensate (BEC) in a symmetric double well, emphasizing its underlying dynamical phase transition. As the nonlinear parameter characterizing the interaction between the degenerate atoms increases, the BEC becomes self-trapped, manifesting an asymmetric distribution of the atomic density profile. The essence of this phenomenon is revealed to be a continuous phase transition and the underlying critical behavior is studied analytically and found to follow a logarithmic scaling law. We then go beyond the mean-field treatment and extend our treatment to discuss the effect of many-body quantum fluctuations on the transition. It is found that the transition point is shifted and the scaling law is broken. In particular, the quantum phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point. The underlying physics is revealed.

arXiv:cond-mat/0609337•Physical Review A•Dec 13, 2006•95 citations

Quantum phase-space picture of Bose-Einstein condensates in a double well

Khan W. Mahmud, Heidi Perry, William P. Reinhardt

We present a quantum phase-space model of the Bose-Einstein condensate (BEC) in a double-well potential. In a quantum two-mode approximation we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase-space information is extracted from the stationary quantum states using the Husimi distribution function. We show that the mean-field phase-space characteristics of a nonrigid physical pendulum arises from the exact quantum states, and that only 4--8 particles per well are needed to reach the semiclassical limit. For a driven double-well BEC, we show that the classical chaotic dynamics is manifest in the dynamics of the quantum states. Phase-space analogy also suggests that a $\ensuremath{\pi}$ phase-displaced wave packet put on the unstable fixed point on a separatrix bifurcates to create a superposition of two pendulum rotor states---a macroscopic superposition state of BEC. We show that the choice of initial barrier height and ramping, following a $\ensuremath{\pi}$ phase imprinting on the condensate, can be used to generate controlled entangled number states with tunable extremity and sharpness.

arXiv:cond-mat/0312016•Physical Review A•Feb 28, 2005•154 citations

Bose-Einstein condensate in a double well potential in the vicinity of a critical point

Barbara Oleś, Paweł Zin, Jan Chwedeńczuk +2 more

We consider a Bose-Einstein condensate with an attractive particle interaction in a symmetric double well potential. It is known that in the mean field description a symmetric solution for the condensate wavefunction becomes unstable when the interactions are stronger than some critical value. We analyze the system around the critical point applying the number conserving Bogoliubov theory and exact diagonalization of the two mode hamiltonian. It allows for estimation of the density fluctuations in the system. Fluctuations of the order parameter, which is defined in the mean field description, turn out to be maximal at the critical point.

Laser Physics•Feb 2, 2010•12 citations
The generalized purity is employed for investigating the process of coherence loss and delocalization of the QQQ function in the Bloch sphere of a two-mode Bose-Einstein condensate in a symmetrical double well with cross collision. Quantum phase transition of the model is signaled by the generalized purity as a function of an appropriate parameter of the Hamiltonian and the number of particles (N)(N)(N). A power-law dependence of the critical parameter with NNN is derived.
We provide an in-depth characterization of a three-mode Bose-Einstein condensate trapped in a symmetric circular triple-well potential. We show how the purity related to the su (3) algebra scales for increasing number of atoms and signals the quantum phase transition between two dynamical regimes in a specific configuration. This measure, which is intrinsically related to particle entanglement, also depicts if some squeezing is occurring when we consider the system's ground state. Unlike the well-known double-well model, the triple-well model exhibits a first-order quantum phase transition, which could be investigated with the current trapping technology.
A binary mixture of Bose-Einstein condensate structures exhibits an incredible richness in terms of holding different kinds of phases. Depending on the ratio of the inter- and intra-atomic interactions, the transition from the mixed to separated phase, which is also known as the miscibility-immiscibility transition, has been reported in different setups. Here, we describe such a quantum phase transition (QPT) in an effective Hamiltonian approach by applying the Holstein-Primakoff transformation in the limit of a large number of particles. We demonstrate that a nontrivial geometric phase near the critical coupling is present, which confirms the connection between the Berry phase and QPT. We also show that, by using the spin form of the Hillery and Zubairy criterion, a two-mode entanglement accompanies this transition in the limit of a large, but not infinite, number of particles.
The quantum nonlinear dynamics of an atomic Bose-Einstein condensate (BEC) in a double-well potential is studied. Using a double-well single-particle potential model system and a two-mode approximation, results showed that the coherent oscillations resulting from tunneling are suppressed when the number of atoms is greater than a critical value. The spectrum if nonresonant light scattered by the condensate to include an asymmetric double peak structure with peak separation and relative heights determined by the number of atoms in the condensate and the interaction strength for hard sphere collisions.
We investigate the nonlinear self-trapping phenomenon of a Bose-Einstein condensate (BEC) in a symmetric double well, emphasizing its underlying dynamical phase transition. As the nonlinear parameter characterizing the interaction between the degenerate atoms increases, the BEC becomes self-trapped, manifesting an asymmetric distribution of the atomic density profile. The essence of this phenomenon is revealed to be a continuous phase transition and the underlying critical behavior is studied analytically and found to follow a logarithmic scaling law. We then go beyond the mean-field treatment and extend our treatment to discuss the effect of many-body quantum fluctuations on the transition. It is found that the transition point is shifted and the scaling law is broken. In particular, the quantum phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point. The underlying physics is revealed.
We present a quantum phase-space model of the Bose-Einstein condensate (BEC) in a double-well potential. In a quantum two-mode approximation we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase-space information is extracted from the stationary quantum states using the Husimi distribution function. We show that the mean-field phase-space characteristics of a nonrigid physical pendulum arises from the exact quantum states, and that only 4--8 particles per well are needed to reach the semiclassical limit. For a driven double-well BEC, we show that the classical chaotic dynamics is manifest in the dynamics of the quantum states. Phase-space analogy also suggests that a $\ensuremath{\pi}$ phase-displaced wave packet put on the unstable fixed point on a separatrix bifurcates to create a superposition of two pendulum rotor states---a macroscopic superposition state of BEC. We show that the choice of initial barrier height and ramping, following a $\ensuremath{\pi}$ phase imprinting on the condensate, can be used to generate controlled entangled number states with tunable extremity and sharpness.
We consider a Bose-Einstein condensate with an attractive particle interaction in a symmetric double well potential. It is known that in the mean field description a symmetric solution for the condensate wavefunction becomes unstable when the interactions are stronger than some critical value. We analyze the system around the critical point applying the number conserving Bogoliubov theory and exact diagonalization of the two mode hamiltonian. It allows for estimation of the density fluctuations in the system. Fluctuations of the order parameter, which is defined in the mean field description, turn out to be maximal at the critical point.