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Physical Review A

Effect of even and odd numbers of atoms in a condensate inside a double-well potential

R. Lü, Mei Zhang, Jiang Zhu, Li You

Published Jul 24, 2008• 9 citations
Publisher

Abstract

We study macroscopic quantum phenomena for an atomic condensate in a double-well potential as realized in recent experiments by Albiez et al. [Phys. Rev. Lett. 95, 010402 (2005)] and Shin et al. [Phys. Rev. Lett 95, 170402 (2005)]. By keeping the leading correction in the usually adopted mapping to an anisotropic spin model, we find that the topological Berry phase, a parity effect due to the even and odd atom numbers of a condensate, can be observed in the tunnel splitting. Our investigation suggests a cleaner, perhaps significantly improved, alternative for observing macroscopic quantum coherence (MQC) in large spin models.

DOI
10.1103/physreva.78.011605

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We present two examples of tunneling in double well potentials. Therst is a study of the localization in a dissipative one-particle system bymeans of an analogy with a spin-1/2 system in a uniform magnetic eld.The second example is an investigation of the tunneling process of a Bose-Einstein Condensate in a double well potential from the point of view ofa many body Hamiltonian. Although the two-mode model for the processis not realistic for large enough number of particles (N 200), for certaininitial conditions, it points out a completely dierent explanation for thenon-observation of tunneling from that given in Michael Albiez et al, Phys.Rev. Lett. 95, 010402 (2005). We observe a \phase transition" related to spectral properties of the Hamiltonian and the initial conditions which, for large enough initial population imbalance, presents occupation probabilitiesconcentrated in doublets.

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We study macroscopic quantum phenomena for an atomic condensate in a double-well potential as realized in recent experiments by Albiez et al. [Phys. Rev. Lett. 95, 010402 (2005)] and Shin et al. [Phys. Rev. Lett 95, 170402 (2005)]. By keeping the leading correction in the usually adopted mapping to an anisotropic spin model, we find that the topological Berry phase, a parity effect due to the even and odd atom numbers of a condensate, can be observed in the tunnel splitting. Our investigation suggests a cleaner, perhaps significantly improved, alternative for observing macroscopic quantum coherence (MQC) in large spin models.
In a previous work [H. Pu, W. Zhang, and P. Meystre, Phys. Rev. Lett. 87, 140405 (2001)]], we have shown that a spinor condensate confined in a periodic or double-well potential exhibits ferromagnetic behavior due to the magnetic dipole-dipole interactions between different wells, and in the absence of external magnetic field, the ground state has a twofold degeneracy. In this work, we demonstrate the possibility of observing macroscopic quantum spin tunneling between these two degenerate states and show how the tunneling rate critically depends on the strength of the transverse field.
We study quantum dynamical properties of a spin-1 atomic Bose-Einstein condensate in a double-well potential. Adopting a mean field theory and single spatial mode approximation, we characterize our model system as two coupled spins. For certain initial states, we find full magnetization oscillations between wells not accompanied by mass (or atom numbers) exchange. We identify dynamic regimes of collective spin variables arising from nonlinear self-interactions that are different from the usual Josephson oscillations. We also discuss magnetization beats and incomplete oscillations of collective spin variables other than the magnetization. Our study points to an alternative approach to observe coherent tunnelling of a condensate through a (spatial) potential barrier.
We investigate the macroscopic quantum spin coherence of a spinor condensate confined in an anisotropic potential. Under the single-mode approximation, we show that a spin-1 Rb condensate can be modeled as a biaxial quantum magnet. A direct consequence of the biaxial anisotropy is that the tunneling splitting oscillates as a function of the external magnetic field applied along the hard axis. We also propose an experimental scheme to detect the oscillatory behavior of the tunneling splitting by employing the Landau-Zener tunneling.
We study the parity effect of the particle number in the interference fringes of a Bose-Einstein condensate released from a double-well potential. For a coherently splitting condensate in the double-well potential, with a decoupled two-mode Bose-Hubbard model, there is well-known phase diffusion because of interatomic interactions. After a specific holding time of the double-well potential, the phase diffusion will make the interference patterns in the density distribution depend strongly on the parity of the total particle number by further overlapping two condensates. This parity effect originates from the quantized relative phase about the total particle number. The experimental scheme to observe this "even-odd" effect of the particle number is discussed.
Abstract We investigate the dynamical evolution and atom number parity effect of bosonic condensates in a double-well potential within the two-mode Bose–Hubbard model (BHM), following a quench from the Josephson to the Fock regime. We demonstrate the different behaviors of systems with even and odd numbers of atoms on a mesoscopic scale by calculating the correlation function  ( t ) , visibility α , number fluctuation  and entanglement entropy S . In contrast to the full collapse and revival of quantum correlations for systems with even numbers of atoms, we find that the correlations for systems with odd numbers will not collapse thoroughly, predicting a nonvanishing interference pattern. We relate this phenomenon to the parity effect of the energy spectrum, explain the effect in the pseudo-angular-momentum representation of the BHM Hamiltonian and suggest its confirmation in experiments.
We present two examples of tunneling in double well potentials. Therst is a study of the localization in a dissipative one-particle system bymeans of an analogy with a spin-1/2 system in a uniform magnetic eld.The second example is an investigation of the tunneling process of a Bose-Einstein Condensate in a double well potential from the point of view ofa many body Hamiltonian. Although the two-mode model for the processis not realistic for large enough number of particles (N 200), for certaininitial conditions, it points out a completely dierent explanation for thenon-observation of tunneling from that given in Michael Albiez et al, Phys.Rev. Lett. 95, 010402 (2005). We observe a \phase transition" related to spectral properties of the Hamiltonian and the initial conditions which, for large enough initial population imbalance, presents occupation probabilitiesconcentrated in doublets.