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Journal of Physics B Atomic Molecular and Optical Physics

Intrinsic decoherence in an ultracold Bose gas confined in a double-well potential

Santiago F. Caballero-Benítez, Vı́ctor Romero-Rochı́n, R. Paredes

Published Apr 13, 2010• 3 citations
Publisher

Abstract

We address the intrinsic decoherence of an N -body interacting bosonic quantum fluid confined in a double-well potential in one dimension, and its effect on the transition from coherent oscillations to self-trapping regimes as a function of the interparticle interaction. Performing a full quantum approach to the N -particle system, we study the transition and the observed decoherence through the analysis of the one-particle reduced density matrix. The results are obtained by following the time evolution of such a matrix. For large systems and because of the interparticle interactions, the system reaches stationary states which can be characterized both by the vanishing of the off-diagonal matrix elements, in what one may call the preferred basis, and by the value of its associated von Neumman entropy. The present results could be useful in analysing experimental realizations, such as those by Albiez et al (2005 Phys. Rev. Lett. 95 010402).

DOI
10.1088/0953-4075/43/9/095301

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We address the intrinsic decoherence of an N -body interacting bosonic quantum fluid confined in a double-well potential in one dimension, and its effect on the transition from coherent oscillations to self-trapping regimes as a function of the interparticle interaction. Performing a full quantum approach to the N -particle system, we study the transition and the observed decoherence through the analysis of the one-particle reduced density matrix. The results are obtained by following the time evolution of such a matrix. For large systems and because of the interparticle interactions, the system reaches stationary states which can be characterized both by the vanishing of the off-diagonal matrix elements, in what one may call the preferred basis, and by the value of its associated von Neumman entropy. The present results could be useful in analysing experimental realizations, such as those by Albiez et al (2005 Phys. Rev. Lett. 95 010402).
The system under study consists of an interacting ultracold Bose gas confined by a finite n -well potential in one dimension ( n = 2, 3 and 4). By numerically solving the time-dependent Schrödinger equation for the effective Hamiltonian that describes the gas confined in each potential, we determine the mean population of particles in each well as a function of time. From this analysis, we obtain a continuous transition from a coherent state to a self-trapped state as a function of the parameter Λ ≈ Ng , which takes into account the number of particles N and the interaction strength g in each system. Three different behaviours as a function of Λ are found: a coherent oscillation regime, a partial-trapped state and a self-trapped state. The partial trapping regime appears to be a novel phase for finite potentials in one dimension. A systematic quantitative study allows us to conclude that the relaxation time observed in the coherent oscillation regime for a two-well potential scales as N 1/2 . Finally, a comparison with an experimental realization of a Bose–Einstein condensate in a two-well potential (Albiez et al 2005 Phys. Rev. Lett. 95 010402) is presented, exhibiting good agreement.
We consider a quantum Bose fluid confined in a triple well potential in 1D within the exact N-body Bose-Hubbard model to investigate the phenomena of intrinsic decoherence and loss of purity. Our study is done by following the time evolution of one-body properties in an N-particle closed environment. We do an exhaustive exploration of initial conditions to characterize these phenomena. Here we illustrate our main findings with a set of relevant Fock and SU(3) coherent states. Our study shows that signatures of stationarity and maximal mixing are a direct consequence of the inter-particle interactions in the closed system and become evident as the number of particles is increased. This fact is confirmed by quantifying the deviations from stationarity by means of a matrix norm.
We examine the spectral structure and many-body dynamics of two and three repulsively interacting bosons trapped in a one-dimensional double-well, for variable barrier height, inter-particle interaction strength, and initial conditions. By exact diagonalization of the many-particle Hamiltonian, we specifically explore the dynamical behavior of the particles launched either at the single-particle ground state or saddle-point energy, in a time-independent potential. We complement these results by a characterization of the cross-over from diabatic to quasi-adiabatic evolution under finite-time switching of the potential barrier, via the associated time evolution of a single particle's von Neumann entropy. This is achieved with the help of the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X)-which also allows us to extrapolate our results for increasing particle numbers.
We study the dynamics of an ultracold gas of interacting bosons confined in a one-dimensional potential composed of nnn wells. We derive an effective NNN-particle Hamiltonian for this system that describes the tunneling of particles between adjacent wells and that includes the interactions among the particles within the same well. The problem is discussed in the light of current research on optical lattices. We demonstrate that the effective Hamiltonian gives the possibility of studying the transition from an ideal insulator to a real conductor when the parameters that modulate the interaction and the tunneling of the particles are varied. To show this we numerically solve Schr\"odinger equation for the case of n=3n=3n=3 wells. We find that for a given number of particles it is possible to establish a weak- and a strong-interaction regime. In the limit of strong interaction the tunneling term can be neglected. One important result in our analysis is that in the weak-interaction regime the system reaches a stationary state as a result of the loss of coherence in the transport of particles through the wells.
Decoherence with recurrences appear in the dynamics of the one-body density matrix of an F=1 spinor Bose–Einstein condensate, initially prepared in coherent states, in the presence of an external uniform magnetic field and within the single mode approximation. The phenomenon emerges as a many-body effect of the interplay of the quadratic Zeeman effect, which breaks the rotational symmetry, and the spin-spin interactions. By performing full quantum diagonalizations, a very accurate time evolution of large condensates is analyzed, leading to heuristic analytic expressions for the time dependence of the one-body density matrix, in the weak and strong interacting regimes, for initial coherent states. We are able to find accurate analytical expressions for both the decoherence and the recurrence times, in terms of the number of atoms and strength parameters, which show remarkable differences depending on the strength of the spin-spin interactions. The features of the stationary states in both regimes are also investigated. We discuss the nature of these limits in light of the thermodynamic limit.
We study ground-state properties and dynamics of a dilute ultracold atomic gas in a double-well potential. The Gaussian barrier separating the two wells derives from the interaction between the atoms and a quantized field of a driven Fabry-Perot cavity. Due to intrinsic atom-field nonlinearity, several interesting phenomena arise which are the focus of this work. For the ground state, there is a critical pumping amplitude in which the atoms self-organize and the intra-cavity-field amplitude drastically increases. In the dynamical analysis, we show that the Josephson oscillations depend strongly on the atomic density and may be greatly suppressed within certain regimes, reminiscent of self-trapping of Bose-Einstein condensates in double-well setups. This pseudo-self-trapping effect is studied within a mean-field treatment valid for large atom numbers. For small numbers of atoms, we consider the analogous many-body problem and demonstrate a collapse-revival structure in the Josephson oscillations.