Quantum dynamics of a Bose gas in finiten-well potentials in one dimension

Abstract

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 N1/2. 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.

Analytical results for Josephson dynamics of ultracold bosons

“…for small Λ) can be approximated as N/(Λω p (2j 0 /N))σ. Thus, assuming Λ and (j 0 /N) are kept fixed so that σ is proportional to √ N, the collapse time is proportional to √ N. This √ N-behavior has been stated before in [25,29]. Our semiclassical formula shows, however, that this statement is only correct for the special case of fixed Λ and j 0 /N, or in the Rabi limit (Λ ≪ 1).…”

Nonlinear dynamics of Rydberg-dressed Bose-Einstein condensates in a triple-well potential

“…Increasing N , we find that the relaxation becomes weaker, such that the quantum dynamics resembles that of the mean-field calculation. Similar dynamics has been investigated in detail in Ref [76]. When approaching to the self-trapping regime (U > U c1 ), only a small fraction of populations can tunnel to other potential wells.…”

Delocalization to self-trapping transition of a Bose fluid confined in a double-well potential: an analysis via one- and two-body correlation properties

“…The atomic transport has shown the existence of Josephson tunneling or macroscopic quantum self-trapping regimes depending on the interatomic interactions and on the initial populations in the wells. These opposite states are similar to the well known superfluid and Mott insulator states observed in optical lattices [2, 3] in the sense that the quantum transition among them is the result of the non-linear condensate self-trapping interactions.The theoretical analysis of this system has been based on the Bose-Hubbard Hamiltonian in the two-mode approximation [4,5,6,7,8,9]. Besides providing a fairly good description of the experimental situation[1], this model has been extensively studied on its own, specially within a mean-field or semiclassical approximation.…”

“…Besides providing a fairly good description of the experimental situation[1], this model has been extensively studied on its own, specially within a mean-field or semiclassical approximation. This model has lead to significant understanding of the richness of the physical problem at hand; additionally, it can incorporate asymmetric two-well potentials and external time-dependent driving fields [4].Beyond the studies within the mean-field approximation, this model is amenable to numerical full quantum calculations, so far up to N = 1000 particles [4,5,8,9]. These results and mean-field calculations agree for a short time while for longer times the full quantum approach shows that the system reaches a state, that one may call "statistically stationary" as we shall specify below, punctuated by coherent revivals.…”

“…For purposes of calculations we use a well-known family of coherent states [11,12] such that the previous requirement is satisfied. We point out here that the particular state with all particles initially in one of the wells, analyzed in most of the studies with full quantum solutions [4,8,9], belongs to the family of such coherent states.…”