The full quantum dynamics of many bosons that are initially completely localized on one site of a symmetric dimer is investigated in the small tunnelling amplitude regime. The number difference of bosons between the two equivalent sites of the dimer exhibits rich behaviour on different timescales, ranging from small amplitude oscillations and collapses and revivals, to coherent tunnelling. We show that this complex quantum evolution is completely accounted for by analytical expressions. A general formula is obtained at a higher order of perturbation theory for the splitting of quasi-degenerate energy levels. The splittings of the two highest pairs provide the characteristic frequencies of the intermediate and long timescale dynamics.
The full quantum dynamics of many bosons that are initially completely localized on one site of a symmetric dimer is investigated in the small tunnelling amplitude regime. The number difference of bosons between the two equivalent sites of the dimer exhibits rich behaviour on different timescales, ranging from small amplitude oscillations and collapses and revivals, to coherent tunnelling. We show that this complex quantum evolution is completely accounted for by analytical expressions. A general formula is obtained at a higher order of perturbation theory for the splitting of quasi-degenerate energy levels. The splittings of the two highest pairs provide the characteristic frequencies of the intermediate and long timescale dynamics.
We present analytical relations for the quantum evolution of the number difference of bosons between the two sites of a double-well potential, by using perturbative results for small tunneling amplitudes in the two-mode approximation. Results are obtained for two different initial conditions: completely localized states and coherent spin states. In the former case both the short and the long time behavior is investigated and the characteristic Bohr frequencies of the energy spectrum are determined. In the latter case we calculate the short time-scale evolution of the number difference. The analytical expressions compare favorably with direct numerical solutions of the quantum problem. Finally, we discuss the corresponding Gross-Pitaevskii (i.e., mean-field) dynamics and we point out the differences between the full quantum evolution and the mean-field evolution.
Analytical expressions for the energy eigenstates of the boson-Hubbard (or quantum discrete-nonlinear Schr\"odinger) dimer are obtained by applying perturbation theory in the small-tunneling-amplitude limit. The results are relevant for a Bose-Einstein condensate trapped in a double-well potential. A detailed comparison with the numerical solutions arising from the direct diagonalization of the Hamiltonian (for even or odd numbers of bosons) is presented, and the limits of validity of the perturbative results are determined. For fixed values of the tunneling amplitude, the accuracy of the perturbative calculation varies with the total number of bosons in different ways, depending on the particular energy level. Results for the fluctuations of the boson-number difference in each eigenstate are also presented.
The collapse and revival of localized states in many-body systems is a quintessential example of a quantum interference phenomenon that cannot be explained purely within mean-field theories. Historically, the majority of previous work on quantum revivals has been in a Schrödinger mechanics context, typically for effectively 1D systems with a focus on the autocorrelation function as the key detection observable. The general revival subject acquires a far greater complexity in the bosonic many-body context that offers a larger variety of observables and intrinsically implies high dimensionality. Here, the focus is on the simplest nontrivial (i.e., not 1D) bosonic many-body system, namely a symmetric two-site Bose-Hubbard model. The non-equilibrium situation of a coherent initial state prepared on one of the two sites of this integrable 2D system in the strongly self-trapping regime is considered. The revival behaviors emerging from the resulting dynamics within expectation values, coherences, and the autocorrelation function are theoretically derived, and the entanglement behavior is illustrated. Several new features, unknown so far in the Schrödinger context and identified here in terms of five ``puzzles'', are encountered and discussed, among them, a synchronized resurgence behavior, differing revivals times depending on the specific observable, and a manifestation of a precession that appears in the underlying mean field dynamics. These new phenomena can be entirely understood through a comprehensive semiclassical theory, building upon the underlying classical (mean-field) phase-space structure. A quantitative comparison of the latter with semiclassical predictions and quantum perturbative calculations yields an overall excellent agreement and confirms that a full semiclassical theory is pivotal for the understanding of these genuinely quantum many-body interference phenomena.
Sufficiently strong intersite interactions in extended-Hubbard and XXZ spin models result in dynamically bound clusters at neighboring sites. We show that the dynamics of these clusters in two-dimensional lattices is remarkably different and richer than that of repulsively bound on-site clusters in gases without intersite interactions. Whereas on-site pairs move in the same lattice as individual particles, nearest-neighbor dimers perform an interacting quantum walk in a different lattice geometry, leading to a peculiar dynamics characterized by multiple timescales. Although this is generally true, it is especially relevant in some lattices, including triangular and diamond lattices for hard-core bosons, and square lattices for soft-core bosons, where dimers move resonantly in either a kagome or a Lieb lattice. As a result, dimers show two very different transport velocities---a fast one comparable to the motion of individual particles, and a very slow one associated to flatband quasilocalization. Moreover, these lattices permit the resonant motion of longer clusters, and, remarkably, trimers move faster than quasi-flatband dimers for sufficiently strong optical lattices. This rich interplay between multiscaled quantum walk dynamics, quasilocalization, and flatband physics may be readily observed in experiments with lanthanide atoms.
Open quantum systems with nearly degenerate energy levels have been shown to exhibit long-lived metastable states in the approach to equilibrium, even when modelled with certain Lindblad-form quantum master equations. This is a result of dramatic separation of timescales due to differences between Liouvillian eigenvalues. These metastable states often have nonzero coherences that die off only in the long-time limit once the system reaches thermal equilibrium. We examine two distinct situations that give rise to this effect: one in which dissipative dynamics couple together states only within a nearly degenerate subspace, and one in which they give rise to jumps over finite-energy splittings, between nearly degenerate subspaces. We find, in each case, that a change of basis can often lead to a representation that more naturally captures the impact of the system-bath interaction than does the energy eigenbasis, revealing that separate timescales are associated with separate processes (e.g., decoherence into a nonenergy eigenbasis, decay of population correlations to the initial state). This approach is paired with the inspection of quantum trajectories, which further provide intuition as to how open system evolution is characterized when coherent oscillations, thermal relaxation, and decoherence all occur simultaneously. Published by the American Physical Society 2024
We study the quantum behaviour of a binary mixture of Bose–Einstein condensates in a double-well potential starting from a two-mode Bose–Hubbard Hamiltonian. We focus on the small tunnelling amplitude regime and apply perturbation theory up to second order. Analytical expressions for the energy eigenvalues and eigenstates are obtained. Then, the quantum evolution of the number difference of bosons between the two potential wells is fully investigated for two different initial conditions: completely localized states and coherent spin states. In the first case both the short- and the long-time dynamics is studied and a rich behaviour is found, ranging from small amplitude oscillations and collapses and revivals to coherent tunnelling. In the second case, the short-timescale evolution of number difference is determined and a more irregular dynamics is evidenced. Finally, the formation of Schrödinger cat states is considered and shown to affect the momentum distribution.