We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space. This enhancement is robust with respect to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition principle in Fock space. It is a genuine quantum many-body effect that lies beyond the reach of any mean-field approach. Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss their relevance in the context of many-body thermalization.
We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space. This enhancement is robust with respect to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition principle in Fock space. It is a genuine quantum many-body effect that lies beyond the reach of any mean-field approach. Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss their relevance in the context of many-body thermalization.
We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space [1]. This enhancement is robust with respect to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition principle in Fock space. It is a genuine quantum many-body effect which lies beyond the reach of any mean-field approach. Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss their relevance in the context of many-body thermalization. We furthermore propose a specific experimental setup in order to detect this many-body coherent backscattering phenomenon with ultracold bosonic atoms.
We present a semiclassical approach to many-body quantum propagation in terms of coherent sums over quantum amplitudes associated with the solutions of corresponding classical nonlinear wave equations. This approach adequately describes interference effects in the many-body space of interacting bosonic systems. The main quantity of interest, the transition amplitude between Fock states when the dynamics is driven by both single-particle contributions and many-body interactions of similar magnitude, is non-perturbatively constructed in the spirit of Gutzwiller's derivation of the van Vleck propagator from the path integral representation of the time evolution operator, but lifted to the space of symmetrized many-body states. Effects beyond mean-field, here representing the classical limit of the theory, are semiclassically described by means of interfering amplitudes where the action and stability of the classical solutions enter. In this way, a genuinely many-body echo phenomenon, coherent backscattering in Fock space, is presented arising due to coherent quantum interference between classical solutions related by time reversal.
We present numerical evidence for the occurrence of coherent backscattering in the Fock space of a small disordered Bose‐Hubbard system consisting of four sites and containing five particles. This many‐body interference phenomenon can most conveniently be seen in time evolution processes that start from a Fock state of the Bose‐Hubbard system. It manifests itself in an enhanced detection probability of this initial state as compared to other Fock states with comparable total energy. We argue that coherent backscattering in Fock space can be experimentally measured with ultracold bosonic atoms in optical lattices using state‐of‐the‐art single‐site detection techniques. A synthetic gauge field can be induced in order to break time‐reversal symmetry within the lattice and thereby destroy coherent backscattering. While this many‐body interference effect is most prominently visible in the presence of eigenstate thermalization, we briefly discuss its significance in the opposite regime of many‐body localization. image
We present a semiclassical approach to many-body quantum propagation in terms of coherent sums over quantum amplitudes associated with the solutions of corresponding classical nonlinear wave equations. This approach adequately describes interference effects in the many-body space of interacting bosonic systems. The main quantity of interest, the transition amplitude between Fock states when the dynamics is driven by both single-particle contributions and many-body interactions of similar magnitude, is non-perturbatively constructed in the spirit of Gutzwiller's derivation of the van Vleck propagator from the path integral representation of the time evolution operator, but lifted to the space of symmetrized many-body states. Effects beyond mean-field, here representing the classical limit of the theory, are semiclassically described by means of interfering amplitudes where the action and stability of the classical solutions enter. In this way, a genuinely many-body echo phenomenon, coherent backscattering in Fock space, is presented arising due to coherent quantum interference between classical solutions related by time reversal.
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.
During the last decades, semiclassical techniques for single particle systems have been successfully developed, to the point that they describe the universal and reproducible quantum fluctuations characteristic of quantum systems with chaotic classical limit. By now they not only give a qualitative and intuitive picture about interference, but also yield quantitatively good results. Motivated by this story of success, the aim of this thesis was to first of all rigorously deduce a semiclassical theory for many-body systems in Fock space from path integrals, thus pushing the work of John Hasbrouck Van Vleck, Richard Feynman, Martin Charles Gutzwiller and Michael Victor Berry to the next level. The central object in this development is the propagator in Fock basis, for which a path integral in complex variables has to be found, from which the corresponding classical theory can be deduced. The main focus of attention there lies the action of the classical trajectories being real thus supporting the explicit, illustrative and manifest study of many-body interference. Then, with the help of this semiclassical propagator, universal many-body interference effects in bosonic and fermionic Fock space are studied several of which are novel predictions due to new qualitative tools developed here. The semiclassical tool for quantum fields, and the picture of many-body interference it provides, is put to test against numerical calculations. For a quantitative comparison, the loop expansion developed by Martin Sieber and Klaus Richter going beyond Michael Berry's diagonal approximation is transfered and adopted to the theory in Fock space. All our predictions then show excellent agreement with quantum mechanical simulations.