N-Level Systems Interacting with Bosons: Semiclassical Limits

G. A. Raggio, H.S. Zivi

Luis Benet, Christof Jung, F. Leyvraz

We prove that a wide class of two-level boson systems interacting through k -body forces is integrable in the semiclassical limit irrespective of the value of the parameters of the model. This class of models includes number-conserving Hamiltonians, and interactions which do not conserve the particle number. Applications to two-component and atom–molecule Bose–Einstein condensates at zero temperature as well as to the bosonic k -body embedded ensembles of Gaussian random matrices in the dense limit are discussed.

Z. F. Ezawa

Jonathan Keeling

The Tavis-Cummings model (the Dicke model treated in the rotating-wave approximation), describing many two-level systems coupled to a single bosonic mode, has been long known to show collective semiclassical oscillations when prepared in an inverted state, with all two-level systems excited and the bosonic mode is empty. This paper discusses how the quantum dynamics approaches this semiclassical result for large numbers of two-level systems, focusing on how the eigenvalues approach their semiclassical limit. The approach to the semiclassical result is found to be slow, scaling like a power of the logarithm of the system size. Considering also the effect of weak detuning between the two-level system and the bosonic field, quantum corrections are again found to decay slowly with system size, such that for a fixed detuning, the quantum effects of detuning are greater than the classical effect.

Julien Dujardin, Thomas Engl, Juan Diego Urbina +1 more

We consider quasi‐stationary scattering of interacting bosonic matter waves in one‐dimensional waveguides, as they arise in guided atom lasers. We show how the truncated Wigner (tW) method, which corresponds to the semiclassical description of the bosonic many‐body system on the level of the diagonal approximation, can be utilized in order to describe such many‐body bosonic scattering processes. Special emphasis is put on the discretization of space at the exact quantum level, in order to properly implement the semiclassical approximation and the tW method, as well as on the discussion of the results to be obtained in the continuous limit. image