A system of Na atoms of n-levels interacting dipolarly with modes of electromagnetic field is considered. The energy surface of the system is constructed from the direct product of the coherent states of U(n) in the totally symmetric representation for the matter times the coherent states of the electromagnetic field. A variational analysis shows that the collective region is divided into zones, inside each of which only one mode of the electromagnetic field contributes to the ground state. In consequence, the polychromatic phase diagram for the ground state naturally divides itself into monochromatic regions. For the case of 3-level atoms in the Ξ-configuration in the presence of 2 modes, the variational calculation is compared with the exact quantum solution showing that both are in agreement.

We apply the energy surface method to study a system of Na three-level atoms interacting with a one-mode radiation field in the Ξ-, Λ-and V -configurations. We obtain an estimation of the ground-state energy, the expectation value of the total number of excitations, and the separatrix of the model in the interaction parameter space, and compare the results with the exact solutions. We have first-and second-order phase transitions, except for the V -configuration which only presents second-order phase-transitions.

We consider Na three-level atoms (or systems) interacting with a one-mode electromagnetic field in the dipolar and rotating wave approximations. The order of the quantum phase transitions is determined explicitly for each of the configurations Ξ, Λ and V , with and without detuning. The semi-classical and exact quantum calculations for both the expectation values of the total number of excitations M = M and photon number n = n have an excellent correspondence as functions of the control parameters. We prove that the ground state of the collective regime obeys sub-Poissonian statistics for the M and n distribution functions. Therefore, their corresponding fluctuations are not well described by the semiclassical approximation. We show that this can be corrected by projecting the variational state to a definite value of M. PACS numbers: 42.50.Ct,42.50.Nn,73.43.Nq,03.65.Fd arXiv:1305.7188v2 [quant-ph] 28 Nov 2013 Semi-classical vs. quantum description of the ground state of three-level atoms. . . 2

We derive an exact analytical solution to the time-dependent Schrödinger equation for transmission of a Gaussian wave packet through an arbitrary potential of finite range. We consider the situation where the initial Gaussian wave packet is sufficiently broad in momentum space to guarantee that the resonance structure of the system is included in the dynamical description. We demonstrate that the transmitted wave packet exhibits a transient behavior which at very large distances and long times may be written as the free evolving Gaussian wave packet solution times the transmission amplitude of the system and hence it reproduces the resonance spectra of the system. This is a novel result that predicts the ultimate fate of the transmitted Gaussian wave packet. We also prove that at a fixed distance and very long times the solution goes as t −3/2 which extends to arbitrary finite range potentials previous analysis on this issue. Our results are exemplified for single and multibarrier systems.

The Jaynes-Cummings Hamiltonian with deformed operators of the field is considered; as a particular case the Kerr-like medium is obtained via an appropriate deformation function. We find that, for an appropriate choice of the parameter of the deformation function, states of the uncoupled basis with a selected fixed number of quanta are in resonance, providing a maximum probability of transition of the atom for these states. Under this condition one may find an appropriate value of the coupling constant such that complete revivals are obtained.

A study of the λ-and N -atomic configurations under dipolar interaction with 2 modes of electromagnetic radiation is presented. The corresponding quantum phase diagrams are obtained by means of a variational procedure. Both configurations exhibit normal and collective (super-radiant) regimes. While the latter in the λ-configuration divides itself into 2 subregions, corresponding to each of the modes, that in the N -configuration may be divided into 2 or 3 subregions depending on whether the field modes divide the atomic system into 2 separate subsystems or not.Our variational procedure compares well with the exact quantum solution. The properties of the relevant field and matter observables are obtained.

Abstract. We introduce a combination of coherent states as variational test functions for the atomic and radiation sectors to describe a system of Na threelevel atoms interacting with a one-mode quantised electromagnetic field, with and without the rotating wave approximation, which preserves the symmetry presented by the Hamiltonian. These provide us with the possibility of finding analytical solutions for the ground and first excited states. We study the properties of these solutions for the V -configuration in the double resonance condition, and calculate the expectation values of the number of photons, the atomic populations, the total number of excitations, and their corresponding fluctuations. We also calculate the photon number distribution and the linear entropy of the reduced density matrix to estimate the entanglement between matter and radiation. For the first time, we exhibit analytical expressions for all of these quantities, as well as an analytical description for the phase diagram in parameter space, which distinguishes the normal and collective regions, and which gives us all the quantum phase transitions of the ground state from one region to the other as we vary the interaction parameters (the matter-field coupling constants) of the model, in functional form.arXiv:1510.06308v1 [quant-ph]

The short-time behavior of quantum decay of an unstable state initially located within an interaction region of finite range is investigated using a resonant expansion of the survival amplitude. It is shown that in general the short-time behavior of the survival probability S(t) has a dependence on the initial state and may behave as either S(t) = 1 − O(t 3/2 ) or 1 − O(t 2 ). These cases are illustrated by solvable models. The experiment reported by Wilkinson et al. [Nature (London) 387, 575 (1997)] does not distinguish between the above short-time behaviors.