Sergio Cordero

Selective transition and complete revivals of a single two-level atom in the Jaynes–Cummings Hamiltonian with an additional Kerr medium

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.

Transient effects and reconstruction of the energy spectra in the time evolution of transmitted Gaussian wave packets

We derive an analytical solution to the time-dependent Schr?dinger equation for the 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 include the full resonance structure of the system in the dynamical description. We find that the transmitted wave packet may be written as the free evolving Gaussian wave packet solution times a transient term. We demonstrate that both at very large distances and very long times the transient term tends to the transmission amplitude of the system and hence the time-evolving solution reproduces the resonance spectra of the system. We also prove that at a fixed distance and very long times the analytical solution is t?3/2 which extends previous analysis on this issue to arbitrary finite-range potentials. Our results are exemplified for a multibarrier system.

Algebraic treatment of the time-dependent Jaynes–Cummings Hamiltonian including nonlinear terms

A generalization of the time-dependent Jaynes–Cummings Hamiltonian is considered including nonlinear terms in the field and/or an intensity-dependent coupling term. Using algebraic methods we find the corresponding time evolution operator of the problem as a product of exponential operators. Also, we study the effect of the atomic motion in the cavity on its quantum state. We found that, when the atom is vibrating classically with a small amplitude A0 (in comparison with the effective length of the cavity L), i.e. A0 ≪ L, the effects of the atom’s motion are negligible but when A0 ∼ L/4, the state of the atom changes drastically. Our study is devoted to a Jaynes–Cummings Hamiltonian with an additional Kerr medium.

A semi-classical versus quantum description of the ground state of three-level atoms interacting with a one-mode electromagnetic field

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 and photon number have excellent correspondence as functions of the control parameters. We prove that the ground state of the collective regime obeys sub-Poissonian statistics for the and n distribution functions. Therefore, their corresponding fluctuations are not well described by the semi-classical approximation. We show that this can be corrected by projecting the variational state to a definite value of .

Symmetry adapted coherent states for three-level atoms interacting with one-mode radiation

We introduce a combination of coherent states as variational test functions for the atomic and radiation sectors to describe a system of Na three-level 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.

A triple point in 3-level systems

The energy spectrum of a 3-level atomic system in the Ξ-configuration is studied. This configuration presents a triple point independently of the number of atoms, which remains in the thermodynamic limit. This means that in a vicinity of this point any quantum fluctuation will drastically change the composition of the ground state of the system. We study the expectation values of the atomic population of each level, the number of photons, and the probability distribution of photons at the triple point.

Variational study of λ and N atomic configurations interacting with an electromagnetic field of two modes

A study of the

Polychromatic phase diagram for n -level atoms interacting with ℓ modes of an electromagnetic field

\lambda

Phase diagrams of systems of two and three levels in the presence of a radiation field

- and

Phase transitions in three-level systems in a cavity

N