The General Squeezed State and Its Atomics Phase Dependence

Saad S. M. Hassan, T. Jarad, Ravinder Rupchand Puri +1 more

The relaxation process of a single two-level atom driven by an intense resonant coherent field is studied in the presence of a broadband squeezed vacuum field. Generalized forms for the self-field operator and the field-dependent damping coefficients are derived. In the steady state, positive atomic inversion (~5%) is shown for some range of the phase of the squeezed vacuum field. The squeezing-induced enhanced and asymmetric coherence (i.e.?non-zero dispersive atomic polarization) induces profound asymmetry in the side-bands of the Mollow fluorescent spectrum and the absorptive?dispersive spectra near the Rabi side-band frequencies. The case of two and three cooperative atoms, instead of a single atom, shows (i)?positive atomic inversion in the steady state for larger interval of the squeeze phase parameter and more enhanced extrema for the atomic polarization components and (ii) the extra side peaks in the fluorescent spectrum become asymmetric and of dispersive-like profile. Dressed-state analysis in the single-atom case with the field-dependent decay process in the presence of the squeezed vacuum field is presented and shows that the inequality of the (field-dependent) decay rates of the dressed states leads to more positive inversion in the dressed states as compared with the normal vacuum case.

A. D. Jannussis, Vasileios Bartzis

M.R. Ferguson, Z. Ficek, Bryan J. Dalton

Master equation methods are used to investigate the effects of a broad-band squeezed vacuum on a three-level atom of the lambda configuration. The two-mode squeezed vacuum is treated as a Markovian reservoir in a non-stationary phase-dependent state. In addition to the squeezed vacuum the atom is driven by two coherent laser fields each of which, depending on the polarization, can couple to one or both of the atomic transitions. We show that in general the optical Bloch equations for the atomic density matrix elements have oscillatory coefficients, thereby necessitating the use of Floquet methods. For the case of equal laser frequencies, which are also equal to the carrier frequency of the squeezed vacuum, the coefficients of the Bloch equations become time independent and stationary solutions for the populations and coherences are obtained by standard matrix methods. For the ordinary vacuum the usual coherent population trapping effect at two-photon resonance is obtained, with the upper state population being zero. An unsqueezed thermal field partially destroys the trapping effect as the upper state population is no longer zero at two-photon resonance. The squeezed vacuum has the effect of improving the trapping in that the coherence hole becomes more pronounced for some values of the relative phase between the squeezed vacuum and the driving fields. The additional effects of a coherence transfer rate between the two optical coherences, which occurs for special choices of angular momentum quantum numbers are also studied. For the case of equal laser frequencies, the inclusion of this coherence transfer process destroys population trapping and reduces the lambda system to a two-level system. However, for the case of unequal laser frequencies, the coherence transfer process in combination with the squeezed vacuum can restore to some extent the population trapping. We show that other features that do not occur for two-level atoms, such as stationary population inversions between pairs of the atomic levels, also depend on the relative phase and can be enhanced in the squeezed vacuum. In the case of unequal frequencies of the driving fields the population in the upper state depends on the relative phase only when the carrier frequency of the squeezed vacuum is equal to one of the two frequencies of the driving fields. When the carrier frequency of the squeezed vacuum is slightly detuned from both frequencies of the driving fields, the population in the upper state is insensitive to the relative phase but is dependent on the degree of squeezing. For large detunings, the population does not show any dependence on the degree of squeezing and its distribution in function of the two-photon detuning is similar to that in the thermal vacuum field.

Barry C. Sanders, Stephen Mark Barnett, P. L. Knight

Fadhel Almalki, Ali M. Mubaraki, Sayed Abdel-Khale +1 more

In this framework, the effect of a Kerr-like medium and the coupling function dependent on the number of photons operator on the interaction between a two-level atom and a non-linear field is studied. A relation between the Kerr-like medium parameter and the field-atom coupling parameter is used to obtain a simplified formula for Rabi frequency. The wave function of the proposed model is obtained, followed by the derivation of the phase distribution and from which the wehrl entropy formula is calculated. The effect of the initial state and the non-linear func?tion dependent on the number of photons operator and the Kerr-like medium on entanglement is calculated through the Wehrl entropy formula, wehrl distribution and the behaviour of photons by studying the correlation function. The entangle?ment decreases when the function dependent on the number of photons operator is taken into account, while the entanglement gradually improves when the squeezed state is considered, and the entanglement decreases significantly when considering the Kerr medium. An oscillatory distribution is formed between the classical and non-classical in the coherent state. The non-classical distribution disappears when considering the squeezed state and the Kerr-like medium.

Jeffrey H. Shapiro, Scott Roger Shepard, N. C. Wong