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中国激光(英文版)

Steady state Behaviour of a Three level Ladder Atomic System with Incoherent Population Pumping in a Squeezed Vacuum

Chen Zhao-yang

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

A study is made of the steady state populations of a three level ladder atom in a squeezed vacuum, driven by a superposition of a monochromatic laser wave with incoherent population pumping. Using the density matrix equations for the system, the steady state populations are calculated numerically and shown graphically as functions of two photon detuning for various cases of the squeezed vacuum and different incoherent pump rates. It is shown that the incoherent population pumping tends to greatly decrease the two photon absorption from the squeezed vacuum.

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Journal of Modern Optics•Mar 1, 1995•18 citations
A study is made of the
steady state populations of a three level ladder atom in a squeezed vacuum, driven by a
superposition of a monochromatic laser wave with incoherent population pumping. Using the
density matrix equations for the system, the steady state populations are calculated
numerically and shown graphically as functions of two photon detuning for various cases of the
squeezed vacuum and different incoherent pump rates. It is shown that the incoherent
population pumping tends to greatly decrease the two photon absorption from the squeezed
vacuum.
A three-level ladder atom driven by two coherent laser fields with rather different frequencies in various kinds of reservoirs is considered. Making use of the master equation and Bloch equation, we calculate numerically and show graphically the steady-state populations versus two-photon detuning. We also discuss and compare the two-photon and one-photon processes occurring for various cases. For a squeezed vacuum, only when the carrier frequency of the squeezed vacuum equals the average of frequencies of the two driving fields and the phase matching condition is fulfilled, will there be a strong two-photon resonant absorption from the squeezed vacuum, a characteristic different from absorption of photons from a classical field; Otherwise, the two-photon ab-sorption rate from the squeezed vacuum will be greatly diminished.
This paper mainly deals with the steady-state population of a moving ladder-type three-level atom,driven by a superposition of a monochromatic laser wave with a broad-band squeezed vacuum,From the Hamiltonian of the atomic system,making use of Born-Markoff approximation,we derive the master equation for the system and the atomic Bloch equations and obtain the steady-state solutions of the optical Bloch equations using numerical calculation.Then we discuss the dependence of the attained population σ_(ii) on parameters such as detuning Δ,Rabi frequencies e_1e_2,phase ,squeezing photon number N and spontaneous decay ratesγ_1 γ_2 etc in different cases by using graphical method.
A theoretical study is carried out for the laser cooling of a moving three-level atom in a ladder configuration, driven by a bichromatic laser fields with a broad-band squeezed vacuum. The friction, diffusion coefficients and the equilibrium temperature are calculated numerically and shown graphically as a function of two-photon detunings for various cases of the squeezed vacuum. It is shown that the relative phases between the two coherent fields and the squeezed vacuum field play an important role in the cooling process. For a suitable choice of parameters, the atomic cooling temperature may be reduced to below that in the case of a vacuum, even down to two orders below the Doppler temperature limit. The efficiency of this cooling scheme is also analyzed.
A theoretical study is made of the steady-state intensity and squeezing properties of the fluorescent light from a three-level-atom system in a ladder configuration, which is subject to spontaneous-emission decay to the electromagnetic-field vacuum. Two cases are examined: in the equispaced (ES) level case, the two atomic transition frequencies are nearly equal and two photon absorption processes occur from a single coherent laser field that couples both transitions and has a small detuning from each; in the non- equispaced (NES) level case, the atomic transition frequencies are rather different and two photon absorption processes occur from two coherent laser fields, each coupled to a single transition and in near resonance with it. In both cases, a situation of small two-photon detuning occurs. Optical Bloch equations for the atomic density matrix in rotating frames are given and matrix expressions for determining the steady-state populations and coherences are obtained. Analytic expressions are also given for special cases. The fluorescent intensity is obtained from the populations of the intermediate and upper states, with the normally ordered variance (NOV) for quadrature components of the fluorescent field involving, in addition, the atomic coherences. The fluorescent intensities are shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases.In both cases, the fluorescent intensities show the well known resonances from the upper state at zero two-photon detuning and from the intermediate state at zero one-photon detuning for the lower transition. However, further resonances are also found. The intermediate-state intensity displays a resonance at zero two-photon detuning. Also, the upper-state intensity shows a resonance at zero one-photon detuning for the upper transition, but only for the NES case; evidently, the transfer rate from upper to lower transition coherences destroys this resonance for the ES case. The time-averaged NOV is also shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases. For the ES case, the quadrature frequency is chosen as the single laser frequency and for the NES case, it is chosen as either the average of the two laser frequencies or the lower transition laser frequency. Squeezing occurs near zero two-photon detuning for both ES and NES cases, though only for the quadrature frequency equal to the average laser frequency in the latter case. It also occurs near zero detuning for the lower transition for both cases, though only for the quadrature frequency equal to the lower transition laser frequency in the NES case. The squeezing minima show a splitting effect for large Rabi frequencies corresponding to two-photon or one-photon Rabi splitting of the dressed atom levels for the situation near two-photon or one-photon resonance, respectively. The large squeezing near two-photon resonance for moderate Rabi frequencies and large one-photon detuning corresponds to essentially pure three-level squeezing, while that near one-photon resonance for weak Rabi frequencies involves two-level squeezing.
This paper mainly studies the radiation pressure of a moving ladder-type three-level atom driven by a superposition of a bichromatic laser wave with a broad-band squeezed vaccum and obtains the steady-state expression for the radiation force.Frist,from the master equations for a moving ladder-type three-level atom driven by a superposition of a bichromatic laser wave with a broad-band squeezed vaccum,we derive the equations for the atomic density matrix element.Second,by choosing proper scaled variables,Bloch equations for the atomic population are obtained.Then,from Heisenberg equation for atomic momentum,considering the adiabatic approximation,the mathematical expression of the mean radiation pressure is obtained.At last,by considering the steady-state case in which the atomic population doesn't vary with time and the condition,the steady-state expression of the radiation pressure is obtained.
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.