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Journal of Modern Optics

Population trapping with quantized fields in two-channel models of atomic excitation

Christopher C. Gerry

Published Nov 1, 1999• 4 citations
Publisher

Abstract

In this paper, we study several models of two-channel atomic excitation involving quantized fields and search for field states that result in the trapping of the atomic population in a single bare state. This trapping is a result of quantum interference between the two channels. We study the following models: a two-level atom resonantly interacting with two quantized field modes, a two-level atom with competing one and three photon transitions, and a Raman coupled model containing both Stokes and anti-Stokes fields. We find a great variety of trapping states of the field, some of the states being highly non-classical. The effects of dissipation on the stability of the trapping states are discussed and a method for generating some of the states is presented.

DOI
10.1080/09500349908231385

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In this paper, we study several models of two-channel atomic excitation involving quantized fields and search for field states that result in the trapping of the atomic population in a single bare state. This trapping is a result of quantum interference between the two channels. We study the following models: a two-level atom resonantly interacting with two quantized field modes, a two-level atom with competing one and three photon transitions, and a Raman coupled model containing both Stokes and anti-Stokes fields. We find a great variety of trapping states of the field, some of the states being highly non-classical. The effects of dissipation on the stability of the trapping states are discussed and a method for generating some of the states is presented.
We investigate the population trapping in a Raman-coupled three-level system interacting with a pump mode and a Stokes mode in a quantized cavity. We show that with an initial atom-field decoupled state and the atomic state prepared in a coherent superposition of two nondegenerate ground states, population trapping occurs when the phase of the atomic dipole is equal to the phase difference of the two modes and the two-mode field state satisfies a specific photon distribution. In the limit of large total photon number, under some specific conditions, the corresponding two-mode trapping state can be identified as a phase difference state. We have studied the variance of superposition mode quadrature and its evolution, statistical properties, and the phase-space properties of the two-mode trapping field state. It has been observed that although under different conditions the two-mode field exhibits both sub- and super-Poissonian statistics, no squeezing is observed in any case.
We consider a \ensuremath{\Lambda}-type three-level atom interacting simultaneously with two quantized cavity fields and a classical field, all of different frequencies. The classical field is of constant amplitude and the quantized cavity fields are dynamical variables. The effective interactions are Raman type with the two cavity fields regarded as Stokes and anti-Stokes modes. The classical field acts as the pump-mode, so that both the pump--Stokes and the pump--anti-Stokes transitions are included. We present analytic expressions for the dressed states of the system in a general situation where the two channels have different coupling strengths. The dressed states are closely related to the two-mode squeezed number states. We find that two-mode squeezing and nontrivial phase correlation occur in the model. The effects of weak cavity damping are also discussed.
The interaction of a two-level atom with a single-mode radiation field through multiphoton transitions is studied in terms of the dressed-state formalism. It is shown that when only certain dressed states are initially excited, population trapping occurs. We particularize these results for some well-known models of one- and two-photon transitions. Photon statistics of the cavity mode is analyzed in terms of the quasiprobability distribution Q(\ensuremath{\alpha}). It is shown that when population trapping occurs some two-time correlation functions become stationary, which allows one to obtain the resonance spectrum as the Fourier transform of the two-time dipole autocorrelation function.
The effect of interference stabilization is shown to exist in a system of two atomic levels coupled by a strong two-color laser field, the two frequencies of which are close to a two-photon Raman-type resonance between the chosen levels, with open channels of one-photon ionization from both of them. We suggest an experiment, in which a rather significant (up to 9090%90) suppression of ionization can take place and which demonstrates explicitly the interference origin of stabilization. Specific calculations are made for H and He atoms and optimal parameters of a two-color field are found. The physics of the effect and its relation with such well-known phenomena as light induced continuum structure and population trapping in a three-level system are discussed.
We study the effect of quantum interference on the population distribution and absorptive properties of a V-type three-level atom driven by two lasers of unequal intensities and different angular frequencies. Three coupling configurations of the lasers to the atom are analysed: (a) both lasers coupled to the same atomic transition, (b) each laser coupled to different atomic transition and (c) each laser coupled to both atomic transitions. Dressed states for the three coupling configurations are identified, and the population distribution and absorptive properties of the weaker field are interpreted in terms of transition dipole moments and transition frequencies among these dressed states. In particular, we find that in the first two cases there is no population inversion between the bare atomic states, but the population can be trapped in a superposition of the dressed states induced by quantum interference and the stronger field. We show, that the trapping of the population, which results from the cancellation of transition dipole moments, does not prevent the weaker field to be coupled to the cancelled (dark) transitions. As a result, the weaker field can be strongly amplified on transparent transitions. In the case of each laser coupled to both atomic transitions the population can be trapped in a linear superposition of the excited bare atomic states leaving the ground state unpopulated in the steady state. Moreover, we find that the absorption rate of the weaker field depends on the detuning of the strong field from the atomic resonances and the splitting between the atomic excited states. When the strong field is resonant to one of the atomic transitions a quasi-trapping effect appears in one of the dressed states. In the quasi-trapping situation all the transition dipole moments are different from zero, which allows the weaker field to be amplified on the inverted transitions. When the strong field is tuned halfway between the atomic excited states, the population is completely trapped in one of the dressed states and no amplification is found for the weaker field.