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Digest on Nonlinear Optics: Materials, Phenomena and Devices

Spontaneous Trapping In A Three-level Atom

David A. Cardimona, M. P. Sharma

Published Jan 1, 1990• 0 citations
Publisher

Abstract

For a 3-level atom in the "V-configuration" (two excited states |1> and |2> each dipole-coupled to a common ground state |g>) interacting with a quantized field, we have found a set of initial atomic state amplitudes for which the usual time-dependent oscillations collapses, and revivals vanish. Preparing the atom initially in this special way forces the atomic population to remain coherently trapped in this configuration. The dressed-state energy of this particular linear combination of bare-atom states is zero, so that eiEt= 1 and the population remains constant in time - as long as the applied field remains on.

DOI
10.1109/nlo.1990.695815

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For a 3-level atom in the "V-configuration" (two excited states |1> and |2> each dipole-coupled to a common ground state |g>) interacting with a quantized field, we have found a set of initial atomic state amplitudes for which the usual time-dependent oscillations collapses, and revivals vanish. Preparing the atom initially in this special way forces the atomic population to remain coherently trapped in this configuration. The dressed-state energy of this particular linear combination of bare-atom states is zero, so that eiEt= 1 and the population remains constant in time - as long as the applied field remains on.
For a three-level atom in the ssV configuration (i.e., having two excited states each dipole-coupled to a common ground state), we have found a particular linear combination of bare-atom states in which Rabi oscillations and their associated collapses and revivals do not occur. Moving to a dressed-state picture, we discover that this particular linear combination state is just that dressed state which is decoupled from all the field modes. It is a dressed state for which the transition dipole moments with the other dressed states are zero. The existence of this decoupled dressed state depends on the tuning of the dressing laser field, which in turn depends on the bare-atom excited-state dipole moments and energy-level separation. When we include spontaneous emission, the population decays from the other dressed states into this decoupled state and remains coherently trapped there, producing a system that experiences no dynamical behavior. This is exact for \ensuremath{\delta}-function photon statistics (i.e., if there is no intensity uncertainty). The trapping becomes less perfect as the photon statistics are allowed to have a greater bandwidth. Also, if the applied field is tuned incorrectly, the spontaneous realignment of the atomic state amplitudes does not result in a totally decoupled dressed state, and the dynamics proceed normally.
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.
In this paper we investigate the sensitivity of coupled atomic transitions to correlations between field modes. In particular, we show that a three-level atom interacting with a cavity field supporting two quantized modes can be highly sensitive to the nature of the correlations between the modes. Correlated two-mode states include the two-mode squeezed state, whereas the SU(2) coherent state is an example of an anticorrelated state. We study in detail the dynamics of a three-level atom in the \ensuremath{\lambda} configuration, interacting with the two modes of an SU(2) coherent state. We show that for certain choices of the atom-field coupling constants, the generalized two-photon Rabi frequency for the system becomes independent of the photon number, leading to a purely periodic behavior in time of the atomic population probabilities; for other choices of the atom-field coupling constants, we observe the usual collapse and revival of the Rabi oscillations. We study also the dynamics of the field, in particular the correlations between the modes. Finally, for comparison purposes, we present a parallel study of the case in which the field modes are initially uncorrelated.