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Journal of Physics B Atomic Molecular and Optical Physics

Effect of three-level atomic state coherence on collapse and revival dynamics

David A. Cardimona, M. P. Sharma, María Alejandra Gómez Ortega

Published Dec 28, 1989• 26 citations
Publisher

Abstract

For a three-level atom with two excited states each dipole-coupled to a common ground state, the authors have found a particular linear combination of the atomic states which will not experience Rabi oscillations and their associated collapses and revivals. If the atom is initially prepared in this combination state, the atomic population will be coherently trapped there, and the dynamical behaviour will be constant in time.

DOI
10.1088/0953-4075/22/24/010

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For a three-level atom with two excited states each dipole-coupled to a common ground state, the authors have found a particular linear combination of the atomic states which will not experience Rabi oscillations and their associated collapses and revivals. If the atom is initially prepared in this combination state, the atomic population will be coherently trapped there, and the dynamical behaviour will be constant in time.
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.
The effects of the coherence between the states of a two-level atom on the phenomenon of collapses and revivals in an undamped binomial state of the electromagnetic field are investigated. It is found that the Rabi oscillations exhibit qualitatively different behaviour for different phases of coherence between the levels. This behaviour in the binomial state of the field is in contrast with that in a coherent state field, in which case the Rabi oscillations are qualitatively the same for all values of the coherence between the two atomic levels.
Interaction of a lossless two-level atom with a monochromatic (classical) field of radiation is considered, as the atom initially possesses a translational state with a number of equidistant and discrete momenta. It is shown that the Rabi oscillations in such an atom evolve as a sequence of collapses and revivals, if the coupling wave deeply saturates the optical transition. Between revivals, the populations undergo subrevivals. Approximate analytical formulae are obtained taking the initial momentum distribution in the form of two shifted Gaussians or a Besselian. A possible experimental realization of such revivals is discussed.