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Revista Mexicana de Física

Atomic spin squeezing in three level atoms

Osvaldo Civitarese, M. Reboiro, Lorena Rebón, Diego Tielas

Published Dec 1, 2008• 1 citation
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Abstract

"The conditions under which squeezing occurs, in a system of Rb atoms and photons, are modelled by describing atom-photon interactions in three atomic levels. The time evolution of the spin population is calculated for different initial conditions. It is found that the use of coherent states does not suffice for the transfer of spin between the atoms."

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"The conditions under which squeezing occurs, in a system of Rb atoms and photons, are modelled by describing atom-photon interactions in three atomic levels. The time evolution of the spin population is calculated for different initial conditions. It is found that the use of coherent states does not suffice for the transfer of spin between the atoms."
Spin squeezing via atom-field interactions is considered within the context of the Tavis-Cummings model. An ensemble of N two-level atoms interacts with a quantized cavity field. For all the atoms initially in their ground states, it is shown that spin squeezing of both the atoms and the field can be achieved provided the initial state of the cavity field has coherence between number states differing by 2. Most of the discussion is restricted to the case of a cavity field initially in a coherent state, but initial squeezed states for the field are also discussed. Optimal conditions for obtaining squeezing are obtained. An analytic solution is found that is valid in the limit that the number of atoms is much greater than unity and is also much larger than the average number of photons, ${\ensuremath{\alpha}}^{2},$ initially in the coherent state of the cavity field. In this limit, the degree of spin squeezing increases with increasing $\ensuremath{\alpha},$ even though the field more closely resembles a classical field for which no spin squeezing could be achieved.
By using the full quantum theory,the time evolution of atomic dipole squeezing parameters of a Λ-type three-level atom interacting with a single-mode coherent cavity field is investigated.The influence of the initial coherent-field intensity,the initial atomic coherence,the initial populations on the two lower atomic levels and their energy splitting on the atomic dipole squeezing are studied.Results show that the amount of dipole squeezing increases while the duration of dipole squeezing decreases with increasing initial field intensity.In the case of degenerate lower atomic states maximum dipole squeezing is reached when the two states have equal initial phases and equal populations.Exchange of initial populations in the lower atomic states does not influence time evolution of diploe squeezing.Atomic energy level splitting is helpful to dipole squeezing generation under certain conditions.