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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum theory of two-photon optical tristability: Part II

Zhicheng Wang, Wenan Guo, Songyi Zheng

Published Oct 28, 1992• 0 citations
Publisher

Abstract

The analysis presented in part I of this paper is applied to the two-photon interaction of a cavity field mode with N three-level atoms in a Lambda configuration instead. Reduction of the three-level two-photon model to an effective two-level two-photon model leads to a given effective interaction Hamiltonian, which incorporates the optical Stark effect. Using the technique developed by Collett, Cardinear, Collett and Walls, the authors calculate the squeezing spectra for the output field for different Stark shift in the good cavity limit. For the same driving field strength, the inclusion of Stark shift changes the transmission strength.

DOI
10.1117/12.130443

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The analysis presented in part I of this paper is applied to the two-photon interaction of a cavity field mode with N three-level atoms in a Lambda configuration instead. Reduction of the three-level two-photon model to an effective two-level two-photon model leads to a given effective interaction Hamiltonian, which incorporates the optical Stark effect. Using the technique developed by Collett, Cardinear, Collett and Walls, the authors calculate the squeezing spectra for the output field for different Stark shift in the good cavity limit. For the same driving field strength, the inclusion of Stark shift changes the transmission strength.
An effective Hamiltonian for the two-photon two-level model is derived form the microscopic Hamiltonian of a three-level atom in a \ensuremath{\Lambda} configuration, interacting through two-photon transitions with a light field. The effective Hamiltonian includes a term describing the optical Stark shift. With this effective Hamiltonian, we study the steady-state equation and the squeezing spectrum for a cavity-field mode interacting with an ensemble of three-level ``\ensuremath{\Lambda}-configuration'' atoms by a two-photon transition. It is shown that significant changes in the transmission characteristics and the squeezing spectrum for the output field result from the inclusion of the Stark shift.
The squeezing spectrum for a cavity field mode interacting with an ensemble of three-level ``\ensuremath{\Lambda}-configuration'' atoms by an effective two-photon transition is calculated. The advantage of the three-level \ensuremath{\Lambda} system as a squeezing medium, that is, optical nonlinearity without atomic saturation, has recently been pointed out by Reid, Walls, and Dalton. We predict perfect squeezing at the turning points for dispersive optical bistability and good squeezing for a range of other cases. Three-level ladder atoms interacting by an effective two-photon transition are also shown to give perfect squeezing in the dispersive limit.
We study the entanglement properties of two three-level Rydberg atoms passing through a single-mode cavity. The interaction of an atom with the cavity field allows the atom to make a transition from the upper most (lower most) to the lower most (upper most) level by emission (absoprtion) of two photons via the middle level. We employ an effective Hamiltonian that describes the system with a Stark shifted two-photon atomic transition. We compute the entanglement of formation of the joint two-atom state as a function of Rabi angle gtgtgt. It is shown that the Stark shift can be used to enhance the magnitude of atomic entanglement over that obtained in the resonant condition for certain parameter values. We find that though the two-atom entanglement generally diminishes with the increase of the two-photon detuning and the Stark shift, it is possible to sustain the entanglement over a range of interaction times by making the detuning and the Stark shift compensate each other. Similar characteristics are obtained for a thermal state cavity field too.
We study the entanglement properties of two three-level Rydberg atoms passing through a single-mode cavity. The interaction of an atom with the cavity field allows the atom to make a transition from the uppermost (lowermost) to the lowermost (uppermost) level by emission (absorption) of two photons via the middle level. We employ an effective Hamiltonian that describes the system with a Stark-shifted two-photon atomic transition. We compute the entanglement of formation of the joint two-atom state as a function of Rabi angle gt . It is shown that the Stark shift can be used to enhance the magnitude of atomic entanglement over that obtained in the resonant condition for certain parameter values. We find that though the two-atom entanglement generally diminishes with the increase of the two-photon detuning and the Stark shift, it is possible to sustain the entanglement over a range of interaction times by making the detuning and the Stark shift compensate each other. Similar characteristics are also obtained for a thermal state cavity field.
The atomic dipole squeezing and the emission spectra in a nondegenerate two-photon Jaynes–Cummings model in the presence of Stark shift for various field inputs are studied. The percentage duration of the atomic dipole squeezing is greatly enhanced by the inclusion of the Stark shift. The emission spectra show an asymmetric central two-peak structure that is quite different from that in the absence of the Stark shift. When the fields are initially in the coherent state, asymmetric coherent sidebands emerge. The effect of atomic coherence on dipole squeezing and the emission spectrum have also been incorporated