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Physical Review A

Squeezing via two-photon transitions

Craig M. Savage, Daniel F. Walls

Published May 1, 1986• 57 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.33.3282

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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.
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 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.
Two-photon bistability in a system of three-level atoms driven by a single-frequency field shows nearly ideal squeezing close to a dynamic instability threshold, occurring in the lower branch of the steady-state bistability curve. The squeezing is maximized and becomes very broad band in the bad cavity limit. Such results which were previously predicted on the basis of an effective two-level model, are demonstrated here and analysed by a full three-level treatment of the atoms. In addition, important restrictions and new features are found.
The interaction of classical and quantized electromagnetic fields with an ensemble of atoms in an optical cavity is considered. Four fields drive a double-lambda level scheme in the atoms, consisting of a pair of lambda systems sharing the same set of lower levels. Two of the fields produce maximum coherence, rho12 = -1/2, between the ground state sublevels 1 and 2. This pumping scheme involves equal intensity fields that are resonant with both the one and two-photon transitions of the lambda system. There is no steady-state absorption of these fields, implying that the fields induce a type electromagnetically-induced transparency (EIT) in the medium. An additional pair of fields interacting with the second lambda system, combined with the EIT fields, leads to squeezing of the atom spin associated with the ground state sublevels. Our method involves a new mechanism for creating steady-state spin squeezing using an optical cavity. As the cooperativity parameter C is increased, the optimal squeezing varies as C^{-1/3}. For experimentally accessible values of C, squeezing as large as 90% can be achieved.
We consider two modes of the electromagnetic field interacting via a three-level atom in a ladder configuration. We calculate the squeezing spectra of the sum and difference of the two output beams. The usefulness of this system as a quantum-nondemolition-measurement scheme is analyzed and a prediction is made using the parameters of a recent experiment by Grangier et al. [Phys. Rev. Lett. 66, 1418 (1991)]. We use a full three-level model in the most general case and in particular the influence of both the one-photon and the two-photon detunings are investigated.
We study the interaction of a three-level atom with a single mode field through multiphoton transition in a cavity, taking explicitly into account the existence of forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. The analytical forms of the absorption spectrum is calculated using the dressed states of the system. The effects of photon multiplicities, mean photon number, detuning, Kerr-like medium, and the intensity-dependent coupling functional on the absorption spectrum are analyzed.