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Physical Review A

Optical pumping method for squeezing and entanglement in the ground-state spin subsystems of macroscopic atomic ensembles

Dmitriy V. Kupriyanov, Igor M. Sokolov, A. V. Slavgorodskii

Published Oct 13, 2003• 3 citations
Publisher

Abstract

We describe the mechanism of squeezing and entanglement in the ground-state spin subsystems of macroscopic atomic ensembles via the process of stimulated cooperative Raman-type scattering of correlated photon pairs. This mechanism is analogous to common optical pumping techniques normally used for depopulation of Zeeman sublevels in macroscopic atomic ensembles. We show that, by the excitation of atoms, oriented in their angular momenta, with nonclassical light consisting of a rare flux of strongly correlated photon pairs, essential correlations in the macroscopic spin fluctuations can be transferred and accumulated. In turn this leads to squeezing or entanglement in the quasispin (alignment) subsystems of macroscopic ensembles. We discuss in particular a scheme for an interferometer that would be available for the control or teleportation of quantum states created in quasispin subsystems. Such squeezed and entangled states can be stored in long-lived spin subsystems and can be further used in quantum information protocols based on the continuous variable technique.

DOI
10.1103/physreva.68.043815

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We describe the mechanism of squeezing and entanglement in the ground-state spin subsystems of macroscopic atomic ensembles via the process of stimulated cooperative Raman-type scattering of correlated photon pairs. This mechanism is analogous to common optical pumping techniques normally used for depopulation of Zeeman sublevels in macroscopic atomic ensembles. We show that, by the excitation of atoms, oriented in their angular momenta, with nonclassical light consisting of a rare flux of strongly correlated photon pairs, essential correlations in the macroscopic spin fluctuations can be transferred and accumulated. In turn this leads to squeezing or entanglement in the quasispin (alignment) subsystems of macroscopic ensembles. We discuss in particular a scheme for an interferometer that would be available for the control or teleportation of quantum states created in quasispin subsystems. Such squeezed and entangled states can be stored in long-lived spin subsystems and can be further used in quantum information protocols based on the continuous variable technique.
In this paper we consider the optical coupling of two four-level atoms via cooperative Raman scattering of correlated photons of the nondegenerate spontaneous parametric radiation. The Raman scattering of twin photons incident on the atoms is additionally stimulated by coherent classical radiation in such a way that it is slightly off resonant for each atom considered independently but resonant for the joint system. We discuss the special excitation conditions when the amplitude of the cooperative stimulated Raman scattering from quantum to classical modes becomes greater than the normal transition rates associated with independent Raman scattering. In certain conditions weak entanglement between the Zeeman sublevels in the ground states of these atoms can appear. The small admixture of entanglement in the system of two atoms leads to strong entanglement between transverse macroscopic spin fluctuations of two spatially separated atomic ensembles coupled by such quantum light. The proposed mechanism of entanglement is relevant to the ground state spin subsystem of two distant macroscopic and optically thin atomic ensembles. Such an entangled state can be stored for a long time and used as a basic Einstein-Podolsky-Rosen system in different applications pursuing the goal of spreading quantum information schemes in atomic subsystems.
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.
A proposal is made for the creation of macroscopic quantum states of collective atomic-ensemble variables by the use of stimulated Raman scattering (SRS), followed by conditional optical measurement. After the completion of the SRS process, one is able to reverse the process and to return all the atoms to their ground states in such a way that reads out an arbitrary quantum state of the collective atomic field and writes this state onto the outgoing optical field. This scheme can be used for the creation of entanglement between two distant atomic ensembles. The quantum analysis of the SRS process treats one-dimensional spatial-temporal propagation accurately. Remarkably, it is found that this multimode problem can be simplified to a two-mode problem involving spatial-temporal wave-packet modes of the optical and atomic collective fields. This improves the understanding of the entanglement created in this system.