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Journal of Physics B Atomic Molecular and Optical Physics

Two-mode squeezed and entangled states of a hybrid system of an atomic ensemble and an optical field via an atom–cavity reservoir

Qing Yang Xu, Xiangming Hu

Published Sep 5, 2013• 4 citations
Publisher

Abstract

We show that it is possible to use an atom–cavity reservoir to prepare the two-mode squeezed and entangled states of a hybrid system of an atomic ensemble and an optical field, which do not directly interact with each other. The essential mechanism is based on the combined effect of a two-mode squeezing interaction and a beam–splitter interaction between the system and the reservoir. The reservoir mechanism is important for quantum networking in that it allows an interface between a localized matter-based memory and an optical carrier of quantum information without direct interaction. (Some figures may appear in colour only in the online journal)

DOI
10.1088/0953-4075/46/18/185501

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We show that it is possible to use an atom–cavity reservoir to prepare the two-mode squeezed and entangled states of a hybrid system of an atomic ensemble and an optical field, which do not directly interact with each other. The essential mechanism is based on the combined effect of a two-mode squeezing interaction and a beam–splitter interaction between the system and the reservoir. The reservoir mechanism is important for quantum networking in that it allows an interface between a localized matter-based memory and an optical carrier of quantum information without direct interaction. (Some figures may appear in colour only in the online journal)
We present a cavity dissipation scheme to prepare a hybrid system of an atomic ensemble and a moving mirror in squeezed and entangled states. This scheme is based on four-wave mixing in the atoms and radiation pressure on the mirror, both of which combine to lead to Bogoliubov interactions of the atoms and the mirror with the cavity fields. Under adiabatic conditions, the cavity fields cause the hybrid Bogoliubov modes to evolve into the vacuum states, which correspond to the two-mode squeezed and entangled states. The dependence of the hybrid entanglement on the system parameters is also presented in and beyond the Bogoliubov interactions.
We show a procedure for engineering effective interactions between two modes in a bimodal cavity. Our system consists of one or more two-level atoms, excited by a classical field, interacting with both modes. The two effective Hamiltonians have forms similar to beam-splitter and quadratic beam-splitter interactions. We also demonstrate that the nonlinear Hamiltonian can be used to prepare an entangled coherent state, also known as a multidimensional entangled coherent state, which has been pointed out as an important entanglement resource. We show that the nonlinear interaction parameter can be enhanced considering NNN independent atoms trapped inside a high-finesse optical cavity.
Quantum correlations, particularly squeezing and entanglement, are essential in quantum technologies such as metrology, computation, and simulation, as well as in foundational studies. In quantum optics, these phenomena are often intertwined: two squeezed beams can be transformed into entangled beams by mixing them at a beam splitter, and vice versa. However, it is less common to encounter states where two beams are simultaneously squeezed individually while retaining global entanglement. These hybrid states evidently present potential possibilities for applications. In this work, we propose a compact single-cavity source based on a nondegenerate optical parametric oscillator operated below threshold, capable of generating such light—signal and idler beams that are quadrature-squeezed individually while maintaining global entanglement. This behavior arises from an additional linear coupling between the signal and idler, resembling a beam-splitter interaction. We discuss two physical implementations of this system: one based on intra-cavity electro-optic modulators and the other on optomechanical interactions. This unique combination of local and non-local quantum correlations opens the door to novel quantum communication and metrology protocols.
We show that, in analogy to light fields, effective bosonic modes of atomic ensembles in the Holstein-Primakoff representation can be prepared in multimode squeezed states, and multipartite continuous-variable cluster and Greenberger-Horne-Zeilinger (GHZ) entangled states. Our scheme uses a cascade of optical cavities, in each of which one atomic ensemble is placed. Through Raman transitions between stable atomic ground states, the atomic ensembles are in the interactions with the cavity and laser fields. Because of the long-lived ground states, the atomic ensembles act as quantum network nodes, whose cluster entangled states are applicable in the one-way quantum computer, and whose GHZ entangled states have potential for quantum communication.
We propose a scheme employing quantum-reservoir engineering to controllably entangle the internal states of two atoms trapped in a high-finesse optical cavity. Using laser and cavity fields to drive two separate Raman transitions between stable atomic ground states, a system is realized corresponding to a pair of two-state atoms coupled collectively to a squeezed reservoir. Phase-sensitive reservoir correlations lead to entanglement between the atoms, and, via local unitary transformations and adjustment of the degree and purity of squeezing, one can prepare entangled mixed states with any allowed combination of linear entropy and entanglement of formation.