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Physical Review A

Light-matter entanglement via dark-state resonances

Fei Wang, Xiangming Hu

Published Sep 29, 2010• 14 citations
Publisher

Abstract

We show that dark-state resonances can be a fundamental mechanism for the entanglement between light and matter. While two optical fields trap an ensemble of three-level $\ensuremath{\Lambda}$ atoms into the dark state, the coherence is created between the two metastable states, and the two fields undergo no absorption. The trapped atoms behave like a coherently coupled two-party reservoir and act on the two fields. As a result, Einstein-Podolsky-Rosen entanglement is obtainable between the atomic ensemble and one collective field under proper parameter conditions. Long-lived atomic coherence and no need of nonclassical input light are the advantages for quantum communications between light and matter based on the present mechanism.

DOI
10.1103/physreva.82.033835

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We show that dark-state resonances can be a fundamental mechanism for the entanglement between light and matter. While two optical fields trap an ensemble of three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ atoms into the dark state, the coherence is created between the two metastable states, and the two fields undergo no absorption. The trapped atoms behave like a coherently coupled two-party reservoir and act on the two fields. As a result, Einstein-Podolsky-Rosen entanglement is obtainable between the atomic ensemble and one collective field under proper parameter conditions. Long-lived atomic coherence and no need of nonclassical input light are the advantages for quantum communications between light and matter based on the present mechanism.
We explore the quantum entanglement between two collective fields via atomic coherence effects. For three-level atoms in V\mathsf{V}V configuration driven by two applied fields on two-photon resonance, one coherent superposition of the excited states is not excited, which is the counterpart of coherent population trapping. The coherence-induced depopulation makes two cavity fields in each collection combine into a quantum-beat, i.e., equivalently, the difference mode of the two components decouples from the driven atoms. The two sum modes, when they are arranged in the four-wave mixinglike interactions, can be prepared in Einstein-Podolsky-Rosen entangled state. Correspondingly, any two individual fields from different collective modes are entangled with each other. Furthermore, the effects of thermal reservoir and laser linewidths are discussed, and a generalization is given to the case in which each quantum beat involves more than two modes.
We show that Einstein–Podolsky–Rosen (EPR) light entanglement is obtainable via the resonant nonlinear interactions enhanced by electromagnetically induced transparency. A three-level system is used as a unified model, where two metastable states are coupled to each other via microwave, or Raman, or two-photon transition, and the upper metastable state is coupled to the excited state. A pair of inner sidebands is amplified as optical cavity modes via the transition from the excited state to the other metastable state. The analysis is presented by using the dressed-atom squeezed-transformed-mode approach. For a proper ratio of the amplitudes of the applied fields, the sum of the variances for two EPR-like operators approaches zero, which corresponds to EPR entanglement.
We propose to couple single atomic qubits to photons incident on a cavity containing an atomic ensemble of a different species that mediates the coupling via Rydberg interactions. Subject to a classical field and the cavity field, the ensemble forms a collective dark state which is resonant with the input photon, while excitation of a qubit atom leads to a secondary ``dark'' state that splits the cavity resonance. The two different dark-state mechanisms yield zero and $\ensuremath{\pi}$ reflection phase shifts and can be used to implement quantum gates between atomic and optical qubits.
An ideal and reversible transfer technique for the quantum state between light and metastable collective states of matter is presented and analyzed in detail. The method is based on the control of photon propagation in coherently driven three-level atomic media, in which the group velocity is adiabatically reduced to zero. Form-stable coupled excitations of light and matter (``dark-state polaritons'') associated with the propagation of quantum fields in electromagnetically induced transparency are identified, their basic properties discussed and their application for quantum memories for light analyzed.
Protocols for quantum communication between massive particles, such as atoms, are usually based on making use of nonclassical light, and/or superhigh finesse optical cavities are normally needed to enhance interaction between atoms and photons. We demonstrate a remarkable result: by using only coherent light, entanglement can be generated between distant free space atomic ensembles, and an unknown quantum state can thus be teleported from one to another. Neither nonclassical light nor cavities are needed in the scheme, which greatly simplifies its experimental implementation.