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Journal of Modern Optics

Collective entangled dark states

Hideomi Nihira, Carlos R. Stroud

Published Sep 10, 2007• 1 citation
Publisher

Abstract

We describe a type of collective entangled dark state which exists when a group of many-level atoms interact simultaneously with both high-Q cavity modes and free space modes of the electromagnetic field. As an example we describe a collection of atoms with a level structure of the form of and show that there are states of this system in which the atoms remain trapped in a collective coherent superposition of ground state levels in spite of the presence of photons in resonant field modes. Efficient methods of generalization of these results to other atomic level structures and cavity fields are described.

DOI
10.1080/09500340701391449

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We describe a type of collective entangled dark state which exists when a group of many-level atoms interact simultaneously with both high-Q cavity modes and free space modes of the electromagnetic field. As an example we describe a collection of atoms with a level structure of the form of and show that there are states of this system in which the atoms remain trapped in a collective coherent superposition of ground state levels in spite of the presence of photons in resonant field modes. Efficient methods of generalization of these results to other atomic level structures and cavity fields are described.
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.
Spontaneous emission of atoms in free space is modified by the presence of other atoms in close vicinity inducing collective super- and subradiance. For two nearby atoms with a single decay channel the entangled antisymmetric superposition state of the two single excited states will not decay spontaneously. No such excited two-atom dark state exists, if the excited state has two independent optical decay channels of different frequencies or polarizations. However, we show that for an excited atomic state with N-1 independent spontaneous decay channels one can find a highly entangled N-particle dark state, which completely decouples from the vacuum radiation field. It does not decay spontaneously, nor will it absorb resonant laser light. Mathematically, we see that this state is the only such state orthogonal to the subspace spanned by the atomic ground states. Moreover, by means of generic numerical examples we demonstrate that the subradiant behavior largely survives at finite atomic distances including dipole-dipole interactions.
An ensemble of identical two level atoms in dark state neither adsorbs nor emits photons due to destructive interference. Dark states have numerous applications. It can be used for the source of energy for nano-devices; the space of dark states is decoherence free and can serve as the carrier for the fault tolerant quantum computations, etc. Since a dark state does not interact with the electromagnetic field it is an eigenstate of Tavis-Cummings Hamiltonian and the preparation of such states requires the exit from this model. We show how to prepare a dark state by the photon pumping and drain from the optical cavity with two atoms, one from which has Stark or Zeeman splitting of energy levels. This splitting is removed before photon drain from the cavity. The dark state yield after one such cycle has the order of energy level splitting. We show the scheme of the experiment, in which such cycles repeat until the dark state is produced with high probability and the results of its computer simulation. The structure of dark states is briefly discussed.
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.