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Journal of Modern Optics

Local entanglement in a bimodal high- Q cavity: Production and utilization

Anna Napoli, Antonio Messina

Published Jun 1, 2002• 3 citations

Abstract

A new conditional scheme for entangling the two quantized modes of a bimodal high-Q cavity field is presented. We show that, injecting one at time k atoms inside the cavity, it is possible to guide the field toward k-dependent linear combinations of k + 1 bimodal Fock states, each one possessing the same total number of photons. The two simple cases corresponding to the passage of one or two atoms only through the resonator are considered. Their practical feasibility against cavity losses, spontaneous emission and other sources of imprecision of the experimental set-up is discussed. Two examples illustrating the usefulness of and the interest toward the creation of such a local entanglement, are reported. The first one relates the specific features of these bimodal entangled states to the occurrence of a non-classical correlation effect in the dynamics of a two-level atom interacting with the entangled cavity. The second one demonstrates that the peculiar entanglement initially stored in the cavity in accordance with our method, provides an effectively exploitable resource to entangle two spatially separated cavities.

DOI: 10.1080/09500340110107162

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A new conditional scheme for entangling the two quantized modes of a bimodal high-Q cavity field is presented. We show that, injecting one at time k atoms inside the cavity, it is possible to guide the field toward k-dependent linear combinations of k + 1 bimodal Fock states, each one possessing the same total number of photons. The two simple cases corresponding to the passage of one or two atoms only through the resonator are considered. Their practical feasibility against cavity losses, spontaneous emission and other sources of imprecision of the experimental set-up is discussed. Two examples illustrating the usefulness of and the interest toward the creation of such a local entanglement, are reported. The first one relates the specific features of these bimodal entangled states to the occurrence of a non-classical correlation effect in the dynamics of a two-level atom interacting with the entangled cavity. The second one demonstrates that the peculiar entanglement initially stored in the cavity in accordance with our method, provides an effectively exploitable resource to entangle two spatially separated cavities.

A single two-level atom can be used to prepare an arbitrary photon number state (Fock state) in a high Q cavity . The atom undergoes a controlled succession of interactions with two cavity modes. One of them contains a coherent field. The atom transfers photons one by one from this field to the initially empty second mode. The scheme can be extended to prepare a quantum superposition of the vacuum with a Fock state, a highly non-classical situation. We discuss the feasibility of the experiment with our present Rydberg-atom cavity QED set-up.

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

N

independent atoms trapped inside a high-finesse optical cavity.

It has been recently shown [1] that, under suitable conditions, the interaction between a three-level atom and the quantized field of a bimodal microcavity may be effectively reduced to the two-photon coupling between a single two-level atom and the electromagnetic field in the resonator. The corresponding Hamiltonian model is characterized by intensity-dependent Stark shifts due to the presence of an intermediate off-resonance atomic level. Assume the cavity field prepared at in an arbitrary state and let an initially excited atom cross the cavity with an appropriately selected velocity. It is possible to show that, exploiting a single conditional measurement of the atomic state immediately after the atom leaves the resonator, the bimodal field is projected into a new state characterized by the same photon number distribution present at More in detail, the experimental scheme we propose makes it possible manipulating only the phases of the initial probability amplitudes of finding a well defined population in the cavity. We prove that the state into which the cavity collapses after a successful atomic measurement is unitarily related to the initial field state and the explicit form of the accomplishing operator is constructed. We wish to remark that, beside its inherent theoretical interest, this simple experimental scheme might also be of relevance in the socalled field of quantum communication [2], where implementing unitary modifications of a quantum state signal represents an issue of topical and central importance. More in general, our proposal provides a systematic procedure for controlling selected properties of a quantum state. We in fact demonstrate that our experimental scheme may be reliably exploited to generate orthogonal states to a prefixed one or to control the squeezing direction.

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We propose a conditional scheme to generate entangled two-photons generalized binomial states inside two separate single-mode high-Q cavities. This scheme requires that the two cavities are initially prepared in entangled one-photon generalized binomial states and exploits the passage of two appropriately prepared two-level atoms one in each cavity. The measurement of the ground state of both atoms is finally required when they exit the cavities. We also give a brief evaluation of the experimental feasibility of the scheme.