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Optics and Spectroscopy

A powerful source of entangled states of light

В. Н. Горбачев, A. Ya. Kazakov, A. I. Trubilko

Published Aug 1, 2005• 0 citations
Publisher

Abstract

The simultaneous interaction of N two-level atoms with a quasi-resonant classical field and two quantized modes is considered under the assumption that the Rabi parameter of the classical mode substantially exceeds the effective Rabi parameters of the quantized modes. It is shown that, in a certain domain of the parameters, the population of the quantized modes exponentially depends on time and the number N . At certain instants of time, the states of the quantized modes prove to be close to the totally entangled state.

DOI
10.1134/1.2034620

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The simultaneous interaction of N two-level atoms with a quasi-resonant classical field and two quantized modes is considered under the assumption that the Rabi parameter of the classical mode substantially exceeds the effective Rabi parameters of the quantized modes. It is shown that, in a certain domain of the parameters, the population of the quantized modes exponentially depends on time and the number N . At certain instants of time, the states of the quantized modes prove to be close to the totally entangled state.
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If a two-level atom is in the two-photon resonance with a quantized mode and simultaneously inter-acts with a quasi-resonance classical field, then a photon exchange is observed in this system between the quantized and classical modes. It is demonstrated that such a physical system can serve as a source of squeezed radiation in the quantized mode. The squeezing can be arbitrarily close to unity, while the radiation amplitude can be relatively large. A situation is discussed when N atoms are in the two-photon resonance with a quantized mode and simultaneously interact with a classical field. The phenomenon of exponential superradiation is described when the number of photons in the quantized mode exponentially depends on the number N of atoms.
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.
We show that the resonant interaction between a two-level atom and a quantized field mode via two-photon transitions leads to extreme quantum entanglement between the atom and quantum field. Nevertheless during the time evolution there are moments at which the atom-field system becomes asymptotically disentangled. We investigate statistical properties of the pure-field states generated at such times. We show that at the quarter of the revival time the field is produced in the pure superposition state (Schrödinger cat state) composed of two coherent states with the same amplitude but which are out of phase by 90° (we obtain approximate analytical solution for this superposition state). We show that the interference between component states leads to non-classical oscillations in the photon number distribution. At the revival time the field is again in the pure state (we present an approximate analytical solution for the corresponding state vector). This pure state is not a superposition state. Nevertheless it exhibits a certain degree of sub-Poissonian photon statistics. We briefly discuss the influence of the Stark shift on the production of superposition states.
We present a general procedure to describe the dynamics of N degenerate quantized fields interacting resonantly with a two–level atom, all coupled with the same strength, within the rotating–wave approximation. Starting from the analysis of the two and three field cases, we generalize the method by identifying dynamical invariants that lead to a factorized form of the time–evolution operator. A unitary transformation reduces the problem to an effective Jaynes–Cummings Hamiltonian, where only one field interacts with the atom and the remaining modes contribute as free fields. Assuming initially coherent fields and an atomic superposition, we compute the atomic inversion and the mean photon number, revealing vacuum Rabi oscillations with a frequency determined by an effective coupling constant that exceeds the individual atom–field coupling, as well as the characteristic collapse-revival behavior.