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Annual Meeting Optical Society of America

Intracavity entangled coherent states and local realism

Barry C. Sanders, B. F. Wielinga, A. Mann

Published Jan 1, 1993• 0 citations
Publisher

Abstract

The generation of entangled coherent states in two coupled cavities is considered. The coupling is provided by a fast variable reflectivity beamsplitter and a nonlinear medium is placed in each of the two cavities. A coherent state in one cavity is split between the two cavities and is subjected to a nonlinear evolution in each cavity and evolves into a superposition of the coherent field with itself 180° out of phase. Two types of nonlinear media are considered: (1) a nonlinear Kerr medium and (2) a medium with large χ(2) and χ(3) nonlinearities. Medium (2) permits an entanglement with variable weighting between approximate coherent states. The two cavities are coupled together again and the result is described as an entangled coherent state.

DOI
10.1364/oam.1993.thdd.14

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The generation of entangled coherent states in two coupled cavities is considered. The coupling is provided by a fast variable reflectivity beamsplitter and a nonlinear medium is placed in each of the two cavities. A coherent state in one cavity is split between the two cavities and is subjected to a nonlinear evolution in each cavity and evolves into a superposition of the coherent field with itself 180° out of phase. Two types of nonlinear media are considered: (1) a nonlinear Kerr medium and (2) a medium with large χ(2) and χ(3) nonlinearities. Medium (2) permits an entanglement with variable weighting between approximate coherent states. The two cavities are coupled together again and the result is described as an entangled coherent state.
Entangled coherent states, with arbitrary weighting of the two product coherent states in the superposition, might be produced by incorporating an optical bistable device in a coupled cavity configuration. This scheme is contrasted with the entangled coherent states that arise due to interaction in an optical Kerr medium and produce only equally weighted entanglements. The entanglement is shown to occur, not between coherent states, but between states which closely approximate coherent states. An interaction which does produce entanglement between true coherent states is introduced but is shown to be unphysical.
We demonstrate several results for the nonlinear interferometer, that emerge from a formalism which elegantly describes the output field of the nonlinear interferometer as two-mode entangled coherent states. We clarify the relationship between squeezing and entangled coherent states, since a weak nonlinear evolution produces a squeezed output, while a strong nonlinear evolution produces a two-mode, two-state entangled coherent state. In between these two extremes exist superpositions of two-mode coherent states manifesting varying degrees of entanglement for arbitrary values of the nonlinearity. The cardinality of the basis set of the entangled coherent states is finite when the ratio \ensuremath{\chi}/\ensuremath{\pi} is rational, where \ensuremath{\chi} is the nonlinear strength. We also show that entangled coherent states can be produced from product coherent states via a nonlinear medium without the need for the interferometric configuration. This provides an important experimental simplification in the process of creating entangled coherent states.
The authors of this paper propose an optical scheme for the generation of entangled coherent states which include the multi-mode and high-dimensional entangled coherent states.The scheme is based on the interaction of nonlinear Kerr medium and optical fields.The authors find that muliti-mode and high-dimensional entangled coherent states can be generated through proper selections of the fields′ initial states,the time of the interaction and the generalized bell measurement.The authors also find that the interaction of nonlinear Kerr media can generate entanglement when the states of input modes are prepared in coherent state and superposed Fock states.
An entangled state, as an essential tool in quantum information processing, may be generated through the interaction between light and matter in cavity quantum electrodynamics. In this paper, we study the interaction between two two-level atoms and a two-mode field in an optical cavity enclosed by a medium with Kerr nonlinearity in the presence of a detuning parameter and Stark effect. It is assumed that the atom–field coupling and third-order susceptibility of the Kerr medium depend on the intensity of the light. In order to investigate the dynamics of the introduced system, we obtain the exact analytical form of the state vector of the considered atom–field system under initial conditions which may be prepared for the atoms (in a coherent superposition of their ground and upper states) and the fields (in a standard coherent state). Then, in order to evaluate the degree of entanglement between the subsystems, we investigate the dynamics of the entanglement by employing the entanglement of formation. Finally, we analyze in detail the influences of the Stark shift, the deformed Kerr medium, the intensity-dependent coupling, and also the detuning parameter on the behavior of this measure for different subsystems. The numerical results show that the amount of entanglement between the different subsystems can be controlled by choosing the evolved parameters appropriately.
The nonlinear Mach-Zehnder interferometer is presented as a device whereby a pair of coherent states can be transformed into an entangled superposition of coherent states for which the notion of entanglement is generalized to include nonorthogonal, but distinct, component states. Each mode is directed to a homodyne detector. We show that there exist nonclassical intensity correlations at the output ports of the homodyne detectors which facilitate a test of local realism. In contradistinction to previous optical schemes which test local realism, the initial state used here possesses a positive Glauber-Sudarshan representation and is therefore a semiclassical state. The nonlinearity itself is responsible for generating the nonclassical state.
We investigate the entanglement between two movable mirrors in an optomechanical cavity, in which a Kerr-down-conversion crystal consisting of a Kerr nonlinear medium and an optical parametric amplifier (OPA) is placed. The effects of the nonlinear media on the entanglement have been analyzed. It is shown that the Kerr nonlinear medium makes the perfect entanglement in some discrete frequency regions. Furthermore, when the input vacuum field is squeezed, the frequency range for producing the entanglement can be effectively extended and the reachable maximal entanglement can be enhanced by the Kerr nonlinear medium, while the OPA medium reduces the degree of the entanglement and necks the frequency range for generating the entanglement. These results suggest that nonlinear media could serve as a new handle to coherently control the entanglement between the vibrational modes of the micromirrors in the optomechanical cavity system.