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Journal of Modern Optics

Entangled Coherent States with Variable Weighting

B. F. Wielinga, Barry C. Sanders

Published Oct 1, 1993• 27 citations
Publisher

Abstract

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.

DOI
10.1080/09500349314551951

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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.
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.
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 approach to generating the entangled photonic states $|{\ensuremath{\Psi}}_{1},{\ensuremath{\Psi}}_{2}\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|{\ensuremath{\Psi}}_{2},{\ensuremath{\Psi}}_{1}\ensuremath{\rangle}$ from two arbitrary states $|{\ensuremath{\Psi}}_{1}\ensuremath{\rangle}$ and $|{\ensuremath{\Psi}}_{2}\ensuremath{\rangle}$ is proposed. The protocol is implemented by the conditionally induced beam-splitter coupling, which leads to the selective swapping between two photonic modes. Such coupling occurs in a quantum system prepared in the superposition of two ground states with only one of them being involved in the swapping. All the entangled states in the category, such as entangled pairs of coherent states or Fock states (NOON states), can be efficiently produced in the same way by this method.
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.
We propose a scheme for the generation of entangled coherent states for two separate cavities connected by an optical fiber. In the scheme, an atom is trapped in the first cavity and driven by a strong classical field. Under the condition that the cavity-fiber coupling is much larger than the atom-cavity coupling, the two cavity modes evolve from a vacuum state to entangled coherent states correlated with the atomic states. During the evolution, the fiber mode is not excited and the fiber loss does not affect the fidelity of the produced state.
A scheme for preparation of coherent superposition of Fock states of electromagnetic field is constructed. The superposition state is created inside the cavity via a strong interaction of a four-level atom with quantum field of the cavity and classic laser fields. We demonstrate the possibility to create desired arbitrary superposition of the cavity Fock states just by changing the relative delay of the fields. Then, as another application of our model, we study a means of creating entanglement of neutral four-level atoms using different sequences of interactions with the cavity and laser fields.