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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Entangled superpositions of distinguishable states via nonlinear wave mixing

Dmitri S. Mogilevtsev, Natalia Korolkova, Jan Peřina

Published Dec 1, 1996• 7 citations
Publisher

Abstract

We propose and investigate a scheme describing the interaction of two field modes in a nonlinear structure including second- and third-order nonlinearities. With the help of exact solutions for both Heisenberg equations of motion and the Schrödinger equation we find three different dynamical regimes of the described scheme. In one of the regimes the generation of different macroscopically distinguishable states is possible. We show that the resulting two-mode wavefunction can contain an infinite set of different Schrödinger-cat states.

DOI
10.1088/1355-5111/8/6/006

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We propose and investigate a scheme describing the interaction of two field modes in a nonlinear structure including second- and third-order nonlinearities. With the help of exact solutions for both Heisenberg equations of motion and the Schrödinger equation we find three different dynamical regimes of the described scheme. In one of the regimes the generation of different macroscopically distinguishable states is possible. We show that the resulting two-mode wavefunction can contain an infinite set of different Schrödinger-cat states.
We suggest a variant of the recently proposed experiment for the generation of a kind of mesoscopic superposition quantum state (a Schr\"odinger-cat-type state), using two coupled parametric down-converter nonlinear crystals [F. De Martini, Phys. Rev. Lett. 81, 2842 (1998)]. We study the parametric oscillator case and find that an entangled Schr\"odinger-cat-type state of two cavities, whose mirrors are placed along the output beams of the nonlinear crystals, can be realized under suitable conditions.
A two-step interaction scheme involving (2) and (3) nonlinear media is suggested for the generation of Schrödinger cat-like states of a single-mode optical field. In the first step, a weak coherent signal undergoes a self-Kerr phase modulation in a (3) crystal, leading to a Kerr kitten , namely a microscopic superposition of two coherent states with opposite phases. In the second step, such a Kerr kitten enters a (2) crystal and, in turn, plays the role of a quantum seed for stimulated phase-sensitive amplification. The output state in the above-threshold regime consists in a quantum superposition of mesoscopically distinguishable squeezed states, i.e. an optical cat-like state. The whole setup does not rely on conditional measurements, and is robust against decoherence, as only weak signals interact with the Kerr medium.
A scheme is proposed for the generation of superpositions of multi-mode coherent states, i.e. multi-mode Schrödinger cat states. In the scheme a -type three-level atom is sent through many cavities filled with coherent fields. The whole system is entangled via the Raman atom-field interaction. Then the detection of the atom leaves the cavity system in a multi-mode cat state. Under certain conditions, such a cat state is identical to a Greenberger-Horne-Zeilinger state and thus can be used to test local realistic theories.
We investigate the dynamics of a two-level atom in a cavity filled with a nonlinear medium. We show that the atom-field detuning δ and the nonlinear parameter χ(3) may be combined to yield a periodic dynamics, allowing the generation of almost exact superpositions of coherent states (Schrödinger cats). By analysing the atomic inversion and the field purity, we verify that any initial atom-field state is recovered at each revival time, and that a coherent field interacting with an excited atom evolves to a superposition of coherent states at each collapse time. We show that a mixed field state (statistical mixture of two coherent states) evolves towards an almost pure field state as well (Schrödinger cat). We discuss the validity of these results by using the field fidelity and the Wigner function.
Abstract Generation of nonclassical states is a necessary requirement for all quantum science and technology protocols. In this regard, Schrödinger cat states, as quantum superpositions of mocroscopically distinguishable coherent states with equal amplitude and opposite phases, have been of great importance in recent years. In this paper, using some appropriate nonlinear optical media, a theoretical scheme is employed to generate various classes of cat-like states with the help of the connection between quantum and nonlinear optics. In fact, we have exploited a single simple method to produce even, odd and also Yurke-Stoler cat-like states by considering different input states such as coherent squeezed, squeezed coherent, photon-added coherent, pair coherent and trio coherent states. To achieve the purpose, we extensively use cross-Kerr interaction and its further generalizations to higher-orders. Projective measurement is the original conception behind the represented approach by which distinct types of nonclassical states are obtained. At last, we pay our attention to the unavoidable effect of field dissipation and show that in most of the above-studied states we may still achieve the cat-like states, however, with attenuated amplitudes.
An exactly solvable case of an interacting Hamiltonian of two bosonic modes is considered to study fundamental properties of the entanglement dynamics for coupled nonlinear oscillators. Such an interaction is of physical importance, either in a two-species Bose–Einstein condensate or in the case of two modes of electromagnetic fields interacting in Kerr media. The time-evolved state is obtained analytically for initial products of two Fock and two coherent states, and the purification times of the subsystems are determined. The possibility of dynamical generation of a quantum superposition state is discussed at such purification times. We also identify the existence of two regimes: the short time, phase spread regime where subsystem entropy rises monotonically and the self-interference regime where it oscillates and a purification phenomenon can be observed. Our results also show that the break time from the first regime to the second one becomes longer, as well as the purification and reversibility times, as the Planck constant becomes much smaller than a typical action in phase space.