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Journal of Optics B Quantum and Semiclassical Optics

Generation of mesoscopic quantum superpositions through Kerr-stimulated degenerate downconversion

Matteo G. A. Paris

Published Nov 16, 1999• 20 citations
Publisher

Abstract

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.

DOI
10.1088/1464-4266/1/6/308

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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.
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.
It is shown that a linear superposition of two macroscopically distinguishable optical coherent states (Schroedinger's cat state) can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a free propagating optical cat state with a large coherent amplitude (alpha>2\\alpha>2alpha>2) and high fidelity (F>0.99F>0.99F>0.99). In contrast to all previous schemes to generate such a state, our scheme does not need photon resolving measurements nor Kerr-type nonlinear interactions.
A method for producing macroscopic quantum superposition states (generally known as Schr\"odinger cat) states for optical fields is presented. The proposed method involves two modes of the field interacting dispersively in a Kerr medium where one of the modes is an arm of a Mach-Zehnder interferometer and the other mode is external to it. If the external mode initially contains a macroscopic quantum state, such as a coherent state, and the vacuum and a single photon state are the inputs to the interferometer, the external field state becomes entangled with the number states associated with the two paths of the interferometer. Selective measurement at the output ports of the interferometer project the external mode into the desired cat states. It is pointed out that the method can also be used to generate cat states out of multimode states initially containing correlations.
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.
Any nonlinear interaction, in principle, can produce non-classical state. The Kerr nonlinearity seems to be the simplest one. Since papers [1-3], it seemed that as the squeezed states, as the Schriidinger cat ones can be produced by the self-modulation. The squeezing was really observed [ 3] in such a scheme. As for cats, Ref. {4,5] mention the large distance of propagation and linear absorption as factors which make the experimental realization unlike. Note that neither the large distance of propagation nor the linear absorption are fundamental reasons why the Schrödinger cat cannot be obtained by such a manner.