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Fortschritte der Physik

Generating Entangled Schrödinger Cat States within a Parametric Oscillator

David Vitali, M. Fortunat, P. Tombesi, F. De Martini

Published May 1, 2000• 4 citations
Publisher

Abstract

We suggest a variant of the proposed experiment for the generation of a new kind of mesoscopic superposition quantum states, using two coupled parametric down-converter nonlinear crystals [F. De Martini, Phys. Rev. Lett. 81 (1998) 2842]. We study the parametric oscillator case and find that an entangled Schr�dinger-cat type state of two cavities, whose mirrors are placed along the output beams of the nonlinear crystals, can be realized under suitable conditions.

DOI
10.1002/(sici)1521-3978(200005)48:5/7<437::aid-prop437>3.0.co;2-g

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We suggest a variant of the proposed experiment for the generation of a new kind of mesoscopic superposition quantum states, using two coupled parametric down-converter nonlinear crystals [F. De Martini, Phys. Rev. Lett. 81 (1998) 2842]. We study the parametric oscillator case and find that an entangled Schr�dinger-cat type state of two cavities, whose mirrors are placed along the output beams of the nonlinear crystals, can be realized under suitable conditions.
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.
Non-Gaussian continuous-variable states play a central role both in the foundations of quantum theory and for emergent quantum technologies. In particular, ``cat states,'' i.e., two-component macroscopic quantum superpositions, embody quantum coherence in an accessible way and can be harnessed for fundamental tests and quantum information tasks alike. Degenerate optical parametric oscillators can naturally produce single-mode cat states and thus represent a promising platform for their realization and harnessing. We show that a dissipative coupling between degenerate optical parametric oscillators extends this to two-mode entangled cat states, i.e., two-mode entangled cat states are naturally produced under such dissipative coupling. While overcoming single-photon loss still represents a major challenge towards the realization of sufficiently pure single-mode cat states in degenerate optical parametric oscillators, we show that the generation of two-mode entangled cat states under such dissipative coupling can then be achieved without additional hurdles. We numerically explore the parameter regime for the successful generation of transient two-mode entangled cat states in two dissipatively coupled degenerate optical parametric oscillators. To certify the cat-state entanglement, we employ a tailored, variance-based entanglement criterion, which can robustly detect cat-state entanglement under realistic conditions.
We theoretically propose a method for on-demand generation of traveling Schr\"odinger cat states, namely, quantum superpositions of distinct coherent states of traveling fields. This method is based on deterministic generation of intracavity cat states using a Kerr-nonlinear parametric oscillator (KPO) via quantum adiabatic evolution. We show that the cat states generated inside a KPO can be released into an output mode by dynamically controlling the parametric pump amplitude. We further show that the quality of the traveling cat states can be improved by using a shortcut-to-adiabaticity technique.
We present an alternative scheme to achieve Schrödinger cat states in a strong coupling hybrid cavity optomechanical system. Under the single-photon strong-coupling regime, the interaction between the atom-cavity-oscillator system can induce the mesoscopic mechanical oscillator to Schrödinger cat states. Comparing to previous schemes, the proposed proposal consider the second order approximation on the Lamb-Dicke parameter, which is more universal in the experiment. Numerical simulations confirm the validity of our derivation.
In this paper, we propose a new theoretical scheme for generating a macroscopic Schrödinger cat state of a mechanical oscillator in a hybrid optomechanical system where a beam of two-level atoms passes through the cavity. In the model under consideration, the cavity field couples to the macroscopic mirror through the optomechanical interaction while it couples to the atom through a generalized Jaynes–Cummings interaction that involves the cavity-mode structure. The motion of the mirror modifies the cavity-mode function and therefore modulates the atom-field interaction, leading to the three-mode atom-field-mirror coupling or, equivalently, polariton-mirror coupling in a dressed picture. This interaction induces a controllable anharmonicity in the energy spectrum of the mechanical oscillator, which provides the possibility of generating a superposition of two time-dependent coherent states of the mechanical oscillator just by performing a conditional measurement on the internal states of the atoms exiting the optomechanical cavity. We also investigate the tripartite atom-field-mirror entanglement, which is controllable by adjusting the parameters of the system. In addition, we explore the effects of the mechanical dissipation and thermal noise on the tripartite quantum correlation in the system as well as the generated mechanical superposition state.