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American Journal of Physics

Quantum superpositions and Schrödinger cat states in quantum optics

Christopher C. Gerry, P. L. Knight

Published Oct 1, 1997• 152 citations
Publisher

Abstract

We describe the properties of a quantum system prepared in superpositions of classically distinguishable states. These states, often called Schrödinger cat states, are of great interest at present. We discuss how they may be realized in quantum optics using nonlinear interactions and cavity quantum electrodynamics. We first describe the quantum properties of field states in a cavity, and demonstrate the interference properties which characterize superposition states and discuss how fragile they are in dissipative environments. Finally, we review current experimental approaches which may realize these states.

DOI
10.1119/1.18698

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We describe the properties of a quantum system prepared in superpositions of classically distinguishable states. These states, often called Schrödinger cat states, are of great interest at present. We discuss how they may be realized in quantum optics using nonlinear interactions and cavity quantum electrodynamics. We first describe the quantum properties of field states in a cavity, and demonstrate the interference properties which characterize superposition states and discuss how fragile they are in dissipative environments. Finally, we review current experimental approaches which may realize these states.
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A Schrödinger-cat state is a coherent superposition of macroscopically distinguishable quantum states, in quantum optics usually realized as superposition of coherent states.Protocols to prepare photonic cats have been presented for atomic systems.Here we investigate in what manner and how well the preparation protocols can be transferred to a solid-state platform, namely, a semiconductor quantum-dot-cavity system.In quantum-dotcavity systems there are many disruptive influences like cavity losses, the radiative decay of the quantum dot, and the coupling to longitudinal acoustic phonons.We show that for one of the protocols these influences kill the quantum coherence between the states forming the cat, while for a second protocol a parameter regime can be identified where the essential characteristics of Schrödinger-cat states survive the environmental influences under conditions that can be realized with current equipment.
A full comprehension of the fuzzy boundary between the classical and the quantum world is still lacking. A deeper understanding of the problem can be obtained form the study of the so-called "Schrödinger cat states", i.e. the paradoxical states arising when the superposition principle of quantum mechanics is extended to the macroscopic world. Quantum optics is, up to now, the most studied field for the experimental realization of these states. A survey of all the proposals made for generating and detecting linear superpositions of classically distinguishable states in quantum optical systems is presented. Then, one of the most recent proposals [P. Tombesi and D. Vitali, Phys. Rev. Lett.77, 411 (1996)] is presented in detail and its experimental feasibility discussed.
Schrödinger cat states, representing coherent superpositions of macroscopically distinguishable states, are indispensable nonclassical resources for continuous-variable quantum information processing. Existing generation protocols typically rely on strong nonlinear interactions, complicated control techniques, or engineered dissipation, posing challenges for experimental implementation. Here, we propose a simple measurement-based protocol for generating Schrödinger cat states in a cavity-QED system by combining coherent driving, dispersive atom--cavity interactions, and atomic postselection. The atom--cavity interaction establishes coherent correlations between the atomic and photonic degrees of freedom, while the subsequent atomic postselection projects the cavity field onto a non-Gaussian superposition state with pronounced Wigner negativity. Numerical simulations based on the Lindblad master equation show that the generated Schrödinger cat states remain robust against moderate cavity dissipation. Our results demonstrate that conditional atomic measurements provide an effective and experimentally accessible approach for preparing nonclassical cavity states without relying on strong optical nonlinearities or engineered dissipation.
In cavity-quantum-electrodynamics experiments, two-level Rydberg atoms and single-photon microwave fields can be seen as qubits. Quantum gates based on resonant and dispersive atom-field effects have been realized, which implement various kinds of conditional dynamics between these qubits. We have also studied the interaction between a single atom and coherent fields stored in the cavity. By progressively increasing the number of photons in these fields, we have explored various aspects of the quantum-classical boundary. We have realized a complementarity experiment demonstrating the continuous evolution of an apparatus from a quantum to a classical behaviour. We have also prepared 'Schrödinger-cat'-like states of the field made of a few photons, and observed their decoherence. We present a brief review of these experiments along with a proposal to study larger systems, i.e. coherent fields with more photons. Fundamental limits to the size of mesoscopic superpositions of field states in a cavity will be briefly discussed.