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Physical Review A

Quantum entanglement in photon-atom scattering

Kam Wai Clifford Chan, C. K. Law, Joseph H. Eberly

Published Aug 27, 2003• 54 citations
Publisher

Abstract

Joint atom-photon states can become nonseparably entangled by momentum conservation in scattering events. The consequences are open for observation in interference experiments in which one particle is used to monitor the evolution of the other. We have previously quantified the degree of available recoil entanglement in spontaneous emission, and present here the extensions to Rayleigh scattering and Raman scattering, with an emphasis on the similarity among the three cases. It is found that such scattering processes have the potential to create a higher degree of entanglement between the scattered photon and the recoiled atom than any reported to date.

DOI
10.1103/physreva.68.022110

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•Jan 1, 2001•90 citations
Joint atom-photon states can become nonseparably entangled by momentum conservation in scattering events. The consequences are open for observation in interference experiments in which one particle is used to monitor the evolution of the other. We have previously quantified the degree of available recoil entanglement in spontaneous emission, and present here the extensions to Rayleigh scattering and Raman scattering, with an emphasis on the similarity among the three cases. It is found that such scattering processes have the potential to create a higher degree of entanglement between the scattered photon and the recoiled atom than any reported to date.
Abstract Quantum entanglement is a basic ingredient in the formalism of quantum mechanics and was held by Heisenberg as its most emblematic feature. But although all its consequences could be foreseen from the start, it took half a century before experiments were carried out to test its more intriguing predictions. One reason was that sufficiently sensitive tools, like lasers, were not yet available, but there was also a lack of interest and imagination among theoreticians, who did not realize its full potential. When experiments were finally realized and opened a ‘weird and ghostlike quantum world’, they were first met with surprise and doubt. In the first experiments on entanglement it was purposely created (using chain-decays or down-conversion), but entanglement is actually a ubiquitous phenomenon appearing in most physical processes, although surviving over so short time-scales that it is usually not observed. The present work deals with ‘measurement-induced entanglement’ in scattering, and starts with a process where its effects can actually be studied in the sub-femtosecond range in a time-resolved manner, the Compton scattering of neutrons. Based on results from this method, the conditions for observing similar effects in other scattering processes are discussed. First, the mechanisms for entanglement creation by a scattering particle are mentioned, then the conditions for observing measurable consequences of it on scattering cross-sections: a very limited number of scattering centers, large zero-point motions of the scatterers and no strong interaction with environment which leads to decoherence.
We suggest a quantum description of Rayleigh light scattering on atoms. We show that an entangled state of the excited atom and the incident photon is formed during the scattering. Due to entanglement, a photon is never completely absorbed by the atom. The formation of the scattering spectrum is considered as a relaxation of incident photons to the reservoir of free space modes that are in thermal equilibrium. Additional excitations of the reservoir modes occurring during scattering are treated as scattered light. We show that even if the frequency of incident photons is incommensurate with an atomic transition frequency, the scattered light spectrum has a maximum at the frequency of incident photons. In addition, the linewidth of the scattered light is much smaller than that of the spontaneous emission of a single atom. Therefore, the process can be considered as elastic.
Spontaneous emission of a photon by an atom is described theoretically in three dimensions with the initial wave function of a finite-mass atom taken in the form of a finite-size wave packet. Recoil and wave-packet spreading are taken into account. The total atom-photon wave function is found in the momentum and coordinate representations as the solution of an initial-value problem. The atom-photon entanglement arising in such a process is shown to be closely related to the structure of atom and photon wave packets which can be measured in the coincidence and single-particle schemes of measurements. Two predicted effects, arising under the conditions of high entanglement, are anomalous narrowing of the coincidence wave packets and, under different conditions, anomalous broadening of the single-particle wave packets. Fundamental symmetry relations between the photon and atom single-particle and coincidence wave-packet widths are established. The relationship with the famous scenario of Einstein-Podolsky-Rosen is discussed.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ‘‘meter’’ measuring the other. We have performed a ‘‘quantum nondemolition’’ measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (‘‘Schrodinger cat’’) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrodinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.