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arXiv:quant-ph/0312119 · Physical Review A

Packet narrowing and quantum entanglement in photoionization and photodissociation

Mikhail Vladimirovich Fedorov, Maxim A. Efremov, Alexey E. Kazakov, Kam Wai Clifford Chan, C. K. Law, Joseph H. Eberly

Published May 26, 2004• 109 citations
arXivHTMLPDF

Abstract

The narrowing of electron and ion wave packets in the process of photoionization is investigated, with the electron-ion recoil taken fully into account. Packet localization of this type is directly related to entanglement in the joint quantum state of the electron and ion, and to Einstein-Podolsky-Rosen localization. Experimental observation of such packet-narrowing effects is suggested via coincidence registration by two detectors, with a fixed position of one and varying position of the other. A similar effect, typically with an enhanced degree of entanglement, is shown to occur in the case of photodissociation of molecules.

DOI
10.1103/physreva.69.052117

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The narrowing of electron and ion wave packets in the process of photoionization is investigated, with the electron-ion recoil taken fully into account. Packet localization of this type is directly related to entanglement in the joint quantum state of the electron and ion, and to Einstein-Podolsky-Rosen localization. Experimental observation of such packet-narrowing effects is suggested via coincidence registration by two detectors, with a fixed position of one and varying position of the other. A similar effect, typically with an enhanced degree of entanglement, is shown to occur in the case of photodissociation of molecules.
A structure of wave packets arising in the process of a bipartite system decay is investigated and its connection with entanglement of quantum states is discussed. As long as the effect of wave packet spreading can be ignored, the ratio R of the single-particle to coincidence wave packet widths is shown to coincide with the degree of entanglement determined by the Schmidt correlation number K. Mathematically single-particle and coincidence schemes correspond to absolute and conditional probability densities. Coordinate and momentum wave-packets for each particle are compared. A series of reciprocity and identity relations between the corresponding wave packet widths is found to occur. Uncertainty relations following from these relations are found. The coordinate and momentum uncertainty products for each particle are shown to be related directly to the degree of entanglement K: the single-particle and coincidence uncertainty products are shown to be, correspondingly, ∼ K ≥ 1 and ∼ 1/K ≤ 1. A series of specific examples are considered.
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.
The problem of two-particle breakup involving Einstein- Podolsky-Rosen entanglement is studied in this thesis. One or both of the fragments in the breakup can be massive. We have examined photoionization, photodissociation, spontaneous emission, Raman scattering and Rayleigh scattering, and identified a generic control parameter that determines the degree of entanglement in these physical systems. This control parameter allows one to find the conditions to achieve very high entanglement. Similarities among the systems are also found in terms of entanglement and wave packet localization, while subtle differences in the evolution of wave packets due to the nature of the participating particles are observed. With the help of a Gaussian model, a concrete relation between entanglement and experimentally measurable quantities is established. The model also explains the apparent entanglement loss in the evolution of wave packets in free space through the notion of phase entanglement, and relates the Heisenberg uncertainty relation and Einstein- Podolsky-Rosen conditional uncertainty to the Schmidt number. It is conjectured that the Schmidt number serves as the upper or lower bound to the uncertainty relations for a generic bipartite breakup.
The two-particle wave function of neutrino and recoil nucleus is found as a solution of an initial-value problem in the far zone for a time longer than the electron capture decay lifetime of a hydrogenlike ion. The neutrino-recoil entanglement arising in such a process is a consequence of the momentum conservation and is closely related to the wave packet structure of the state. Because of neutrino mixing, the joint wave packet involves the coherent superposition of the neutrino mass eigenstate packets. This is the new physical realization of the Einstein-Podolsky-Rosen thought experiment, which has no analogue in quantum optics and quantum informatics. A class of possible experiments for the registration of a neutrino and a recoil nucleus is proposed. It is shown that, due to spatial correlations, neutrino and recoil oscillations can be observed in the coincidence experiment.
In this paper, we shed new light on the molecular photoionization of a diatomic molecule. We will elaborate the differences and analogy between a quantum optical and light–matter interaction approach in a study of K-shell photoionization of N 2 in which the photoelectron and the subsequently emitted Auger electron are both measured in coincidence in the body fixed frame of the molecule. The two electrons form an entangled state inside a double slit. By changing the photon energy we create different types of interference in the photoelectron and the Auger electron wave.
Einstein-Podolsky-Rosen (EPR) entanglement introduced in 1935 deals with two particles that are entangled in their positions and momenta. Here we report the first experimental demonstration of EPR position-momentum entanglement of narrow-band photon pairs generated from cold atoms. By using two-photon quantum ghost imaging and ghost interference, we demonstrate explicitly that the narrow-band photon pairs violate the separability criterion, confirming EPR entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons. Our new source of EPR-entangled narrow-band photons is expected to play an essential role in spatially multiplexed quantum information processing, such as, storage of quantum correlated images, quantum interface involving hyperentangled photons, etc.