Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0412107 · Physical Review A

Spontaneous emission of a photon: Wave-packet structures and atom-photon entanglement

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

Published Sep 22, 2005• 79 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.72.032110

Related papers

High-entanglement regimes in the Weisskopf-Wigner theory for spontaneous decay

J. C. C. Capella, Alejandro Fonseca, Pablo L. Saldanha +1 more

In this work we review the Weisskopf-Wigner formalism for spontaneous emission considering the spatial modes of light as well as external atomic degrees of freedom, which we introduce in the theory by modeling the atom as a wave packet in momentum space with a given initial uncertainty. We perform a purity calculation in order to quantify the entanglement encoded in the momentum variables of the atom-photon system. Our purity calculations reveal two high-entanglement regimes depending on the initial atomic momentum uncertainty: (1) the Recoil entanglement regime (which arises in the small momentum uncertainty region) where recoil effects dominate the mechanisms that originate entanglement, and (2) the Doppler entanglement regime (in the large momentum uncertainty region) where homogeneous Doppler shifts in the emitted photon's frequency play the fundamental part in the build up of quantum correlations in the system. Physical considerations are made to explain the nature of each entanglement regime as well as provide their respective thresholds.

arXiv:2505.19979•Physical Review A•Oct 1, 2025•0 citations

Entanglement and Wave Packet Structures in Photoionization and Other De- cay Processes of Bipartite Systems

Mikhail Vladimirovich Fedorov

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.

CRC Press eBooks•Mar 27, 2009•0 citations

Space-time description of photon emission from an atom

Ole Keller

Starting from the postulate that the electromagnetic field appearing in the transverse set of microscopic Maxwell-Lorentz equations governing field-matter interactions, properly normalized, can be looked upon as describing one-photon-emission and -absorption processes in space and time, a first-quantized initiation of photon emission by a single atom is presented. The wave function for the emerging photon is introduced as a six-vector object constructed from the complex analytical signals of the Riemann-Silberstein vectors belonging to opposite photon helicities. When the atom is no longer electrodynamically active, the emitted photon is described in first quantization by the so-called energy wave function well known for photons in free space. From the momentum representation of the emerging photon wave function a condition on the analytical part of the transverse atomic current density is established which ensures that precisely one photon is emitted. A propagator description of the emerged photon dynamics in the coordinate representation is established. The photon propagator is introduced as a two-component spinor, where upper and lower tensor components are constructed, respectively, from positive and negative helicity combinations of the propagators describing the time-space evolution of the transverse electric and magnetic fields. It is shown that the emission region for the photon coincides with the region in space where the transverse atomic current density is nonvanishing. For a photon emitted in an electric dipole transition the emission region essentially is the near-field zone of the atom, and this zone therefore determines the initial (and best) spatial confinement of the photon. The photon emerging from an atom active for a finite time necessarily is of the polychromatic sort and the associated wave packet essentially is confined between spherical shells moving outwards with the vacuum speed of light. To illustrate the main principles of the fundamental theory in a heuristic fashion we apply it to a study of the emission of a one-photon sinusoidal wavetrain from a pointlike atom. It is found that the atomic current density needed to create just one photon is independent of the oscillation period in the train and thus depends only on the number of periods in the wave train. An explicit expression for the one-photon energy is derived, and it is shown that only for extremely short pulse trains pronounced deviations from the textbook result, $E=\ensuremath{\Elzxh}{\ensuremath{\omega}}_{0},$ occur. The radial energy flow in the coupled atom-photon system in the near-field zone of the atom is investigated, and the cycle-averaged outwards energy transport carried by the emerging photon in a given distance from the atom is determined.

Physical Review A•Jul 18, 2000•44 citations

Localization of the relative position of two atoms induced by spontaneous emission

L. Zheng, C. Li, Yahui Li +1 more

We reexamine the back-action of emitted photons on the wave packet evolution about the relative position of two cold atoms. We show that photon recoil resulting from the spontaneous emission can induce the localization of the relative position of the two atoms through the entanglement between the spatial motion of individual atoms and their emitted photons. The obtained result provides a more realistic model for the analysis of the environment-induced localization of a macroscopic object.

arXiv:quant-ph/0501080•Physical Review A•Jun 9, 2005•9 citations

Quantum Optics of Atomic Wave-Packets

Kazimierz Rza̧żewski, Luis Plaja, Luis Pumares +2 more

Recent progress in production and control of the atomic wave-packets calls for re-examination of the most fundamental quantum optical processes.We have examined the evolution of the atomic wave-packet resonantly driven by the monochromatic laser beam and the spontaneous emission from an extended atom.We stress the role of Doppler shifts in the dephasing of the atomic dipole.New echects of single laser pulse photon echo and homogeneous Doppler modification of the emission line are discussed.

Acta Physica Polonica A•Jul 1, 1994•3 citations

Spontaneous and stimulated emissions of a preformed quantum free-electron wave function

Yiming Pan, Avraham Gover

Do the prior history and the wave-packet size and form of a free electron have a physical effect in its interaction with light? Here we answer these fundamental questions on the interpretation of the electron quantum wave function by analyzing spontaneous and stimulated emissions of a quantum electron wave packet, interacting with a general, quantized radiation field. For coherent radiation (Glauber state), we confirm that stimulated emission and absorption of photons depends on the preinteraction-history-dependent size, exhibiting spectral cutoff when it exceeds the interacting radiation wavelength. Furthermore, stimulated emission of an optically modulated electron wave packet has a characteristic harmonic emission spectrum beyond the cutoff, which depends on the modulation features. In either case, there is no wave-packet-dependent radiation of the Fock state, and particularly the vacuum state spontaneous emission is wave-packet independent. The classical-to-quantum transition of radiation from the point-particle to the plane-wave limits, and the effects of wave-packet modulation indicate a way of measuring the wave-packet size of a single electron wave function, and suggest an alternative direction for exploring light-matter interaction.

arXiv:1805.08210•Physical Review A•May 7, 2019•65 citations
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.
In this work we review the Weisskopf-Wigner formalism for spontaneous emission considering the spatial modes of light as well as external atomic degrees of freedom, which we introduce in the theory by modeling the atom as a wave packet in momentum space with a given initial uncertainty. We perform a purity calculation in order to quantify the entanglement encoded in the momentum variables of the atom-photon system. Our purity calculations reveal two high-entanglement regimes depending on the initial atomic momentum uncertainty: (1) the Recoil entanglement regime (which arises in the small momentum uncertainty region) where recoil effects dominate the mechanisms that originate entanglement, and (2) the Doppler entanglement regime (in the large momentum uncertainty region) where homogeneous Doppler shifts in the emitted photon's frequency play the fundamental part in the build up of quantum correlations in the system. Physical considerations are made to explain the nature of each entanglement regime as well as provide their respective thresholds.
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.
Starting from the postulate that the electromagnetic field appearing in the transverse set of microscopic Maxwell-Lorentz equations governing field-matter interactions, properly normalized, can be looked upon as describing one-photon-emission and -absorption processes in space and time, a first-quantized initiation of photon emission by a single atom is presented. The wave function for the emerging photon is introduced as a six-vector object constructed from the complex analytical signals of the Riemann-Silberstein vectors belonging to opposite photon helicities. When the atom is no longer electrodynamically active, the emitted photon is described in first quantization by the so-called energy wave function well known for photons in free space. From the momentum representation of the emerging photon wave function a condition on the analytical part of the transverse atomic current density is established which ensures that precisely one photon is emitted. A propagator description of the emerged photon dynamics in the coordinate representation is established. The photon propagator is introduced as a two-component spinor, where upper and lower tensor components are constructed, respectively, from positive and negative helicity combinations of the propagators describing the time-space evolution of the transverse electric and magnetic fields. It is shown that the emission region for the photon coincides with the region in space where the transverse atomic current density is nonvanishing. For a photon emitted in an electric dipole transition the emission region essentially is the near-field zone of the atom, and this zone therefore determines the initial (and best) spatial confinement of the photon. The photon emerging from an atom active for a finite time necessarily is of the polychromatic sort and the associated wave packet essentially is confined between spherical shells moving outwards with the vacuum speed of light. To illustrate the main principles of the fundamental theory in a heuristic fashion we apply it to a study of the emission of a one-photon sinusoidal wavetrain from a pointlike atom. It is found that the atomic current density needed to create just one photon is independent of the oscillation period in the train and thus depends only on the number of periods in the wave train. An explicit expression for the one-photon energy is derived, and it is shown that only for extremely short pulse trains pronounced deviations from the textbook result, $E=\ensuremath{\Elzxh}{\ensuremath{\omega}}_{0},$ occur. The radial energy flow in the coupled atom-photon system in the near-field zone of the atom is investigated, and the cycle-averaged outwards energy transport carried by the emerging photon in a given distance from the atom is determined.
Do the prior history and the wave-packet size and form of a free electron have a physical effect in its interaction with light? Here we answer these fundamental questions on the interpretation of the electron quantum wave function by analyzing spontaneous and stimulated emissions of a quantum electron wave packet, interacting with a general, quantized radiation field. For coherent radiation (Glauber state), we confirm that stimulated emission and absorption of photons depends on the preinteraction-history-dependent size, exhibiting spectral cutoff when it exceeds the interacting radiation wavelength. Furthermore, stimulated emission of an optically modulated electron wave packet has a characteristic harmonic emission spectrum beyond the cutoff, which depends on the modulation features. In either case, there is no wave-packet-dependent radiation of the Fock state, and particularly the vacuum state spontaneous emission is wave-packet independent. The classical-to-quantum transition of radiation from the point-particle to the plane-wave limits, and the effects of wave-packet modulation indicate a way of measuring the wave-packet size of a single electron wave function, and suggest an alternative direction for exploring light-matter interaction.