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:2009.09576

Spontaneous transition rates near the focus of a parabolic mirror with identification of the vectorial modes involved

R. Gutiérrez-Jáuregui, Rocío Jáuregui

Published Sep 21, 2020• 0 citations
arXivHTMLPDF

Abstract

Each natural mode of the electromagnetic field within a parabolic mirror exhibits spatial localization and polarization properties that can be exploited for the quantum control of its interaction with atomic systems. The region of localization is not restricted to the focus of the mirror leading to a selective response of atomic systems trapped on its vicinity. We report calculations of the spontaneous emission rates for an atom trapped inside the mirror accounting for all atomic polarizations and diverse trapping regions. It is shown that electric dipole transitions can be enhanced near the focus of a deep parabolic mirror with a clear identification of the few vectorial modes involved. Out of the focus the enhancement vanishes gradually, but the number of relevant modes remains small. Ultimately this represents a quantum electrodynamic system where internal and external degrees of freedom cooperate to maximize a selective exchange and detection of single excitations.

DOI
10.48550/arxiv.2009.09576

Related papers

Spontaneous transition rates near the focus of a parabolic mirror with identification of the vectorial modes involved

R. Gutiérrez-Jáuregui, Rocío Jáuregui

Each natural mode of the electromagnetic field within a parabolic mirror exhibits spatial localization and polarization properties that can be exploited for the quantum control of its interaction with atomic systems. The region of localization is not restricted to the focus of the mirror leading to a selective response of atomic systems trapped on its vicinity. We report calculations of the spontaneous emission rates for an atom trapped inside the mirror accounting for all atomic polarizations and diverse trapping regions. It is shown that electric dipole transitions can be enhanced near the focus of a deep parabolic mirror with a clear identification of the few vectorial modes involved. Out of the focus the enhancement vanishes gradually, but the number of relevant modes remains small. Ultimately this represents a quantum electrodynamic system where internal and external degrees of freedom cooperate to maximize a selective exchange and detection of single excitations.

Scientific Reports•Oct 15, 2020•3 citations

Single-Photon Single-Ion Interaction in Free Space Configuration in Front of a Parabolic Mirror

Magdalena Stobińska, Robert Alicki

The efficient interaction between single photons and single matter objects in free space is of key importance for quantum technologies. An experimental setup for testing this possibility involves single two-level ion trapped at the focus of a parabolic metallic mirror. We study the conditions for the setup, under which the assumption about the free-space mode structure of the radiation field in the vicinity of the atom is justified. In our analysis we apply vectorial properties of light by including the polarization degree of freedom. We look for possible changes in the spontaneous emission rate of the atom resulting from the presence of the parabolic boundary conditions.

arXiv:0905.4014•Open Systems & Information Dynamics•Dec 1, 2012•5 citations

Radiative Response of Atomic Systems Illuminated with Approximate Spherical Vector Waves

F. Camas-Aquino, R. Jáuregui

The natural electromagnetic modes spontaneously emitted by an atom in free space are spherical vector waves (SVWs). Each SVW mode is uniquely linked to a specific dynamical--spherical--multipole--moment of the atomic system. In this work, we introduce a general formalism for evaluating spherical multipole transition rates under different boundary conditions, considering the superposition between a given SVW and the modes resulting from the boundary conditions. This formalism is applied to study the radiative properties of an atomic system trapped near the focus of a 4$π$ optical array. By appropriately selecting the external light field, the juxtaposed lenses of the optical array allow the atom to be illuminated with approximate spherical vector waves. Explicit expressions for the resulting multipole transition rates are presented as a function of the numerical aperture of the lenses. The feasibility of enhancing and inhibiting electric dipole-forbidden transitions using such an array, under current experimental capabilities, is briefly discussed.

arXiv:2605.27558•May 26, 2026•0 citations

QED with a parabolic mirror

G. Alber, József Zsolt Bernád, Magdalena Stobińska +2 more

We investigate the quantum electrodynamics of a single two-level atom located at the focus of a parabolic cavity. We first work out the modifications of the spontaneous emission induced by the presence of this boundary in the optical regime, where the dipole and the rotating-wave approximations apply. Furthermore, the single-photon state that leaves the cavity asymptotically is determined. The corresponding time-reversed single-photon quantum state is capable of exciting the atom in this extreme multimode scenario with near-unit probability. Using semiclassical methods, we derive a photon-path representation for the relevant transition amplitudes and show that it constitutes a satisfactory approximation for a wide range of wavelengths.

arXiv:1305.2488•Physical Review A•Aug 14, 2013•29 citations

Spontaneous Emission of a Polarized Atom in a Medium Between Two Parallel Mirrors

Wang De-Hua, Huang Kai-Yun, Qiang Xu

Using the photon closed orbit theory, the spontaneous emission rate of a polarized atom in a medium between two parallel mirrors is derived and calculated. It is found that the spontaneous emission rate of a polarized atom between the mirrors is related to the atomic position and the polarization direction. The results show that in the vicinity of the mirror, the variation of the spontaneous emission rate depends crucially on the atomic polarization direction. With the increase of the polarization angle, the oscillation in the spontaneous emission rate becomes decreased. For the polarization direction parallel to the mirror plane, the oscillation is the greatest; while for the perpendicular polarization direction, the oscillation is nearly vanished. The agreement between our result and the quantum electrodynamics result suggests the correctness of our calculation. This study further verifies that the atomic spontaneous emission process can be effectively controlled by changing the polarization orientation of the atom.

Communications in Theoretical Physics•Jan 1, 2010•2 citations

Nonlinear Quantum Optics With Structured Light: Tightly Trapped Atoms in the 3D Focus of Vectorial Waves

R. Gutiérrez-Jáuregui, Rocío Jáuregui

Atomic gases tightly trapped near the focus of an electromagnetic wave interact with photons that exhibit a complex structure, displaying strong gradients of field amplitude and local polarization that can lead to topological phase singularities. We illustrate the consequences of this structure on a paradigmatic nonlinear optical process: three-wave mixing. The process begins by proper selection of the pump field, whose spatial structure is tailored to present huge gradients of the EM field that enhance atomic excitations through forbidden transitions. Atoms can then be depopulated via two electric dipole decays in a cascade configuration, thus providing the three necessary waves. The properties of the down-converted photons are conditioned to those of the pump field through phase matching conditions. It is emphasized that the expression of the photons must incorporate both the structure of the vectorial EM modes and the spatial configuration of the atomic trap. Due to the three-dimensional focusing, the slowly varying envelope approximation becomes inadequate when describing the scattered EM field. We discuss an alternative using a Green function formalism valid for any configuration of the field that also allows to identify the phase matching conditions. Spherical vectorial waves exemplify most concepts here discussed, including the possibility of observing nonlinear quantum phenomena at the single photon level.

Frontiers in Physics•Jun 16, 2022•3 citations
Each natural mode of the electromagnetic field within a parabolic mirror exhibits spatial localization and polarization properties that can be exploited for the quantum control of its interaction with atomic systems. The region of localization is not restricted to the focus of the mirror leading to a selective response of atomic systems trapped on its vicinity. We report calculations of the spontaneous emission rates for an atom trapped inside the mirror accounting for all atomic polarizations and diverse trapping regions. It is shown that electric dipole transitions can be enhanced near the focus of a deep parabolic mirror with a clear identification of the few vectorial modes involved. Out of the focus the enhancement vanishes gradually, but the number of relevant modes remains small. Ultimately this represents a quantum electrodynamic system where internal and external degrees of freedom cooperate to maximize a selective exchange and detection of single excitations.
Each natural mode of the electromagnetic field within a parabolic mirror exhibits spatial localization and polarization properties that can be exploited for the quantum control of its interaction with atomic systems. The region of localization is not restricted to the focus of the mirror leading to a selective response of atomic systems trapped on its vicinity. We report calculations of the spontaneous emission rates for an atom trapped inside the mirror accounting for all atomic polarizations and diverse trapping regions. It is shown that electric dipole transitions can be enhanced near the focus of a deep parabolic mirror with a clear identification of the few vectorial modes involved. Out of the focus the enhancement vanishes gradually, but the number of relevant modes remains small. Ultimately this represents a quantum electrodynamic system where internal and external degrees of freedom cooperate to maximize a selective exchange and detection of single excitations.
The efficient interaction between single photons and single matter objects in free space is of key importance for quantum technologies. An experimental setup for testing this possibility involves single two-level ion trapped at the focus of a parabolic metallic mirror. We study the conditions for the setup, under which the assumption about the free-space mode structure of the radiation field in the vicinity of the atom is justified. In our analysis we apply vectorial properties of light by including the polarization degree of freedom. We look for possible changes in the spontaneous emission rate of the atom resulting from the presence of the parabolic boundary conditions.
The natural electromagnetic modes spontaneously emitted by an atom in free space are spherical vector waves (SVWs). Each SVW mode is uniquely linked to a specific dynamical--spherical--multipole--moment of the atomic system. In this work, we introduce a general formalism for evaluating spherical multipole transition rates under different boundary conditions, considering the superposition between a given SVW and the modes resulting from the boundary conditions. This formalism is applied to study the radiative properties of an atomic system trapped near the focus of a 4πππ optical array. By appropriately selecting the external light field, the juxtaposed lenses of the optical array allow the atom to be illuminated with approximate spherical vector waves. Explicit expressions for the resulting multipole transition rates are presented as a function of the numerical aperture of the lenses. The feasibility of enhancing and inhibiting electric dipole-forbidden transitions using such an array, under current experimental capabilities, is briefly discussed.
We investigate the quantum electrodynamics of a single two-level atom located at the focus of a parabolic cavity. We first work out the modifications of the spontaneous emission induced by the presence of this boundary in the optical regime, where the dipole and the rotating-wave approximations apply. Furthermore, the single-photon state that leaves the cavity asymptotically is determined. The corresponding time-reversed single-photon quantum state is capable of exciting the atom in this extreme multimode scenario with near-unit probability. Using semiclassical methods, we derive a photon-path representation for the relevant transition amplitudes and show that it constitutes a satisfactory approximation for a wide range of wavelengths.
Using the photon closed orbit theory, the spontaneous emission rate of a polarized atom in a medium between two parallel mirrors is derived and calculated. It is found that the spontaneous emission rate of a polarized atom between the mirrors is related to the atomic position and the polarization direction. The results show that in the vicinity of the mirror, the variation of the spontaneous emission rate depends crucially on the atomic polarization direction. With the increase of the polarization angle, the oscillation in the spontaneous emission rate becomes decreased. For the polarization direction parallel to the mirror plane, the oscillation is the greatest; while for the perpendicular polarization direction, the oscillation is nearly vanished. The agreement between our result and the quantum electrodynamics result suggests the correctness of our calculation. This study further verifies that the atomic spontaneous emission process can be effectively controlled by changing the polarization orientation of the atom.
Atomic gases tightly trapped near the focus of an electromagnetic wave interact with photons that exhibit a complex structure, displaying strong gradients of field amplitude and local polarization that can lead to topological phase singularities. We illustrate the consequences of this structure on a paradigmatic nonlinear optical process: three-wave mixing. The process begins by proper selection of the pump field, whose spatial structure is tailored to present huge gradients of the EM field that enhance atomic excitations through forbidden transitions. Atoms can then be depopulated via two electric dipole decays in a cascade configuration, thus providing the three necessary waves. The properties of the down-converted photons are conditioned to those of the pump field through phase matching conditions. It is emphasized that the expression of the photons must incorporate both the structure of the vectorial EM modes and the spatial configuration of the atomic trap. Due to the three-dimensional focusing, the slowly varying envelope approximation becomes inadequate when describing the scattered EM field. We discuss an alternative using a Green function formalism valid for any configuration of the field that also allows to identify the phase matching conditions. Spherical vectorial waves exemplify most concepts here discussed, including the possibility of observing nonlinear quantum phenomena at the single photon level.