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:0910.2648

Reflectance of a quantum mirror

Pablo L. Saldanha

Published Oct 14, 2009• 0 citations
arXivHTMLPDF

Abstract

The problem of the reflectance of a photon by a metallic mirror whose position is treated quantum mechanically is considered. The interaction between the metallic surface and the light is treated classically. It is shown that the reflectance depends on the spread of the wavefunction describing the reflecting surface along its normal. Considering this decrease on the mirror reflectance, it is shown by first principles that it is impossible to achieve a highly entangled state between a photon and a mirror when the photon can be reflected only once.

DOI
10.48550/arxiv.0910.2648

Related papers

Quantum channels from reflections on moving mirrors

Giulio Gianfelici, Stefano Mancini

Light reflection on a mirror can be thought as a simple physical effect. However if this happens when the mirror moves a rich scenario opens up. Here we aim at analyzing it from a quantum communication perspective. In particular, we study the kind of quantum channel that arises from (Gaussian) light reflection upon an accelerating mirror. Two competing mechanisms emerge in such a context, namely photons production by the mirror's motion and interference between modes. As consequence we find out a quantum amplifier channel and quantum lossy channel respectively below and above a threshold frequency (that depends on parameters determining mirror's acceleration). Exactly at the threshold frequency the channel behaves like a purely classical additive channel, while it becomes purely erasure for large frequencies. In addition the time behavior of the channel is analyzed by employing wave packets expansion of the light field.

arXiv:1704.04635•Scientific Reports•Nov 10, 2017•8 citations

Mirror Geometry as the Physical Origin of Quantum Uncertainty

Andrzej Statowski

This work introduces a geometric reinterpretation of Heisenberg’s uncertainty principle using a mirror as a physical operator that separates conjugate variables into two independent information spaces. Position is encoded in the real space, while momentum is transformed into a reflection angle in the mirror space. This separation preserves quantum mechanics while allowing full state information without violating Heisenberg’s inequality. The model naturally reproduces entanglement as a correlation between the original and reflected states. ─── Conceptual Introduction (for general readers) Quantum mechanics states that position and momentum cannot be measured simultaneously with arbitrary precision. This is usually interpreted as a fundamental limit of nature. In this work, we propose a different view: A mirror creates a second information space. 1. In this space: the position of a particle remains in the real world, the momentum of the particle becomes a reflection angle. Thus: position lives in one space, momentum lives in another, and the conflict between them disappears. The uncertainty principle is not broken — its geometry is changed. This simple idea leads to a powerful reinterpretation of quantum information. ─── Formal Model (for scientific readers) 2.1 Two Hilbert Spaces We define two independent Hilbert spaces: [ \mathcal{H}R \quad \text{(real space)} ] [ \mathcal{H}{R'} \quad \text{(mirror space)} ] The full state becomes: [ |\Psi\rangle = |\psiR\rangle \otimes |\psi{R'} 2. \rangle ] Position and momentum no longer coexist in the same space. ─── 2.2 Mirror Operator The mirror is defined as a linear operator: [ \hat{M}: \mathcal{H}R \rightarrow \mathcal{H} {R'} ] acting as: [ \hat{M}|\psiR(x)\rangle = |\psi{R'}(x')\rangle ] with: [ x' = f(x) ] where (f) is the geometric reflection. ─── 2.3 Momentum Becomes Reflection Angle In mirror space, momentum is replaced by a geometric observable: [ \hat{\theta} = g(\hat{p}) ] Example mapping: [ \theta = \arctan\left(\frac{p}{p_0}\right) ] Thus: position → real space momentum → angle in mirror space And therefore: [ [\hat{x}, \hat{\theta}] = 0 ] This is the mathematical heart of the model. ─── 2.4 Modified Uncertainty Relation Standard quantum mechanics: [ \Delta x \cdot \Delta p \geq \frac{\hbar}{2} ] In the mirror model: [ \Delta x \in \mathcal{H}R ] [ \Delta \theta \in \mathcal{H}{R'} ] Thus: [ \Delta x \cdot \Delta \theta \quad \text{is not constrained by Heisenberg} ] because (x) and (\theta) are not conjugate variables in the same space. ─── 2.5 Entanglement as Mirror Correlation The original and reflected states form a natural entangled pair: [ |\Psi\rangle = \sumi ci |xi\rangle \otimes | \thetai\rangle ] A change in position immediately changes the reflection angle: [ x \rightarrow x + \delta x ] [ \theta \rightarrow \theta + \delta\theta ] This reproduces quantum entanglement as a geometric correlation. ─── Main Conclusion A mirror acts as a geometric operator that: separates conjugate variables into two spaces, 3. 1. transforms momentum into reflection angle, allows full state information without violating Heisenberg, provides a physical model of entanglement, extends quantum mechanics without contradicting it. This is the third pillar of the broader theoretical framework developed in earlier works.

•Sep 10, 2026•0 citations

Decay of an emitting dipole between two parallel mirrors

R. R. Chance, Alfred Prock, R. Silbey

A classical treatment is presented for the modification of the emission rate of an atom between two parallel mirrors. For the case of two perfectly reflecting mirrors, the results are identical with previous treatments of this problem using a quantum mechanical approach. The purely classical treatment has the advantage of being able to treat nonperfectly reflecting mirrors.

The Journal of Chemical Physics•Feb 1, 1975•30 citations

Reflection of Atoms by Light

V. I. Balykin, Vladilen S Letokhov

In the reflection of atoms by evanescent wave the amplitude of the light field can be changed not necessarily adiabatically slow in comparison with relaxation of internal atomic motion. An approach to describe the reflection of atoms by evanescent wave is the dressed state picture. An atomic mirror can be formed also by a focused elliptical laser beam, in which atoms intersect near the waist of the laser beam. A simple evanescent wave allows one to create a high homogeneous field along the surface of an atomic mirror, without a limitation on the intensity of the field in an evanescent wave. The size of an atomic mirror is usually restricted by the laser intensity required by the reflection. There are several processes at the reflection of atom by light which could lead to non ideal properties of the mirror. One of the remarkable properties of an atomic mirror is its ability to reflect atoms in a certain quantum state.

CRC Press eBooks•Apr 23, 2020•0 citations

Temperature effects on fidelity of reflection from absorbing Bragg mirrors

Dalibor Čevizović, Alexei Vladimirovich Chizhov

In the paper, we consider the quantum effects in reflection of the electromagnetic field from an absorbing Bragg mirror. The special emphasis is placed on the study of the influence of thermal noises of the mirror environment on the fidelity of reflection. Taking the incident light field in coherent and Fock states, we show that the fidelity of reflection turns out to be strongly dependent on the quantum state, and on the level of thermal noise and absorption of the mirror.

Journal of Physics Conference Series•Jan 20, 2016•0 citations

Spontaneous emission of atomic dipoles near two-sided semi-transparent mirrors

Dawson, Benjamin, Nicholas Furtak-Wells, Thomas Mann +2 more

Atom-field interactions near optical interfaces have a wide range of applications in quantum technology. Motivated by this, this paper revisits the spontaneous emission of atomic dipoles in the presence of a two sided semi-transparent mirror. First we review the main properties of the quantised electromagnetic field near a semi-transparent mirror. To do so, we employ a quantum mirror image detector method which maps the experimental setup which we consider here onto analogous free space scenarios. We emphasise that the local density of states of the electromagnetic field depends on the reflection rates of both sides of the mirror surface. Hence it is not surprising that also the spontaneous decay rate of an atomic dipole in front of a semi-transparent mirror depends on both reflectance rates. Although the effect which we describe here only holds for relatively short atom-mirror distances, it can aid the design of novel photonics devices.

arXiv:2004.10897•Apr 22, 2020•0 citations
The problem of the reflectance of a photon by a metallic mirror whose position is treated quantum mechanically is considered. The interaction between the metallic surface and the light is treated classically. It is shown that the reflectance depends on the spread of the wavefunction describing the reflecting surface along its normal. Considering this decrease on the mirror reflectance, it is shown by first principles that it is impossible to achieve a highly entangled state between a photon and a mirror when the photon can be reflected only once.
Light reflection on a mirror can be thought as a simple physical effect. However if this happens when the mirror moves a rich scenario opens up. Here we aim at analyzing it from a quantum communication perspective. In particular, we study the kind of quantum channel that arises from (Gaussian) light reflection upon an accelerating mirror. Two competing mechanisms emerge in such a context, namely photons production by the mirror's motion and interference between modes. As consequence we find out a quantum amplifier channel and quantum lossy channel respectively below and above a threshold frequency (that depends on parameters determining mirror's acceleration). Exactly at the threshold frequency the channel behaves like a purely classical additive channel, while it becomes purely erasure for large frequencies. In addition the time behavior of the channel is analyzed by employing wave packets expansion of the light field.
This work introduces a geometric reinterpretation of Heisenberg’s uncertainty principle using a mirror as a physical operator that separates conjugate variables into two independent information spaces. Position is encoded in the real space, while momentum is transformed into a reflection angle in the mirror space. This separation preserves quantum mechanics while allowing full state information without violating Heisenberg’s inequality. The model naturally reproduces entanglement as a correlation between the original and reflected states. ─── Conceptual Introduction (for general readers) Quantum mechanics states that position and momentum cannot be measured simultaneously with arbitrary precision. This is usually interpreted as a fundamental limit of nature. In this work, we propose a different view: A mirror creates a second information space. 1. In this space: the position of a particle remains in the real world, the momentum of the particle becomes a reflection angle. Thus: position lives in one space, momentum lives in another, and the conflict between them disappears. The uncertainty principle is not broken — its geometry is changed. This simple idea leads to a powerful reinterpretation of quantum information. ─── Formal Model (for scientific readers) 2.1 Two Hilbert Spaces We define two independent Hilbert spaces: [ \mathcal{H}R \quad \text{(real space)} ] [ \mathcal{H}{R'} \quad \text{(mirror space)} ] The full state becomes: [ |\Psi\rangle = |\psiR\rangle \otimes |\psi{R'} 2. \rangle ] Position and momentum no longer coexist in the same space. ─── 2.2 Mirror Operator The mirror is defined as a linear operator: [ \hat{M}: \mathcal{H}R \rightarrow \mathcal{H} {R'} ] acting as: [ \hat{M}|\psiR(x)\rangle = |\psi{R'}(x')\rangle ] with: [ x' = f(x) ] where (f) is the geometric reflection. ─── 2.3 Momentum Becomes Reflection Angle In mirror space, momentum is replaced by a geometric observable: [ \hat{\theta} = g(\hat{p}) ] Example mapping: [ \theta = \arctan\left(\frac{p}{p_0}\right) ] Thus: position → real space momentum → angle in mirror space And therefore: [ [\hat{x}, \hat{\theta}] = 0 ] This is the mathematical heart of the model. ─── 2.4 Modified Uncertainty Relation Standard quantum mechanics: [ \Delta x \cdot \Delta p \geq \frac{\hbar}{2} ] In the mirror model: [ \Delta x \in \mathcal{H}R ] [ \Delta \theta \in \mathcal{H}{R'} ] Thus: [ \Delta x \cdot \Delta \theta \quad \text{is not constrained by Heisenberg} ] because (x) and (\theta) are not conjugate variables in the same space. ─── 2.5 Entanglement as Mirror Correlation The original and reflected states form a natural entangled pair: [ |\Psi\rangle = \sumi ci |xi\rangle \otimes | \thetai\rangle ] A change in position immediately changes the reflection angle: [ x \rightarrow x + \delta x ] [ \theta \rightarrow \theta + \delta\theta ] This reproduces quantum entanglement as a geometric correlation. ─── Main Conclusion A mirror acts as a geometric operator that: separates conjugate variables into two spaces, 3. 1. transforms momentum into reflection angle, allows full state information without violating Heisenberg, provides a physical model of entanglement, extends quantum mechanics without contradicting it. This is the third pillar of the broader theoretical framework developed in earlier works.
In the reflection of atoms by evanescent wave the amplitude of the light field can be changed not necessarily adiabatically slow in comparison with relaxation of internal atomic motion. An approach to describe the reflection of atoms by evanescent wave is the dressed state picture. An atomic mirror can be formed also by a focused elliptical laser beam, in which atoms intersect near the waist of the laser beam. A simple evanescent wave allows one to create a high homogeneous field along the surface of an atomic mirror, without a limitation on the intensity of the field in an evanescent wave. The size of an atomic mirror is usually restricted by the laser intensity required by the reflection. There are several processes at the reflection of atom by light which could lead to non ideal properties of the mirror. One of the remarkable properties of an atomic mirror is its ability to reflect atoms in a certain quantum state.
Atom-field interactions near optical interfaces have a wide range of applications in quantum technology. Motivated by this, this paper revisits the spontaneous emission of atomic dipoles in the presence of a two sided semi-transparent mirror. First we review the main properties of the quantised electromagnetic field near a semi-transparent mirror. To do so, we employ a quantum mirror image detector method which maps the experimental setup which we consider here onto analogous free space scenarios. We emphasise that the local density of states of the electromagnetic field depends on the reflection rates of both sides of the mirror surface. Hence it is not surprising that also the spontaneous decay rate of an atomic dipole in front of a semi-transparent mirror depends on both reflectance rates. Although the effect which we describe here only holds for relatively short atom-mirror distances, it can aid the design of novel photonics devices.