Interactions between charged particles and light occur in real space and time, yet quantum field theory usually describes them in momentum space. Whereas this approach is well suited for calculating emission probabilities and cross sections, it is insensitive to spatial and temporal phenomena such as, for instance, radiation formation, quantum coherence, and wave packet spreading. These effects are becoming increasingly important for experiments involving electrons, photons, atoms, and ions, particularly with the advent of attosecond spectroscopy and metrology. Here, we propose a general method for describing the emission of photons in phase space via a Wigner function. Several effects for Cherenkov radiation are predicted, absent in classical realm or in quantum theory in momentum space, such as a finite spreading time of the photon, finite duration of the flash and a quantum shift of the photon arrival time. The photon spreading time turns out to be negative near the Cherenkov angle, the flash duration is defined by the electron packet size, and the temporal shift can be both positive and negative. The characteristic time scales of these effects lie in the atto- and femtosecond ranges, thereby illustrating atomic origins of these macroscopic phenomena. The near-field distribution of the photon field resembles the electron packet shape, thus making ``snapshots'' of the emitter wave function. Our approach can easily be generalized to the other types of radiation and extended to scattering, decay, and annihilation processes, bringing tomographic methods of quantum optics to particle physics.Interactions between charged particles and light occur in real space and time, yet quantum field theory usually describes them in momentum space. Whereas this approach is well suited for calculating emission probabilities and cross sections, it is insensitive to spatial and temporal phenomena such as, for instance, radiation formation, quantum coherence, and wave packet spreading. These effects are becoming increasingly important for experiments involving electrons, photons, atoms, and ions, particularly with the advent of attosecond spectroscopy and metrology. Here, we propose a general method for describing the emission of photons in phase space via a Wigner function. Several effects for Cherenkov radiation are predicted, absent in classical realm or in quantum theory in momentum space, such as a finite spreading time of the photon, finite duration of the flash and a quantum shift of the photon arrival time. The photon spreading time turns out to be negative near the Cherenkov angle, the flash duration is defined by the electron packet size, and the temporal shift can be both positive and negative. The characteristic time scales of these effects lie in the atto- and femtosecond ranges, thereby illustrating atomic origins of these macroscopic phenomena. The near-field distribution of the photon field resembles the electron packet shape, thus making ``snapshots'' of the emitter wave function. Our approach can easily be generalized to the other types of radiation and extended to scattering, decay, and annihilation processes, bringing tomographic methods of quantum optics to particle physics.

quant-pharXiv:2512.21783Dec 29, 2025

Phase-space-density limitation in laser cooling without spontaneous emission

T. Chanelière, D. Comparat, Hans Lignier

We study the possibility to enhance the phase-space density of noninteracting particles submitted to a classical laser field without spontaneous emission. We clearly state that, when no spontaneous emission is present, a quantum description of the particle motion is more reliable than semiclassical description, which can lead to large errors especially if no care is taken to smooth structures smaller than the Heisenberg uncertainty principle. Whatever the definition of position-momentum phase-space density, its gain is severely bounded especially when started from a thermal sample. More precisely, the maximum of the position-momentum phase-space density can only increase by a factor $M$ for $M$ -level particles. This bound comes from a transfer between the external and internal degrees of freedom. Therefore, it is impossible to increase the position-momentum phase-space density in the same internal state.We study the possibility to enhance the phase-space density of noninteracting particles submitted to a classical laser field without spontaneous emission. We clearly state that, when no spontaneous emission is present, a quantum description of the particle motion is more reliable than semiclassical description, which can lead to large errors especially if no care is taken to smooth structures smaller than the Heisenberg uncertainty principle. Whatever the definition of position-momentum phase-space density, its gain is severely bounded especially when started from a thermal sample. More precisely, the maximum of the position-momentum phase-space density can only increase by a factor $M$ for $M$-level particles. This bound comes from a transfer between the external and internal degrees of freedom. Therefore, it is impossible to increase the position-momentum phase-space density in the same internal state.

arXiv:1806.06906Physical Review ADec 27, 20186 citations

How long is a photon?

Sky Nelson-Isaacs

A photon has the strange property that it travels along a null interval with zero proper time, hence its emission and absorption points are, in a sense, a singular event. For their part, the emission and absorption processes have a finite duration which determines the spectral content of the photon. The question in the title points to the conceptual difficulty in `stitching' together these three intervals, which all correspond to the same physical entity but have fundamentally incompatible temporal descriptions. A previously developed model for quantum wavefunction propagation solves this apparent dilemma by formulating the life cycle of a photon in terms of recursive Fourier transforms on dual spaces. Because it doesn't treat space as dependent on time, and it is built on the Fourier transform whose phase is an invariant in special relativity as well as the foundation of the uncertainty principle, the model is a promising candidate framework for making quantum mechanics compatible with relativity. The model proposes to serve as an improved Klein-Gordon equation, or relativistically compatible replacement for Schrödinger's equation.A photon has the strange property that it travels along a null interval with zero proper time, hence its emission and absorption points are, in a sense, a singular event. For their part, the emission and absorption processes have a finite duration which determines the spectral content of the photon. The question in the title points to the conceptual difficulty in `stitching' together these three intervals, which all correspond to the same physical entity but have fundamentally incompatible temporal descriptions. A previously developed model for quantum wavefunction propagation solves this apparent dilemma by formulating the life cycle of a photon in terms of recursive Fourier transforms on dual spaces. Because it doesn't treat space as dependent on time, and it is built on the Fourier transform whose phase is an invariant in special relativity as well as the foundation of the uncertainty principle, the model is a promising candidate framework for making quantum mechanics compatible with relativity. The model proposes to serve as an improved Klein-Gordon equation, or relativistically compatible replacement for Schrödinger's equation.

quant-pharXiv:2610.14088Oct 9, 20260 citations

Photon states and spontaneous emission

P. E. Gordon, N. M. Chase

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoFeb 1, 19854 citations

Mathematical Models of Photons

Imants Bersons, Rita Veilande, Ojārs Balcers

Foundations of PhysicsAug 1, 20231 citation

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-level particles. This bound comes from a transfer between the external and internal degrees of freedom. Therefore, it is impossible to increase the position-momentum phase-space density in the same internal state.