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Physical Review Letters

Unruh and Cherenkov Radiation from a Negative Frequency Perspective

Anatoly A. Svidzinsky, Arash Azizi, J. Ben-Benjamin, Marlan O. Scully, William George Unruh

Published Feb 12, 2021• 25 citations
Publisher

Abstract

A ground-state atom uniformly accelerated through the Minkowski vacuum can become excited by emitting an Unruh-Minkowski photon. We show that from the perspective of an accelerated atom, the sign of the frequency of the Unruh-Minkowski photons can be positive or negative depending on the acceleration direction. The accelerated atom becomes excited by emitting an Unruh-Minkowski photon which has negative frequency in the atom's frame, and decays by emitting a positive-frequency photon. This leads to interesting effects. For example, the photon emitted by accelerated ground-state atom cannot be absorbed by another ground-state atom accelerating in the same direction, but it can be absorbed by an excited atom or a ground-state atom accelerated in the opposite direction. We also show that similar effects take place for Cherenkov radiation. Namely, a Cherenkov photon emitted by an atom cannot be absorbed by another ground-state atom moving with the same velocity, but can be absorbed by an excited atom or a ground-state atom moving in the opposite direction.

DOI
10.1103/physrevlett.126.063603

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hep-thCross-listedarXiv:2604.09456•Apr 13, 2026
A ground-state atom uniformly accelerated through the Minkowski vacuum can become excited by emitting an Unruh-Minkowski photon. We show that from the perspective of an accelerated atom, the sign of the frequency of the Unruh-Minkowski photons can be positive or negative depending on the acceleration direction. The accelerated atom becomes excited by emitting an Unruh-Minkowski photon which has negative frequency in the atom's frame, and decays by emitting a positive-frequency photon. This leads to interesting effects. For example, the photon emitted by accelerated ground-state atom cannot be absorbed by another ground-state atom accelerating in the same direction, but it can be absorbed by an excited atom or a ground-state atom accelerated in the opposite direction. We also show that similar effects take place for Cherenkov radiation. Namely, a Cherenkov photon emitted by an atom cannot be absorbed by another ground-state atom moving with the same velocity, but can be absorbed by an excited atom or a ground-state atom moving in the opposite direction.
Free quantum field theory in flat space-time is often believed to be well established, holding no surprises. We hope, by the end of this paper, to have demonstrated that surprises still exist. For example, we will show that a uniformly accelerated atom in Minkowski space-time emits entangled photon pairs in a squeezed state which mimics entanglement of the Minkowski vacuum in that the entanglement is between Minkowski modes which are dominantly in opposite causal wedges of the space-time. Similar emission of photon pairs occurs if an atom is held above the black hole event horizon. Namely, a ground-state atom becomes excited by emitting a ``negative'' -energy photon under the horizon and then spontaneously decays back to the ground state by emitting a positive-energy photon outside the horizon, which propagates away from the black hole.
Emission of photons by atoms can occur into modes which extend into a region causally disconnected with the emitter.For example, a uniformly accelerated ground-state atom emits a photon into the Unruh-Minkowski mode which is exponentially larger in the causally disconnected region.This makes an impression that photon emission is acausal.Here we show that conventional quantum optical analysis yields that a detector atom will not detect the emitted photon in the region noncausally connected with the emitter.However, joint excitation probability of atoms in the causally disconnected regions can be correlated due to entanglement of Minkowski vacuum and be much larger than the product of independent excitation probabilities.Moreover, atoms uniformly accelerated in the same Rindler wedge cannot become simultaneously excited without changing the state of the field, that is, the Unruh-Minkowski photon emitted by one atom cannot be absorbed by the other atom.We discuss examples demonstrating interesting features of Minkowski vacuum entanglement.
Recently, a new physical picture for the spontaneous excitation of a uniformly accelerated two-level atom has been put forward [1]. Following a quantum optical approach it is based on the distinction of the two competing mechanisms which operate to excite an atom in the quantum vacuum: vacuum fluctuations and radiation reaction. Vacuum fluctuations tend to excite an atom in its ground state and de-excite it in an excited state. On the other hand, radiation reaction leads always to a loss of internal excitation energy. For an inertial atom in the ground state, the two contributions cancel exactly, so that a very sublime balance between vacuum fluctuations and radiation reaction prevents the spontaneous excitation of the atom [2]. If the atom is in the excited state, both contribution add up to the well-known spontaneous emission rate. It has been shown in [1] that uniform acceleration will disturb this balance. Spontaneous transitions from the ground state to the excited state become possible: the Unruh effect [3].
We find that uniformly accelerated motion of a mirror yields excitation of a static two-level atom with simultaneous emission of a real photon. This occurs because of virtual transitions with probability governed by the Planck factor involving the photon frequency ν and the Unruh temperature. The result is different from the Unruh radiation of an accelerated atom, which is governed by the frequency of the atom, ω, rather than frequency of the emitted photon. We also find that the excitation probability oscillates as a function of the atomic position because of interference between contributions from the waves incident on and reflected from the mirror.
We consider a gedanken experiment with a beam of atoms in their ground state that are accelerated through a single-mode cavity. We show that taking into account of the ``counterrotating'' terms in the interaction Hamiltonian leads to the excitation of an atom with simultaneous emission of a photon into a field mode. In free space, when the atom-field interaction is turning on/off adiabatically, the only nonadiabatic effect that causes the excitation is the time-dependent Doppler shift. The resulting ratio of emission and absorption probabilities is exponentially small and is described by the Unruh factor. In the opposite case of rapid turn on of the interaction on the cavity boundaries the above ratio is much greater and radiation is produced with an intensity which can exceed the intensity of radiation in free space by many orders of magnitude. In both cases real photons are produced. The cavity field at steady state has a thermal density matrix. However, under some conditions laser gain is possible. We present a detailed discussion of how the acceleration of atoms affects the generated cavity field in different situations. We identify a common physical mechanism behind the Unruh effect and similar QED radiation processes.
We compute the quantum radiation emitted by wavepackets of relativistic single electrons, both at rest and undergoing uniform acceleration in the Minkowski vacuum of the electromagnetic field. We find that the cubic terms in the original nonlinear action of electrodynamics should be considered in obtaining the quantum radiation to the leading order. We show that the quantum radiation from a single-electron wavepacket at rest vanishes exactly. For a uniformly accelerated electron, the quantum radiated power has secular growth in the long-time regime. We demonstrate that this secular growth has a classical interpretation, and argue that the resummed quantum radiation at late times would not diverge. Regarding experimental proposals for the detection of the Unruh effect from the quantum radiation in the `blind spots' of classical radiation we ascertain that quantum corrections in the two blind spots are fully contributed by the transverse deviation correlators, where the dominant contributions are irrelevant to the Unruh effect in electron microscopes.