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Asymmetric excitation of left- vs right-handed photons in accelerating waveguides

Adrian del Rio

TL;DR

This work demonstrates a quantum anomaly for electric-magnetic duality in Maxwell theory confined inside a helically accelerating waveguide. By employing a covariant phase-space quantization with duality-preserving boundary conditions and a self-dual formulation, the authors construct in/out Fock spaces and perform a Bogoliubov analysis to track helicity mixing. The key result is a nonzero vacuum expectation value of the duality charge, \langle in|:Q:|in\rangle, arising from frame-dragging and spectral asymmetry between right- and left-handed photon modes, given by a topological sum over mode sets. The finding provides a concrete analogue of the axial anomaly for spin-1 fields in flat spacetime with noninertial boundaries and suggests experimental routes, including analogue gravity platforms and squeezed-state enhancements, to detect a helicity imbalance of vacuum photons.

Abstract

The electromagnetic duality symmetry of Maxwell's equations in vacuum implies that the circular polarization $Q$ of classical electromagnetic waves is conserved. In quantum field theory, the normal-ordered operator $\hat Q$ represents the difference between the number operators of right- and left-handed photons. Previous studies have shown that its expectation value is not conserved for observers propagating in a gravitational field. Here, we show that this Noether symmetry can also be realized in empty waveguides with duality-preserving boundary conditions, and we quantize the source-free Maxwell theory inside a long, cylindrical waveguide undergoing both linear and rotational acceleration from rest. In the vacuum $|0\rangle$ associated to inertial observers, we find that the expectation value $\langle 0| \hat Q |0\rangle $ fails to be conserved for observers co-moving with the waveguide. In particular, frame-dragging effects induce a spectral asymmetry between the right- and left-handed field modes at late times. As a consequence, accelerated detectors co-moving with the rotating waveguide can detect photon-pair excitations from the quantum vacuum, exhibiting an imbalance between opposite helicity modes. This is a relativistic quantum effect, which shows that the classical conservation law associated with duality symmetry is broken in the quantum theory even in flat spacetime, provided we work with non-inertial systems. Our analysis provides a concrete proof of concept for testing this effect in analogue gravity platforms.

Asymmetric excitation of left- vs right-handed photons in accelerating waveguides

TL;DR

This work demonstrates a quantum anomaly for electric-magnetic duality in Maxwell theory confined inside a helically accelerating waveguide. By employing a covariant phase-space quantization with duality-preserving boundary conditions and a self-dual formulation, the authors construct in/out Fock spaces and perform a Bogoliubov analysis to track helicity mixing. The key result is a nonzero vacuum expectation value of the duality charge, \langle in|:Q:|in\rangle, arising from frame-dragging and spectral asymmetry between right- and left-handed photon modes, given by a topological sum over mode sets. The finding provides a concrete analogue of the axial anomaly for spin-1 fields in flat spacetime with noninertial boundaries and suggests experimental routes, including analogue gravity platforms and squeezed-state enhancements, to detect a helicity imbalance of vacuum photons.

Abstract

The electromagnetic duality symmetry of Maxwell's equations in vacuum implies that the circular polarization of classical electromagnetic waves is conserved. In quantum field theory, the normal-ordered operator represents the difference between the number operators of right- and left-handed photons. Previous studies have shown that its expectation value is not conserved for observers propagating in a gravitational field. Here, we show that this Noether symmetry can also be realized in empty waveguides with duality-preserving boundary conditions, and we quantize the source-free Maxwell theory inside a long, cylindrical waveguide undergoing both linear and rotational acceleration from rest. In the vacuum associated to inertial observers, we find that the expectation value fails to be conserved for observers co-moving with the waveguide. In particular, frame-dragging effects induce a spectral asymmetry between the right- and left-handed field modes at late times. As a consequence, accelerated detectors co-moving with the rotating waveguide can detect photon-pair excitations from the quantum vacuum, exhibiting an imbalance between opposite helicity modes. This is a relativistic quantum effect, which shows that the classical conservation law associated with duality symmetry is broken in the quantum theory even in flat spacetime, provided we work with non-inertial systems. Our analysis provides a concrete proof of concept for testing this effect in analogue gravity platforms.

Paper Structure

This paper contains 25 sections, 7 theorems, 186 equations.

Table of Contents

  1. Introduction
  2. Electric-magnetic duality in empty waveguides
  3. Review of some standard results
  4. A self-dual formulation of Maxwell equations inside a waveguide
  5. Description of the waveguide model: boundary conditions and dynamics
  6. Preliminary example: electric and magnetic modes allowed in a perfectly conducting waveguide
  7. Electric/magnetic modes allowed in our waveguide model
  8. Right- and left-handed potentials inside the waveguide model
  9. Acceleration of the waveguide and frame-dragging of basis vectors
  10. Quantization at early times
  11. Classical covariant phase space (standard variables)
  12. Classical covariant phase space (self-dual variables)
  13. Quantization: construction of the in Fock space
  14. Quantization at late times
  15. A late-time mode basis for the classical covariant phase space
  16. ...and 10 more sections

Key Result

Lemma A.1

For $m>-1$ and any pair of zeros $j_{mn}$, $j_{mn'}$ of $J_m(x)$, we have

Theorems & Definitions (7)

  • Lemma A.1
  • Lemma A.2
  • Lemma A.3
  • Lemma A.4
  • Lemma A.5
  • Corollary A.1
  • Proposition A.1