PT-symmetric spectral singularity and negative-frequency resonance

Abstract

Vacuum consists of a bath of balanced and symmetric positive and negative frequency fluctuations. Media in relative motion or accelerated observers can break this symmetry and preferentially amplify negative frequency modes as in Quantum Cherenkov radiation and Unruh radiation. Here, we show the existence of a universal negative frequency-momentum mirror symmetry in the relativistic Lorentzian transformation for electromagnetic waves. We show the connection of our discovered symmetry to parity-time (PT ) symmetry in moving media and the resulting spectral singularity in vacuum fluctuation related effects. We prove that this spectral singularity can occur in the case of two metallic plates in relative motion interacting through positive and negative frequency plasmonic fluctuations (negative frequency resonance). Our work paves the way for understanding the role of PT -symmetric spectral singularities in amplifying fluctuations and motivates the search for PT -symmetry in novel photonic systems.

Spin photonic forces in non-reciprocal waveguides

“…When the velocity is large enough (v motion > ω/k x ), the complex-conjugate component of the negative-momentum mode is transformed to the positive-momentum positivefrequency region, resulting in flipping of negative-momentum to positive-momentum. A similar transformation for plasmonic mode in moving metal-insulator-metal waveguide structure is explained in detail in [41]. This essentially means that the slab-waveguide is moving fast enough for the backward propagating mode to appear as forward propagating in the reference frame of the particle; consequently switching the sign of momentum from negative to positive at the Cherenkov velocity.…”

“…alongx direction. Our calculations are fully relativistic and the details can be found in the appendix [41]. It can be seen that for a moving slab-waveguide, the propagation characteristics are asymmetrical and non-reciprocal.…”

“…In region (ii) and (iii), regular relation between electric and magnetic fields is used to compute the electric fields. Since the direction of motion is perpendicular to the direction of interface between slab and the surrounding vacuum, the boundary conditions on the tangential components of the fields hold true for moving medium as well [40,41]. Boundary conditions are applied at the two interface on E x and H y components to solve for the dispersion relation and the modal fields in moving-slab waveguide.…”

Spectral singularities, threshold gain, and output intensity for a slab laser with mirrors

“…where '≈' labels approximate equalities in which we neglect terms of order κ ℓ 0 and (κ 0 /m) According to (14), (25), and (41),…”

Effective action study of the 𝒫𝒯-symmetric (iϕ3)6−𝜖 theory and the Yang–Lee edge singularity

“…The experimental test of predictions within PT -symmetric theories have been stressed in many articles (for instance Refs. [18][19][20]). In fact, there is a growing interest in that direction and it seems to be a matter of time to the full acceptance of non-Hermitian theories to share in solving existing problems in the current Hermitian description of a natural phenomena.…”