Invariant operator theory for the single-photon energy in time-varying media

Nuri Ünal

Toshio Inagaki

Jeong-Ryeol Choi

After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption that the theory of Lewis–Riesenfeld invariants is applicable in quantum optics, it is shown in the present work that this widely accepted notion is valid only for light described by a time-independent Hamiltonian, i.e., for light in media satisfying the conditions, ε(i) = ε(0), μ( t ) = μ(0), and σ( t ) = 0 simultaneously. The use of the Lewis–Riesenfeld invariant operator method in quantum optics leads to a marvelous result: the energy of a single photon propagating through time-varying linear media exhibits nontrivial time dependence without a change of frequency.

A. Stevens, Christophe Caloz

We study the squeezing of light beams in a system combining beam splitters and time-varying media. First, we derive the input-output operator transformations for time-varying media. Integrating these with the input-output operator transformations of beam splitters allows describing arbitrary sequences of beam splitters and time-varying media. We show that a specific configuration—beam splitter, time-varying medium, beam splitter, time-varying medium—enables simultaneous single- and two-mode squeezing. This dual squeezing mechanism leverages the benefits of both types of squeezing, offering potential advantages for high-precision, non-demolition measurements.

N. Ionescu-Pallas, J. Maurer

N. Ionescu-Pallas, J. Maurer