Quantizing the electromagnetic field near two-sided semitransparent mirrors

Abstract

This paper models light scattering through flat surfaces with finite transmission, reflection and absorption rates, with wave packets approaching the mirror from both sides. While using the same notion of photons as in free space, our model also accounts for the presence of mirror images and the possible exchange of energy between the electromagnetic field and the mirror surface. To test our model, we derive the spontaneous decay rate and the level shift of an atom in front of a semitransparent mirror as a function of its transmission and reflection rates. When considering limiting cases and using standard approximations, our approach reproduces well-known results but it also paves the way for the modelling of more complex scenarios.

A Physically-Motivated Quantisation of the Electromagnetic Field on Curved Spacetimes

“…An infinite set of evenly spaced energy levels, as is present here, has been proven to be unique to the simple harmonic oscillator [ 66 ]. Hence this Hamiltonian must take the form [ 5 ] where the are a set of independent ladder operators for each mode, obeying the canonical commutation relations …”

“…This is also consistent with the Hamiltonian being a direct operator-valued promotion of its classical form Comparing Equations ( 11 ) and ( 15 ) allows us to determine the zero point energy in Minkowski space, which coincides with the energy expectation value of the vacuum state of the electromagnetic field. In quantum optics, Equations ( 11 ) and ( 14 ) often serve as the starting point for further investigations [ 5 , 36 , 46 ].…”

“…Using this Hamiltonian and demanding consistency of the dynamics of expectation values with classical electrodynamics, especially with Maxwell’s equations, is sufficient to then obtain expressions for and without having to invoke vector potentials and without having to choose a specific gauge. Generalising the work by the authors of [ 35 ] from flat Minkowski space to curved space times, we obtain field observables which could be used, for example, to model photonics experiments in curved spacetimes in a similar fashion to how quantum optics typically models experiments in Minkowski space [ 5 , 36 , 46 ].…”

“…For many theorists the question “what is a photon?” remains highly nontrivial [ 1 ]. It is in principle possible to uniquely define single photons in free space [ 2 ]; however, the various roles that photons play in light–matter interactions [ 3 ], the presence of boundary conditions in experimental scenarios [ 4 , 5 ] and our ability to arbitrarily shape single photons [ 6 ] all lead to a multitude of possible additional definitions. Yet this does not stop us from utilising single photons for tasks in quantum information processing, especially for quantum cryptography, quantum computing, and quantum metrology [ 7 ].…”

Journeys from quantum optics to quantum technology

“…Other open questions are, "Is there a Hamiltonian to describe the propagation of light through a beamsplitter?" [27] and "How can we model the light scattering from two-sided optical cavities?" [28].…”