QED of lossy cavities: Operator and quantum-state input-output relations

Abstract

Within the framework of exact quantization of the electromagnetic field in dispersing and absorbing media the input-output problem of a high-Q cavity is studied, with special emphasis on the absorption losses in the coupling mirror. As expected, the cavity modes are found to obey quantum Langevin equations, which could be also obtained from quantum noise theories, by appropriately coupling the cavity modes to dissipative systems, including the effect of the mirror-assisted absorption losses. On the contrary, the operator input-output relations obtained in this way would be incomplete in general, as the exact calculation shows. On the basis of the operator input-output relations the problem of extracting the quantum state of an initially excited cavity mode is studied and input-output relations for the s-parametrized phase-space function are derived, with special emphasis on the relation between the Wigner functions of the quantum states of the outgoing field and the cavity field.

On the Problem of Electromagnetic-Field Quantization

“…The problem of quantization of electromagnetic field in material media remains important in view of recent trends in the flourishing cavity QED [17], [19], [47], [72], [80] and for experiments in quantum optics in media [7], [32], [33], [58], [81], [96], which may result in a better understanding of the interaction of light with matter. Among other possible applications of the electromagnetic wave propagation in time-dependent media are the modulation of microwave power [71], wave propagation in ionized plasma [53], and magnetoelastic delay lines [82], [83] (see also [13] and the references therein).…”

Ab InitioFew-Mode Theory for Quantum Potential Scattering Problems

“…On the theoretical side, there are still various challenges [79,80,137]. One of them is the high openness of these systems, which has cast doubts on the applicability of input-output models for quantum plasmonics [32,33,35,138]. Consequently, much effort has been invested into developing alternative quantum mechanical descriptions [137], for example by quantizing quasi-modes, which have had much success in the semi-classical domain [55,59,62].…”

Quantized fluctuational electrodynamics for three-dimensional plasmonic structures

“…The normalization factors j 0,e (r, ω) and j 0,m (r, ω) have been determined to be j 0,e (r, ω) = 4π ω 2 ε 0 ε i (r, ω) [26,31] and j 0,m (r, ω) = 4π ω 2 µ 0 µ i (r, ω) [25,34].…”