Quantum description of radiative decay in optical cavities

Abstract

We present, for the first time, the quantum mechanical description of light-matter interaction in the presence of optical cavities that are characterized by radiative losses. Unique to radiative losses is the unitary evolution and their full preservation of the coherence, in stark contrast to the usually considered dissipative losses. We elucidate the reduction of exact quantum electrodynamic equations to a form similar to the familiar Jaynes-Cummings model through the introduction and study of a new class of noise operators. The dynamics of this henceforth inherently dissipative model are then presented by formulating the resulting equations of motion. Furthermore, an inputoutput formalism is established, which provides a direct connection to the dynamics of output states accessible with detectors. The application-oriented cases of coherent and pulsed laser pumping are discussed as inputs. Finally the single-photon dynamics in an optical cavity with significant radiative loss -whose importance has to be contextualized in view of the prospects of light-matter interaction applications -are reviewed according to the proposed model. The formulation is kept as general as possible to emphasise the universal applicability to different implementations of quantum optical systems but from our own background we have an application in mind in the context of nanooptics.

Second Quantization of Scattering Modes of Absorptive Photonic Nanostructures

“…Since the classical eigenmodes of the system are already subjected to losses, absorptive losses can be introduced into the freely evolving quantum system. The key to finding dissipation in a quantum context is the input-output formalism introduced in [8].…”

“…In terms of the input-output formalism, the central difference between absorptive and non-absorptive systems is the construction of output states. For non-absorptive systems, output states can be calculated from input states by applying time-reversal [8]. In absorptive systems this procedure fails, because the wave equation ( 7) is no longer invariant under timereversal.…”

“…Assume that an atom is coupled to a leaky cavity mode of Gaussian lineshape. In [8] it is shown that the light-matter coupling strength for such a scenario reads…”

“…The quantitative quantum description of optical systems, therefore, often requires a large amount of heuristic modeling, phenomenological inference and/or experimental input. In two earlier contributions we tried to overcome this problem by first achieving proper field normalization of scattering modes [7] as a necessary step towards quantizing the field and then demonstrating how discrete eigenmodes can emerge from the resulting quantum field theory in systems with optical resonances [8]. In the process we found means to determine light-matter coupling paramters quantitatively, discussed the emergence of dissipative dynamics due to radiation losses and established an input-output formalism linking cavity and scattering dynamics.…”

“…Although the resulting Hamiltonian remains fully unitary, losses manifest under a change of basis as discussed in [8]. Compared to the lossless case, the system Hamiltonian exhibits additional terms that give rise to more complex dynamics.…”