Cavity quantum electrodynamics with spin ensembles: from the semiclassical to the quantum regime

Abstract

Spin ensembles inside a cavity act as light-matter interfaces that play an eminentrole in the development of future quantum devices. An apparent asset of ensemble-based systems is the collective enhancement of the coupling strength, facilitating astrong interaction between the light and matter components. Particularly promisingin this regard, due to their convenient handling and integrability, are solid statespin ensembles such as nitrogen-vacancy centers in diamond, phosphorous donors in silicon, or rare earth doped crystals. Such ensemble-based setups, however, are almost inevitably inhomogeneously broadened as the different spins of the ensemble typically have different local environments leading to a spectral distribution in their transition frequencies. This so-called inhomogeneous broadening is a major source for decoherence in solid state systems and a major challenge to be addressed for future technical applications.In this thesis, we aim to provide the theoretical framework necessary to describeand understand various effects of inhomogeneously broadened spin ensembles coupled to a single-mode cavity—a system that has been realized in numerous different quantum optical setups and in very different parameter regimes.For macroscopic spin ensembles, i.e., ensembles consisting of a vast number ofspins, quantum fluctuations of the individual spins can typically be neglected, allowing a semiclassical description based on Maxwell-Bloch equations. Here, we study two prominent effects in the strongly nonlinear regime namely optical bistability, resembling a first-order phase transition, and critical slowing down. In particular, we show that the onset of bistability not only depends on the width of the spectral spin distribution but also strongly depends on its exact shape. Furthermore, we analyze the transient times of the cavity amplitude which show a power-law divergence when an external parameter is changed in the vicinity of the phase transition.This critical slowdown is demonstrated in collaboration with the group ofJörg Schmiedmayer at the Atominstitut of TU Wien. In the experiment, negativelycharged nitrogen vacancy centers in diamond are strongly coupled to a superconducting microwave resonator showing transient times of up to 11 hours.In mesoscopic spin ensembles with moderate numbers of constituents, quantumfluctuations gain importance, and semiclassical methods fail. We study thiscrossover between the semiclassical and the quantum regime using a cumulant expansion approach to study the semiclassical-to-quantum boundary for inhomogeneously broadened spin ensembles inside a cavity. In addition, we develop a time-adaptivevariational renormalization group method to calculate the full quantumdynamics of spin ensembles containing up to one hundred spins. With the aid ofthis method, we examine mesoscopic spin ensembles whose spin distributions form a comb-shaped structure. These so-called atomic frequency combs have promising properties for the storage of quantum information. On the one hand, we show that arbitrary multi-photon states are absorbed by the comb-shaped spin ensembleand re-emitted into the cavity at periodic time intervals. On the other hand, wedemonstrate that by means of such a spin ensemble a coherent input pulse can beconverted into periodic pulses of non-classical light.Finally, we address spin echoes, which are a fundamental part in nuclear magneticresonance as well as in electron spin resonance. Specifically, we transfer the Hahnecho to the strong coupling regime, where we find a new dynamical phenomenonfeaturing a periodic sequence of self-sustained echoes after a conventional Hahn echo pulse. In collaboration with the group of Hans Hübl at the Technical UniversityMunich, a first demonstration of this intriguing multiecho signature is presented inan electron spin resonance experiment with phosphorus donors in silicon.