We study the dynamics of a spin ensemble strongly coupled to a single-mode resonator driven by external pulses. When the mean frequency of the spin ensemble is in resonance with the cavity mode, damped Rabi oscillations are found between the spin ensemble and the cavity mode which we describe very accurately, including the dephasing effect of the inhomogeneous spin broadening. We demonstrate that a precise knowledge of this broadening is crucial both for a qualitative and a quantitative understanding of the temporal spin-cavity dynamics. On this basis we show that coherent oscillations between the spin ensemble and the cavity can be enhanced by a few orders of magnitude, when driving the system with pulses that match special resonance conditions. Our theoretical approach is tested successfully with an experiment based on an ensemble of negatively charged nitrogen-vacancy centers in diamond strongly coupled to a superconducting coplanar single-mode waveguide resonator.
We study the dynamics of a spin ensemble strongly coupled to a single-mode resonator driven by external pulses. When the mean frequency of the spin ensemble is in resonance with the cavity mode, damped Rabi oscillations are found between the spin ensemble and the cavity mode which we describe very accurately, including the dephasing effect of the inhomogeneous spin broadening. We demonstrate that a precise knowledge of this broadening is crucial both for a qualitative and a quantitative understanding of the temporal spin-cavity dynamics. On this basis we show that coherent oscillations between the spin ensemble and the cavity can be enhanced by a few orders of magnitude, when driving the system with pulses that match special resonance conditions. Our theoretical approach is tested successfully with an experiment based on an ensemble of negatively charged nitrogen-vacancy centers in diamond strongly coupled to a superconducting coplanar single-mode waveguide resonator.
Hybrid quantum systems, which combines the advantages of different quantum systems, play an essential role in the realisation of quantum computation, especially as quantum memory. This thesis discusses the very promising hybrid quantum system based on the ensemble of negatively charged nitrogen-vacancy centers (NV-centers) in diamond and superconducting microwave cavities. The decoherence of this system, due to the inhomogeneous spin broadening, seems to be the major obstacle of utilising the NV-centers as a quantum information storage. This works focuses on the study of the dynamics of our NV-center spin ensemble strongly coupled to a superconducting resonator driven by pulse sequences with a carrier frequency equaling the cavity frequency. A precise knowledge of the spin broadening, which has a non-Lorentzian distribution, led to the observation of the so called 'cavity protection effect'. Furthermore this work demonstrates the enhancement of the damped Rabi oscillations between the spin ensemble and the cavity mode through appropriate chosing of the microwave pulses, which could change in the order of two magnitudes. Last we also confirmed the theoretical analysis of the crossover from markovian to non-markovian dynamics for our system, which is achieved for increasing coupling strength.
We present a theoretical study of the nonlinear dynamics and stationary states of an inhomogeneously broadened spin ensemble coupled to a single-mode cavity driven by an external drive with constant amplitude. Assuming a sizable number of constituents within the ensemble allows us to use a semiclassical approach and to formally reduce the theoretical description to the Maxwell-Bloch equations for the cavity and spin amplitudes. We explore the critical slowing-down effect, quench dynamics, and asymptotic behavior of the system near a steady-state dissipative phase transition accompanied by a bistability effect. Some of our theoretical findings have recently been successfully verified in a specific experimental realization based on a spin ensemble of negatively charged nitrogen-vacancy centers in diamond strongly coupled to a single-mode microwave cavity [see A. Angerer et al., Sci. Adv. 3, e1701626 (2017)].
Based on the experiments [S. Putz et al., Nat. Phys. 10, 720 (2014); Nat. Photonics 11, 36 (2017)] on the hybrid quantum system of a superconducting microwave cavity coupled strongly to an inhomogeneous broadening spin ensemble, we use the exact master equation theory to investigate its non-Markovian decoherence dynamics under external driving fields. In the experiments, the spin ensemble is made of negatively charged nitrogen-vacancy defects in diamond. The exact master equation theory generalizes the fluctuation-dissipation relation and depicts in details the transient non-Markovian decoherence, in which the dissipation (relaxation) and fluctuations (noise or dephasing) dynamics is well described and the non-Markovian memory effect can be well characterized. We study the physical picture of the transient non-Markovian decoherence dynamics and explore how the non-Markovian decoherence induced by the inhomogeneous broadening of the spin ensemble is suppressed in the strong-coupling regime. We also show how the spectral hole burning generates localized bound states for the further decoherence suppression. Furthermore, we investigate the two-time correlations to show the relationships between quantum fluctuations and quantum memory.
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.
We explore controllable quantum dynamics of a hybrid system, which consists of an array of mutually coupled superconducting resonators (SRs) with each containing a nitrogen-vacancy center spin ensemble (NVE) in the presence of inhomogeneous broadening. We focus on a three-site model, which compared with the two-site case, shows more complicated and richer dynamical behavior, and displays a series of damped oscillations under various experimental situations, reflecting the intricate balance and competition between the NVE-SR collective coupling and the adjacent-site photon hopping. Particularly, we find that the inhomogeneous broadening of the spin ensemble can suppress the population transfer between the SR and the local NVE. In this context, although the inhomogeneous broadening of the spin ensemble diminishes entanglement among the NVEs, optimal entanglement, characterized by averaging the lower bound of concurrence, could be achieved through accurately adjusting the tunable parameters.
We study experimentally and theoretically a dense ensemble of negatively charged nitrogen-vacancy centers in diamond coupled to a high-Q superconducting coplanar waveguide cavity mode at low temperature. The nitrogen-vacancy centers are modeled as effective spin-one defects with inhomogeneous frequency distribution. For a large enough ensemble the effective magnetic coupling of the collective spin dominates the mode losses and inhomogeneous broadening of the ensemble and the system exhibits well-resolved normal-mode splitting in probe transmission spectra. We use several theoretical approaches to model the probe spectra and the number and frequency distribution of the spins. This analysis reveals an only slowly temperature-dependent q-Gaussian energy distribution of the defects with a yet unexplained decrease of effectively coupled spins at very low temperatures below 100mK. Based on the system parameters we predict the possibility to implement an extremely stable maser by adding an external pump to the system.