Ultrastrong coupling phenomena beyond the Dicke model

We study effective light-matter interactions in a circuit QED system consisting of a single $LC$ resonator, which is coupled symmetrically to multiple superconducting qubits. Starting from a minimal circuit model, we demonstrate that in addition to the usual collective qubit-photon coupling the resulting Hamiltonian contains direct qubit-qubit interactions, which have a drastic effect on the ground and excited state properties of such circuits in the ultrastrong coupling regime. In contrast to a superradiant phase transition expected from the standard Dicke model, we find an opposite mechanism, which at very strong interactions completely decouples the photon mode and projects the qubits into a highly entangled ground state. These findings resolve previous controversies over the existence of superradiant phases in circuit QED, but they more generally show that the physics of two- or multi-atom cavity QED settings can differ significantly from what is commonly assumed.Comment: 11 pages, 8 figure

Quantum Simulation of Non-perturbative Cavity QED with Trapped Ions

We discuss the simulation of non-perturbative cavity-QED effects using systems of trapped ions. Specifically, we address the implementation of extended Dicke models with both collective dipole-field and direct dipole-dipole interactions, which represent a minimal set of models for describing light-matter interactions in the ultrastrong and deep-strong coupling regime. We show that this approach can be used in state-of-the-art trapped ion setups to investigate excitation spectra or the transition between sub- and superradiant ground states, which are currently not accessible in any other physical system. Our analysis also reveals the intrinsic difficulty of accessing this non-perturbative regime with larger numbers of dipoles, which makes the simulation of many-dipole cavity QED a particularly challenging test case for future quantum simulation platforms.Comment: 10 pages, 5 figure

Super-correlated radiance in nonlinear photonic waveguides

We study the collective decay of two-level emitters coupled to a nonlinear waveguide, for example, a nanophotonic lattice or a superconducting resonator array with strong photon-photon interactions. Under these conditions, a new decay channel into bound photon pairs emerges, through which spatial correlations between emitters are established by regular interference as well as interactions between the photons. We derive an effective Markovian theory to model the resulting decay dynamics of an arbitrary distribution of emitters and identify collective effects beyond the usual phenomena of super- and subradiance. Specifically, in the limit of many close-by emitters, we find that the system undergoes a supercorrelated decay process where all the emitters are either in the excited state or in the ground state but not in any of the intermediate states. The predicted effects can be probed in state-of-the-art waveguide QED experiments and provide a striking example of how the dynamics of open quantum systems can be modified by many-body effects in a nonharmonic environment

Breakdown of gauge invariance in ultrastrong-coupling cavity QED

We revisit the derivation of Rabi- and Dicke-type models, which are commonly used for the study of quantum light-matter interactions in cavity and circuit QED. We demonstrate that the validity of the two-level approximation, which is an essential step in this derivation, depends explicitly on the choice of gauge once the system enters the ultrastrong coupling regime. In particular, while in the electric dipole gauge the two-level approximation can be performed as long as the Rabi frequency remains much smaller than the energies of all higher-lying levels, it can dramatically fail in the Coulomb gauge, even for systems with an extremely anharmonic spectrum. We extensively investigate this phenomenon both in the single-dipole (Rabi) and multi-dipole (Dicke) case, and considering the specific examples of dipoles confined by double-well and by square-well potentials, and of circuit QED systems with flux qubits coupled to an LC resonator.Comment: See also related independent work arxiv:1805.0635

Ultrastarke Licht-Materie Kopplung mit supraleitenden Schaltkreisen

Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers“Circuit quantum electrodynamics (QED)” bezeichnet ein junges Forschungsfeld in dem effective Licht-Materiewechselwirkungen anhand der Kopplung von supraleitenden Qubits (“künstliche Atome”) und Mikrowellenphotonen untersucht werden. Im Vergleich zu traditionellen Resonator QED Systemen mit Atomen und optischen Photonen kann in diesen künstlichen Systemen die Kopplungsstärke um viele Größenordnungen erhöht und dadurch vergleichbar mit der absoluten Energie der Photonen werden. In diesem Regime der sogenannten ultrastarken Kopplung (USK) gelten die bekannten Gesetze der Quantenoptik nicht mehr und neue exotische Phänomene treten zu Tage. In dieser Dissertation werden die grundlegenden physikalischen Eigenschaften von Circuit- und Resonator-QED Systemen anhand von einfachen Modellen beschrieben und diskutiert. Dazu wird insbesondere durch verschiedene explizite Herleitungen gezeigt, dass in diesem Regime das oft verwendete Dicke Model seine Gültigkeit verliert und durch ein erweitertes Dicke Model (EDM) ersetzt werden muss. Im Bereich USK sagt dieses Model einen neuartigen, subradianten Grundzustand voraus, in welchem die Qubits oder Atome von den Photonen komplett entkoppelt, aber gleichzeitig untereinander stark verschränkt sind. Durch die Ableitung von weiter vereinfachten effektiven Modellen kann diese Phase, so wie auch viele andere Eigenschaften des Grundzustands und der angeregten Zustände von stark-wechselwirkenden Licht-Materie Systemen, verstanden werden. Dadurch konnten mit dieser Dissertation auch jahrelang kontrovers diskutierte Fragen in diesem Feld, wie zum Beispiel die Existenz eines superradianten Phasenübergangs, endgültig geklärt werden. Basierend auf diesem neuen grundlegenden Verständnis werden in dieser Dissertation des Weiteren ein Protokoll diskutiert, um stark verschränkte Zustände aus dem subradianten Vakuum zu extrahieren und die Möglichkeit das EDM mit Hilfe gefangener Ionen zu simulieren im Detail analysiert.In circuit quantum electrodynamics (QED) effective light-matter interactions can be studied in terms of superconducting two-level systems (“artificial atoms”) coupled to microwave resonators. Compared to regular cavity QED systems with atoms and optical photons, the achievable coupling strengths in such artificial systems can be enhanced by many orders of magnitude and even exceed the bare energies of the photons and atoms. In this so-called ultra-strong coupling (USC) regime the simple physics of the Jaynes-Cummings model is no longer valid and new exotic phenomena emerge. This thesis addresses the physics of circuit and cavity QED systems beyond the standard description based on the Dicke model. First of all, a rigorous derivation of the effective circuit QED Hamiltonian is presented, which shows that the Dicke model is no longer valid in the USC regime of circuit QED. Instead, a new model, the Extended Dicke model (EDM), is identified as a physically consistent description. In the remainder of the thesis, the physics of the EDM is studied, first in the case of non-interacting qubits. From this analysis a new ground state phase, the subradiant phase, is found, where the qubits decouple from the photons, but at the same time they are strongly entangled with each other. In a next step the cases of repulsively and attractively interacting qubits are discussed. From this analysis it can be shown that the origin of the usual superradiant phase transition is related to the presence of attractive qubit-qubit interactions and not to the presence of a cavity mode, as commonly understood. In the successive parts of the thesis also the excited states of the EDM are discussed, in particular in the low photon- frequency regime. In this limit the photons behave as effective particles moving in a potential landscape determined by the coupling to the qubits. Several symmetry-breaking transition in the qubit excited states are found and ways to probe them are discussed. Finally, as an application of these new USC effects a scheme to extract entanglement from the subradiant vacuum and a quantum simulation scheme of the EDM with trapped ions are proposed and analyzed.13

Validity of the semiquantum approximation in the ultrastrong coupling regime of cavity QED

With the recent advancements made in the coupling of quantum systems, reaching the (ultra)strong coupling regime, where the coupling constant exceeds the dissipation rate and approaches the frequencies of the coupled systems, is getting closer. In this regime, the much used semiclassical model is no longer valid, and the solving of the full quantum master equation can be computationally too demanding. Thus, we must develop a new approach to be able to simulate the system. One solution is to use the semiquantum approximation. In this thesis, we present a systematic way of employing the semiquantum approximation and compare it to the full master equation. Our aim is to determine the range for the coupling strength where the semiquantum model is applicable. We chose to do the comparison of the semiquantum approximation and the master equation within the Rabi model, which can be used to describe e.g. the interaction of light and matter. The Rabi model describes a system with a coupled two-level system and a harmonic oscillator. It was chosen because its behaviour is reasonably well known. We compared the semiquantum approximation to the quantum master equation in two cases. First we studied the steady state results from the two models, and then moved on to the spectral properties. The results show that the steady state and the spectrum obtained from the semiquantum model agree with the ones obtained by using the master equation, until the coupling reaches a considerable fraction of the resonant frequency of the oscillator, while still exceeding the experimentally reasonable dissipation rate by an order of magnitude. In the future, one could use the semiquantum approximation in the field of cavity optomechanics. There a mechanical oscillator is coupled to optical radiation confined in a cavity, e.g. a Fabry-Pérot cavity. Especially in optomechanics, the solving of the master equation can turn out to be a formidable task, and by using the semiquantum approximation one could reduce the computation time considerably