Abstract We investigate light–matter interactions in multi-element optical resonators and provide a roadmap for the identification of structural resonances and the description of the interaction of single extended cavity modes with quantum emitters or mechanical resonators. Using a first principle approach based on the transfer matrix formalism we analyze, both numerically and analytically, the static and dynamical properties of three- and four-mirror cavities. We investigate in particular conditions under which the confinement of the field in specific subcavities allows for enhanced light–matter interactions in the context of cavity quantum electrodynamics and cavity optomechanics.
Abstract We investigate light–matter interactions in multi-element optical resonators and provide a roadmap for the identification of structural resonances and the description of the interaction of single extended cavity modes with quantum emitters or mechanical resonators. Using a first principle approach based on the transfer matrix formalism we analyze, both numerically and analytically, the static and dynamical properties of three- and four-mirror cavities. We investigate in particular conditions under which the confinement of the field in specific subcavities allows for enhanced light–matter interactions in the context of cavity quantum electrodynamics and cavity optomechanics.
Small optical microresonators are structures which confine light to volumes with dimensions on the order of one wavelength and provide an important means for controlling light-matter interaction in integrated optics. In this Paper, we would like to present our work on the study of the interaction of single quantum emitters or nanoparticles located in the confined optical field of a single-mode microresonator. The interaction possibilities between a general photonic system and a quantum system are discussed, with special focus on the effect of resonant microcavities. For the case of the optical microresonator used in our experiments, we present a model based on the transfer matrix method which can analytically describe the radiative enhancement of even complex resonator geometries. This allows not only the optimization of resonator geometries, but gives accurate information on the radiative processes occurring in the cavity, allowing the extraction of information normally inaccessible in optical measurements.
The interaction of an ensemble of N two-level quantum emitters with a single-mode electromagnetic field is described by the Tavis-Cummings model. There, the collectively enhanced light-matter coupling strength is given by gN=Ng1, where g1 is the ensemble-averaged single-emitter coupling strength. This model has been employed to describe and to analyze numerous cavity-based experiments. Here, we show that this is only justified if the effective scattering rate into noncavity modes is negligible compared to the cavity's free-spectral range. In terms of experimental parameters, this requires that the optical depth of the ensemble is low, a condition that is violated in several state-of-the-art experiments. We give quantitative conditions for the validity of the Tavis-Cummings model and derive a more general Hamiltonian description that takes into account the cascaded interaction of the photons with all consecutive emitters. We show that the predictions of our cascaded model can differ quantitatively and even qualitatively from those obtained with the Tavis-Cummings model. Finally, we present experimental data, for which the deviation from the predictions of the Tavis-Cummings model is apparent. Our findings are relevant for all experiments in which optically dense ensembles of quantum emitters are coupled to an optical resonator.
We present a general framework for cavity quantum electrodynamics with strongly frequency-dependent mirrors. The method is applicable to a variety of reflectors exhibiting sharp internal resonances as can be realized, for example, with photonic-crystal mirrors or with two-dimensional atomic arrays around subradiant points. Our approach is based on a modification of the standard input-output formalism to explicitly include the dynamics of the mirror's internal resonance. We show how to directly extract the interaction parameters from the comparison with classical transfer matrix theory and how to treat the non-Markovian dynamics of the cavity field mode introduced by the mirror's internal resonance. As an application within optomechanics, we illustrate how a non-Markovian Fano-resonance cavity with a flexible photonic-crystal mirror can provide both sideband resolution as well as strong heating suppression in optomechanical cooling. This approach, amenable to a wide range of systems, opens up possibilities for using hybrid frequency-dependent reflectors in cavity quantum electrodynamics for engineering novel forms of light-matter interactions.
In the field of optomechanics, one typically studies the interaction of a single mechanical resonator and a single optical cavity mode. In this thesis, we investigate collective quantum effects in optomechanical systems with two or more optical and mechanical modes. First, we study the generation and destruction of entanglement between two mechanical resonators effected by optical cavity fields. We also describe how the optomechanical interaction can be employed to mediate strong coherent coupling and entanglement between a micromechanical membrane and a single atom. Secondly, we show that a configuration with two optical and a single mechanical mode can lead to enhanced nonlinear interactions, which can be exploited for quantum non-demolition measurements of the phonon and photon numbers. Finally, we explore the quantum many-body dynamics of optomechanical arrays. In particular, we research into the transition from a disordered state due to quantum noise to a state with phasecoherent mechanical oscillations. As an intermediate step towards this study, we also investigate the nonlinear classical dynamics of single- and multi-mode optomechanical setups and compare theoretical predictions to experimental data.
We study a microscopic model, the Mirror-Oscillator-Field (MOF) model proposed in [1], for describing optomechanical interactions. In contrast with the conventional approach where the mirror-field interaction is understood as arising from the radiation pressure of an optical field inducing the motion of the mirror’s CoM, the MOF model incorporates the dynamics of the internal degrees of freedom of the mirror that couple to the optical field directly. Considering the mirror’s internal and mechanical degrees of freedom as two separate degrees of freedom we derive the optomechanical properties of the coupled mirror and field system. The major advantage in this approach is that it provides a self-consistent treatment of the three relevant subsystems (the mirror’s motion, its internal degrees of freedom and the field) including their back-actions on each other, thereby giving a more accurate account of the coupled internal and external dynamics. The optical and the mechanical properties of a mirror arising from its dynamical interaction with the field are obtained without imposing any boundary conditions on the field additionally, as is done in the conventional way. We find that our results agree with those from the boundary condition approach in the appropriate limits and more generally the model provides a framework within which one can study optomechanical elements with different internal structures and mechanical properties, which makes it suited for studying hybrid systems. Considering the quantum dynamics of the coupled subsystems we look at the entanglement between the mirror’s motion and the field, showing that the internal degrees of the mirror, in the appropriate parameter regimes, can act as a means to coherently transfer quantum correlations between the field and the mechanics thus leading to a larger optomechanical entanglement. We then use the MOF model to study the entanglement between the motion of an atom and a field for the setup in [95] and find a larger optomechanical entanglement when the field is closer to the internal resonance. We also study the interaction between two mirrors as described by the MOF model, specifically looking at the entanglement between the motion of their centers of mass. Conclusively, we see that including the dynamics of the internal degrees of freedom of a mirror, which is the quintessential mediator of interaction between the mirror center of mass and the field, leads to qualitatively different physics, specifically in the quantum regime, thus giving a physically more complete treatment of mirror-field interactions.
We present a systematic study of the properties of systems composed of N two-level quantum emitters coupled to a single cavity mode, for light-matter interaction strengths ranging from the weak to the ultrastrong and deep-strong coupling regimes. Beginning with an analysis of the energy spectrum as a function of the light-matter coupling strength, we examine systems with varying numbers of emitters, from a pair to large collections, approaching the thermodynamic limit $(N\ensuremath{\rightarrow}\ensuremath{\infty})$. Additionally, we explore the emission properties of these systems under incoherent excitation of the emitters, employing a general theoretical framework for open cavity-QED systems, which is valid across all light-matter interaction regimes and preserves gauge invariance within truncated Hilbert spaces. Furthermore, we study the influence of the emitter-environment interaction on the spectral properties of the system. Specifically, when each emitter interacts independently with its own reservoir, we observe the emergence of an emission peak at the cavity's resonant frequency for even values of N. Our analysis also clarifies the evolution of the system as the number of emitters increases, ultimately converging toward an equivalent system composed of two interacting single-mode bosonic fields.