As atom-cavity systems are becoming more sophisticated, the limitations of the Jaynes-Cummings model are becoming more apparent. In this paper, we therefore take a more dynamical approach to the modelling of atom-cavity systems and do not reduce the electromagnetic field inside the resonator to a single mode. Our approach shows that the decay rate Gamma_cav of an emitter inside a subwavelength cavity with metallic mirrors can be much larger than its free space decay rate Gamma_free due to constructive interference effects of the emitted light. In general, however, we find that Gamma_cav = Gamma_free to a very good approximation which might explain why atom-cavity experiments with planar mirrors have not been able to operate in the so-called strong coupling regime.
As atom-cavity systems are becoming more sophisticated, the limitations of the Jaynes-Cummings model are becoming more apparent. In this paper, we therefore take a more dynamical approach to the modelling of atom-cavity systems and do not reduce the electromagnetic field inside the resonator to a single mode. Our approach shows that the decay rate Gamma_cav of an emitter inside a subwavelength cavity with metallic mirrors can be much larger than its free space decay rate Gamma_free due to constructive interference effects of the emitted light. In general, however, we find that Gamma_cav = Gamma_free to a very good approximation which might explain why atom-cavity experiments with planar mirrors have not been able to operate in the so-called strong coupling regime.
As atom-cavity systems are becoming more sophisticated, the limitations of the Jaynes-Cummings model are becoming more apparent. In this paper, we therefore take a more dynamical approach to the modelling of atom-cavity systems and do not reduce the electromagnetic field inside the resonator to a single mode. Our approach shows that the decay rate [Formula: see text] of an emitter inside a subwavelength cavity with metallic mirrors can be much larger than its free space decay rate [Formula: see text] due to constructive interference effects of the emitted light. In general, however, we find that [Formula: see text] to a very good approximation which might explain why atom-cavity experiments with planar mirrors have not been able to operate in the so-called strong coupling regime.
Strong coupling between a single resonator mode and a single quantum emitter is key to a plethora of experiments and applications in quantum science and technology and is commonly described by means of the Jaynes–Cummings model. Here, we show that the Jaynes–Cummings model only applies when the cavity does not significantly change the emitter’s decay rate into free-space. Most notably, the predictions made by the Jaynes–Cummings model become increasingly wrong when approaching the ideal emitter-resonator systems with no free-space decay channels. We present a Hamiltonian that provides, within the validity range of the rotating wave approximation, a correct theoretical description that applies to all regimes. As minimizing the coupling to free-space modes is paramount for many cavity-based applications, a correct description of strong light-matter interaction is therefore crucial for developing and optimizing quantum protocols.
Strong coupling between a single resonator mode and a single quantum emitter is key to a plethora of experiments and applications in quantum science and technology and is commonly described by means of the Jaynes-Cummings model. Here, we show that the Jaynes-Cummings model only applies when the cavity does not significantly change the emitter's emission rate into free-space. Most notably, the predictions made by the Jaynes-Cummings model become increasingly wrong when approaching the ideal emitter-resonator systems with no free-space decay channels. We present a Hamiltonian that provides, within the validity range of the rotating wave approximation, a correct theoretical description that applies to all regimes. As minimizing the coupling to free-space modes is paramount for many cavity-based applications, a correct description of strong light-matter interaction is therefore crucial for developing and optimizing quantum protocols.
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.
The interaction of light with matter is at the heart of quantum optics, which itself enables insight into the fundamental aspects of quantum mechanics. First experimental access to this research field has been realized by coupling atoms to light. Here, the transition between discrete energy states of the atom is associated with the absorption and emission of a photon, a single quantum of the electromagnetic field. As a central aspect of quantum optics, the light-emitter interaction can be significantly enhanced by placing the emitter in optical cavity that is on resonance with the emitter. In recent years, this has led to a rapidly evolving research field known as cavity quantum electrodynamics (CQED). In CQED two different regimes are distinguished: the strong and the weak coupling regimes. In the strong coupling regime, the emitted photon is reflected from the cavity mirrors and eventually reabsorbed by the emitter. In contrast, the weak coupling regime describes the irreversible emission, where the photon leaks out of the cavity before it can be reabsorbed. Both the weak and strong coupling regimes enabled fundamental experiments for a better understanding of quantum optical phenomena. \n \n \n \nCQED grants access to the quantum world and hence offers potentially revolutionizing applications, particularly in the field of quantum information processing. A central aspect for the successful implementation of quantum applications is the system's scalability. Unfortunately, placing atoms deterministically inside a cavity remains technologically elaborate and hence minimizes the prospect of scaling a atom-CQED system. \n \nA possibility to address this issue is to implement CQED in the solid state, where sophisticated fabrication strategies allow miniaturization and scalability of the system. Particularly the development of self-assembled quantum dots (QD) in semiconductors represent a promising route. QDs can be considered as artificial atoms that mimic the atomic two-level system. These structures interact strongly with light and therefore have the potential for replacing atoms in CQED. As a central advantage, QDs are naturally trapped, which greatly simplifies the deterministic incorporation into the cavity. \n \nIn recent years, many efforts have been made to couple self-assembled QDs to microcavities. Generally, the successful implementation of CQED requires a cavity with a high quality factor Q and a low mode volume. In a majority of the approaches, the high Q/small mode volume cavities were monolithically defined around the QD, embedding the QD at a fixed position inside the cavity. Both the weak and strong coupling regimes have been reached with these systems. However, for future applications they suffer from several disadvantages. The fixed position of the QD inside the cavity minimizes the prospects for spectral tunability and spatial positioning the QD inside the cavity. Furthermore, prospects for further increasing of the cavity Q-factor and minimization of the mode volume remain limited in these systems. \n \nIn this thesis the mentioned disadvantages are addressed by developing a fully tunable miniaturized Fabry-Pérot microcavity with low mode volume. The design enables both spatial positioning of the emitter inside the cavity and spectral tunability. Successful coupling of a single QD to the microcavity is demonstrated including the strong coupling regime. Further a new approach to decrease the cavity mode volume is presented, where we demonstrate weak coupling is achieved
As discussed in Section 4.4 the strong coupling regime of cavity QED is reached when the emitter-cavity coupling rate gcav dominates over the cavity loss rate κ and other decay modes of the emitter γ , i.e., gcav > κ/2, γ . The strong coupling regime is not only ideal to test the field quantization formalism and the resulting Jaynes- Cummings model [56, 344], but also the basis for many scalable quantum computation and networking protocols [345-347]. Here, the cavity mediates deterministic light-matter interaction on the single-photon single-emitter level, allowing the realization of quantum gates and interfaces between stationary and flying qubits. In classical information processing, strong coupling can be used to achieve ultrafast all-optical switches with ultralow switching energies, reaching the one-photon level [348]. Thus, strongly coupled solid state emitters promise to provide a scalable quantum and classical optical information processing platform.