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.
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.
A single two-level emitter coupled to a single mode of an electromagnetic resonator constitutes the most fundamental instance of light--matter interaction. Realizations of this type of system are investigated in the field of cavity quantum electrodynamics (cavity QED). Particularly important are schemes in which the coupling is strong enough to exceed the spontaneous emission rate as well as cavity damping. In this case, the coherent exchange of excitation between source and photon is the dominating process, providing the unique possibility to deterministically control the quantum evolution of the system. Great progress has recently been accomplished, technologically as well as conceptually, and the focus section in this issue of Journal of Optics B: Quantum and Semiclassical Optics features five articles highlighting important recent developments in the field. Strong coupling between single atoms and the electromagnetic cavity field have been achieved in two distinct regimes, the optical and the microwave region. The latter is represented by the micromaser, a high-Q microwave cavity pumped by a beam of highly excited Rydberg atoms. It has proved to be an almost ideal system for the generation of non-classical field states. A constraint in these experiments is the fact that the field inside the cavity can only be examined indirectly, by analysing the occupation of atoms leaving the cavity. While only two atomic states were previously identified for this purpose, V A Reshetov shows in his article (pages 119--126) that more information on the field may be extracted by taking advantage of the Zeeman substructure of the atomic levels. In the optical domain of cavity QED, by contrast, the state of the resonator field may be probed directly by measuring the light leaking from the cavity using photodetectors. In order to minimize damping, high-quality cavities must be employed. In most optical experiments these are Fabry--Perot resonators with ultra-high reflectivity mirrors, with losses as low as a few parts per million being state of the art. At the same time, the coupling of atoms and photons is enhanced by reducing the length of the cavity, so that strong coupling conditions are reached. A very attractive application of this type of cavity QED setup is the possibility of exerting control over the quantum dynamics of the system. An impressive example is the implementation of quantum feedback, reported in the paper by W P Smith and L A Orozco (pages 127--134). Using information gained from detecting a single photon escaping from the cavity, active feedback is applied to halt the dynamical evolution of the system. This is the first time active feedback has been used to modify the quantum evolution of a system at the single-photon level. The authors discuss how detunings between the subsystems affect the quantum feedback, an issue particularly relevant for ensembles of atoms with a spread in detuning. Perfect quantum feedback in this case requires the use of additional parameters to control the system. The majority of optical cavity QED experiments performed so far have used as a medium atoms traversing the cavity on random trajectories, such as, for example, thermal atomic beams. In this case, the observation of quantum effects is degraded in two ways. The Doppler effect and the finite transit time lead to line broadening, while the spatial structure of the cavity mode results in atoms in different locations experiencing different coupling with the photonic field. J E Reiner et al (pages 135--142) investigate the impact of these effects on quantum fluctuations in their cavity QED system. In order to overcome line broadening, they have developed a continuous cold atomic beam, extracted from a magneto-optical trap. An even better control of broadening effects and fluctuating coupling strength is provided by trapping the atoms inside the cavity and cooling them to temperatures at which their position spread is smaller than the optical wavelength. Much recent activity has been devoted to developing such an ultimate cavity QED system. A Vukics et al (pages 143--153) present a theoretical proposal for dynamically trapping and cooling atoms inside a cavity. By driving the atoms with a standing wave injected from the side of the cavity and by weakly exciting the cavity field itself, they predict three-dimensional trapping of the atom for periods around 1 second, an extremely long time on the typical scale of cavity QED dynamics. The essential component of their scheme is the interference between the two driving fields, determining the temperature of the particle and the stable trapping positions. In the quest for better confinement of radiation, lately, an appealing alternative to the Fabry--Perot cavity has been investigated -- the optical microsphere resonator. A sphere with a diameter of a few tens of microns, it supports so-called whispering gallery modes near its circumference, for which quality factors up to 10 10 have been measured. In order to exploit the correspondingly low field damping rates for cavity QED, a method must be found to couple atomic or solid state emitters to these modes. S Göotzinger et al (pages 154--158) report the coupling of single nanocrystals on the surface of a microsphere through the evanescent field of the mode. Selective excitation of a single nano-emitter was accomplished with a scanning confocal microscope. The system is a promising candidate for cavity QED with single-quantum emitters. The ability to fully control the quantum dynamics of atoms and light is beginning to spawn early applications. The most notable example is quantum information processing. This requires the coherent manipulation of single-quantum systems, which is ideally provided by cavity QED interaction in the strong-coupling limit. The development of practical devices will be among the principal future tasks for research in the field. This will include physical systems, which have not been covered in this issue, such as semiconductors, quantum dots as emitters, or photonic crystals as resonator structures. Cavity QED is therefore guaranteed to remain a vigorous field in the years to come.
The physics of strong light-matter coupling has been addressed in different scientific communities over the last three decades. Since the early eighties, atoms coupled to optical and microwave cavities have led to pioneering demonstrations of cavity quantum electrodynamics, Gedanken experiments, and building blocks for quantum information processing, for which the Nobel Prize in Physics was awarded in 2012. In the framework of semiconducting devices, strong coupling has allowed investigations into the physics of Bose gases in solid-state environments, and the latter holds promise for exploiting light-matter interaction at the single-photon level in scalable architectures. More recently, impressive developments in the so-called superconducting circuit QED have opened another fundamental playground to revisit cavity quantum electrodynamics for practical and fundamental purposes. This book aims at developing the necessary interface between these communities, by providing future researchers with a robust conceptual, theoretical and experimental basis on strong light-matter coupling, both in the classical and in the quantum regimes. In addition, the emphasis is on new forefront research topics currently developed around the physics of strong light-matter interaction in the atomic and solid-state scenarios.
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.
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.
By embedding a single quantum emitter inside a nanoresonator that strongly localizes optical field, it is possible to achieve a very strong light-matter interaction. The strength of this interaction is characterized by the coherent emitter-field coupling strength (g), which increases with reduction in the optical mode volume and which also sets the limit on the operational speed of such a system. With InAs quantum dots inside GaAs photonic crystal cavities, coupling strengths of 40 GHz can be reached (much greater than the record values in atom-cavity QED systems), while nanometallic cavities could increase them over 100 GHz, as a result of the further reduction in the mode volume. Such a quantum dot-nanocavity platform is of interest for various quantum technologies, as well as in optical switching/computing.
Controlling quantum emitters (atoms, molecules, quantum dots, etc.), light, and its interactionsis a key issue for implementing all-optical devices and information processing at thequantum level. This generally necessitates a strong coupling of emitters to photonic modes,as achieved by a high-Q cavity, for efficient manipulation of the atoms and field dynamicsthrough cavity quantum electrodynamics (cQED).The integration of the principles of quantum optics at the nanoscale in a plasmonic platformhas been envisioned, on the basis of a possible strong coupling between a quantum emitter andthe surface plasmon polaritons (SPPs) via their strong mode confinement. Recent progressshowed the possibility to reach such a strong coupling regime, allowing the development ofquantum plasmonics where a SPP mode takes the role of the cavity mode. However, its applicationappears notoriously limited in practical situations due to the intrinsic presence ofnumerous and lossy modes, which complicates the description and the interpretation of theinteraction, and introduces strong decoherence in the system, in particular for strong coupling.In this work, a detailed overview of quantum control applied to ion trapping, cQED, and plasmonics,is presented. The first part of the thesis is a study of adiabatic processes in trappedion systems and cQED:- We summarize quantum computation processes using quantum gates, and control usingadiabatic laser pulses with atomic systems.- We design arbitrary quantum gates with ions manipulated with laser pulses.- Models for cQED are derived and applied for the production of photon states leakingfrom a cavity.In the second part, we develop a formalism to describe the quantum dynamics of emitters closeto nanoscale structures, and numerics showing the strong coupling regime and the couplingof emitters via plasmon modes. More specifically:- We provide a general field quantization procedure for spherically layered systems.- Effective models using the field quantization are derived, and we show they are analogousto cQED models.- We describe the interaction of localized plasmons (LSPs) with quantum emitters.- The coupling/entanglement of emitters by adiabatic passage through lossy plasmonicmodes of a nanosphere is shown.