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.
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 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
Cavity quantum electrodynamics (cavity QED) describes electromagnetic fields in a confined space and the radiative properties of atoms in such fields. The simplest example of such system is a single atom interacting with one mode of a high-finesse resonator. Besides observation and exploration of fundamental quantum mechanical effects, this system bears a high potential for applications quantum information science such as, e.g., quantum logic gates, quantum communication and quantum teleportation. In this thesis I present an experiment on the deterministic coupling of a single neutral atom to the mode of a high-finesse optical resonator. In Chapter 1 I describe our basic techniques for trapping and observing single cesium atoms. As a source of single atoms we use a high-gradient magneto-optical trap, which captures the atoms from background gas in a vacuum chamber and cools them down to millikelvin temperatures. The atoms are then transferred without loss into a standing-wave dipole trap, which provides a conservative potential required for experiments on atomic coherence such as quantum information processing and metrology on trapped atoms. Moreover, shifting the standing-wave pattern allows us to deterministically transport the atoms (Chapter 2). In combination with non-destructive fluorescence imaging of individual trapped atoms, this enables us to control their position with submicrometer precision over several millimeters along the dipole trap. The cavity QED system can distinctly display quantum behaviour in the so-called strong coupling regime, i.e., when the coherent atom-cavity coupling rate dominates dissipation in the system. This sets the main requirements on the resonator's properties: small mode volume and high finesse. Chapter 3 is devoted to the manufacturing, assembling, and testing of an ultra-high finesse optical Fabry-Perot resonator, stabilized to the atomic transition. In Chapter 4 I present the transportation of single atoms into the cavity and their coupling to the cavity mode. The strong coupling manifests itself in a strong reduction of the cavity transmission probed by a weak external laser. The atoms remain trapped and coupled to the cavity mode for several seconds until we move them out of the cavity for final analysis of their number and position.
Cavity quantum electrodynamics (cavity QED) describes the interactions of single atoms and single photons in a resonator. In the laboratory, state-of-the-art experiments are able to observe the dynamics of these simple yet fundamental quantum systems. The recent development of quantum information science has also introduced a new role for cavity QED systems as quantum interfaces, in which information can be coherently mapped between photonic and atomic quantum bits. Groundbreaking optical cavity QED experiments in the past twenty years would not have been possible without the technological development of mirror coatings with extremely low scatter and absorption losses. Thermal noise has typically played a smaller role in cavity QED experiments but in certain instances is nevertheless important to consider. In this chapter, we begin with an overview of optical cavity QED experiments and some of the central questions that they address. It is hoped that this description, while by no means exhaustive, will provide a window for the nonspecialist into basic techniques and motivations in the field. We then turn to focus on the roles played by scattering and absorption loss and mechanical loss. We discuss how these losses have set limits on feasible experiments and the extent to which improvements may be possible. Experimental realizations of cavity QED systems An idealized cavity QED system consists of one atom placed between two highly reflective mirrors (Figure 17.1). In this model, a single atomic transition interacts with photons in a single cavity mode; the atom is often pictured at an antinode of the cavity standing wave, where it has a maximal dipole interaction with the cavity field.
In order to study quantum effects such as state superposition and entanglement, one would like to construct simple systems for which the damping rates are slow relative to the rate of coherent evolution. One such system is strong-coupling cavity quantum electrodynamics (QED), in which a single atom is coupled to a single mode of a high finesse optical cavity. In recent years, optical trapping techniques have been applied to the cavity QED system, allowing an individual atom to remain coupled to the cavity for long periods of time. For the purpose of future cavity QED experiments, one would like to gain as much control over the trapped atom as possible; in particular, one would like to cool the center of mass motion of the atom, to measure the magnetic field at the location of the atom, and to be able to prepare the atom in a given internal state. In the first part of this thesis, I present a scheme for driving Raman transitions inside the cavity that can be used to achieve these goals. After giving a detailed theoretical treatment of the Raman scheme, I describe how it can be implemented in the lab and discuss some preliminary experimental results. In the second part of this thesis, I present a number of simple field theory models. These models were developed in an attempt to understand some of the central ideas of theoretical physics by looking at how the ideas work in a highly simplified context. The hope is that by reducing the mathematical complexity of an actual theory, the underlying physical concepts can be more easily understood.
Cavity quantum electrodynamics (QED) in the strong-coupling regime provides the opportunity to monitor and control the dynamics of a simple quantum system. A single Cesium atom interacts strongly with single-photon fields in the mode of a high-finesse optical cavity. When the resulting coherent coupling rate dominates dissipation in the system, strong coupling is realized and the system displays distinctively quantum behavior. The coupling between atomic internal states and the quantized cavity field allows for diverse protocols in quantum state preparation, quantum communication, and quantum logic. However, the atom's external or motional state must also be taken into account. My research develops cavity QED in the limit where the coherent atom-field coupling dominates the atomic kinetic energy and thus significantly affects the atomic center-of-mass motion. In this regime, the interaction of the atom with the cavity field provides both a means of controlling atomic motion and a signal for detecting that motion in real time with high signal-to-noise. The sensing capability of the ``atom-cavity microscope" is exploited to trap single atoms with single-photon fields and to monitor their orbits in real time as they are bound in the cavity. Such real-time position sensing is the basis for a detailed strategy and ongoing experiment to actively stabilize select aspects of an atom's motion within the cavity. As the cavity-enabled position measurement approaches the standard quantum limit, this work begins to realize a quantum servo for atomic position and to address questions of optimal state estimation and state preparation. In combination with other progress in cavity QED, it furthers the goal of controlled atom-field interactions for quantum information science.
Light has always been the most important carrier of information. Most of the information received by a human is visual. Technological breakthroughs have been made by changing from copper networks to networks based on optical data processing using laser light. In the last fifteen years, however, research has gone much further. We can now generate and control new sources of nonclassical light which are constructed from single atoms in a resonator. The systems for generating this new light are the micromaser in the microwave regime and the microlaser in the optical regime. Fundamental properties as well as possible applications have been investigated in a common European effort within the TMR network Microlasers and Cavity QED . Funded by the European Commission seventeen teams have been working together sharing their knowledge about the fundamental interaction of light with matter. These Focus articles will highlight several important findings of this collaboration. From the selection of papers one can immediately see the wide range of research that has been done in this European project. New quantum effects have been found in the interaction of a single light mode with single atoms and new properties of the corresponding field states have been explored. The fundamental forces acting on atoms in a cavity field have been simulated. This will open new ways to cool an ensemble of atoms in a cavity. In addition it has been shown that cold atoms can be transported in a waveguide. Regarding semiconductor microlasers the quantum noise of vertical surface emitting lasers (VCSELs) has been understood experimentally as well as theoretically. The focus articles also demonstrate that the ability to manipulate quantum characteristics of light will have direct applications in information technology. Systems based on cavity QED are candidates for future processing of quantum information. One of the most challenging tasks therefore is to understand the dissipative effects and to actively control the decay of atomic states. A clear understanding of all these decoherence effects then allows for the development of error avoiding quantum codes that stabilize quantum algorithms within the realm of cavity QED. At this point we take the opportunity to thank the authors and the reviewers of these articles for preparing and ensuring high-quality presentations. We are convinced that this cluster of articles will give the readers a broad insight into an inspiring piece of modern physics. Focus on Microlaser and Cavity QED Contents Coherent states sometimes look like squeezed states and vice versa: the Paul trap Michael Martin Nieto and D Rodney Truax Error avoiding quantum codes and dynamical stabilization of Grover's algorithm Michael Mussinger, Aldo Delgado and Gernot Alber Schrödinger-cat entangled state reconstruction in the Penning trap Michol Massini, Mauro Fortunato, Stefano Mancini, Paolo Tombesi and David Vitali Nonlocality of the Schrödinger cat Krzysztof Wódkiewicz Driving atoms into decoherence-free states Almut Beige, Daniel Braun and Peter L Knight Transport of cold atoms in a miniature guide M Key, W Rooijakkers and E A Hinds Quantum noise in VCSELs J-P Hermier, I Maurin, E Giacobino, P Schnitzer, R Michalzik, K J Ebeling, A Bramati and A Z Khoury A physical explanation of excess quantum noise due to non-orthogonal modes A M van der Lee, M P van Exter, N J van Druten and J P Woerdman Collective light forces on atoms in a high-finesse cavity T Fischer, P Maunz, T Puppe, P W H Pinkse and G Rempe Tunable whispering gallery modes for spectroscopy and CQED experiments Wolf von Klitzing, Romain Long, Vladimir S Ilchenko, Jean Hare and Valérie Lefèvre-Seguin Matthias Freyberger and Wolfgang Schleich Abteilung für Quantenphysik, Universität Ulm, Germany