Spontaneous emission of a source, such as an atom, is often thought of as an inherent property of the source, but is a result of the interaction between the radiating source dipole and the vacuum electromagnetic field. Therefore, the radiation emitted from an atom can be altered by suitably modifying the surrounding vacuum field [1] with a cavity. This has been verified by experiments initiated in the 1980s using atoms which are passed through a cavity and show enhanced[2] or inhibited[3] spontaneous emission. This field, called cavity quantum electrodynamics (QED), is currently addressing important issues in semiconductor nanostructures, in particular, high-efficiency light-emitting diodes for communications and single photon sources for quantum cryptography. [4,5] For example, quantum cryptography has emerged as a significant field of study over the last fifteen years, because it offers the promise of private communication whose security is assured by the laws of physics. Most implementations of quantum cryptography so far have used a protocol introduced by Bennet and Brassard, which uses four different states of a quantum system (generally known as BB84) [6 ]. For example, the message can be encoded on the polarization state of single photons, with a random choice between two non-othogonal polarization bases when the photons are sent (by Alice) and recieved (by Bob). Since an eavesdropper (Eve) does not know what bases have been chosen, any measurement she makes will impose a back-action on the states of the transmitted photons, which can be easily detected. Using error correction and privacy amplification, Alice and Bob can distill the transmitted message into a secure key about which Eve knows arbitrarily little.
Spontaneous emission of a source, such as an atom, is often thought of as an inherent property of the source, but is a result of the interaction between the radiating source dipole and the vacuum electromagnetic field. Therefore, the radiation emitted from an atom can be altered by suitably modifying the surrounding vacuum field [1] with a cavity. This has been verified by experiments initiated in the 1980s using atoms which are passed through a cavity and show enhanced[2] or inhibited[3] spontaneous emission. This field, called cavity quantum electrodynamics (QED), is currently addressing important issues in semiconductor nanostructures, in particular, high-efficiency light-emitting diodes for communications and single photon sources for quantum cryptography. [4,5] For example, quantum cryptography has emerged as a significant field of study over the last fifteen years, because it offers the promise of private communication whose security is assured by the laws of physics. Most implementations of quantum cryptography so far have used a protocol introduced by Bennet and Brassard, which uses four different states of a quantum system (generally known as BB84) [6 ]. For example, the message can be encoded on the polarization state of single photons, with a random choice between two non-othogonal polarization bases when the photons are sent (by Alice) and recieved (by Bob). Since an eavesdropper (Eve) does not know what bases have been chosen, any measurement she makes will impose a back-action on the states of the transmitted photons, which can be easily detected. Using error correction and privacy amplification, Alice and Bob can distill the transmitted message into a secure key about which Eve knows arbitrarily little.
By investigating the interaction of single atoms with a cavity, pioneering experiments in the 1980's demonstrated that the spontaneous emission from an atom is intimately tied to the electromagnetic vacuum field distribution. By adjusting the field distribution with a cavity a discrete mode distribution was created, and enhanced and inhibited spontaneous emission from the atom was observed. We have demonstrated a semiconductor analog of the single-atom cavity experiments using a single InAs quantum dot (QD) as an artificial atom. With this solid-state implementation it is possible to make compact, regulated single-photon sources with high efficiency and high repetition rate for applications such as quantum cryptography.
Introduction Ever since 1916/17 when Einstein argued [45] [46] that spontaneous emission must occur if matter and radiation are to achieve thermal equilibrium, physicists have believed that spontaneous emission is an inherent quantum mechanical property of atoms and that excited atoms inevitably radiate. This view, however, overlooks the fact that spontaneous emission is a consequence of the coupling of quantized energy states of atoms with the quantized radiation field, and is a manifestation of quantum noise or of emission ‘stimulated’ by ‘vacuum fluctuations’. An infinity of vacuum states is available to the photon radiated by an excited atom placed in free space, leading to the effective irreversibility of such emissions. If these vacuum states are modified, as for example by placing an excited atom between closely spaced mirrors or in a small cavity (essentially the Casimir effect), spontaneous emission can be greatly inhibited or enhanced or even made reversible. Recent advances in atomic and optical techniques have made it possible to control and manipulate spontaneous emission. A whole new branch of quantum optics called ‘cavity QED’ has developed since 1987 utilizing these dramatic changes in spontaneous emission rates in cavities to construct new kinds of microscopic masers or micromasers that operate with a single atom and a few photons or with photons emitted in pairs in a two-photon transition.
In 1946, E. M. Purcell predicted that the radiative lifetime of an emitter is not an intrinsic property but can be modified by structuring the surrounding electromagnetic field [36]. By inserting a semiconductor quantum dot (QD) in an optical cavity, one can accelerate or inhibit its spontaneous emission. In the present article, we show that the QD spontaneous emission can be deterministically controlled to fabricate bright sources of quantum light. QDs in cavities: basics, motivation, first demonstrations Light-matter coupling We note f the ground state of the QD and e its excited state. For a cavity mode close to resonance with the QD optical transition, we consider only the states with 0 or 1 photon in the cavity mode. The states ∣ e, 0〉 and ∣ f, 1〉 are coupled through light–matter interaction, with a constant g , where h g = ∣〈 e, 0∣ Ed ∣ f, 1∣, with d the dipole of the optical transition e → f and E the electric field at the QD position. Each of the states ∣ e, 0 > and ∣ f, 1 > are also coupled to continua of states: continuum of the free-space optical mode, phonons of the semiconductor matrix, etc. [4]. Here, we consider only the coupling to the continuum of the free-space optical mode, related to the cavity losses, with a constant γ c . When g << γ c , the photon emitted by the recombination of an exciton efficiently escapes outside the cavity. The QD optical transition radiative recombination rate can be accelerated (Purcell effect) or inhibited.
Though QD arrays have initially been mostly studied in an attempt to improve semiconductor lasers, much attention has been recently devoted to the revolutionary prospects opened by the unique properties of single QDs. These artificial atoms allow to mimic in solid-state systems some of the quantum optics experiments performed on atoms since the early 80’s. Recent demonstrations of coherent control experiments on QDs illustrate this fruitful analogy [10]. We will focus here our discussion on the impact of QDs on two other fields, solid-state cavity quantum electrodynamics (CQED) and the generation of quantum states of light. A single QD can be used to emit triggered single photon pulses and photon pairs, whereas its narrow emission spectrum permits to implement microcavities very efficiently to tailor its emission properties. By combining both kind of effects, it is possible to control simultaneously the number of emitted photons as well as their quantum state and to build a solid-state singlemode source of single photons (singlemode S4P) as proposed [11] and demonstrated recently by our group [12]. This novel device represents the ultimate step in a field which has been extremely active in the last 15 years, spontaneous emission (SE) control in optoelectronic devices using confined electronic and/or photonic systems [13]. Before reviewing the development of this single mode S4P, based on a single QD in a pillar microcavity, we will briefly discuss its potential applications in the field of quantum information processing and quantum communications (QIPC).
In the pursuit of developing a quantum information network, photons appear to be the most convenient carriers to interconnect distant ports. The need to get on-demand single photons that is one and only one photon, with a high reliability, is the main driving force for the development of bright solid-state sources. One important parameter is the brightness defined as the probability that one collected pulse contains a single photon. For some applications like quantum information processing or long distance quantum communications, the emitted single photons must be also indistinguishable, so that can make use of their quantum interference to implement effective photon-photon interactions. To reach the ideal source of single and indistinguishable photons, different systems are explored : defects in diamond (NV centers), trapped atoms or ions, single molecules or semiconductor quantum dots.By coupling a semiconductor quantum dot to an optical cavity, the spontaneous emission of the emitter can be modified to obtain bright single-photon sources. An innovative technique was developed by Pr. Pascale Senellart and her team at the Laboratory of Photonics and Nanostructures (LPN) from CNRS that allows making such sources in a very reproducible way.This work explores the performance of single quantum dot coupled to micropillars. Various techniques are used in order to increase the single photon purity and indistinguishability while keeping a high source brightness. First, the cavity was modified using an adiabatic architecture such that a strong acceleration of the spontaneous emission was implemented. Then, a technique to apply an electric bias on the micropillars has been developed. The combination of the electric bias with a resonant optical excitation of the quantum dot allows to generation purely indistinguishable photons with a high brightness.The results developed in this thesis open a vast field of novel applications in quantum technologies, from quantum cryptography, metrology to quantum imaging.
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.