Quantum stabilization of a single-photon emitter in a coupled microcavity-- half-cavity system Experimental verification of quantum transformation between photon and electron spin View project Terahertz Nondestructive Evaluation of Fiber-reinforced Composites View project
C. Y. Chang, L. Lanco, P. Senellart, David S. Citrin
We analyze the quantum dynamics of a two-level emitter in a resonant microcavity with optical feedback provided by a distant mirror (i.e., a half-cavity) with a focus on stabilizing the emitter-microcavity subsystem. Our treatment is fully carried out in the framework of cavity quantum electrodynamics. Specifically, we focus on the dynamics of a perturbed dark state of the emitter to ascertain its stability (existence of time oscillatory solutions around the candidate state) or lack thereof. In particular, we find conditions under which multiple feedback modes of the half cavity contribute to the stability, showing certain analogies with the Lang-Kobayashi equations, which describe a laser diode subject to classical optical feedback.
We analyze the quantum dynamics of a two-level emitter in a resonant microcavity with optical feedback provided by a distant mirror (i.e., a half-cavity) with a focus on stabilizing the emitter-microcavity subsystem. Our treatment is fully carried out in the framework of cavity quantum electrodynamics. Specifically, we focus on the dynamics of a perturbed dark state of the emitter to ascertain its stability (existence of time oscillatory solutions around the candidate state) or lack thereof. In particular, we find conditions under which multiple feedback modes of the half cavity contribute to the stability, showing certain analogies with the Lang-Kobayashi equations, which describe a laser diode subject to classical optical feedback.
We analyze the quantum dynamics of a two-level emitter in a resonant microcavity with optical feedback provided by a distant mirror (i.e., a half cavity) with a focus on stabilizing the emitter-microcavity subsystem. Our treatment is fully carried out in the framework of cavity quantum electrodynamics. Specifically, we focus on the dynamics of a perturbed subradiant state of the emitter-microcavity subsystem to ascertain its stability (existence of time oscillatory solutions around the candidate state) or lack thereof. In particular, we find conditions under which multiple feedback modes of the half cavity contribute to the stability, showing certain analogies with the Lang-Kobayashi equations, which describe a laser diode subject to classical optical feedback.
We propose a scheme to control cavity quantum electrodynamics in the single photon limit by delayed feedback. In our approach a single emitter-cavity system, operating in the weak coupling limit, can be driven into the strong coupling-type regime by an external mirror: The external loop produces Rabi oscillations directly connected to the electron-photon coupling strength. As an expansion of typical cavity quantum electrodynamics, we treat the quantum correlation of external and internal light modes dynamically and demonstrate a possible way to implement a fully quantum mechanical time-delayed feedback. Our theoretical approach proposes a way to experimentally feedback control quantum correlations in the single photon limit.
We present an analytical solution of the single-photon quantum feedback in a cavity quantum electrodynamics system based on a half-cavity setup coupled to a structured continuum. Our exact analytical expression constitutes an important benchmark for quantum-feedback models and allows us to unravel the necessary conditions for the previously reported numerical result that a single-emitter-cavity system, which is initially in the weak-coupling regime, can be driven into the strong-coupling regime via the proposed quantum-feedback mechanism [A. Carmele et al., Phys. Rev. Lett. 110, 013601 (2013)]. We specify the phase relations between the cavity mode and the delay time and state explicitly the theoretical limit for a feedback effect in the single-photon regime. Via the photon-path representation, we prove that the stabilization phenomenon relies on a destructive interference effect and we discuss the stabilization time in the weak- and strong-coupling limits.
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 purpose of this article is to study two-photon dynamics induced by the coherent feedback control of a cavity quantum electrodynamics (cavity-QED) system coupled to a waveguide. In this setup, the two-level system in the cavity can work as a photon source, and the photon emitted into the waveguide can reinteract with the cavity-QED system many times after the transmission and reflection in the waveguide, during which the feedback can tune the number of the photons in and out of the cavity. We analyze the dynamics of two-photon processes in this coherent feedback network in two scenarios: the continuous mode coupling scheme and the discrete periodic mode coupling scheme between the waveguide and cavity. The difference of these coupling schemes is due to their relative scales and the number of semitransparent mirrors for coupling. Specifically, in the continuous mode coupling scheme, the generation of two-photon states is influenced by the length of the feedback loop by the waveguide and the coupling strength between the waveguide and the cavity-QED system. By tuning the length of the waveguide and the coupling strength, we are able to generate two-photon states efficiently. In the discrete periodic mode coupling scheme, the Rabi oscillation in the cavity can be stabilized and there are no notable two-photon states in the waveguide.
Multi-photon lasing has been realized in systems with strong nonlinear interactions between emitters and cavity modes, where single-photon processes are suppressed. Coherence between the internal states of a quantum emitter, or among multiple emitters, plays a key role. Such continuous nonclassical sources of light can find applications in quantum computation, quantum sensing, quantum metrology, and quantum communication.
This thesis explores the multi-photon lasing phenomena in various quantum dot-photonic crystal cavity quantum electrodynamic (QED) setups. Exciton-phonon interactions are inevitable in such systems and are incorporated using the polaron-transformed master equation. The Born-Markov approximation is employed to obtain the reduced density matrix rate equation. Using quantum laser theory, we derived the Scully-Lamb laser rate equations and evaluated the single- and multi-photon excess emission rates defined as the difference between emission and absorption rates into the cavity mode without mean-field approximations. We investigated cooperative two-photon lasing, correlated emission lasing, hyperradiant lasing, non-degenerate two-mode two-photon lasing, and continuous variable entanglement in open quantum systems with single or multiple semiconductor quantum dots (two-level, three-level, and four-level) driven coherently/incoherently and coupled to single/ bimodal cavities.