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arXiv:0806.4162 · Physical Review A

Investigations of a coherently driven semiconductor optical cavity QED system

Kartik A. Srinivasan, Christopher P. Michael, Raviv Perahia, Oskar J. Painter

Published Sep 30, 2008• 23 citations
arXivHTMLPDF

Abstract

Chip-based cavity quantum electrodynamics (QED) devices consisting of a self-assembled InAs quantum dot (QD) coupled to a high quality factor GaAs microdisk cavity are coherently probed through their optical channel using a fiber taper waveguide. We highlight one particularly important aspect of this all-fiber measurement setup, which is the accuracy to which the optical coupling level and optical losses are known relative to typical free-space excitation techniques. This allows for precise knowledge of the intracavity photon number and measurement of absolute transmitted and reflected signals. Resonant optical spectroscopy of the system under both weak and strong driving conditions are presented, which when compared with a quantum master equation model of the system allows for determination of the coherent coupling rate between QD exciton and optical cavity mode, the different levels of elastic and inelastic dephasing of the exciton state, and the position and orientation of the QD within the cavity. Pump-probe measurements are also performed in which a far off-resonant red-detuned control laser beam is introduced into the cavity. Rather than producing a measurable ac Stark shift in the exciton line of the QD, we find that this control beam induces a saturation of the resonant system response. The broad photoluminescence spectrum resulting from the presence of the control beam in the cavity points to sub-band-gap absorption in the semiconductor, and the resulting free-carrier generation, as the likely source of system saturation.

DOI
10.1103/physreva.78.033839

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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. 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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.

Journal of Optics B Quantum and Semiclassical Optics•Feb 1, 2004•0 citations
Chip-based cavity quantum electrodynamics (QED) devices consisting of a self-assembled InAs quantum dot (QD) coupled to a high quality factor GaAs microdisk cavity are coherently probed through their optical channel using a fiber taper waveguide. We highlight one particularly important aspect of this all-fiber measurement setup, which is the accuracy to which the optical coupling level and optical losses are known relative to typical free-space excitation techniques. This allows for precise knowledge of the intracavity photon number and measurement of absolute transmitted and reflected signals. Resonant optical spectroscopy of the system under both weak and strong driving conditions are presented, which when compared with a quantum master equation model of the system allows for determination of the coherent coupling rate between QD exciton and optical cavity mode, the different levels of elastic and inelastic dephasing of the exciton state, and the position and orientation of the QD within the cavity. Pump-probe measurements are also performed in which a far off-resonant red-detuned control laser beam is introduced into the cavity. Rather than producing a measurable ac Stark shift in the exciton line of the QD, we find that this control beam induces a saturation of the resonant system response. The broad photoluminescence spectrum resulting from the presence of the control beam in the cavity points to sub-band-gap absorption in the semiconductor, and the resulting free-carrier generation, as the likely source of system saturation.
Cavity quantum electrodynamic (cQED) systems have attracted extensive research interest in the past decades as the main driving force of quantum optics. First experimental demonstrations focused on the enhancement of spontaneous emission and optical nonlinearities related to a single quantum emitter confined in a microcavity. Major technological effort was needed to enter the strong coupling regime of single emitter cQED to study for instance the non-harmonicity of resulting Jaynes-Cummings ladder and to perform quantum non-demolition measurements at the heart of quantum optics. Corresponding milestone experiments paved the way towards the realization of a wide variety of non-classical light sources bringing the concept of photonic quantum networks to a practical level. cQED systems can be realized using atomic, superconducting and semiconductor platforms. In view of future applications in the quantum information technology, the solid state platform of microcavities with embedded quantum emitters is the most attractive one as it promises low-cost mass production as well as interoperability with the integrated electronic circuit technology of today. Therefore, quantum dot (QD)-microcavity systems are very attractive for further investigations in this field. Indeed, even though cQED effects have been studied for many years now, there are still fundamental aspects remaining to be explored. One example is the exploration of a strongly coupled cQED system under coherent optical excitation which is one of the primary goals of this work. The work presented in this thesis aims at a deeper understanding of cQED effects in semiconductor based implementations of this central topic of quantum optics. It includes comprehensive spatially-resolved studies of the QD-micropillar system in the both weak and strong coupling regime. For this purpose an advanced 90 degree excitation and detection scheme, suitable for efficient wavelength-independent driving of the coupled exciton (X) and cavity mode (C) system, was implemented. This flexible and powerful technique enables access to the three-dimensional emission characteristics of QD-micropillars providing important new insight into cQED effects which is the central aspect of the first part of this thesis. The performed studies show for instance a pronounced anticorrelation (correlation) of the directional emission characteristics down to the single emitter level in the weak (strong) coupling regime demonstrating directly their fundamentally different nature. Related investigations of the lasing regime present a straightforward characterization method to demonstrate lasing action in high-Beta microlasers without the need for time consuming studies employing photon statistics. The second part of the thesis addresses another very important yet unexplored fundamental aspect of cQED. The main focus is on coherently-driven strongly-coupled QD-microcavity systems. Of particular interest is the regime where the coherent excitation dresses the X-C polariton at high excitation powers. This regime is found at the crossover from a quantum (Jaynes Cummings) to a semi-classical (Mollow Triplet-like) system and can be observed between the limiting cases of an anharmonic and a harmonic ladder solely by varying the excitation strength. An indispensable condition for the first observation of this transitory regime is driving the system through the matter (X) component, which distinguishes this work from previous studies. Counterintuitively, significant cavity losses with respect to the coupling strength are required to create the highly coherent state of the laser-dressed polariton. Moreover, this work pioneers in resonance fluorescence (RF) studies of strongly-coupled QD-microcavity systems and reveals that strong X-C coupling suppresses the RF substantially. Additionally, injection pulling of a single polariton is observed for the first time in the QD-microcavity system, which links this classical effect of injection locking, which is also found in macroscopic lasers, to the quantum regime. Complementary studies on long range off-resonant X-C coupling, mutual coupling of two QD Xs as well as temperature stability of the coherent coupling regime deepen the fundamental understanding of the strong light-matter interaction in semiconductor systems.
We theoretically study the bichromatic driving of a solid-state cavity quantum electrodynamics (QED) system as a means of probing cavity dressed state transitions and observing the coherent interaction between the system and the light field. We show that this method can enable the observation of the higher order cavity dressed states, supersplitting and ac-Stark shift in a solid-state system comprised of a quantum dot (QD) strongly coupled to a photonic crystal cavity for the on- and far off-resonant cases. For the off-resonant case, phonons mediate off-resonant coupling between the QD and the photonic resonator, a phenomenon unique to solid-state cavity QED.
The models presented simulate pumping techniques that can be used on modern semiconductor devices which are capable of coupling a quantum dot and cavity mode in order to determine a more efficient method of producing a single-photon emitter while taking into consideration typical parameters which are achievable given today's standards of coupling strength. Cavity quantum electrodynamics are incorporated in the calculations as we compare various pumping schemes for the system that either use on-resonant laser excitation or nonresonant excitation due to a wetting layer. In particular, we look to study how antibunching effects change for each method as the cavity finesse is increased toward the strong coupling regime. Experimentally these studies are equivalent to nonlinear pump-probe measurements, where a strong pump, either resonant or nonresonant, is used to excite the coupled system, and the resulting state is characterized using a weak, resonant probe beam.
In this work we present an extensive experimental and theoretical investigation of different regimes of strong field light–matter interaction for cavity-driven quantum dot (QD) cavity systems. The electric field enhancement inside a high-Q micropillar cavity facilitates exceptionally strong interaction with few cavity photons, enabling the simultaneous investigation for a wide range of QD-laser detuning. In case of a resonant drive, the formation of dressed states and a Mollow triplet sideband splitting of up to 45 μ eV is measured for a mean cavity photon number . In the asymptotic limit of the linear AC Stark effect we systematically investigate the power and detuning dependence of more than 400 QDs. Some QD-cavity systems exhibit an unexpected anomalous Stark shift, which can be explained by an extended dressed 4-level QD model. We provide a detailed analysis of the QD-cavity systems properties enabling this novel effect. The experimental results are successfully reproduced using a polaron master equation approach for the QD-cavity system, which includes the driving laser field, exciton-cavity and exciton-phonon interactions.
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.