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Experiments in two-mode cavity QED

D. G. Norris

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Cavity quantum electrodynamics (QED) allows the study of light-matter in-teractions at the most basic level, through precise identification of the coherent and incoherent (dissipative) parts of the system evolution. We present measurements of light from a cavity QED system consisting of a high-finesse optical resonator coupled to a beam of cold Rb atoms. The novelty of the design lies in the interplay of two degenerate and orthogonal polarization modes. One mode (driven) behaves as the canonical cavity mode of the Jaynes-Cummings Hamiltonian, coherently exciting the atoms with a modest coupling strength; the other mode (undriven) collects a small fraction of spontaneously emitted light and provides a probe of the dissipative processes. We first demonstrate the ability to detect individual atoms passing through the cavity modes in real time by coincidence detection of photons from the un-driven mode. Calculation of statistics and correlation functions from the complete photon detection record allows the determination of detection probabilities and the reconstruction of atomic trajectories. We next present evidence of quantum coher-ence that is created, modified, and measured in the excitation-spontaneous emission cycle. The coherence appears as a long-lived quantum beat at the ground-state Larmor frequency, visible in the intensity autocorrelation function of the undriven mode. Quantum jumps of the atomic state, occurring in between the detections of photons from the cavity, result in substantial changes in the frequency and spectral width of the beats. We present the results of a full quantum Monte Carlo calculation in order to quantitatively explain the measurements.

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Summary form only given. The second order intensity correlation function can provide evidence of the non-classical nature of an electric field, as well as information about the dynamics which produce the field. In practice, this is a conditional measurement of the probability to detect a photon given that another photon was detected in coincidence or some time before. We have measured the correlation function of the photons escaping from a strongly coupled cavity QED system consisting of a high finesse interferometer traversed by a beam of optically pumped Rb atoms. In this regime, the rate of reversible exchange of energy between the atoms and the cavity is larger than the cavity decay and spontaneous emission rates, and the saturation photon number is less than one. The correlations exhibit the non-classical features of antibunching and sub-Poissonian statistics, and an oscillation related to the exchange of energy taking place in the coupled system of atoms and cavity field. We view the initial photon detection as causing a projection of the system into a well defined initial state from which it coherently evolves back to steady state. A full characterization of this conditional evolution requires the measurement of the electric field as it evolves from the initial state.

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Cavity quantum electrodynamics (QED) allows the study of light-matter in-teractions at the most basic level, through precise identification of the coherent and incoherent (dissipative) parts of the system evolution. We present measurements of light from a cavity QED system consisting of a high-finesse optical resonator coupled to a beam of cold Rb atoms. The novelty of the design lies in the interplay of two degenerate and orthogonal polarization modes. One mode (driven) behaves as the canonical cavity mode of the Jaynes-Cummings Hamiltonian, coherently exciting the atoms with a modest coupling strength; the other mode (undriven) collects a small fraction of spontaneously emitted light and provides a probe of the dissipative processes. We first demonstrate the ability to detect individual atoms passing through the cavity modes in real time by coincidence detection of photons from the un-driven mode. Calculation of statistics and correlation functions from the complete photon detection record allows the determination of detection probabilities and the reconstruction of atomic trajectories. We next present evidence of quantum coher-ence that is created, modified, and measured in the excitation-spontaneous emission cycle. The coherence appears as a long-lived quantum beat at the ground-state Larmor frequency, visible in the intensity autocorrelation function of the undriven mode. Quantum jumps of the atomic state, occurring in between the detections of photons from the cavity, result in substantial changes in the frequency and spectral width of the beats. We present the results of a full quantum Monte Carlo calculation in order to quantitatively explain the measurements.
Summary form only given. The second order intensity correlation function can provide evidence of the non-classical nature of an electric field, as well as information about the dynamics which produce the field. In practice, this is a conditional measurement of the probability to detect a photon given that another photon was detected in coincidence or some time before. We have measured the correlation function of the photons escaping from a strongly coupled cavity QED system consisting of a high finesse interferometer traversed by a beam of optically pumped Rb atoms. In this regime, the rate of reversible exchange of energy between the atoms and the cavity is larger than the cavity decay and spontaneous emission rates, and the saturation photon number is less than one. The correlations exhibit the non-classical features of antibunching and sub-Poissonian statistics, and an oscillation related to the exchange of energy taking place in the coupled system of atoms and cavity field. We view the initial photon detection as causing a projection of the system into a well defined initial state from which it coherently evolves back to steady state. A full characterization of this conditional evolution requires the measurement of the electric field as it evolves from the initial state.
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.
Cavity quantum electrodynamics (QED), the system of a single atom interacting with a single mode of a high finesse optical resonator, has tremendous potential for use in quantum logic, quantum information processing, and in enabling observation of quantum mechanical effects in the laboratory. The work of this thesis demonstrates a number of steps toward realizing these goals, by employing an experimental system with the strongest atom-field coupling achieved to date in optical cavity QED. The effects of strong coupling in cavity QED are studied for single cold atoms measured one at a time, in real time. The passage of single atoms through the cavity is employed to map out the frequency response of the system, and to demonstrate that quantum rather than semiclassical theory provides the correct theoretical model. The mechanical effects of strong coupling on single atoms are explored, these experiments demonstrating the first trapping of single atoms with single photons. Additionally, strong coupling enables high signal-to-noise ratio for monitoring atomic position at single photon field strengths; this capability is employed to investigate the motion of atoms trapped within the cavity. The transmitted cavity field is used to reconstruct the trajectories of single atoms, thereby realizing a new form of microscopy - the Atom-Cavity Microscope. Technical developments necessary to create the cavities used in this experiment are detailed. Ideas for future extensions to the experiment are proposed; a zero light-shift dipole force trap, and measurement of photon statistics of a single strongly coupled atom (which realizes a photon blockade device) are discussed.
We study the light generated by spontaneous emission into a mode of a cavity QED system under weak excitation of the orthogonally polarized mode. Operating in the intermediate regime of cavity QED with comparable coherent and decoherent coupling constants, we find an enhancement of the emission into the undriven cavity mode by more than a factor of 18.5 over that expected by the solid angle subtended by the mode. A model that incorporates three atomic levels and two polarization modes quantitatively explains the observations.
We use an optical cavity in the regime of intermediate coupling between atom and cavity mode to detect single moving atoms. Degenerate polarization modes allow excitation of the atoms in one mode and collection of spontaneous emission in the other while keeping separate the two sources of light; we obtain a higher confidence and efficiency of detection by adding cavity-enhanced Faraday rotation. Both methods greatly benefit from coincidence detection of photons, attaining fidelities in excess of 99% in less than $1\text{ }\ensuremath{\mu}\text{s}$. Detailed studies of the second-order intensity autocorrelation function of light from the signal mode reveal evidence of antibunched photon emissions and the dynamics of single-atom transits.
We study the light generated by spontaneous emission into a mode of a cavity QED system under weak excitation of the orthogonally polarized mode. Operating in the intermediate regime of cavity QED with comparable coherent and decoherent coupling constants, we find an enhancement of the emission into the undriven cavity mode by more than a factor of 18.5 over that expected by the solid angle subtended by the mode. A model that incorporates three atomic levels and two polarization modes quantitatively explains the observations.