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arXiv:0906.2690 · Physical Review A

Pulse shaping by coupled cavities: Single photons and qudits

Chun‐Hsu Su, Andrew D. Greentree, William J. Munro, Kae Nemoto, Lloyd C. L. Hollenberg

Published Sep 9, 2009• 17 citations
arXivHTMLPDF

Abstract

Dynamic coupling of cavities to a quantum network is of major interest to distributed quantum information processing schemes based on cavity quantum electrodynamics. This can be achieved by actively tuning a mediating atom-cavity system. In particular, we consider the dynamic coupling between two coupled cavities, each interacting with a two-level atom, realized by tuning one of the atoms. One atom-field system can be controlled to become maximally and minimally coupled with its counterpart, allowing high fidelity excitation confinement, $Q$ switching, and reversible state transport. As an application, we first show that simple tuning can lead to emission of near-Gaussian single-photon pulses that is significantly different from the usual exponential decay in a passive cavity-based system. The influences of cavity loss and atomic spontaneous emission are studied in detailed numerical simulations, showing the practicality of these schemes within the reach of current experimental solid-state technology. We then show that when the technique is employed to an extended coupled-cavity scheme involving a multilevel atom, arbitrary temporal superposition of single photons can be engineered in a deterministic way.

DOI
10.1103/physreva.80.033811

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Dynamic coupling of cavities to a quantum network is of major interest to distributed quantum information processing schemes based on cavity quantum electrodynamics. This can be achieved by actively tuning a mediating atom-cavity system. In particular, we consider the dynamic coupling between two coupled cavities, each interacting with a two-level atom, realized by tuning one of the atoms. One atom-field system can be controlled to become maximally and minimally coupled with its counterpart, allowing high fidelity excitation confinement, QQQ switching, and reversible state transport. As an application, we first show that simple tuning can lead to emission of near-Gaussian single-photon pulses that is significantly different from the usual exponential decay in a passive cavity-based system. The influences of cavity loss and atomic spontaneous emission are studied in detailed numerical simulations, showing the practicality of these schemes within the reach of current experimental solid-state technology. We then show that when the technique is employed to an extended coupled-cavity scheme involving a multilevel atom, arbitrary temporal superposition of single photons can be engineered in a deterministic way.
The ability to control the temporal shape of single-photon pulses is highly desirable in quantum information processing. For instance, it has been shown that Gaussian pulses are best suited for linear optics quantum computing1. By mimicking the time-reversal of a spontaneous emission event, it also allows to optimize the absorption of the prepared photons by a quantum emitter. In this work we investigate the potential of using fast modifications of the detuning between an atomic system and a cavity mode during photon emission to reach this goal. We compare two approaches consisting of varying the emitter or cavity frequency. The latter, achievable by a fast modification of the refractive index of a solid state cavity, will be shown to have negligible influence on the photon spectrum. It allows to create Gaussian pulses interacting with a fidelity to the target photons of 99%, as well as time-reversed photons absorbed by an atom in a cavity with a probability of 93%.
Summary form only given. In quantum information processing, a qubit is realised as a superposition of atomic or ionic eigenstates, or as a superposition of the states of a photon. A coupling between these different types of qubits is necessary to perform quantum operations or quantum transmissions, e.g. in a quantum network where single atoms or ions are entangled with individual photons. To generate such an entanglement in a controlled way, a triggered source for single photons, a photon pistol, will be needed. Our scheme will lead to the emission of one photon into a single, predetermined mode of the radiation field in response to a trigger event. This photon is emitted from an atom strongly coupled to a high-finesse optical cavity, and the trigger is a classical light pulse. The device combines cavity-QED with an adiabatic transfer technique. We consider a single lambda-type three-level atom being placed inside an empty cavity.
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.
We study analytically the dynamics of cavity QED nodes in a practical quantum network. Given a single 3-level ΛΛΛ-type atom or quantum dot coupled to a micro-cavity, we derive several necessary and sufficient criteria for the coherent trapping and generation of a single photon pulse with a given waveform to be realizable. We prove that these processes can be performed with practical hardware -- such as cavity QED systems which are operating deep in the weak coupling regime -- given a set of restrictions on the single-photon pulse envelope. We systematically study the effects of spontaneous emission and spurious cavity decay on the transfer efficiency, including the case where more than one excited state participates in the dynamics. This work should open the way to very efficient optimizations of the operation of quantum networks.
Control of the temporal waveform of photons produced during spontaneous emission from single quantum emitters provides a crucial tool in the establishment of hybrid quantum systems, optimization of quantum state transfer protocols and mitigation of effects due interferometric instability for network architectures based on flying qubits. We describe a method to generate photons of any temporal waveform from emitters of any excited state lifetime, limited only by the timing resolution of control hardware. We show how the temporal waveform of photons can be controlled by deterministically varying the population of an excited state which undergoes spontaneous emission. Our broadly applicable approach has only two requirements for a candidate quantum emitter: modulation of the (1) amplitude and (2) relative phase of a field coupling a ground state to the excited manifold. We detail how to identify optimal excitation pulses by employing variational algorithms to feed back on atomic populations. Additionally, we develop Quantum Monte Carlo based tools to determine photon-number statistics and establish techniques to identify optimal excitation strengths and post-selection thresholds for photon generation protocols. We situate our work in the context of other prior research on bespoke single photon sources and networking including post-emission pulse shaping, temporal gating and cavity-based methods. In comparison, our free-space process has greater flexibility in producing any waveform, requires less infrastructure, and can be readily applied across a wide range of quantum emitters. We discuss the applications and limits of this technique, including how increasing photon emission probabilities affects achievable temporal-mode overlap fidelities between emitted and target photon waveforms.
In this article, we discuss the one-excitation dynamics of a quantum system consisting of two two-level atoms each interacting with one of two coupled single-mode cavities via spontaneous emission. When the atoms and cavities are tuned into resonance, a wide variety of time-evolution behaviors can be realized by modulating the atom-cavity coupling strength ggg and the cavity-cavity hopping strength $\ensuremath{\lambda}$. The dynamics is solved rigorously via the eigenproblem of an ordinary coupled linear system and simple analytical solutions are derived at several extreme situations of ggg and $\ensuremath{\lambda}$. In the large hopping limit where $g\ensuremath{\ll}\ensuremath{\lambda}$, the behavior of the system is the linear superposition of a fast and slow periodic oscillation. The quantum state transfers from one atom to the other atom accompanied with weak excitation of the cavity mode. In the large coupling limit where $g\ensuremath{\gg}\ensuremath{\lambda}$, the time-evolution behavior of the system is characterized by the usual slowly varying carrier envelope superimposed upon a fast and violent oscillation. At a certain instant, the energy is fully transferred from the one quantum subsystem to the other. When the two interaction strengths are comparable in magnitude, the dynamics acts as a continuous pulse having irregular frequency and line shape of peaks and valleys, and the complicated time-evolution behaviors are ascribed to the violent competition between all the one-excitation quantum states. The coupled quantum system of atoms and cavities makes a good model to study cavity quantum electrodynamics with great freedoms of many-body interaction.