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Superradiance, the enhanced collective emission of energy from a coherent ensemble of quantum systems, has been typically studied in atomic ensembles. In this work we study theoretically the enhanced emission of energy from coherent ensembles of harmonic oscillators. We show that it should be possible to observe harmonic oscillator superradiance for the first time in waveguide arrays in integrated photonics. Furthermore, we describe how pairwise correlations within the ensemble can be measured with this architecture. These pairwise correlations are an integral part of the phenomenon of superradiance and have never been observed in experiments to date., Comment: 7 pages, 3 figures

Using a gradient echo memory, we experimentally demonstrate cross phase modulation (XPM) between two optical pulses; one stored and one freely propagating through the memory medium. We explain how this idea can be extended to enable substantial nonlinear interaction between two single photons that are both stored in the memory. We present semi-classical and quantum simulations along with a proposed experimental scheme to demonstrate the feasibility of achieving large XPM at single photon level.

We analyze in detail the proposal for a two-qubit gate for travelling single-photon qubits recently presented by C. Ottaviani \emph{et al}. [Phys. Rev. A \textbf{73}, 010301(R) (2006)]. The scheme is based on an ensemble of five-level atoms coupled to two quantum and two classical light fields. The two quantum fields undergo cross-phase modulation induced by electromagnetically induced transparency. The performance of this two-qubit quantum phase gate for travelling single-photon qubits is thoroughly examined in the steady-state and transient regimes, by means of a full quantum treatment of the system dynamics. In the steady-state regime, we find a general trade-off between the size of the conditional phase shift and the fidelity of the gate operation. However, this trade-off can be bypassed in the transient regime, where a satisfactory gate operation is found to be possible, significantly reducing the gate operation time., Comment: 12 pages, 15 figures

We present a full quantum treatment of a five-level atomic system coupled to two quantum and two classical light fields. The two quantum fields undergo a cross-phase modulation induced by electro-magnetically induced transparency. The performance of this configuration as a two-qubit quantum phase gate for travelling single-photons is examined. A trade-off between the size of the conditional phase shift and the fidelity of the gate is found. Nonetheless, a satisfactory gate performance is still found to be possible in the transient regime, corresponding to a fast gate operation., Comment: 4 pages, 3 figures

We present phase-space techniques for the modelling of spontaneous emission in two-level bosonic atoms. The positive-P representation is shown to give a full and complete description and can be further developed to give exact treatments of the interaction of degenerate bosons with the electromagnetic field in a given experimental situation. The Wigner representation, even when truncated at second order, is shown to need a doubling of the phase-space to allow for a positive-definite diffusion matrix in the appropriate Fokker-Planck equation and still fails to agree with the full quantum results of the positive-P representation. We show that quantum statistics and correlations between the ground and excited states affect the dynamics of the emission process, so that it is in general non-exponential., Comment: 16 pages, 6 figures

A single three-level atom driven by a longitudinal mode of a high-Q cavity is used to implement two-qubit quantum phase gates for the intracavity field. The two qubits are associated to the zero-and one-photon Fock states of each of the two opposite circular polarization states of the field. The three-level atom yields the conditional phase gate provided the two polarization states and the atom interact in a $V$-type configuration and the two photon resonance condition is fulfilled. Microwave and optical implementations are discussed with gate fidelities being evaluated against several decoherence mechanisms such as atomic velocity fluctuations or the presence of a weak magnetic field. The use of coherent states for both polarization states is investigated to assess the entanglement capability of the proposed quantum gates.

A novel effect of population transfer in a five-level system is analyzed. This population transfer effect is found to be a version of a Raman process, which is facilitated and assisted by coherence effects, acting to close other available decay channels., Comment: International Wokshop and Seminar on Rydberg Physics, 19 April - 14 May 2004, Dresden, Germany

Large optical nonlinearities occurring in a coherently prepared atomic system are shown to produce phase shifts of order $\pi$. Such an effect may be observed in ultracold rubidium atoms where it could be feasibly exploited toward the realization of a polarization phase gate., Comment: Foundations of Quantum Information, Camerino, 16th-19th April 2004, Italy

We present the quantum theory of a polarization phase-gate that can be realized in a sample of ultracold rubidium atoms driven into a tripod configuration. The main advantages of this scheme are in its relative simplicity and inherent symmetry. It is shown that the conditional phase shifts of order $\pi$ can be attained., Comment: X International Conference on Quantum Optics, Minsk, Belarus

We analyse the properties of the second order correlation functions of the electromagnetic field in atom-cavity systems that approximate two-level systems. It is shown that a recently-developed polariton formalism can be used to account for all the properties of the correlations, if the analysis is extended to include two manifolds - corresponding to the ground state and the states excited by a single photon - rather than just two levels., Comment: 4 pages, 2 figures, published version

We analyze the nonlinear optical response of a four-level atomic system driven into a tripod configuration. The large cross-Kerr nonlinearities that occurr in such a system are shown to produce nonlinear phase shift of order $\pi$. Such a substantial shift may be observed in a cold atomic gas in a magneto-optical trap where it coupl be fasibly exploited towards the realization of a polarization quantum phase gate. The experimental feasibility of such a gate is here examined in detail., Comment: Corrected version

We explore the photon statistics of light emitted from a system comprising a single four--level atom strongly coupled to a high-finesse optical cavity mode which is driven by a coherent laser field. In the weak driving regime this system is found to exhibit a photon blockade effect. For intermediate driving strengths we find a sudden change in the photon statistics of the light emitted from the cavity. Photon antibunching switches to photon bunching over a very narrow range of intracavity photon number. It is proven that this sudden change in photon statistics occurs due to the existence of robust quantum interference of transitions between the dressed states of the atom-cavity system. Furthermore, it is shown that the strong photon bunching is a nonclassical effect for certain values of driving field strength, violating classical inequalities for field correlations., Comment: 14 pages, 11 figures

We present a complete analytical solution for a single four-level atom strongly coupled to a cavity field mode and driven by external coherent laser fields. The four-level atomic system consists of a three-level subsystem in an EIT configuration, plus an additional atomic level; this system has been predicted to exhibit a photon blockade effect. The solution is presented in terms of polaritons. An effective Hamiltonian obtained by this procedure is analyzed from the viewpoint of an effective two-level system, and the dynamic Stark splitting of dressed states is discussed. The fluorescence spectrum of light exiting the cavity mode is analyzed and relevant transitions identified., Comment: 12 pages, 9 figures