Cross phase modulation in a five--level atomic medium: Semiclassical theory

The interaction of a five-level atomic system involving electromagnetically induced transparency with four light fields is investigated. Two different light-atom configurations are considered, and their efficiency in generating large nonlinear cross-phase shifts compared. The dispersive properties of those schemes are analyzed in detail, and the conditions leading to group velocity matching for two of the light fields identified. An analytical treatment based on amplitude equations is used in order to obtain approximate solutions for the susceptibilities, ehich are shown to fit well with the numerical simulations of the full Bloch equations in a large parameter region.Comment: New version: section on pulse propagation added, reference list expanded; 17 pages, 15 figure

Non-conditioned generation of Schroedinger cat states in a cavity

We investigate the dynamics of a two-level atom in a cavity filled with a nonlinear medium. We show that the atom-field detuning $\delta$ and the nonlinear parameter $\chi^{(3)}$ may be combined to yield a periodic dynamics and allowing the generation of almost exact superpositions of coherent states ({\sl Schr\"odinger} cats). By analysing the atomic inversion and the field purity, we verify that any initial atom-field state is recovered at each revival time, and that a coherent field interacting with an excited atom evolves to a superposition of coherent states at each collapse time. We show that a mixed field state (statistical mixture of two coherent states) evolves towards a pure field state ({\sl Schr\"odinger} cat) as well. We discuss the validity of those results by using the field fidelity and the {\sl Wigner} function.Comment: REVTeX4, 8 pages, 7 figures, link to an external animation fil

Field correlations and effective two level atom-cavity systems

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 versio

Assessment of a quantum phase gate operation based on nonlinear optics

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 figure

Polarization phase gate with a tripod atomic system

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 versio

Polariton Analysis of a Four-Level Atom Strongly Coupled to a Cavity Mode

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 figure

Theory of Photon Blockade by an Optical Cavity with One Trapped Atom

In our recent paper [1], we reported observations of photon blockade by one atom strongly coupled to an optical cavity. In support of these measurements, here we provide an expanded discussion of the general phenomenology of photon blockade as well as of the theoretical model and results that were presented in Ref. [1]. We describe the general condition for photon blockade in terms of the transmission coefficients for photon number states. For the atom-cavity system of Ref. [1], we present the model Hamiltonian and examine the relationship of the eigenvalues to the predicted intensity correlation function. We explore the effect of different driving mechanisms on the photon statistics. We also present additional corrections to the model to describe cavity birefringence and ac-Stark shifts. [1] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).Comment: 10 pages, 6 figure

Effect of atomic beam alignment on photon correlation measurements in cavity QED

Quantum trajectory simulations of a cavity QED system comprising an atomic beam traversing a standing-wave cavity are carried out. The delayed photon coincident rate for forwards scattering is computed and compared with the measurements of Rempe et al. [Phys. Rev. Lett. 67, 1727 (1991)] and Foster et al. [Phys. Rev. A 61, 053821 (2000)]. It is shown that a moderate atomic beam misalignment can account for the degradation of the predicted correlation. Fits to the experimental data are made in the weak-field limit with a single adjustable parameter--the atomic beam tilt from perpendicular to the cavity axis. Departures of the measurement conditions from the weak-field limit are discussed.Comment: 15 pages and 13 figure

Cavity QED quantum phase gates for a single longitudinal mode of the intracavity field

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 with the zero- and one-photon Fock states of each of the two opposite circular polarization states of the field. The three-level atom mediates 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 satisfied. 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