Phase-space analysis of bosonic spontaneous emission

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 figure

Quantum theory of a polarization phase-gate in an atomic tripod configuration

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, Belaru

Prospects for photon blockade in four level systems in the N configuration with more than one atom

We show that for appropriate choices of parameters it is possible to achieve photon blockade in idealised one, two and three atom systems. We also include realistic parameter ranges for rubidium as the atomic species. Our results circumvent the doubts cast by recent discussion in the literature (Grangier et al Phys. Rev Lett. 81, 2833 (1998), Imamoglu et al Phys. Rev. Lett. 81, 2836 (1998)) on the possibility of photon blockade in multi-atom systems.Comment: 8 page, revtex, 7 figures, gif. Submitted to Journal of Optics B: Quantum and Semiclassical Optic

A proposal for an optical implementation of a universal quantum phase gate

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

Entanglement and four wave mixing effects in the dissipation free nonlinear interaction of two photons at a single atom

We investigate the nonlinear interaction between two photons in a single input pulse at an atomic two level nonlinearity. A one dimensional model for the propagation of light to and from the atom is used to describe the precise spatiotemporal coherence of the two photon state. It is shown that the interaction generates spatiotemporal entanglement in the output state similar to the entanglement observed in parametric downconversion. A method of generating photon pairs from coherent pump light using this quantum mechanical four wave mixing process is proposed.Comment: 10 pages, including 3 figures, correction in eq.(7), updated references, final version for publication in PR

Controlling quantum entanglement through photocounts

We present a protocol to generate and control quantum entanglement between the states of two subsystems (the system ${\cal S}$) by making measurements on a third subsystem (the monitor ${\cal M}$), interacting with ${\cal S}$. For the sake of comparison we consider first an ideal, or instantaneous projective measurement, as postulated by von Neumann. Then we compare it with the more realistic or generalized measurement procedure based on photocounting on ${\cal M}$. Further we consider that the interaction term (between ${\cal S}$ and ${\cal M}$) contains a quantum nondemolition variable of ${\cal S}$ and discuss the possibility and limitations for reconstructing the initial state of ${\cal S}$ from information acquired by photocounting on ${\cal M}$.Comment: 12 pages, 3 figures, accepted for publication in Phys. Rev

Optimized phase switching using a single atom nonlinearity

We show that a nonlinear phase shift of pi can be obtained by using a single two level atom in a one sided cavity with negligible losses. This result implies that the use of a one sided cavity can significantly improve the pi/18 phase shift previously observed by Turchette et al. [Phys. Rev. Lett. 75, 4710 (1995)].Comment: 6 pages, 3 figures, added comments on derivation and assumption

Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach

We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump pump, Stokes signal, and Raman coherence idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions