Quantum theory of resonantly enhanced four-wave mixing: mean-field and exact numerical solutions

We present a full quantum analysis of resonant forward four-wave mixing based on electromagnetically induced transparency (EIT). In particular, we study the regime of efficient nonlinear conversion with low-intensity fields that has been predicted from a semiclassical analysis. We derive an effective nonlinear interaction Hamiltonian in the adiabatic limit. In contrast to conventional nonlinear optics this Hamiltonian does not have a power expansion in the fields and the conversion length increases with the input power. We analyze the stationary wave-mixing process in the forward scattering configuration using an exact numerical analysis for up to $10^3$ input photons and compare the results with a mean-field approach. Due to quantum effects, complete conversion from the two pump fields into the signal and idler modes is achieved only asymptotically for large coherent pump intensities or for pump fields in few-photon Fock states. The signal and idler fields are perfectly quantum correlated which has potential applications in quantum communication schemes. We also discuss the implementation of a single-photon phase gate for continuous quantum computation.Comment: 10 pages, 11 figure

Efficient photon counting and single-photon generation using resonant nonlinear optics

The behavior of an atomic double lambda system in the presence of a strong off-resonant classical field and a few-photon resonant quantum field is examined. It is shown that the system possesses properties that allow a single-photon state to be distilled from a multi-photon input wave packet. In addition, the system is also capable of functioning as an efficient photodetector discriminating between one- and two-photon wave packets with arbitrarily high efficiency.Comment: 4 pages, 2 figure

Full quantum solutions to the resonant four-wave mixing of two single-photon wave packets

We analyze both analytically and numerically the resonant four-wave mixing of two co-propagating single-photon wave packets. We present analytic expressions for the two-photon wave function and show that soliton-type quantum solutions exist which display a shape-preserving oscillatory exchange of excitations between the modes. Potential applications including quantum information processing are discussed.Comment: 7 pages, 3 figure

Threshold and linewidth of a mirrorless parametric oscillator

Abstract: We analyze the above-threshold behavior of a mirrorless parametric oscillator based on resonantly enhanced four wave mixing in a coherently driven dense atomic vapor. It is shown that, in the ideal limit, an arbitrary small flux of pump photons is sufficient to reach the oscillator threshold. We demonstrate that due to the large group velocity delays associated with coherent media, an extremely narrow oscillator linewidth is possible, making a narrow-band source of non-classical radiation feasible

Nonlinear optics via double dark resonances

Double dark resonances originate from a coherent perturbation of a system displaying electromagnetically induced transparency. We experimentally show and theoretically confirm that this leads to the possibility of extremely sharp resonances prevailing even in the presence of considerable Doppler broadening. A gas of 87Rb atoms is subjected to a strong drive laser and a weak probe laser and a radio frequency field, where the magnetic coupling between the Zeeman levels leads to nonlinear generation of a comb of sidebands.Comment: 6 pages, 9 figure

Coherent Control of Stationary Light Pulses

We present a detailed analysis of the recently demonstrated technique to generate quasi-stationary pulses of light [M. Bajcsy {\it et al.}, Nature (London) \textbf{426}, 638 (2003)] based on electromagnetically induced transparency. We show that the use of counter-propagating control fields to retrieve a light pulse, previously stored in a collective atomic Raman excitation, leads to quasi-stationary light field that undergoes a slow diffusive spread. The underlying physics of this process is identified as pulse matching of probe and control fields. We then show that spatially modulated control-field amplitudes allow us to coherently manipulate and compress the spatial shape of the stationary light pulse. These techniques can provide valuable tools for quantum nonlinear optics and quantum information processing.Comment: 27 pages, 10 figure

Phase Coherence and Control of Stored Photonic Information

We report the demonstration of phase coherence and control for the recently developed "light storage" technique. Specifically, we use a pulsed magnetic field to vary the phase of atomic spin excitations which result from the deceleration and storing of a light pulse in warm Rb vapor. We then convert the spin excitations back into light and detect the resultant phase shift in an optical interferometric measurement. The coherent storage of photon states in matter is essential for the practical realization of many basic concepts in quantum information processing.Comment: 5 pages, 3 figures. Submitted to Phys. Rev. Let

Resonantly enhanced nonlinear optics in semiconductor quantum wells: An application to sensitive infrared detection

A novel class of coherent nonlinear optical phenomena, involving induced transparency in quantum wells, is considered in the context of a particular application to sensitive long-wavelength infrared detection. It is shown that the strongest decoherence mechanisms can be suppressed or mitigated, resulting in substantial enhancement of nonlinear optical effects in semiconductor quantum wells.Comment: 4 pages, 3 figures, replaced with revised versio

Towards non-classical light storage via atomic-vapor Raman scattering

We present experimental work that investigates whether quantum information carried by light can be stored via reversible mapping of the quantum state of such light onto a collective atomic coherence. Such a quantum memory could be utilized to allow quantum communication over long, lossy channels. Current efforts concentrate on writing a photon-number-squeezed state of light onto a collective coherence between the ground-state hyperfine levels of 87Rb atoms in a warm vapor cell, and subsequent on-demand retrieval of this light. In this approach, intensity squeezing between the written and retrieved photon fields provides evidence for storage of a photon-number-squeezed state of light. The scheme is based on spontaneous Raman transitions that create the atomic coherence, and at the same time convert control fields into signal fields that propagate under conditions of electromagnetically induced transparency. We present experimental results demonstrating the storage and retrieval of light using this method, and discuss techniques for measuring intensity squeezing between these photon fields