Pairwise entanglement and readout of atomic-ensemble and optical wave-packet modes in traveling-wave Raman interactions

We analyze quantum entanglement of Stokes light and atomic electronic polarization excited during single-pass, linear-regime, stimulated Raman scattering in terms of optical wave-packet modes and atomic-ensemble spatial modes. The output of this process is confirmed to be decomposable into multiple discrete, bosonic mode pairs, each pair undergoing independent evolution into a two-mode squeezed state. For this we extend the Bloch-Messiah reduction theorem, previously known for discrete linear systems (S. L. Braunstein, Phys. Rev. A, vol. 71, 055801 (2005)). We present typical mode functions in the case of one-dimensional scattering in an atomic vapor. We find that in the absence of dispersion, one mode pair dominates the process, leading to a simple interpretation of entanglement in this continuous-variable system. However, many mode pairs are excited in the presence of dispersion-induced temporal walkoff of the Stokes, as witnessed by the photon-count statistics. We also consider the readout of the stored atomic polarization using the anti-Stokes scattering process. We prove that the readout process can also be decomposed into multiple mode pairs, each pair undergoing independent evolution analogous to a beam-splitter transformation. We show that this process can have unit efficiency under realistic experimental conditions. The shape of the output light wave packet can be predicted. In case of unit readout efficiency it contains only excitations originating from a specified atomic excitation mode

Quantum efficiency of single-photon sources in the cavity-QED strong-coupling regime

We calculate the integrated-pulse quantum efficiency of single-photon sources in the cavity quantum electrodynamics (QED) strong-coupling regime. An analytical expression for the quantum efficiency is obtained in the Weisskopf-Wigner approximation. Optimal conditions for a high quantum efficiency and a temporally localized photon emission rate are examined. We show the condition under which the earlier result of Law and Kimble [J. Mod. Opt. 44, 2067 (1997)] can be used as the first approximation to our result.Comment: 8 pages, 3 figures, final version, tex file uploade

Quantum-Fluctuation-Initiated Coherence in Multi-Octave Raman Optical Frequency Combs

We show experimentally and theoretically that the spectral components of a multi-octave frequency comb spontaneously created by stimulated Raman scattering in a hydrogen-filled hollow-core photonic crystal fiber exhibit strong self coherence and mutual coherence within each 12 ns driving laser pulse. This coherence arises in spite of the field's initiation being from quantum zero-point fluctuations, which causes each spectral component to show large phase and energy fluctuations. This points to the possibility of an optical frequency comb with nonclassical correlations between all comb lines.Comment: Accepted for publication, Physical Review Letters, 201

Proposal for a QND which-path measurement using photons

A scheme is proposed for experimentally realizing the famous two-slit gedaenken experiment using photons. As elegantly discussed for electrons by Feynman, a particle's quantum pathways interfere to produce fringes in the probability density for the particle to be found at a particle location. If the path taken by the particle is experimentally determined, the complementarity principle says that the fringes must disappear. To carry out this experiment with photons is difficult because normally the act of determining a photon's location destroys it. We propose to overcome this difficulty by putting a type-2 optical parametric amplifier (OPA) in each arm of a Mach-Zehnder interferometer, and observing fringes at the output. An OPA responds to an input photon by increasing its probability to produce a pair of photons with polarization orthogonal to the input, the detection of which allows partial inference about the path taken by the input photon without destroying it. Thus, the measurement is of the quantum nondemolition (QND) type

Tomographic reconstruction of quantum states in N spatial dimensions

Most quantum tomographic methods can only be used for one-dimensional problems. We show how to infer the quantum state of a non-relativistic N-dimensional harmonic oscillator system by simple inverse Radon transforms. The procedure is equally applicable to finding the joint quantum state of several distinguishable particles in different harmonic oscillator potentials. A requirement of the procedure is that the angular frequencies of the N harmonic potentials are incommensurable. We discuss what kind of information can be found if the requirement of incommensurability is not fulfilled and also under what conditions the state can be reconstructed from finite time measurements. As a further example of quantum state reconstruction in N dimensions we consider the two related cases of an N-dimensional free particle with periodic boundary conditions and a particle in an N-dimensional box, where we find a similar condition of incommensurability and finite recurrence time for the one-dimensional system.Comment: 8 pages, 1 figur

Photon temporal modes: a complete framework for quantum information science

Field-orthogonal temporal modes of photonic quantum states provide a new framework for quantum information science (QIS). They intrinsically span a high-dimensional Hilbert space and lend themselves to integration into existing single-mode fiber communication networks. We show that the three main requirements to construct a valid framework for QIS -- the controlled generation of resource states, the targeted and highly efficient manipulation of temporal modes and their efficient detection -- can be fulfilled with current technology. We suggest implementations of diverse QIS applications based on this complete set of building blocks.Comment: 17 pages, 13 figure

Modematching an optical quantum memory

We analyse the off-resonant Raman interaction of a single broadband photon, copropagating with a classical `control' pulse, with an atomic ensemble. It is shown that the classical electrodynamical structure of the interaction guarantees canonical evolution of the quantum mechanical field operators. This allows the interaction to be decomposed as a beamsplitter transformation between optical and material excitations on a mode-by-mode basis. A single, dominant modefunction describes the dynamics for arbitrary control pulse shapes. Complete transfer of the quantum state of the incident photon to a collective dark state within the ensemble can be achieved by shaping the control pulse so as to match the dominant mode to the temporal mode of the photon. Readout of the material excitation, back to the optical field, is considered in the context of the symmetry connecting the input and output modes. Finally, we show that the transverse spatial structure of the interaction is characterised by the same mode decomposition.Comment: 17 pages, 4 figures. Brief section added treating the transverse spatial structure of the memory interaction. Some references added. A few typos fixe