State Reduction for Correlated Photons and Eigenstates of Unitarily and Non-unitarily Displaced Number Operator

Abstract

The number-quadrature minimum-uncertainty states after rotation and displacement emerge in the parametric down-conversion followed by photon number measurement in the idler mode when the coherent state inputs. Again, the state generated in the signal mode by the reduction is described by the principally measurable quantum-statistical tools.     

Generation of amplitude squeezed states of light from phase squeezed coherent states

Abstract

We propose a scheme to generate a displaced macroscopic superposition of phase squeezed coherent states by incorporating an optical parametric oscillator (OPO) and a nonlinear Kerr medium in a Mach-Zhender interferometer configuration. We show that the phase squeezed coherent state generated by the OPO evolves into a macroscopic superposition of phase squeezed coherent states on spending a specific amount of time inside a Kerr medium. The phase space displacement is achieved by the interference of the intense reference beam with the signal in the final beam splitter of the interferometer. The noise of the reference beam contaminating the signal is prevented by making this beam splitter highly reflective. We have calculated the photon number uncertainty of the outcoming beam and have shown that it is smaller than the usual amplitude squeezed coherent state's value.     

High-power,high-repetition-rate picosecond optical parametric oscillators for the near-to mid-infrared

Abstract

We report high-repetition-rate, singly-resonant, picosecond optical parametric oscillators based on the nonlinear crystals LiB₃O₅ and KTiOAsO₄ which are synchronously pumped by a self-mode-locked Ti:sapphire laser operating at 81 MHz. These devices allow tunable pulse generation from 1·116-3·160 μm to be achieved. The LiB₃O₅ system produces average nearinfrared output powers of 325 mW and is continuous tuning over the wavelength range 1·16-2·26 μm. For 1·8 ps input pump pulses, transform-limited signal pulses with durations of 1-1·2 ps and idler pulses with durations of 2-2·2 ps have been generated over 1·2-2·2 μm, without requirement for dispersion compensation. The KTiOAsO₄ system produces average near-infrared output powers of 403 mW, with the signal tuning over 1·116-1·281 μm and idler tuning over 2·260-3·160 μm. Without dispersion compensation, signal (idler) pulses with durations between 1·01-1·03 (1·61-2·91) ps have been obtained for 1·2 ps input pump pulses.     

Femtosecond optical parametric oscillators based on periodically poled lithium niobate

Abstract

We describe two configurations of collinearly pumped femtosecond optical parametric oscillator based on periodically poled lithium niobate and tunable in the infrared from 975 nm to 4.98 μm. Maximum output powers of 240 mW for the signal and 106 mW for the idler were recorded with 25 mW of average power measured at 4.88 μm. An overall conversion efficiency of 35% and slope efficiencies for the signal of 46% at a wavelength of 1.04 μm and 70% at 1.1 μm were measured. Interferometric autocorrelations of the signal and idler pulses at various wavelengths within the tuning range have been obtained and imply nearly transform-limited pulse durations of about 140fs for the signal and about 190fs for the idler.     

Homodyne tomography of classical and non-classical light

Abstract

States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.     

A variable lateral-shearing Sagnac interferometer with high numerical aperture for measuring the complex spatial coherence function of light

Abstract

We combine a telescopic imaging system with a common-path, lateral-shearing interferometer and use phase-shifting interferometry to measure the complex spatial coherence function (or mutual intensity) of a linearly-polarized optical field. Our telescopic design increases the numerical aperture of the system without distorting the shape of the wave front, and therefore without changing the phase difference between lateral positions in the optical field. Our method of generating lateral-sheared images introduces no additional astigmatism. To demonstrate the use of the interferometer we extract the information contained in the complex spatial coherence function to reconstruct the amplitude and phase of a coherent optical field, and we also show how the spatial coherence function evolves from a coherent field to a partially coherent one as light traverses a random multiple-scattering medium.     

Entanglement distillation from Gaussian input states by coherent photon addition

The entanglement between Gaussian entangled states can be increased by non-Gaussian operations. We design a new scheme, named coherent photon addition, which can coherently add one photon generated by a spontaneous parametric down-conversation process to Gaussian quadrature-entangled light pulses created by a non-degenerate optical parametric amplifier. This operation can increase the entanglement of input two-mode Gaussian states as an entanglement distillation, and provides us with a new method of non-Gaussian operation. This scheme can also help us to study the decoherence of adding one- to two-mode Gaussian states from coherent photon addition to normal photon addition.     

Quantum dynamical properties of a two-photon non linear Jaynes-cummings model

Abstract

In this paper a two-photon Jaynes-Cummings model interacting with a Kerr-like medium is studied. It is assumed that the electromagnetic field is in different states such as coherent, squeezed vacuum and pair coherent, and that the atom is initially in the excited state. The temporal evolution of the population of the excited level, and the second-order coherence function are studied. The results obtained show that this system has some similarities with the two-mode Stark system. Two photon entanglement are analysed at different initial conditions.     

Spatiotemporal Dynamics of Optical Parametric Oscillators

Abstract

The coupling of diffraction and the x ⁽²⁾ nonlinearity is shown to lead to pattern formation in parametric oscillators in optical cavities. In particular the threshold for the generation of signal and idler waves is lowered by an off-axis emission for negative detunings. The output intensity is spatially modulated just above threshold while more complicated patterns appear for larger values of the pump amplitude. Competition between domains of rolls with different orientations leads to long transients until boundary effects prevail. In the case of finite-size input beams, the roll orientation is locally perpendicular to the boundary and the pattern tends to rotate. Finally, the effect of spatial structures on the spectrum of quantum fluctuations of the vacuum is considered and discussed.     

Rotating correlations in partially coherent fields

Abstract

Partially coherent optical fields whose cross-spectral density functions rotate on propagation are examined. The general theory for rotating partially coherent fields in the space-frequency domain is derived for both scalar and electromagnetic approaches. Differences between the results obtained with full and partial coherence is discussed. A numerical example is given for rotating intensity distributions.     

Radiance Functions of Partially Coherent Fields

Abstract

The behaviour of the spectral radiance in fields generated by planar, secondary, quasi-homogeneous sources is investigated. Examples are presented which show how both the spectral intensity and the degree of coherence of the source affect the spatial and the angular distribution of the spectral radiance. These examples clearly show the influence of source coherence on the radiometric behaviour of partially coherent optical fields.     

Simulations of continuum coherent states and its use in quantum cryptographic systems

Abstract

The continuum states formalism is suitable for field quantization in optical fibre; however, they are harder to use than discrete states. On the other hand, a Hermitian phase operator can be defined only in a finite dimensional space. We approximated a coherent continuum state by a finite tensor product of coherent states, each one defined in a finite dimensional space. Using this, in the correct limit, we were able to obtain some statistical properties of the photon number and phase of the continuum coherent states from the probability density functions of the individual, finite dimensional, coherent states. Then, we performed a simulation of the BB84 protocol, using the continuum coherent states, in a fibre interferometer commonly used in quantum cryptography. We observed the fluctuations of the mean photon number in the pulses that arrive at Bob, which occurs in the practical system, introduced by the statistical property of the simulation.     

Coherence phenomena in coupled pptical resonators

Abstract

We predict a variety of photonic coherence phenomena in passive and active coupled ring resonators. Specifically, the effective dispersive and absorptive steady-state response of coupled resonators is derived, and used to determine the conditions for coupled-resonator-induced transparency and absorption, lasing without gain, and cooperative cavity emission. These effects rely on coherent photon trapping, in direct analogy with coherent population trapping phenomena in atomic systems. We also demonstrate that the coupled-mode equations are formally identical to the two-level atom Schrödinger equation in the rotating-wave approximation, and use this result for the analysis of coupled-resonator photon dynamics. Notably, because these effects are predicted directly from coupled-mode theory, they are not unique to atoms, but rather are fundamental to systems of coherently coupled resonators.     

Parametric oscillation with squeezed vacuum reservoirs

Employing the quantum Hamiltonian describing the interaction of a two-mode light (signal–idler modes) generated by a non-degenerate parametric oscillator (NDPO) with two uncorrelated squeezed vacuum reservoirs (USVR), we derive the master and the Fokker–Planck equations. The corresponding Fokker–Planck equation for the Q-function is then solved employing a propagator method developed by K. Fesseha [J. Math. Phys. 33 2179 (1992)]. Making use of this Q-function, we calculate the quadrature fluctuations of the optical system. From these results we infer that the signal–idler modes are in squeezed states. When the NDPO operates below threshold we show that, for a large squeezing parameter, a squeezing amounting to a noise suppression approaching 100% below the vacuum level in one of the quadratures can be achieved.     

Transferring the spatial state of an entangled photon pair to a single photon by photon detection

We show theoretically that the spatial state of entangled photons generated by parametric down-conversion can be transferred to the spatial state of an idler photon by signal photon detection. This study considered the general condition with an arbitrary pump field profile and the detection of a signal photon at an arbitrary distance from a nonlinear crystal where the entangled photons are generated. Upon the detection of a signal photon, the two-photon state function of the entangled state can be transferred to a single-photon state function of the idler field due to the EPR type correlation between the signal and idler fields. The spatial state of the idler field contains more information on the original two-photon state.     

Nonlinear quantum optical computing via measurement

Abstract

We show how the measurement induced model of quantum computation proposed by Raussendorf and Briegel (2001, Phys. Rev. Letts., 86, 5188) can be adapted to a nonlinear optical interaction. This optical implementation requires a Kerr nonlinearity, a single photon source, a single photon detector and fast feed forward. Although nondeterministic optical quantum information proposals such as that suggested by KLM (2001, Nature, 409, 46) do not require a Kerr nonlinearity they do require complex reconfigurable optical networks. The proposal in this paper has the benefit of a single static optical layout with fixed device parameters, where the algorithm is defined by the final measurement procedure.     

Evolution of Coherent States in a Dispersionless Fibre with Saturable Nonlinearity and the Generation of Macroscopic Quantum-superposition States

Abstract

We study the evolution of a initially coherent state of an electromagnetic field propagating in a Kerr medium with saturable nonlinearity. By using the quantum phase distribution formalism, we analyse the dependence of the output signal phase configuration upon input field amplitude. We observe that the saturation of the nonlinear contribution of the refractive index of the propagation medium introduces interference effects that compromise the observation of macroscopically well distinguishable components of the output state. For input amplitudes much larger than a characteristic saturation amplitude the final state differs from the input state only by an overall phase shift. Possible relevance of the present results in the experimental search of Schrödinger cat-like states using semiconductor-doped glass optical fibres is discussed.     

The Interferometer as an Optical Network

Abstract

We consider a generic interferometric set-up as a device to record interference fringes. The system is characterized by two variable transmission beam-splitters. A coherent signal is measured and its noise properties are manipulated by mixing in a squeezed vacuum through the second input port. The performance is optimized either by minimizing the noise at the dark and the light fringes, or alternatively by keeping it below the standard quantum limit for all phase angles observed. The analysis is carried out using a quantum optical network formalism generalizing the classical Jones calculus. The results obtained are interpreted and explained using the Wigner function for the output signals.     

Squeezing and Sub-poisson Statistics in Three-mode Interactions

Abstract

A unique approach to the photon statistics in nonlinear optical interactions is suggested based on the use of moment equations and generalized superposition of coherent fields and quantum noise. Non-classical features such as squeezing of fluctuations and sub-Poisson statistics are derived for finite interaction times in the three-mode interaction process and limits of the model are provided.