Photon-number Correlations Research Articles

Low-noise macroscopic twin beams

Applying a multiphoton-subtraction technique to two-color macroscopic squeezed vacuum state of light generated via high-gain parametric down conversion we conditionally prepare a new state of light: bright multi-mode low-noise twin beams. The obtained results demonstrate up to 8-fold suppression of noise in each beam while preserving and even moderately improving the nonclassical photon number correlations between the beams. The prepared low-noise macroscopic state, containing up to 2000 photons per mode, is not among the states achievable through nonlinear optical processes. The proposed technique substantially improves the usefulness of twin beams for quantum technologies.

Projective filtering of the fundamental eigenmode from spatially multimode radiation

Lossless filtering of a single coherent (Schmidt) mode from spatially multimode radiation is a problem crucial for optics in general and for quantum optics in particular. It becomes especially important in the case of nonclassical light that is fragile to optical losses. An example is bright squeezed vacuum generated via high-gain parametric down conversion or four-wave mixing. Its highly multiphoton and multimode structure offers a huge increase in the information capacity provided that each mode can be addressed separately. However, the nonclassical signature of bright squeezed vacuum, photon-number correlations, are highly susceptible to losses. Here we demonstrate lossless filtering of a single spatial Schmidt mode by projecting the spatial spectrum of bright squeezed vacuum on the eigenmode of a single-mode fiber. Moreover, we show that the first Schmidt mode can be captured by simply maximizing the fiber-coupled intensity. Importantly, the projection operation does not affect the targeted mode and leaves it usable for further applications.

Raman-Free, Noble-Gas-Filled Photonic-Crystal Fiber Source for Ultrafast, Very Bright Twin-Beam Squeezed Vacuum.

We report a novel source of twin beams based on modulational instability in high-pressure argon-filled hollow-core kagome-style photonic-crystal fiber. The source is Raman-free and manifests strong photon-number correlations for femtosecond pulses of squeezed vacuum with a record brightness of ∼2500 photons per mode. The ultra-broadband (∼50 THz) twin beams are frequency tunable and contain one spatial and less than 5 frequency modes. The presented source outperforms all previously reported squeezed-vacuum twin-beam sources in terms of brightness and low mode content.

Schmidt modes in the angular spectrum of bright squeezed vacuum

We study the spatial properties of high-gain parametric down-conversion (PDC). From the Hamiltonian we find the Schmidt modes, apply the Bloch-Messiah reduction, and calculate analytically the measurable quantities, such as the angular distributions of photon numbers and photon-number correlations. Our approach shows that the Schmidt modes of PDC radiation can be considered the same as for the low-gain (biphoton) case while the Schmidt eigenvalues strongly depend on the parametric gain. Its validity is confirmed by comparison with several experimental results, obtained by us and by other groups.

Photon-number correlations in waveguide lattices with second order coupling

We introduce second-order coupling into the transport and coupling of photons in waveguide lattices. Second-order coupling, as well as high-order couplings, can be significant in long, compact or some special lattices, and is important for large-scale quantum circuits. Photon-number correlations with various amounts of second-order couplings are calculated. Some distinctive and interesting effects arise, and these are helpful for our comprehension of quantum walks in waveguide lattices.

Time-multiplexed measurements of nonclassical light at telecom wavelengths

We report the experimental reconstruction of the statistical properties of an ultrafast pulsed type-II parametric down conversion source in a periodically poled KTP waveguide at telecom wavelengths, with almost perfect photon-number correlations. We used a photon-number-resolving time-multiplexed detector based on a fiber-optical setup and a pair of avalanche photodiodes. By resorting to a germane data-pattern tomography, we assess the properties of the nonclassical light states states with unprecedented precision.

Delayed-choice quantum eraser with thermal light.

We report a random delayed-choice quantum eraser experiment. In a Young's double-slit interferometer, the which-slit information is learned from the photon-number fluctuation correlation of thermal light. The reappeared interference indicates that the which-slit information of a photon, or wave packet, can be "erased" by a second photon or wave packet, even after the annihilation of the first. Different from an entangled photon pair, the jointly measured two photons, or wave packets, are just two randomly distributed and randomly created photons of a thermal source that fall into the coincidence time window. The experimental observation can be explained as a nonlocal interference phenomenon in which a random photon or wave packet pair, interferes with the pair itself at distance.

Interference of macroscopic beams on a beam splitter: phase uncertainty converted into photon-number uncertainty

Squeezed-vacuum twin beams, commonly generated through parametric down-conversion, are known to have perfect photon-number correlations. According to the Heisenberg principle, this is accompanied by a huge uncertainty in their relative phase. By overlapping bright twin beams on a beam splitter, we convert phase fluctuations into photon-number fluctuations and observe this uncertainty as a typical ‘U-shape’ of the output photon-number distribution. This effect, although reported for atomic ensembles and giving hope for phase super-resolution, has never been observed for light beams. The shape of the normalized photon-number difference distribution is similar to the one that would be observed for high-order Fock states. It can be also mimicked by classical beams with artificially mixed phase, but without any perspective for phase super-resolution. The probability distribution at the beam splitter output can be used for filtering macroscopic superpositions at the input.

Mode reconstruction of a light field by multiphoton statistics

We present a simple method to reconstruct the mode distribution of multimode classical and nonclassical optical fields using a single measurement of higher-order photon number correlation functions. Knowing the underlying number and structure of occupied modes of a light field plays a crucial role in minimizing loss and decoherence of quantum information. Typically, full characterization of the mode structure involves a series of several separate measurements in spatial, temporal, frequency, and polarization domains. We experimentally demonstrate reconstruction of up to three modes with excellent agreement and study the robustness of our method in experimentally realizable regimes.

Direct observation of the degree of correlations using photon-number-resolving detectors

Optical parametric down-conversion is a common source for the generation of nonclassical correlated photonic states. Using a parametric down-conversion source and photon-number-resolving detectors, we measure the two-mode photon-number distribution of up to 10 photons for different degrees of correlation. The degree of correlation is controlled by collecting different spatial and spectral single modes for each polarization and varying the amount of spectral and spatial overlap between them. Clear evidence for photon-number correlations is presented despite detector imperfections such as low detection efficiency and other distorting effects. Two criteria, derived directly from the raw data, are shown to be good measures for the degree of correlation. Additionally, using a fitting technique, we find a connection between the measured photon-number distribution and the degree of correlation of the reconstructed original two-mode state. These observations are only possible as a result of the detection of high photon number events.

Experimental realization of quantum illumination.

We present the first experimental realization of the quantum illumination protocol proposed by Lloyd [Science 321, 1463 (2008)] and S. Tan etal. [Phys. Rev. Lett. 101, 253601 (2008)], achieved in a simple feasible experimental scheme based on photon-number correlations. A main achievement of our result is the demonstration of a strong robustness of the quantum protocol to noise and losses that challenges some widespread wisdom about quantum technologies.

Multiphoton nonclassical correlations in entangled squeezed vacuum states

Photon-number correlation measurements are performed on bright squeezed vacuum states using a standard Bell-test setup, and quantum correlations are observed for conjugate polarization-frequency modes. We further test the entanglement witnesses for these states and demonstrate the violation of the separability criteria, which infers that all the macroscopic Bell states, containing typically $10^6$ photons per pulse, are polarization entangled. The study also reveals the symmetry of macroscopic Bell states with respect to local polarization transformations.

Two-photon and three-photon blockades in driven nonlinear systems

Photon blockade, in analogy to Coulomb's or phonon blockades, is a phenomenon when a single photon in a nonlinear cavity blocks the transmission of a second photon. This effect can occur in Kerr-type systems driven by a laser due to strong nonlinear photon-photon interactions. We predict the occurrence of higher-order photon blockades where the transmission of more than two photons is effectively blocked by single- and two-photon states. This photon blockade can be achieved by tuning the frequency of the laser driving field to be equal to the sum of the Kerr nonlinearity and the cavity resonance frequency. We refer to this phenomenon as two-photon blockade or two-photon state truncation via nonlinear scissors, and can also be interpreted as photon-induced tunneling. We also show that, for a driving-field frequency fulfilling another resonance condition and for higher strengths of the driving field, even a three-photon blockade can occur but less clearly than in the case of single- and two-photon blockades. We demonstrate how various photon blockades can be identified by analyzing photon-number correlations, coherence and entropic properties, Wigner functions, and spectra of squeezing. We show that two- and three-photon blockades can, in principle, be observed in various cavity and circuit quantum electrodynamical systems for which the standard single-photon blockade was observed without the need of using higher-order driving interactions or Kerr media exhibiting higher-order nonlinear susceptibility.

Measuring high-order photon-number correlations in experiments with multimode pulsed quantum states

We implement a direct detection scheme based on hybrid photodetectors to experimentally investigate high-order correlations for detected photons by means of quantities that can be experimentally accessed. We show their usefulness in fully characterizing a multimode twin-beam state in comparison with classical states and, in particular, we introduce a nonclassicality criterion based on a simple linear combination of high-order correlation functions. Our scheme is self-consistent, allowing the estimation of all the involved parameters (quantum efficiency, number of modes and average energy) directly from the same experimental data. Results are in very good agreement with theory, thus suggesting the exploitation of our scheme for reliable state characterization in quantum technology.

Sub-shot noise photon-number correlation in stimulated and spontaneous Raman processes

The light initially prepared in a coherent state runs the stimulated and spontaneous Raman processes in a second-order nonlinear medium. Using analytical expressions of field operators for the light modes, we determine the quantum statistical properties of the modes in the stimulated and spontaneous Raman processes. By a choice of phase, we obtain a boson-pair property correlating the pump and vibration modes and such a property correlating the pump and anti-Stokes modes. The Stokes and vibration modes exhibit the boson-pair property for all initial phase differences between the pump mode and the other ones. In the spontaneous Raman process only the Stokes and vibration modes show such a property.

Testing spectral filters as Gaussian quantum optical channels

We experimentally investigate the mode characteristics of multimode radiation fields propagating through frequency-dependent Gaussian channels. After manipulating the twin beams emitted from a conventional parametric downconversion source via spectral filtering, we study the changes in their mode characteristics, utilizing the joint normalized correlation functions. While filtering reduces the number of spectral modes, it also leads to an apparent mode mismatch, which destroys the perfect photon-number correlation between the twin beams, and influences the mode properties of heralded states.

Three-photon states in nonlinear crystal superlattices

It has been a longstanding goal in quantum optics to realize controllable sources generating joint multiphoton states, particularly, photon triplet with arbitrary spectral characteristics. We demonstrate that such sources can be realized via cascaded parametric down-conversion (PDC) in superlattice structures of nonlinear and linear segments. We consider scheme that involves two parametric processes: $\omega_{0}\rightarrow\omega_{1}+\omega_{2}$, $\omega_{2}\rightarrow\omega_{1}+\omega_{1}$ under pulsed pump and investigate spontaneous creation of photon triplet as well as generation of high-intensity mode in intracavity three-photon splitting. We show preparation of Greenberger-Horne-Zeilinger polarization entangled states in cascaded type-II and type-I PDC in framework of consideration dual-grid structure that involves two periodically-poled crystals. We demonstrate the method of compensation of the dispersive effects in non-linear segments by appropriately chosen linear dispersive segments of superlattice for preparation heralded joint states of two polarized photons. In the case of intracavity three-photon splitting, we concentrate on investigation of photon-number distributions, third-order photon-number correlation function as well as the Wigner functions. These quantities are observed both for short interaction time intervals and in over transient regime, when dissipative effects are essential.

CHOOSING A PHOTOEMISSIVE DETECTOR SUITABLE FOR PHOTON-NUMBER STATISTICS OF PULSED FIELDS

We investigate the possibility of using linear detectors that exhibit a response to dark just resolved from that corresponding to a single detected photon to reconstruct the photon-number statistics of pulsed fields containing sizeable numbers of photons per pulse. We demonstrate that by applying a self-consistent procedure to analyze the output pulses of such detectors, we can properly measure statistical distributions of the number of detected photons and photon number correlations. The lack of fulfillment of such minimal requirements impairs the possibility of reliable shot-by-shot determinations of photon numbers.

PHOTON-NUMBER CORRELATION OF A CLASSICAL EXOTIC STATE IN THE MESOSCOPIC REGIME

We demonstrate that by using a pair of hybrid photodetectors, it is possible to quantify the photon-number correlation coefficient between the components of a classical state described by non-trivial statistics and by a non-Gaussian Wigner function. The measurements, performed in the quite unexplored mesoscopic domain (up to 100 photons incident onto the detector), are in good agreement with the theoretical predictions, and thus open the possibility of performing further tests on this exotic state for its application in the field of quantum information.

Field-quadrature and photon-number correlations produced by parametric processes

In a previous paper [Opt. Express 13, 4986 (2005)], formulas were derived for the field-quadrature and photon-number variances produced by multiple-mode parametric processes. In this paper, formulas are derived for the quadrature and number correlations. The number formulas are used to analyze the properties of basic devices, such as two-mode amplifiers, attenuators and frequency convertors, and composite systems made from these devices, such as cascaded parametric amplifiers and communication links. Amplifiers generate idlers that are correlated with the amplified signals, or correlate pre-existing pairs of modes, whereas attenuators decorrelate pre-existing modes. Both types of device modify the signal-to-noise ratios (SNRs) of the modes on which they act. Amplifiers decrease or increase the mode SNRs, depending on whether they are operated in phase-insensitive (PI) or phase-sensitive (PS) manners, respectively, whereas attenuators always decrease these SNRs. Two-mode PS links are sequences of transmission fibers (attenuators) followed by two-mode PS amplifiers. Not only do these PS links have noise figures that are 6-dB lower than those of the corresponding PI links, they also produce idlers that are (almost) completely correlated with the signals. By detecting the signals and idlers, one can eliminate the effects of electronic noise in the detectors.