The correlation properties of the pump field in spontaneous parametric down-conversion are crucial in determining the degree of entanglement of generated signal and idler photons. We find theoretically that continuous-variable entanglement of the transverse positions and momenta of these photons can be achieved only if the coherence of the pump beam is sufficiently high. The positions of signal and idler photons are found to be correlated, even for an incoherent pump. However, the momenta of the signal and idler photons are not anti-correlated, even though transverse momentum is conserved.
We report the efficient generation of high-gain parametric down-conversion, including pump depletion, with pump powers as low as 100 $μ$W (energies $0.1$~$μ$J/pulse) and conversion efficiencies up to 33\%. In our simple configuration, the pump beam is tightly focused into a bulk periodically poled lithium niobate crystal placed in free space. We also observe a change in the photon number statistics for both the pump and down-converted beams as the pump power increases to reach the depleted pump regime. The experimental results are a clear signature of the interplay between the pump and the dow…
Resonant optical pumping in dense atomic media is discussed, where the absorption length is less than the smallest characteristic dimension of the sample. It is shown that reabsorption and multiple scattering of spontaneous photons (radiation trapping) can substantially slow down the rate of optical pumping. A very slow relaxation out of the target state of the pump process is then sufficient to make optical pumping impossible. As model systems an inhomogeneously and a radiatively broadened 3-level system resonantly driven with a strong broad-band pump field are considered.
Most investigations of multipartite entanglement have been concerned with temporal modes of the electromagnetic field, and have neglected its spatial structure. We present a simple model which allows to generate tripartite entanglement between spatial modes by parametric down-conversion with two symmetrically-tilted plane waves serving as a pump. The characteristics of this entanglement are investigated. We also discuss the generalization of our scheme to 2N+1-partite entanglement using 2N symmetrically-tilted plane pump waves. Another interesting feature is the possibility of entanglement loc…
We study the quantum correlations induced by spontaneous parametric down-conversion (SPDC) of a frequency comb. We derive a theoretical method to find the output state corresponding to a pump with an arbitrary spectral profile. After applying it to the relevant example of a spectrally chirped pump, we run an optimization algorithm to numerically find the pump profiles maximizing some target functions. These include the number of independently squeezed modes and the variances of nullifiers defining cluster states used in many continuous-variable quantum information protocols. To assess the adva…
We experimentally investigate the parametric down-conversion process in a nonlinear bulk crystal, driven by two non-collinear pump modes. The experiment shows the emergence of bright hot-spots in modes shared by the two pumps, in analogy with the phenomenology recently observed in 2D nonlinear photonic crystals. By exploiting the spatial walk-off between the two extraordinary pump modes we have been able to recreate a peculiar resonance condition, reported by a local enhancement of the parametric gain, which corresponds to a transition from a three-mode to a four-mode coupling. From a quantum …
Correlated photon pairs produced by a spontaneous parametric down conversion (SPDC) process can be used for secure quantum communication over long distances including free space transmission over a link through turbulent atmosphere. We experimentally investigate the possibility to utilize the intrinsic strong correlation between the pump and output photon spatial modes to mitigate the negative targeting effects of atmospheric beam wander. Our approach is based on a demonstration observing the deflection of the beam on a spatially resolved array of single photon avalanche diodes (SPAD-array).
We present theoretical and experimental study of preparing maximally entangled two-photon polarization states, or Bell states, using femtosecond pulse pumped spontaneous parametric down-conversion (SPDC). First, we show how the inherent distinguishability in femtosecond pulse pumped type-II SPDC can be removed by using an interferometric technique without spectral and amplitude post-selection. We then analyze the recently introduced Bell state preparation scheme using type-I SPDC. Theoretically, both methods offer the same results, however, type-I SPDC provides experimentally superior methods …
We study the chronocyclic character, i.e. the joint temporal and spectral properties, of the single-photon constituents of photon pairs generated by spontaneous parametric down conversion. In particular we study how single photon properties, including purity and single-photon chirp, depend on photon pair properties, including the type of signal-idler spectral and correlations and the level of pump chirp.
Surface spontaneous parametric down-conversion is predicted as a consequence of continuity requirements for electric- and magnetic-field amplitudes at a discontinuity of chi2 nonlinearity. A generalization of the usual two-photon spectral amplitude is suggested to describe this effect. Examples of nonlinear layered structures and periodically-poled nonlinear crystals show that surface contributions to spontaneous down-conversion can be important.
Coincidence-structures in the transverse plane of Type-II spontaneous parametric down-conversion carrying orbital angular momentum are obtained. Azimuthal symmetry breaking around the pump beam direction reveals itself on these quantum images. Analytical expressions for the amplitude probability of the down conversion process are shown including the nonlinear polarizability components.
We present an experiment of preparing Werner state via spontaneous parametric down-conversion and controlled decoherence of photons in this paper. In this experiment two independent BBO (beta-barium borate) crystals are used to produce down-conversion light beams, which are mixed to prepare Werner state.
The recoil effects of spontaneous photon emissions during optical pumping of a trapped three-level atom are exactly calculated. Without resort to the Lamb-Dicke approximation, and considering arbitrary detuning and saturation of the pump laser, the density of recoil shifts in phase space is derived. It is shown that this density is not of Gaussian shape, and that it becomes isotropic in phase space only for a branching ratio corresponding to fluorescence scattering but unfavorable for optical pumping. The dependence of its anisotropy on the laser saturation is discussed in the resonant case, a…
Strong correlations in two conjugate variables are the signature of quantum entanglement and have played a key role in the development of modern physics. Entangled photons have become a standard tool in quantum information and foundations. An impressive example is position-momentum entanglement of photon pairs, explained heuristically through the correlations implied by a common birth zone and momentum conservation. However, these arguments entirely neglect the importance of the `quantumness', i.e. coherence, of the driving force behind the generation mechanism. We study theoretically and expe…
Recent work using spontaneous parametric down-conversion (SPDC) has made possible investigations of the Einstein-Podolsky-Rosen paradox in its original (position-momentum) form. We propose an experiment that uses SPDC photon pairs to measure through which slit a photon passes while simultaneously observing double-slit interference.
We propose a novel scheme to generate polarization entanglement from spatially-correlated photon pairs. We experimentally realized a scheme by means of a spatial correlation effect in a spontaneous parametric down-conversion and a modified Michelson interferometer. The scheme we propose in this paper can be interpreted as a conversion process from spatial correlation to polarization entanglement.
We implement experimentally a method to generate photon-number$-$path and polarization entangled photon pairs using ``beamlike'' type-II spontaneous parametric down-conversion (SPDC), in which the signal-idler photon pairs are emitted as two separate circular beams with small emission angles rather than as two diverging cones.
We present a first experimental test of the existence of Spontaneus Parametric Up Conversion, predicted by a specific local realistic model based on Wigner function formalism. The measurement has been made using a ccd camera on the emission of a LiIO3 crystal pumped by a 351 nm and/or a 789 (1064) nm lasers. We obtain an upper limit of 160 times on the ratio between intensity of Spontaneus Parametric Up Conversion and Spontaneous Parametric Down conversion.
We study the two-photon detection amplitude of the down-converted beams in spontaneous parametric down-conversion when the physical variable of orbital angular momentum is involved, taking into account both conservation and non-conservation of angular momentum. Agreeing with experimental observations, our theoretical calculation shows that spatial structure of the two-photon detection amplitude of the down-converted beams carries important information about conservation or non-conservation of orbital angular momentum in spontaneous parametric down-conversion.
Using a basic Mach-Zehnder interferometer, we demonstrate experimentally the measurement of the photonic de Broglie wavelength of an entangled photon pair (a biphoton) generated by spontaneous parametric down-conversion. The observed interference manifests the concept of the photonic de Broglie wavelength. The result also provides a proof-of-principle of the quantum lithography that utilizes the reduced interferometric wavelength.
We investigate intensity of the parametric down conversion of ultrashort, ultraviolet pulse both in a low- and high-conversion regime. In the first regime, we develop a simple analytical expressions for the photon flux of the fluorescence. Numerical simulations using three-dimensional stochastic Wigner method provide results in the latter regime. We find that the perturbative approximation for the photon flux as a function of the wavelength of the signal and the observation angle, quantitatively describes even the non-perturbative regime. For short pump pulses the intensity of the fluorescence…
In order to fulfil the continuity requirements for electric- and magnetic-field amplitudes at discontinuities of chi2 nonlinearity additional photon pairs have to be emitted in the area of discontinuity. Generalized two-photon spectral amplitudes can be used to describe properties of photon pairs generated in this process that we call surface spontaneous parametric down-conversion. The spectral structure of such photon pairs is similar to that derived for photon pairs generated in the volume. Surface and volume contributions to spontaneous down-conversion can be comparable as an example of non…
Coherence properties of the down-converted beams generated in spontaneous parametric down-conversion are investigated in detail using an iCCD camera. Experimental results are compared with those from a theoretical model developed for pulsed pumping with a Gaussian transverse profile. The results allow to tailor the shape of correlation area of the signal and idler photons using pump-field and crystal parameters. As an example, splitting of a correlation area caused by a two-peak pump-field spectrum is experimentally studied.
We investigate the quantum state generated by optical parametric down-conversion in a $χ^{(2) } $ medium driven by two noncollinear light modes. The analysis shows the emergence of multipartite, namely 3- or 4-partite, entangled states in a subset of the spatio-temporal modes generated by the process. These appear as bright spots against the background fluorescence, providing an interesting analogy with the phenomenology recently observed in two-dimensional nonlinear photonic crystals. We study two realistic setups: i) Non-critical phase-matching in a periodically poled Lithium Tantalate slab,…
We theoretically discuss one-photon and two-photon double-slit interferences for spontaneous and stimulated parametric down-conversions. We show that the two-photon sub-wavelength interference can exist in a general spontaneous parametric down-conversion (SPDC) for both type I and type II crystals. We propose an alternative way to observe sub-wavelength interference by a joint-intensity measurement which occurs for only type I crystal in a higher gain of SPDC. When a signal beam injects into the crystal, it may create two interference patterns by two stimulated down-converted beams, showing no…
We present a novel yet simple approach to produced multiple entangled photon pairs through spontaneous parametric downconversion. We have developed Gaussian masks to subdivide the pump beam before passing it through a nonlinear medium. In this way, we are able to observe simultaneous separate down-converted emission cones with spatial overlap. The technique we employ can be used to greatly increase the dimensionality of entangled photonic systems generated from spontaneous parametric down conversion, affording greater scalability to optical quantum computing than previously explored.
We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motions fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined…
Quantum networks require interfacing stationary and flying qubits. These flying qubits are usually nonclassical states of light. Here we consider two of the leading source technologies for nonclassical light, spontaneous parametric down-conversion and single semiconductor quantum dots. Down-conversion delivers high-grade entangled photon pairs, whereas quantum dots excel at producing single photons. We report on an experiment that joins these two technologies and investigates the conditions under which optimal interference between these dissimilar light sources may be achieved.
We investigate the third order spontaneous parametric down-conversion process in a nonlinear media with inversion centers. Specifically, we analyze in details the three-photon differential count rate in unit frequency and angular regions, total count rate and measurement time for rutile and calcite crystals which have comparatively large cubic susceptibilities. Special attention is given to consideration of limited frequency and angular detection ranges in order to calculate experimentally available detection rate values.
We report a proof-of-principle experiment demonstrating that appropriately chosen set of Hermite-Gaussian modes constitutes a Schmidt decomposition for transverse momentum states of biphotons generated in the process of spontaneous parametric down conversion. We experimentally realize projective measurements in Schmidt basis and observe correlations between appropriate pairs of modes. We perform tomographical state reconstruction in the Schmidt basis, by direct measurement of single-photon density matrix eigenvalues.
Correlations in twin beams composed of many photon pairs are studied using an intensified CCD camera. Joint signal-idler photon-number distribution and quantum phase-space quasi-distributions determined from experimental data have nonclassical features.
We discuss the Bloch-Messiah decomposition for the broadband squeezed light generated by type-I parametric down-conversion with monochromatic pump. Using an exact solution for this process, we evaluate the squeezing parameters and the corresponding squeezing eigenmodes. Next, we consider the Magnus expansion of the quantum-mechanical evolution operator for this process and obtain its first three approximation orders. Using these approximated solutions, we evaluate the corresponding approximations for the Bloch-Messiah decomposition. Our results allow us to conclude that the first-order approxi…
We consider novel method for implementation of hybrid entanglement between microscopic and macroscopic states on output of spontaneous parametric down converter through the depletion of the pump wave. The generated signal, idler and pumping fields show weak entanglement. We characterize it and show the limits of applicability of the depleted pump regime. Testing method of the hybrid entanglement is proposed. The hybrid entanglement is tested by conditional generation of maximally entangled states of two qubits and qutrits regardless of its smallness. Possibilities to enhance the hybrid entangl…
We present a novel interferometric technique for performing ellipsometric measurements. This technique relies on the use of a non-classical optical source, namely, polarization-entangled twin photons generated by spontaneous parametric down-conversion from a nonlinear crystal, in conjunction with a coincidence-detection scheme. Ellipsometric measurements acquired with this scheme are absolute; i.e., they do not require source and detector calibration.
We present an experimental characterization of the statistics of multiple photon pairs produced by spontaneous parametric down-conversion realized in a nonlinear medium pumped by high-energy ultrashort pulses from a regenerative amplifier. The photon number resolved measurement has been implemented with the help of a fiber loop detector. We introduce an effective theoretical description of the observed statistics based on parameters that can be assigned direct physical nterpretation. These parameters, determined for our source from the collected experimental data, characterize the usefulness o…
In the non-linear optical process of type-II spontaneous parametric down-conversion, we present on an experiment showing that the two-photon detection amplitude of the down-converted beams does not generally reproduce the transverse profile of the pump beam that carries non-zero orbital angular momentum. We explain this observation by that orbital angular momentum is not conserved in the type-II non-linear process due to the broken rotational symmetry of the Hamiltonian.
We show that in parametric down-conversion the coherence properties of a temporally partially coherent pump field get entirely transferred to the down-converted entangled two-photon field. Under the assumption that the frequency-bandwidth of the down-converted signal-idler photons is much larger than that of the pump, we derive the temporal coherence functions for the down-converted field, for both infinitely-fast and time-averaged detection schemes. We show that in each scheme the coherence function factorizes into two separate coherence functions with one of them carrying the entire statisti…
We report on the demonstration of correlated photon pair generation in quasi-phase-matched superlattice AlGaAs waveguides with a high coincidence-to-accidental ratio (CAR); with a continuous (CW) pump, the observed CAR (>100) is more than two order of magnitudes improvement over previously reported spontaneous down conversion (SPDC) schemes in AlGaAs waveguides with a pulsed pump.
Starting from the standard Hamiltonian describing the optical non-linear process of spontaneous parametric down-conversion, we theoretically show that the generated entangled photon-pairs carry non-negligible orbital angular momentum in the degrees of freedom of relative movement in the type-II cases due to spatial symmetry breaking. We also show that the orbital angular momentum carried by photon-pairs in these degrees of freedom escapes detection in the traditional measurement scheme, which demands development of new techniques for further experimental investigations.
The multiphoton states generated by high-gain spontaneous parametric down-conversion (SPDC) in presence of large losses are investigated theoretically and experimentally. The explicit form for the two-photon output state has been found to exhibit a Werner structure very resilient to losses for any value of the gain parameter, g. The theoretical results are found in agreement with the experimental data. The last ones are obtained by quantum tomography of the state generated by a high-gain SPDC.
A rigorous description of volume and surface spontaneous parametric down-conversion in 1D nonlinear layered structures is developed considering exact continuity relations for the fields' amplitudes at the boundaries. The nonlinear process is described by the quantum momentum operator that provides the Heisenberg equations which solution is continuous at the boundaries. The transfer-matrix formalism is applied. The volume and surface contributions are clearly identified. Numerical analysis of a structure composed of 20 alternating GaN/AlN layers is given as an example.
We show that the transfer of the plane wave spectrum of the pump beam to the fourth-order transverse spatial correlation function of the two-photon field generated by spontaneous parametric down-conversion leads to the conservation and entanglement of orbital angular momentum of light. By means of a simple experimental setup based on fourth-order (or two-photon) interferometry, we show that our theoretical model provides a good description for down-converted fields carrying orbital angular momentum.
Spontaneous parametric down-conversion (SPDC) sources are an important technology for quantum sensing and imaging. We demonstrate a general simulation method, based on modeling from first principles, reproducing the spectrally and spatially resolved absolute counts of a SPDC experiment. By simulating additional processes and effects we accomplish good agreement with the experimental results. This method is broadly applicable and allows for the separation of contributing processes, virtual characterization of SPDC sources, and enables the simulation of many quantum based applications.
We present a theory for the quantum state of photon pairs generated from spontaneous parametric down conversion nonlinear process in which the influence of the final sizes of nonlinear optical crystals on eigen optical modes is explicitly taken into consideration. We find that these photon pairs are not in entangled quantum states. Polarization correlations between the signal beam and the idler beam are explained. We also show that the two photons generated from SPDC are not spatially separated, therefore the polarization correlation between the signal and idler beams is not an evidence for qu…
We study the spatial correlations of quantum fluctuations that can be observed in multi-mode spontaneous parametric down-conversion in the regime of high gain. A stochastic model has been solved numerically to obtain quantitative results beyond the stationary plane-wave pump approximation. The pulsed shape of the pump beam and other features of the system, such as spatial walk-off and diffraction are taken into account. Their effect on the spatial quantum correlations predicted by the plane-wave pump theory is investigated, both for near field and far field measurements, in a type I and in a t…
We study how one-particle correlations transfer to manifest as two-particle correlations in the context of parametric down-conversion (PDC), a process in which a pump photon is annihilated to produce two entangled photons. We work in the polarization degree of freedom and show that for any two-qubit generation process that is both trace-preserving and entropy-nondecreasing, the concurrence $C(ρ)$ of the generated two-qubit state $ρ$ follows an intrinsic upper bound with $C(ρ)\leq (1+P)/2$, where $P$ is the degree of polarization of the pump photon. We also find that for the class of two qubit …
In this paper we show that by suitably tailoring the dispersion characteristics of a Bragg reflection waveguide (BRW) mode, it is possible to achieve efficient photon pair generation over a large pump bandwidth while maintaining narrow signal bandwidth. The structure proposed consists of a high index core BRW with a periodically poled GaN core and periodically stratified cladding made up of alternate layers of $Al_{0.02}Ga_{0.98}N$ and $Al_{0.45}Ga_{0.55}N$. Such photon-pair generators should find applications in realizing compact and stable sources for quantum information processing.
We report an experimental self-calibrating tomography scheme for entanglement characterization in high-dimensional quantum systems using Schmidt decomposition techniques. The self-tomography technique based on maximal likelihood estimation was developed for characterizing non-ideal measurements in Schmidt basis allowing us to infer both Schmidt eigenvalues and detecting efficiencies.
We provide a general decomposition of the two-photon state produced by spontaneous parametric down-conversion in Hermite-Gaussian modes, in the case that the pump beam is described by a Hermite-Gaussian beam of any order. We show that the spatial correlations depend explicitly on the order of the pump beam, as well as other experimental parameters. We use the decomposition to demonstrate a few interesting cases. Our results are applicable to the engineering of two-photon spatial entanglement, in particular for non-Gaussian states.
We provide an estimate on the absolute values of the emission rate of photon pairs produced by spontaneous parametric down conversion in a bulk crystal when all interacting fields are in single transverse Gaussian modes. Both collinear and non-collinear configurations are covered, and we arrive at a fully analytical expression for the collinear case. Our results agree reasonably well with values found in typical experiments, which allows this model to be used for understanding the dependency on the relevant experimental parameters.
Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as effects of entanglement or equivalently in terms of interfering probability amplitudes, and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence…
We show that a spontaneous release of virtual photon pairs can occur in a quantum optical system in the ultrastrong coupling regime. In this regime, which is attracting interest both in semiconductor and superconducting systems, the light-matter coupling rate ΩR becomes comparable to the bare resonance frequency of photons ω0. In contrast to the dynamical Casimir effect and other pair creation mechanisms, this phenomenon does not require external forces or time dependent parameters in the Hamiltonian.
We show that the wave packet of a biphoton generated via spontaneous parametric down conversion is strongly anisotropic. Its anisotropic features manifest themselves very clearly in comparison of measurements performed in two different schemes: when the detector scanning plane is perpendicular or parallel to the plane containing the crystal optical axis and the laser axis. The first of these two schemes is traditional whereas the second one gives rise to such unexpected new results as anomalously strong narrowing of the biphoton wave packet measured in the coincidence scheme and very high degr…
We investigate the effect of the cumulative phase on the photon statistics of the three-mode state whose evolution is described by the trilinear Hamiltonian $\hat{H}_{I}=i\hbarκ\big(\hat{a}\hat{b}\hat{c}^{\dagger}-\hat{a}^{\dagger}\hat{b}^{\dagger}c\big)$, wherein the pump is taken to be quantized (and prepared in a coherent state) and the signal and idler modes are initially seeded with coherent states. We provide a brief review of the two-mode squeezed coherent states generated by non-degenerate coherently-stimulated parametric down-conversion, whereby the nonlinear crystal is driven by a st…
