We study the quantum properties of the polarization of the light produced in type II spontaneous parametric down-conversion in the framework of a multi-mode model valid in any gain regime. We show that the the microscopic polarization entanglement of photon pairs survives in the high gain regime (multi-photon regime), in the form of nonclassical correlation of all the Stokes operators describing polarization degrees of freedom.
The theory of parametric down conversion of the vacuum, based on a real zeropoint, or "vacuum" electromagnetic field, has been treated in earlier articles. The same theory predicts a hitherto unsuspected phenomenon - parametric up conversion of the vacuum. This article describes how the phenomenon may be demonstrated experimentally.
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 use photon counters to obtain the joint photon counting statistics from twin-beam non-degenerate parametric down conversion, and we demonstrate directly, and with no auxiliary assumptions, that these twin beams are nonclassical.
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.
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.
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.
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.
Multipartite entanglement and nonclassicality of four-mode Gaussian states generated in two simultaneous nonlinear processes involving parametric down-conversion and frequency up-conversion are analyzed assuming the vacuum as the initial state. Suitable conditions for the generation of highly entangled states are found. Transfer of the entanglement from the down-converted modes into the up-converted ones is also suggested. The analysis of the whole set of states reveals that sub-shot-noise intensity correlations between the equally-populated down-converted modes, as well as the equally-populat…
High-gain parametric down-conversion (PDC) is a source of bright squeezed vacuum, which is a macroscopic nonclassical state of light and a promising candidate for quantum information applications. Here we study its properties, such as the intensity spectral width and the spectral width of pairwise correlations.
Photon-added coherent states have been realized in optical parametric down-conversion by Zavatta {\em et al} [Science 306 (2004) 660-662]. In this report, it is established that the states generated in the process are {\em ideal} photon-added coherent states. It is shown that the scheme can generate higher order photon-added coherent states. A comparative study of the down-conversion process and atom-cavity interaction in generating the photon-added coherent states is presented.
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 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…
In this paper we report our systematic study of a promising absolute calibration technique of analog photo-detectors, based on the properties of parametric down conversion. Our formal results and a preliminary uncertainty analysis show that the proposed method can be effectively developed with interesting applications to metrology.
The phenomenon of parametric down conversion from the vacuum may be understood as a process in classical electrodynamics, in which a nonlinear crystal couples the modes of the pumping field with those of the zeropoint, or "vacuum" field. This is an entirely local theory of the phenomenon, in contrast with the presently accepted nonlocal theory. The new theory predicts a hitherto unsuspected phenomenon - parametric up conversion from the vacuum.
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.
We introduce an effective numerical method of density matrix determination of fiber coupled single photon generated in process of spontaneous parametric down conversion in type I non-collinear configuration. The presented theory has been successfully applied in case of source exploited in Phys. Rev. Lett. 99, 123601 (2007) to demonstrate the experimental characterization of spectral state of single photon.
We solve analytically master equations that describe a cavity filled with a kerr medium, taking into account the dissipation induced by the environment, and parametric down conversion processes. We use superoperator techniques.
We show how stimulated parametric processes can be employed in experiments on beyond the diffraction limit to overcome the problem of low visibility obtained by using spontaneous down conversion operating in the high gain regime. We further show enhancement of the count rate by several orders when stimulated parametric processes are used. Both the two photon counts and the visibility can be controlled by the phase of the stimulating coherent beam.
A theory of spontaneous parametric down-conversion, which gives rise to a quantum state that is entangled in multiple parameters, such as three-dimensional wavevector and polarization, allows us to understand the unusual characteristics of fourth-order quantum interference in many experiments, including ultrafast type-II parametric down-conversion, the specific example illustrated in this paper. The comprehensive approach provided here permits the engineering of quantum states suitable for quantum information schemes and new quantum technologies.
We describe parametric down conversion process in a two-level atomic gas, where the atoms are in a superposition state of relevant energy levels. This superposition results in splitting of the phase matching condition into three different conditions. Another, more important, peculiarity of the system under discussion is the nonsaturability of amplification coefficients with increasing pump wave intensity, under "sideband" generation conditions.
An experimental scheme for preparing a polarization entangled W states from four photons emitted by parametric down-conversion is proposed. We consider two different configurations and a method of improving the yield by using single photon sources. In the proposed scheme, one uses only linear optical elements and photon detectors, so that this scheme is feasible by current technologies.
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.
There is a serious flaw in the proposal [arXiv:1603.06857] for the achievement of unity efficiency in SPDC. This is a replacement due to mistakes in the table of probabilities. Numbers have been corrected.
In recent development of quantum technologies, a frequency conversion of quantum signals has been studied widely. We investigate the optic-microwave entanglement that is generated by applying an electro-optomechanical frequency conversion scheme to one mode in an optical two-mode squeezed vacuum state. We quantify entanglement of the converted two-mode Gaussian state, where surviving entanglement of the state is analyzed with respect to the parameters of the electro-optomechanical system. Furthermore, we show that there exists an upper bound for the entanglement that survives after the convers…
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…
Quantum entanglement associated with transverse wave vectors of down conversion photons is investigated based on the Schmidt decomposition method. We show that transverse entanglement involves two variables: orbital angular momentum and transverse frequency. We show that in the monochromatic limit high values of entanglement are closely controlled by a single parameter resulting from the competition between (transverse) momentum conservation and longitudinal phase matching. We examine the features of the Schmidt eigenmodes, and indicate how entanglement can be enhanced by suitable mode selecti…
While single boson entanglement is known to be equivalent to standard non-identical particle entanglement, the use of fermionic entanglement is constrained by a parity superselection rule. Nevertheless we show that within the framework of second quantization, where local modes play the role of qubits, the analogy with ordinary entanglement holds: two entangled spinless fermion modes can be used to teleport a single local fermion mode and to perform standard dense coding. Entanglement concentration and dilution are possible for fermions. We clarify the meaning of our results by discussing the c…
Spontaneous parametric down conversion has been largely exploited as a tool for absolute calibration of photon counting detectors, photomultiplier tubes or avalanche photodiodes working in Geiger regime. In this work we investigate the extension of this technique from very low photon flux of photon counting regime to the absolute calibration of analog photodetectors at higher photon flux. Moving toward higher photon rate, i.e. at high gain regime, with the spontaneous parametric down conversion shows intrinsic limitations of the method, while the stimulated parametric down conversion process, …
By utilizing the nondegenerate optical parametric amplifier, the quantum state transfer from a pump state with high frequency to a signal state of lower frequency is studied theoretically. The noiseless state transfer is characterized by frequency conversion efficiency and noise figure. It is shown that the quantum state can be well preserved during the frequency conversion as long as the optical parametric amplifier is operated far below the threshold, and meanwhile injected with an input idler field with a power density about ten times greater than that of the pump. The dependence of the noi…
We propose a method for generation of a single-cycle squeezed light by parametric down-conversion in a chirped quasi-phase-matched nonlinear crystal. We find an exact quantum solution for this process valid for an arbitrary parametric gain, and discover an ultrabroadband squeezing in the down-converted light with flat squeezing spectrum comprising the full optical octave. We describe a scheme for observation of this kind of squeezing using second-harmonic generation as an ultrafast correlator.
We investigate how entanglement can be perfectly transfered between continuous variable and qubits system. We find that a two-mode squeezed vacuum state can be converted to the product state of an infinitive number of two-qubit states while keeping the entanglement. The reverse process is also possible. The interaction Hamitonian is a kind of non-linear Jaynes-Cumings Hamiltonian.
We describe an experiment in which photon pairs from a pulsed parametric down-conversion source were coupled into single-mode fibers. Detecting one of the photons heralded the presence of the other photon in its fiber with a probability of 83%. The heralded photons were then used in a simple multi-photon interference experiment to illustrate their potential for quantum information applications.
The primary goal of entanglement theory is to determine convertibility conditions for two quantum states. Up until now, this has always been done with the use of entanglement monotones. With the exception of the negativity, such quantities tend to be rather uncomputable. We instead promote the idea of conversion witnesses in this paper. A conversion witness is a function on pairs of states and whose value determines whether a state can be converted into another. We construct a conversion witness that can be efficiently computed for arbitrary states in systems of any size. This conversion witne…
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 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.
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 observe polarization-entanglement between four photons produced from a single down-conversion source. The non-classical correlations between the measurement results violate a generalized Bell inequality for four qubits. The characteristic properties and its easy generation with high interferometric contrast make the observed four-photon state well-suited for implementing advanced quantum communication schemes such as multi-party quantum key distribution, secret sharing and telecloning.
We verified operational approach based on direct measurement of entanglement degree for bipartite systems. In particular spectral distributions of single counts and coincidence for pure biphoton states generated by train of short pump pulses have been measured and entanglement quantifier calculated. The approach gives upper bound of entanglement stored in total biphoton states, which can reach extremely high value up to $10^{4}-10^{5}$.
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.
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…
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…
We study the harmonic entanglement and squeezing in a two-mode radiation produced in a degenerate parametric down conversion process coupled to a two-mode vacuum reservoir employing the linearization procedure. It is found that there is a quadrature entanglement between the harmonically related fundamental and second-harmonic modes and the superimposed radiation exhibits a significant two-mode squeezing. The entanglement exits even when there is no two-mode squeezing, since the correlation leading to these phenomena are essentially different. In addition, the more the external coherent light i…
We examine the modal, spectral, and polarization entanglement properties of photon pairs generated in a nonlinear, periodically poled, two-mode waveguide (1-D planar or 2-D circular) via nondegenerate spontaneous parametric down-conversion. Any of the possible degrees of freedom -- mode number, frequency, or polarization -- can be used to distinguish the down-converted photons while the others serve as attributes of entanglement. Distinguishing the down-converted photons based on their mode numbers enables us to efficiently generate spectral or polarization entanglement that is either narrowba…
The measurement of high-dimensional entangled states of orbital angular momentum prepared by spontaneous parametric down-conversion can be considered in two separate stages: a generation stage and a detection stage. Given a certain number of generated modes, the number of measured modes is determined by the measurement apparatus. We derive a simple relationship between the generation and detection parameters and the number of measured entangled modes.
We report generation of near-infrared photon pairs in fundamental spatial modes via type-II spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate (KTiOPO4) nonlinear waveguide supporting multiple transverse modes. This demonstrates experimentally a versatile scheme for controlling the spatial characteristics of the produced nonclassical light based on exploitation of intermodal dispersion. The down-converted photons are characterized by the measurement of the beam quality factors in the heralded regime.
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.
In this work the degree of entanglement of two-photon states generated by parametric-down conversion with a phase mismatch is computed in terms of the temperature of the nonlinear medium where the interaction takes place. The minimum interaction time, named {\it birth time of entanglement}, needed before entanglement is attained, is computed in terms of the temperature and of the phase mismatch. Our results show that, for each value of the phase mismatch, there is a critical temperature above which entanglement disappears. We are able to identify the regions of parameters, temperature and mism…
We propose two schemes to generate four-photon polarization-entangled states from the second-order emission of the spontaneous parametric down-conversion process. By using linear optical elements and the coincidence-detection, the four indistinguishable photons emitted from parametric down-conversion source result in the Greenberger-Horne-Zeilinger (GHZ) state or the superposition of two orthogonal GHZ states. For this superposition state, under particular phase settings we analyze the quantum correlation function and the local hidden variable (LHV) correlation. As a result, the Bell inequalit…
Spontaneous parametric down conversion (SPDC) has been largely exploited as a tool for absolute calibration of photon-counting detectors, i.e detectors registering very small photon fluxes. In [J. Opt. Soc. Am. B 23, 2185 (2006)] we derived a method for absolute calibration of analog detectors using SPDC emission at higher photon fluxes, where the beam is seen as a continuum by the detector. Nevertheless intrinsic limitations appear when high-gain regime of SPDC is required to reach even larger photon fluxes. Here we show that stimulated parametric down conversion allow one to avoid this limit…
We experimentally analyze the complete photon number statistics of parametric downconversion and ascertain the influence of multimode effects. Our results clearly reveal a difference between single mode theoretical description and the measured distributions. Further investigations assure the applicability of loss-tolerant photon number reconstruction and prove strict photon number correlation between signal and idler modes.
Heralding of single photon at 1550 nm from pump pulsed non degenerate spontaneous parametric downconversion is demonstrated. P(1) and P(2) of our source are 0.1871 and 2.4 x 10 ^-3 respectively. Triggering of our source is 2.16 x 10^5 trigger.s^-1. This source may be used in QKD system.
