We investigate the spatio-temporal structure of the bi-photon entanglement in parametric down-conversion (PDC) and we demonstrate its non-factorable X-shaped geometry. Such a structure gives access to the ultra-broad bandwidth of PDC, and can be exploited to achieve a bi-photon temporal localization in the femtosecond range. This extreme localization is connected to our ability to resolve the photon positions in the source near-field. The non factorability opens the possibility of tailoring the temporal entanglement by acting on the spatial degrees of freedom of twin photons.
Within the Wigner-PDC picture of photon entanglement, detection "errors" are not independent (though they may look, on average), nor can they be controlled by means of a technological improvement on the detectors. Those two elements make possible the interpretation of experimental evidence without the need to exclude local realism: for that reason, we propose the abandonment of the usual (photon, particle-based) description of (PDC-generated) light states, in favour of an also quantum, but field-theoretical description (QED), a description that finds a one-to-one equivalent in the Wigner-PDC a…
A parametric down-conversion (PDC) source can be used as either a triggered single photon source or an entangled photon source in quantum key distribution (QKD). The triggering PDC QKD has already been studied in the literature. On the other hand, a model and a post-processing protocol for the entanglement PDC QKD are still missing. In this paper, we fill in this important gap by proposing such a model and a post-processing protocol for the entanglement PDC QKD. Although the PDC model is proposed to study the entanglement-based QKD, we emphasize that our generic model may also be useful for ot…
We report the observation of beatings of the coincidence event rate in a Hong-Ou-Mandel interference (HOMI) between signal and idler photons from a parametric downconversion (PDC) process inside a multi-mode KTP waveguide. As explanation we introduce bi-photonic states entangled in their broadband frequency modes generated by waveguide mode triples and propose a suitable entanglement detection scheme.
We show that the possibility of distinguishing between single and two photon detection events is not a necessary requirement for the proof that recent operational realization of entanglement swapping cannot find a local realistic description. We propose a simple modification of the experiment, which gives a richer set of interesting phenomena.
In this work the Schmidt number of the two-photon state generated by parametric-down conversion (PDC) is evaluated in the framework of a fully spatio-temporal model for PDC. A comparison with the results obtained in either purely spatial or purely temporal models shows that the degree of entanglement of the PDC state cannot be trivially reduced to the product of the Schmidt numbers obtained in models with lower dimensionality, unless the detected bandwidth is very narrow. This result is a consequence of the non-factorability of the state in the spatial and temporal degrees of freedoms of twin …
Pulsed parametric downconversion (PDC) processes generate photon pairs with a rich spectral-temporal structure, which offer an attractive potential for quantum information and communication applications. In this paper, we investigate the four-dimensional chronocyclic Wigner function of the PDC state, which naturally lends itself to the pulsed characteristics of these states. From this function we derive the conditioned time-bandwidth product of one of the pair photons, a quantity which is not only a valid measure of entanglement between the PDC photons but also allows to highlight a remarkable…
We investigate the coupling efficiency of parametric downconversion light (PDC) into single and multi-mode optical fibers as a function of the pump beam diameter, crystal length and walk-off. We outline two different theoretical models for the preparation and collection of either single-mode or multi-mode PDC light (defined by, for instance, multi-mode fibers or apertures, corresponding to bucket detection). Moreover, we define the mode-matching collection efficiency, important for realizing a single-photon source based on PDC output into a well-defined single spatial mode. We also define a mu…
Invariant entangled states remain unchanged under simultaneous identical unitary transformations of all their subsystems. We experimentally generate and characterize such invariant two-, four-, and six-photon polarization entangled states. This is done only with a suitable filtering procedure of multiple emissions of entangled photon pairs from a single source, without any interferometric overlaps. We get the desired states utilizing bosonic emission enhancement due to indistinguishability. The setup is very stable, and gives high interference contrasts. Thus, the process is a very likely cand…
Storage and retrieval of parametric down-conversion (PDC) photons are demonstrated with electromagnetically induced transparency (EIT). Extreme frequency filtering is performed for THz order of broadband PDC light and the frequency bandwidth of the light is reduced to MHz order. Storage and retrieval procedures are carried out for the frequency filtered PDC photons. Since the filtered bandwidth [full width at half-maximum (FWHM) = 9 MHz] is within the EIT window (FWHM = 12.6 MHz), the flux of the PDC light is successfully stored and retrieved. The nonclassicality of the retrieved light is conf…
We explore a promising method of generating pure heralded single photons. Our approach is based on parametric downconversion in a periodically-poled waveguide. However, unlike conventional downconversion sources, the photon pairs are counter-propagating: one travels with the pump beam in the forward direction while the other is backpropagating towards the laser source. Our calculations reveal that these downconverted two-photon states carry minimal spectral correlations within each photon-pair. This approach offers the possibility to employ a new range of downconversion processes and materials…
Parametric down-conversion (PDC) is one of the most widely used methods to create pure single-photon states for quantum information applications. However little attention has been paid to higher-order photon components in the PDC process, yet these ultimately limit the prospects of generating single-photons of high quality. In this paper we investigate the impacts of higher-order photon components and multiple frequency modes on the heralding rates and single-photon fidelities. This enables us to determine the limits of PDC sources for single-photon generation. Our results show that a perfectl…
In this work we propose and analyse a scheme where the full spatio-temporal correlation of twin photons/beams generated by parametric down-conversion is detected by using its inverse process, i.e. sum frequency generation. Our main result is that, by imposing independently a temporal delay Δt and a transverse spatial shift Δx between two twin components of PDC light, the up-converted light intensity provides information on the correlation of the PDC light in the full spatio-temporal domain, and should enable the reconstruction of the peculiar X-shaped structure of the correlation predicted in …
We experimentally demonstrate a source of nearly pure single photons in arbitrary temporal shapes heralded from a parametric down-conversion (PDC) source at telecom wavelengths. The technology is enabled by the tailored dispersion of in-house fabricated waveguides with shaped pump pulses to directly generate the PDC photons in on-demand temporal shapes. We generate PDC photons in Hermite-Gauss and frequency-binned modes and confirm a minimum purity of 0.81, even for complex temporal shapes.
We propose and demonstrate experimentally a new method based on the spatial entanglement for the absolute calibration of analog detector. The idea consists on measuring the sub-shot-noise intensity correlation between two branches of parametric down conversion, containing many pairwise correlated spatial modes. We calibrate a scientific CCD camera and a preliminary evaluation of the statistical uncertainty indicates the metrological interest of the method.
Parametric down conversion (PDC) is widely interpreted in terms of photons, but, even among supporters of this interpretation, many properties of the photon pairs have been described as "mind-boggling" and even "absurd". In this article we argue that a classical description of the light field, taking account of its vacuum fluctuations, leads us to a consistent and rational account of all PDC phenomena. "Nonlocality" in quantum optics is simply an artifact of the Photon Concept. We also predict a new phenomenon, namely the appearance of a second, or satellite PDC rainbow.
Multipartite Bell-GHZ nonclassicality from interwoven frustrated down-conversion
International Centre for Theory of Quantum Technologies, University of Gdansk（格但斯克大学国际量子技术理论中心）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Institute of Theoretical Physics and Astrophysics, University of Gdańsk（格但斯克大学理论与天体物理研究所）；Faculty of Physics, Ludwig Maximilian University（路德维希-马克西米利安大学物理学院）；Institute of Theoretical and Applied Informatics, Polish Academy of Sciences（波兰科学院理论与应用信息学研究所）
Bragg-reflection waveguides emitting broadband parametric down-conversion (PDC) have been proven to be well suited for the on-chip generation of polarization entanglement in a straightforward fashion [R. T. Horn et al., Sci. Rep. 3, 2314 (2013)]. Here, we investigate how the properties of the created states can be modified by controlling the relative temporal delay between the pair of photons created via PDC. Our results offer an easily accessible approach for changing the coherence of the polarization entanglement, in other words, to tune the phase of the off-diagonal elements of the density …
We study distinguishing information in the context of quantum interference involving more than one parametric downconversion (PDC) source and in the context of polarization-entangled photon pairs based on PDC. We arrive at specific design criteria for two-photon sources so that when used as part of complex optical systems, such as photon-based quantum information processing schemes, distinguishing information between the photons is eliminated guaranteeing high visibility interference. We propose practical techniques which lead to suitably engineered two-photon states that can be realistically …
Parametric down-conversion (PDC) offers the possibility to control the fabrication of non-Gaussian states such as Fock states. However, in conventional PDC sources energy and momentum conservation introduce strict frequency and photon number correlations, which impact the fidelity of the prepared state. In our work we optimize the preparation of single-photon Fock states from the emission of waveguided PDC via spectral filtering. We study the effect of correlations via photon number resolving detection and quantum interference. Our measurements show how the reduction of mixedness due to filter…
A highly attenuated laser pulse which gives a weak coherent state is widely used in quantum key distribution (QKD) experiments. A weak coherent state has multi-photon components, which opens up a security loophole to the sophisticated eavesdropper. With a small adjustment of the hardware, we prove that the decoy state method can close this loophole and substantially improve the QKD performance. We also propose a few practical decoy state protocols, study statistical fluctuations and perform experimental demonstrations. Moreover, we apply the methods from entanglement distillation protocols bas…
Many recent experiments employ several parametric down conversion (PDC) sources to get multiphoton interference. Such interference has applications in quantum information. We study here how effects due to photon statistics, misalignment, and partial distinguishability of the PDC pairs originating from different sources may lower the interference contrast in the multiphoton experiments.
Parametric down-conversion (PDC) sources can be used for quantum key distribution (QKD). One can use a PDC source as a triggered single photon source. Recently, there are various practical proposals of the decoy state QKD with triggering PDC sources. In this paper, we generalize the passive decoy state idea, originally proposed by Mauerer and Silberhorn. The generalized passive decoy state idea can be applied to cases where either threshold detectors or photon number resolving detectors are used. The decoy state protocol proposed by Adachi, Yamamoto, Koashi and Imoto (AYKI) can be treated as a…
We propose an optical parametric down conversion (PDC) scheme that does not suffer a trade-off between the state-purity of single-photon wave-packets and the rate of packet production. This is accomplished by modifying the PDC process by using a microcavity to engineer the density of states of the optical field at the PDC frequencies. The high-finesse cavity mode occupies a spectral interval much narrower than the bandwidth of the pulsed pump laser field, suppressing the spectral correlation, or entanglement, between signal and idler photons. Spectral filtering of the field occurs prior to pho…
We present a way for entanglement purification based on two parametric down-conversion (PDC) sources with cross-Kerr nonlinearities. It is comprised of two processes. The first one is a primary entanglement purification protocol for PDC sources with nondestructive quantum nondemolition (QND) detectors by transferring the spatial entanglement of photon pairs to their polarization. In this time, the QND detectors act as the role of controlled-not (CNot) gates. Also they can distinguish the photon number of the spatial modes, which provides a good way for the next process to purify the entangleme…
Parametric downconversion (PDC) in semiconductor Bragg-reflection waveguides (BRW) is routinely exploited for photon-pair generation in the telecommunication range. Contrary to many conventional PDC sources, BRWs offer possibilities to create spectrally broadband but nevertheless indistinguishable photon pairs in orthogonal polarizations that simultaneously incorporate high frequency entanglement. We explore the characteristics of co-propagating twin beams created in a type-II ridge BRW. Our PDC source is bright and efficient, which serves as a benchmark of its performance and justifies its ex…
Parametric downconversion (PDC) is a technique of ubiquitous experimental significance in the production of non-classical, photon-number correlated twin beams. Standard theory of PDC as a two-mode squeezing process predicts and homodyne measurements observe a thermal photon number distribution per beam. Recent experiments have obtained conflicting distributions. In this paper, we explain the observation by an a-priori theoretical model solely based on directly accessible physical quantities. We compare our predictions with experimental data and find excellent agreement.
Two-photon time-frequency entanglement is a valuable resource in quantum information. Resolving the wavepacket of ultrashort pulsed single-photons, however, is a challenge. Here, we demonstrate remote spectral shaping of single photon states and probe the coherence properties of two-photon quantum correlations in the time-frequency domain, using engineered parametric down-conversion (PDC) and a quantum pulse gate (QPG) in nonlinear waveguides. Through tailoring the joint spectral amplitude function of our PDC source we control the temporal mode structure between the generated photon pairs and …
Frequency conversion (FC) and type-II parametric down-conversion (PDC) processes serve as basic building blocks for the implementation of quantum optical experiments: type-II PDC enables the efficient creation of quantum states such as photon-number states and Einstein-Podolsky-Rosen-states (EPR-states). FC gives rise to technologies enabling efficient atom-photon coupling, ultrafast pulse gates and enhanced detection schemes. However, despite their widespread deployment, their theoretical treatment remains challenging. Especially the multi-photon components in the high-gain regime as well as …
Optical parametric down-conversion (PDC) is a central tool in quantum optics experiments. The number of collected down-converted modes greatly affects the quality of the produced photon state. We use Silicon Photomultiplier (SiPM) number-resolving detectors in order to directly observe the photon-number distribution of a PDC source, and show its dependence on the number of collected modes. Additionally, we show how the stimulated emission of photons and the partition of photons into several modes determine the overall photon number. We present a novel analytical model for the optical crosstalk…
Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavi…
Parametric down-conversion (PDC) is the established standard for the practical generation of a multiplicity of quantum optical states. These include two-mode squeezed vacuum, heralded non-Gaussian states and entangled photon pairs. Detailed theoretical studies provide insight into the time-frequency (TF) structure of PDC, which are governed by the complex-valued joint spectral amplitude (JSA) function. However in experiments, the TF structure of PDC is mostly characterised by intensity measurementsthat forbid access to the important phase of the JSA. In this paper, we present an amplitude-sens…
We explore the feasibility of using high conversion-efficiency periodically-poled crystals to produce photon pairs for photon-counting detector calibrations at 1550 nm. The goal is the development of an appropriate parametric down-conversion (PDC) source at telecom wavelengths meeting the requirements of high-efficiency pair production and collection in single spectral and spatial modes (single-mode fibers). We propose a protocol to optimize the photon collection, noise levels and the uncertainty evaluation. This study ties together the results of our efforts to model the single-mode heralding…
In this paper we experimentally study the statistical properties of a bright squeezed vacuum state containing up to 10^13 photons per mode (10 uJ per pulse), produced via high gain parametric down conversion (PDC). The effects of bunching and superbunching of photons were observed for a single mode PDC radiation by second-order intensity correlation function measurements with analog detectors.
Light beams with orbital angular momentum (OAM) are convenient carriers of quantum information. They can be also used for imparting rotational motion to particles and provide high resolution in imaging. Due to the conservation of OAM in parametric down-conversion (PDC), signal and idler photons generated at low gain have perfectly anti-correlated OAM values. It is interesting to study the OAM properties of high-gain PDC, where the same OAM modes can be populated with large, but correlated, numbers of photons. Here we investigate the OAM spectrum of high-gain PDC and show that the OAM mode cont…
We make a thorough study of the spreading of quantum coherence (QC), as quantified by the $l_{1}$-norm QC, when a qubit (a two-level quantum system) is subjected to noise quantum channels commonly appearing in quantum information science. We notice that QC is generally not conserved and that even incoherent initial states can lead to transitory system-environment QC. We show that for the amplitude damping channel the evolved total QC can be written as the sum of local and non-local parts, with the last one being equal to entanglement. On the other hand, for the phase damping channel (PDC) enta…
Multi-photon states can be produced in multiple parametric down conversion (PDC) processes. The nonlinear crystal in such a case is pumped with high power. In theory, the more populated these states are, the deeper is the conflict with local realistic description. However, the interference contrast in multi-photon PDC experiments can be quite low for high pumping. We show how the contrast can be improved. The idea employs currently accessible optical devices, the multiport beam splitters. They are capable of splitting the incoming light in one input mode to $M$ output modes. Our scheme works a…
Spontaneous parametric down conversion (PDC), in the perturbative limit, can be considered as a probabilistic splitting of one input photon into two output photons. Conversely, sum-frequency generation (SFG) implements the reverse process of combining two input photons into one. Here we show that a single-photon projective measurement in the temporal-mode basis of the output photon of a two-photon SFG process effects a generalized measurement on the input two-photon state. We describe the positive-operator-valued measure (POVM) associated with such a measurement, and show that its elements are…
We investigate the dispersion properties of ridge Bragg-reflection waveguides to deduce their phasematching characteristics. These are crucial for exploiting them as sources of parametric down-conversion (PDC). In order to estimate the phasematching bandwidth we first determine the group refractive indices of the interacting modes via Fabry-Perot experiments in two distant wavelength regions. Second, by measuring the spectra of the emitted PDC photons we gain access to their group index dispersion. Our results offer a simple approach for determining the PDC process parameters in the spectral d…
Counter-propagating parametric conversion processes in non-linear bulk crystals have been shown to feature unique properties for efficient narrowband frequency conversion. In quantum optics, the generation of photon pairs with a counter-propagating parametric down-conversion process (PDC) in a waveguide, where signal and idler photons propagate in opposite directions, offers unique material-independent engineering capabilities. However, realizing counter-propagating PDC necessitates quasi-phase-matching (QPM) with extremely short poling periods. Here, we report on the generation of counter-pro…
Due to their strict photon-number correlation, the twin beams produced in parametric down-conversion (PDC) work well for heralded state generation. Often, however, this state manipulation is distorted by the optical losses in the herald and by the higher photon-number contributions inevitable in the PDC process. In order to find feasible figures of merit for characterizing the heralded states, we investigate their normalized factorial moments of the photon number that can be accessed regardless of the optical losses in the detection. We then perform a measurement of the joint photon statistics…
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 group…
Parametric down-conversion (PDC) is mostly known in the low-gain (spontaneous) regime, in which the correlated photon pairs are produced. Spontaneous PDC (SPDC) plays a very important role for quantum optics as a variety of quantum states is produced via SPDC. In the high-gain case PDC leads to generation of bright states having up to hundreds mW mean power. With such states almost any nonlinear optical interaction or light-matter interaction becomes more efficient. Even being macroscopically bright, the produced states maintain nonclassical properties as, for example, the fluctuations of elec…
We present a scheme, based only on linear optics and standard photon detection, that allows to generate heralded multiphoton entangled states of arbitrary photon number from spontaneous parametric downconversion (PDC) in the weak interaction regime. The scheme also works in the strong interaction regime, i.e., for the production of large photon numbers, when photon-number resolving detectors with nearly perfect quantum efficiency are used. In addition, the same setup can be used for quantum metrology as multiphoton interferometer with sensitivity at the Heisenberg limit.
We analyze the generation rates and preparation fidelities of photon triplet states in pulsed cascaded parametric down-conversion (PDC) under realistic experimental circumstances. As a model system, we assume a monolithically integrated device with negligible interface loss between the two consecutive PDC stages. We model the secondary down-conversion process in terms of a lossy channel and provide a detailed analysis of noise contributions. Taking variable pump powers into account, we estimate the impact of higher-order photon contributions and conversion processes on the achievable coinciden…
High dimensional quantum states are of fundamental interest for quantum information processing. They give access to large Hilbert spaces and, in turn, enable the encoding of quantum information on multiple modes. One method to create such quantum states is parametric down-conversion (PDC) in waveguide arrays (WGAs) which allows for the creation of highly entangled photon-pairs in controlled, easily accessible spatial modes, with unique spectral properties. In this paper we examine both theoretically and experimentally the PDC process in a lithium niobate WGA. We measure the spatial and spectra…
We propose an efficient quantum key distribution protocol based on the photon-pair generation from parametric down-conversion (PDC). It uses the same experimental setup as the conventional protocol, but a refined data analysis enables detection of photon-number splitting attacks by utilizing information from a built-in decoy state. Assuming the use of practical detectors, we analyze the unconditional security of the new scheme and show that it improves the secure key generation rate by several orders of magnitude at long distances, using a high intensity PDC source.
We demonstrate a method to generate entangled photons with controlled spatial shape by parametric down conversion (PDC) in a 2D nonlinear crystal. A compact and novel crystal source was designed and fabricated, generating directly path entangled photons without the use of additional beam-splitters. This crystal supports two PDC processes, emitting biphotons into two beamlike modes simultaneously. Two coherent path entangled amplitudes of biphotons were created and their interference observed. Our method enables the generation of entangled photons with controlled spatial, spectral and polarizat…
The generation of heralded pure Fock states via spontaneous parametric down conversion (PDC) relies on perfect photon-number correlations in the output modes. Correlations in any other degree of freedom, however, degrade the purity of the heralded state. In this paper, we investigate spectral entanglement between the two output modes of a periodically poled waveguide. With the intent of generating heralded 1- and 2-photon Fock states, we expand the output state of the PDC to second order in photon number. We explore the effects of spectral filtering and inefficient detection, of the heralding …
Single-photon addition to multimode quantum fields at telecom wavelengths using lithium niobate and its doped variants
School of Quantum Technology, Defence Institute of Advanced Technology（国防先进技术研究院量子技术学院）；Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France（卡斯勒·布罗塞尔实验室，索邦大学，法国国家科学研究中心，巴黎文理研究大学，法兰西学院）
We review some recent experimental progresses concerning Foundations of Quantum Mechanics and Quantum Information obtained in Quantum Optics Laboratory "Carlo Novero" at IENGF. More in details, after a short presentation of our polarization entangled photons source (based on precise superposition of two Type I PDC emission) and of the results obtained with it, we describe an innovative double slit experiment where two degenerate photons produced by PDC are sent each to a specific slit. Beyond representing an interesting example of relation between visibility of interference and "welcher weg" k…
The future of quantum photonic technology depends on the realization of efficient sources of single photons, the ideal carriers of quantum information. Parametric downconversion (PDC) is a promising route to create highly coherent, spectrally pure single photons for quantum photonics using versatile group-velocity matching (GVM) and tailored nonlinearities. However, the functionality to actively control the poling period of nonlinear crystals used in PDC is currently missing, yet would enable to dynamically modify the wavelength of single photons produced in the PDC process. Here a detailed GV…
We present a pulsed and integrated, highly non-degenerate parametric downconversion (PDC) source of heralded single photons at telecom wavelengths, paired with heralding photons around 800 nm. The active PDC section is combined with a passive, integrated wavelength division demultiplexer on-chip, which allows for the spatial separation of signal and idler photons with efficiencies of more than 96.5 %, as well as with multi-band reflection and anti-reflection coatings which facilitate low incoupling losses and a pump suppression at the output of the device of more than 99 %. Our device is capab…
We present an integrated source of polarization entangled photon pairs in the telecom regime, which is based on type II-phasematched parametric down-conversion (PDC) in a Ti-indiffused waveguide in periodically poled lithium niobate. The domain grating -- consisting of an interlaced bi-periodic structure -- is engineered to provide simultaneous phase-matching of two PDC processes, and enables the direct generation of non-degenerate, polarization entangled photon pairs with a brightness of $B=7\times10^3$ pairs/(s mW GHz). The spatial separation of the photon pairs is accomplished by a fiber-op…
We present and discuss perspectives of current developments on advanced quantum optical circuits monolithically integrated in the lithium niobate platform. A set of basic components comprising photon pair sources based on parametric down conversion (PDC), passive routing elements and active electro-optically controllable switches and polarisation converters are building blocks of a toolbox which is the basis for a broad range of diverse quantum circuits. We review the state-of-the-art of these components and provide models that properly describe their performance in quantum circuits. As an exa…
We demonstrate a general method of engineering the joint quantum state of photon pairs produced in spontaneous parametric downconversion (PDC). The method makes use of a superlattice structure of nonlinear and linear materials, in conjunction with a broadband pump, to manipulate the group delays of the signal and idler photons relative to the pump pulse, and realizes a joint spectral amplitude with arbitrary degree of entanglement for the generated pairs. This method of group delay engineering has the potential of synthesizing a broad range of states including factorizable states crucial for q…
