Method and system for producing entangled photons

Abstract

A poled nonlinear optical structure for generating pairs of entangled photons from a pump photon comprises a plurality of domains, and is being characterized by a mismatch parameter. A polarization of the domains is periodically reversed to define a periodic poling pattern. A Fourier transform of the poling pattern as a function of the mismatch parameter has two peaks at two different values of the mismatch parameter, and is devoid of peaks at other values of the mismatch parameter.

Description

[0001] METHOD AND SYSTEM FOR PRODUCING ENTANGLED PHOTONS

[0002] RELATED APPLICATION

[0003] This application claims the benefit of priority of U. S. Provisional Patent Application No. 63 / 777,078 filed on March 25, 2025, the contents of which are incorporated herein by reference in their entirety.

[0004] FIELD AND BACKGROUND OF THE INVENTION

[0005] The present invention, in some embodiments thereof, relates to nonlinear optics and, more particularly, but not exclusively, to method and system for producing entangled photons.

[0006] Polarization-entangled and wavelength-entangled states of photon pairs (polarization Bell states and wavelength Bell states, respectively) are useful in many quantum technologies and experiments in quantum optics. A known approach to generating these states is by leveraging nonlinear optical processes, specifically spontaneous parametric down-conversion (SPDC) and spontaneous four-wave mixing (SFWM) in bulk nonlinear crystals and nonlinear optical waveguides. SPDC, being proportional to a second-order susceptibility / J2’, typically exhibits higher efficiency compared to SFWM

[0015] , which relies on the third-order nonlinear susceptibility χ(3).

[0007] Known schemes for the generation of photonic polarization Bell states include post- selection at a beam splitter, the Sagnac loop or crossed crystals. Recently, it was demonstrated

[0017] that polarization-entangled photon pairs can also be obtained using modal birefringence in a microcavity or employing domain-engineered bulk nonlinear crystals. In this study the nonlinear medium supports two type II collinear non-degenerate SPDC processes: |

[0008]

[0009] VltW) and |JH(.>7thereby forming a polarization Bell state immediately after the nonlinear medium.

[0010] SUMMARY OF THE INVENTION

[0011] According to an aspect of some embodiments of the present invention there is provided a poled nonlinear optical structure for generating pairs of entangled photons from a pump photon, the structure comprises a plurality of domains, and is being characterized by a mismatch parameter, wherein a polarization of the domains is periodically reversed to define a periodic poling pattern, and wherein a Fourier transform of the poling pattern as a function of the mismatch parameter is a phase-matching function having two peaks at two different values of the mismatch parameter, and devoid of peaks at other values of the mismatch parameter.According to some embodiments of the invention the two peaks are in-phase with respect to each other.

[0012] According to some embodiments of the invention the two peaks are out of phase with respect to each other.

[0013] According to some embodiments of the invention the two peaks are of substantially equal height in absolute value.

[0014] According to some embodiments of the invention the two peaks are of substantially equal width.

[0015] According to some embodiments of the invention the poling pattern is characterized by a fixed poling period along a length of the optical structure.

[0016] According to some embodiments of the invention the optical structure is made of a material selected from the group consisting of potassium titanyl phosphate (KTP), Lithium Niobate (LN), Lithium Tantalate (LT), Stoichiometric Lithium Tantalate (SLT), Potassium Titanyl Arsenate (KTA), Rubidium Titanium Phosphate (RTP), and Rubidium Titanium Arsenate Phosphate (RTA).

[0017] According to some embodiments of the invention the phase-matching function is selected to ensure type II spontaneous parametric down-conversion (SPDC).

[0018] According to an aspect of some embodiments of the present invention there is provided a method of generating pairs of entangled photons, comprises directing a beam of pump photons onto the poled nonlinear optical structure as delineated above and optionally and preferably as further detailed below.

[0019] According to some embodiments of the invention the beam is directed to ensure a single pass of the beam though the optical structure.

[0020] According to an aspect of some embodiments of the present invention there is provided a system for generating pairs of entangled photons. The system comprises the poled nonlinear optical structure as delineated above and optionally and preferably as further detailed below, and an unpoled optical structure. The poled and unpoled structures being arranged along an axis in a manner that pairs of entangled photons exiting the poled structure enter the unpoled structure.

[0021] According to some embodiments of the invention the poled nonlinear optical structure is a poled nonlinear optical crystal, and the unpoled optical structure is an unpoled optical crystal.

[0022] According to some embodiments of the invention the unpoled crystal is rotated by about 90° relative to the poled crystal, so as to compensate for group velocity walk off of the pairs of entangled photons.According to some embodiments of the invention a length of the unpoled crystal is about half a length of the poled optical structure.

[0023] According to some embodiments of the invention the poled nonlinear optical structure is a poled waveguide, and the unpoled optical structure is an unpoled waveguide.

[0024] According to some embodiments of the invention the unpoled waveguide is selected to support propagation of photons at a polarization state that is rotated by about 90° relative to a polarization state of the pairs of entangled photons upon exiting the poled waveguide, so as to compensate for group velocity walk off of the pairs of entangled photons.

[0025] According to some embodiments of the invention the system comprises a polarization rotating optical element between the poled and the unpoled waveguides. According to some embodiments of the invention the polarization rotating optical element is configured to rotate a polarization state of the pairs of entangled photons by about 90°.

[0026] According to some embodiments of the invention a length of the unpoled waveguide is about half a length of the poled waveguide.

[0027] According to some embodiments of the invention the system comprises an optical element constituted to split each pair of entangled photons into separate optical paths.

[0028] According to some embodiments of the invention the optical element is configured for converting a mixed frequency-polarization state of the pair of entangled photons into a polarizationentangled state.

[0029] According to some embodiments of the invention the optical element comprises a fiber adddrop filter (ADF).

[0030] According to some embodiments of the invention the optical element comprises a dichroic mirror. According to some embodiments of the invention the optical element comprises at least one element selected from the group consisting of a prism, a grating, and a thin film.

[0031] According to some embodiments of the invention the optical element comprises the optical element is configured for converting a mixed frequency-polarization state of the pair of entangled photons into a frequency-entangled state.

[0032] According to some embodiments of the invention the system comprises an optical cavity characterized by a resonance frequency matching a frequency of the pump photon.

[0033] According to some embodiments of the invention the optical cavity is arranged to allow the pump photon to propagate therein unidirectionally. According to some embodiments of the invention the optical cavity is configured to ensure a single pass of the pairs of entangled photons through the optical structure.According to some embodiments of the invention the optical element comprises the optical element comprises polarizing beam splitter.

[0034] According to an aspect of some embodiments of the present invention there is provided a light emission system comprises the optical structure or system as delineated above and optionally and preferably as further detailed below.

[0035] According to an aspect of some embodiments of the present invention there is provided a communication system comprises the optical structure or system as delineated above and optionally and preferably as further detailed below.

[0036] According to an aspect of some embodiments of the present invention there is provided a quantum teleportation system comprises the optical structure or system as delineated above and optionally and preferably as further detailed below.

[0037] According to an aspect of some embodiments of the present invention there is provided a quantum cryptography system comprises the optical structure or system as delineated above and optionally and preferably as further detailed below.

[0038] According to an aspect of some embodiments of the present invention there is provided a quantum computer comprises the optical structure or system as delineated above and optionally and preferably as further detailed below.

[0039] According to an aspect of some embodiments of the present invention there is provided a quantum metrology inspection system, comprises the optical structure or system as delineated above and optionally and preferably as further detailed below.

[0040] According to an aspect of some embodiments of the present invention there is provided a quantum simulation system, comprises the optical structure or system as delineated above and optionally and preferably as further detailed below.

[0041] Unless otherwise defined, all technical and / or scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the invention pertains. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of embodiments of the invention, exemplary methods and / or materials are described below. In case of conflict, the patent specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and are not intended to be necessarily limiting.

[0042] Implementation of the method and / or system of embodiments of the invention can involve performing or completing selected tasks manually, automatically, or a combination thereof. Moreover, according to actual instrumentation and equipment of embodiments of the method and / or system ofthe invention, several selected tasks could be implemented by hardware, by software or by firmware or by a combination thereof using an operating system.

[0043] For example, hardware for performing selected tasks according to embodiments of the invention could be implemented as a chip or a circuit. As software, selected tasks according to embodiments of the invention could be implemented as a plurality of software instructions being executed by a computer using any suitable operating system. In an exemplary embodiment of the invention, one or more tasks according to exemplary embodiments of method and / or system as described herein are performed by a data processor, such as a computing platform for executing a plurality of instructions. Optionally, the data processor includes a volatile memory for storing instructions and / or data and / or a non-volatile storage, for example, a magnetic hard-disk and / or removable media, for storing instructions and / or data. Optionally, a network connection is provided as well. A display and / or a user input device such as a keyboard or mouse are optionally provided as well.

[0044] BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0045] Some embodiments of the invention are herein described, by way of example only, with reference to the accompanying drawings. With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of embodiments of the invention. In this regard, the description taken with the drawings makes apparent to those skilled in the art how embodiments of the invention may be practiced.

[0046] In the drawings:

[0047] FIG. 1 is a schematic illustration of an experimental setup used according to some embodiments of the present invention.

[0048] FIGs. 2A-B show spectral characterization of the source, as obtained in experiments performed according to some embodiments of the present invention.

[0049] FIGs. 3A-C show a reconstructed density matrix, as obtained in experiments performed according to some embodiments of the present invention.

[0050] FIGs. 4A and 4B show polarization entanglement visibility, as obtained in experiments performed according to some embodiments of the present invention.

[0051] FIG. 5 is a schematic illustration of a poled nonlinear optical structure according to some embodiments of the present invention.

[0052] FIGs. 6A and 6B are schematic illustrations of a system for generating pairs of entangled photons according to some embodiments of the present invention.DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION

[0053] The present invention, in some embodiments thereof, relates to nonlinear optics and, more particularly, but not exclusively, to method and system for producing entangled photons.

[0054] Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not necessarily limited in its application to the details of construction and the arrangement of the components and / or methods set forth in the following description and / or illustrated in the drawings and / or the Examples. The invention is capable of other embodiments or of being practiced or carried out in various ways.

[0055] Referring now to the drawings, FIG. 5 illustrates a poled nonlinear optical structure 10 according to some embodiments of the present invention. Structure 10 can be used for generating pairs 12 of entangled photons 12a, 12b from a pump photon 14. For clarity of presentation, photons 12a and 12b are illustrated spaced apart from each other. However, this need not necessarily be the case, since, photons 12a and 12b can be collinear or occupy the same spatial location.

[0056] Structure 10 may be embodied in a variety of physical forms. In some embodiments of the present invention, structure 10 is a bulk nonlinear optical crystal, such as a domain-engineered crystal of potassium titanyl phosphate (KTP), which was employed in the experimental demonstration described in the Examples section below. Other bulk crystal materials suitable for structure 10 include, without limitation, Lithium Niobate (LN), Lithium Tantalate (LT), Stoichiometric Lithium Tantalate (SLT), Potassium Titanyl Arsenate (KTA), Rubidium Titanium Phosphate (RTP), and Rubidium Titanium Arsenate Phosphate (RTA). Each of these materials exhibits a second-order nonlinear susceptibility χ(2)that can be engineered according to some embodiments of the present invention by periodic poling.

[0057] In some embodiments, structure 10 is a nonlinear optical waveguide, such as a periodically poled waveguide fabricated in any of the above-listed materials, for example a periodically poled lithium niobate (PPLN) waveguide, a periodically poled KTP (PPKTP) waveguide, or a waveguide formed in Lithium Tantalate, Stoichiometric Lithium Tantalate, KTA, RTP, or RTA. A waveguide geometry confines the interacting optical fields to a small cross-sectional area over the full length of the structure, which may enhance the nonlinear interaction efficiency and the spectral brightness of the generated photon pairs compared to a bulk crystal geometry. In some embodiments, structure 10 may be integrated on a photonic chip, for example as a ridge waveguide or a strip waveguide etched into a thin-film nonlinear optical material such as thin-film lithium niobate (TFLN), enabling compatibility with integrated photonic circuits.Structure 10 preferably comprise a plurality of domains 16, and is characterized by a mismatch parameter. The mismatch parameter can be conveniently defined in terms of the difference Δk=kP−(ks+ki) between the wavenumber kPof the pump photon 14 and the sum ks+kiof the wavenumbers ksand kiof photons 12a, 12b, respectively. This characterization of the domains is convenient because it expresses the deviation from conservation of momentum in the crystal. Other equivalent characterizations of the mismatch parameter are also contemplated.

[0058] According to some embodiments of the present invention the polarization of domains 16 is periodically reversed to define a periodic poling pattern 18.

[0059] FIG. 5 illustrates a configuration in which poling pattern 18 is characterized by a fixed poling period along the entire length of structure 10. In these embodiments, the spatial interval between successive reversals of the domain polarization remains constant throughout the crystal or waveguide. A uniform periodic poling is advantageous from the standpoint of fabrication complexity. The poling period can be selected to satisfy a quasi-phase-matching (QPM) condition for type II SPDC at a pump wavelength. For example, the poling period can be equal about half the central wavelength of the generated photon pairs. In the experimental demonstration described in the Examples section that follows, the poling period was about 46 μm along the crystallographic X-axis of a KTP crystal. It is to be understood, however, that the present embodiments also contemplate an alternative configuration in which the poling pattern is a non-uniform or chirped poling pattern. In this vase the poling period varies along the length of structure 10. For example, the poling pattern can be a chirped poling pattern. Aperiodic poling pattern may be designed to tailor a joint spectral amplitude of the generated photon pair 12 for a particular application.

[0060] The Fourier transform of poling pattern 18, as a function of the mismatch parameter, is a phasematching function which optionally and preferably has two peaks at two different values of the mismatch parameter. In various exemplary embodiments of the invention phase-matching function is devoid of peaks at other values of the mismatch parameter. The two peaks are typically peaks of two distinct lobes of the phase-matching function. Preferably, the two lobes are sufficiently separated as a function of the mismatch parameter so that the overlap between the lobes is less than a predetermined threshold (e.g., less than 10% or less than 1% of the average height of the peaks). A representative example of a phase-matching function suitable for the present embodiments is provided in the Examples section that follows.

[0061] In some embodiments of the present invention, the two peaks of the phase-matching function are in-phase with respect to each other. In these embodiments, the complex amplitudes of the two peaks carry the same sign. In this configuration, the joint spectral amplitude of the generated photonpairs is symmetric under exchange of the frequencies of photons 12a and 12b, and the corresponding two-photon state takes the form of a symmetric superposition of the two frequency-polarization terms. Alternatively, the two peaks can be out of phase with respect to each other. For example, the relative phase between the two peaks can be about π, so that the complex amplitudes of the two peaks carry opposite signs. In the experimental demonstration described in the Examples section that follows, a π-phase difference between the two lobes of the phase-matching function was employed, resulting in an antisymmetric joint spectral amplitude. The choice between an in-phase and an out-of-phase configuration determines the symmetry of the joint spectral amplitude and thereby the specific Bell state generated by structure 10.

[0062] In some embodiments of the present invention, the two peaks are of equal, or substantially equal (e.g., within tolerance of less than 10%) height in absolute value. Equal-height peaks ensure that the two frequency-polarization terms in the generated two-photon state are produced with equal probability amplitudes, providing a maximally entangled Bell state. In the experimental demonstration described in the Examples section that follows, the crystal design was arranged so that the two lobes of the phase-matching function had substantially equal heights. In some embodiments, the two peaks are of equal or substantially equal (e.g., within a tolerance of less than 10%) width, meaning that the spectral bandwidth of each peak, for example as measured by the full width at half maximum (FWHM) of the peak in the phase-matching function, is the same or nearly the same for both peaks. Equal widths of the two peaks contribute to the spectral indistinguishability of the two terms in the joint spectral amplitude. In the experimental demonstration described below, the FWHM of each lobe was about 6 nm, and the two lobes were designed to have equal widths. The conditions of equal height and equal width of the two peaks may be achieved simultaneously, or individually, as desired.

[0063] In some embodiments of the present invention, the phase-matching function of structure 10 is selected to ensure type II SPDC. In type II SPDC, the signal 12a and idler 12b photons of the generated pair 12 are emitted with orthogonal polarizations: one photon carries horizontal (H) polarization and the other carries vertical (V) polarization with respect to a defined reference frame. This orthogonality of the polarizations of the two photons in each pair is a feature that distinguishes type II SPDC from type I SPDC, in which both photons of a pair share the same polarization. In the context of the present embodiments, type II phase matching gives rise to two distinct nonlinear processes supported simultaneously by structure 10: a first process in which pump photon 14 at frequency ωPgenerates signal photon 12a at frequency ω1with H polarization and idler photon 12b at frequency ω2with V polarization, and a second process in which pump photon 14 generates signalphoton 12a at frequency ω2with H polarization and idler photon 12b at frequency ω1with V polarization, where ω1and ω2are two central frequencies corresponding to the two peaks of the phasematching function. The coherent superposition of these two processes, with the relative phase determined by the phase relationship between the two peaks of the phase-matching function, directly produces a polarization-entangled two-photon state at the output of structure 10 without requiring any post-selection or interferometric manipulation. In the experimental demonstration described in the Examples section that follows, type II SPDC was facilitated by aligning the pump polarization with the crystallographic Y axis of the KTP crystal, enabling interaction via the d23 nonlinear coefficient. The phase-matching function was designed so that both type II processes were simultaneously phase-matched at the two peak positions, as described in detail in the Examples section.

[0064] Reference is now made to FIGs. 6A and 6B, which are schematic illustrations of a system 20 for generating pairs 12 of entangled photons 12a, 12b according to some embodiments of the present invention. System 20 comprises poled nonlinear optical structure 10 as described above, and an unpoled optical structure 22. Poled structure 10 and unpoled structure 22 are arranged along a common optical axis 24 in a manner that photon pairs 12 exiting poled structure 10 enter unpoled structure 22. The arrangement along axis 24 allows the photon pairs generated in structure 10 to propagate collinearly into structure 22 without requiring any additional beam-steering or coupling optics between the two structures in their basic configuration.

[0065] In some embodiments of the invention, poled nonlinear optical structure 10 is a poled nonlinear optical crystal, and unpoled optical structure 22 is an unpoled optical crystal (FIG. 6A). The unpoled crystal 22 can be made of the same material as, or a material compatible with, poled crystal 10, so that the birefringent properties of the two crystals are matched.

[0066] In type II SPDC, the signal and idler photons of each pair travel at different group velocities within the birefringent crystal because they carry orthogonal polarizations, and this difference in group velocities causes the two photons to separate temporally as they propagate through poled crystal 10. This temporal separation, is referred to herein as temporal walk-off. It was found by the inventors that the temporal walk-off may introduces a time-ordering distinguishability between the two photons, and that this reduces the quality of polarization entanglement. Thus, in some embodiments, the unpoled crystal is oriented relative to the poled crystal, so as to compensate for the group velocity walk-off of photon pairs 12. This configuration exchanges the roles of the fast and slow polarization axes in crystal 22, and at least partially reverses the temporal walk-off accumulated in crystal 10. The rotation is such that after the rotation, the unpoled crystal 22 is oriented such that its fast polarization axis is aligned with the slow polarization axis of the poled crystal 10, reversing the group velocitywalk-off. Typically, unpoled crystal 22 is rotated by about 90° relative to poled crystal 10. In some embodiments, a length of unpoled crystal 22 is about half a length of poled optical structure 10, which provides approximately full compensation of the temporal walk-off for photon pairs generated at the center of poled crystal 10. In the experimental demonstration described in the Examples section, the poled KTP crystal was 4 mm long, and an unpoled 2 mm-long KTP crystal was placed immediately after it with its ZY plane oriented perpendicularly to that of the poled crystal.

[0067] In some embodiments of the present invention, poled nonlinear optical structure 10 is a poled waveguide, and unpoled optical structure 22 is an unpoled waveguide (FIG. 6B). In a waveguide geometry, the group velocity walk-off between the two polarized photons (e.g., orthogonally polarized photons) 12a, 12b depends on the modal birefringence of the waveguide. In some embodiments, unpoled waveguide 22 is selected to support propagation of photons at a polarization state that is rotated by about 90° relative to a polarization state of photon pairs 12 upon exiting poled waveguide 10. These embodiments are useful because they compensate, at least partially, for the aforementioned group velocity walk-off. In some embodiments, a length of unpoled waveguide 22 is about half a length of poled waveguide 10, for the same reasons as described above for the crystal embodiment.

[0068] System 20 may optionally and preferably comprise a polarization rotating optical element 26 between poled waveguide 10 and unpoled waveguide 22. Element 26 may be, for example, a halfwave plate, a Faraday rotator, a fiber polarization rotator, or any other optical element configured to rotate the polarization state of the photon pairs before they enter unpoled waveguide 22. The advantage of element 26 is that the walk-off compensation in unpoled waveguide 22 can act on the correct polarization components.

[0069] In some embodiments of the present invention, system 20 comprises an optical cavity 28 characterized by a resonance frequency matching the frequency coPof pump photon 14. Cavity 28 may be, for example, a Fabry-Perot cavity formed by two partially reflective mirrors arranged on either side of poled structure 10 along axis 24, a ring cavity comprising a set of mirrors or beam splitters arranged in a closed loop that includes poled structure 10, a bow-tie cavity comprising four mirrors arranged in a bow-tie configuration that includes poled structure 10, or any other resonant optical structure that supports a standing or travelling wave at the pump frequency ωP. The resonance of cavity 28 at the pump frequency enhances the circulating pump power inside the cavity relative to the input pump power, which optionally and preferably increases the rate of photon pair generation in structure 10.

[0070] Optical cavity 28 may optionally and preferably be arranged to allow pump photon 14 to propagate therein unidirectionally, for example by incorporating an optical isolator or a Faradayrotator within the cavity loop in the case of a ring cavity geometry or a bow-tie cavity geometry, so that the pump field circulates in only one direction around the loop. Unidirectional propagation of the pump suppresses back-reflection and the associated noise that may otherwise degrade the quality of the generated entangled state. In some embodiments, optical cavity 28 is configured to ensure a single pass of pairs 12 of entangled photons through poled optical structure 10. This can be achieved, for example, by arranging the cavity mirrors or output couplers to be dominantly transmissive at the signal and idler wavelengths and dominantly reflective at the pump wavelength, so that photon pair 20 can exit cavity 28 after a single traversal of structure 10 without being resonantly enhanced or reflected back through the nonlinear medium.

[0071] In some embodiments of the present invention, system 20 comprises an optical element 30 constituted to split photon pair 12 into separate optical paths. Optical element 30 receives the collinear biphoton field exiting unpoled structure 22 and directs photon 12a and photon 12b of each pair into respective distinct spatial modes or fiber channels, so that the two photons can be independently manipulated and detected. In some embodiments, optical element 30 is configured for converting a mixed frequency-polarization state of pair 12 of entangled photons into a polarization-entangled state. In the mixed frequency-polarization state, the two photons carry different frequencies and different polarizations, so that the frequency and polarization degrees of freedom are correlated. By splitting the two photons according to their frequency, optical element 30 traces out the frequency degree of freedom and yields a reduced state that is entangled in polarization alone.

[0072] In experiments performed by the Inventors, a fiber add-drop filter (ADF) was used as optical element 30. A fiber ADF transmits photons below a cut-on frequency ω0 into one output port and photons above ω0 into another output port, with the cut-on frequency ω0 lying between the two spectral lobes of the biphoton joint spectral amplitude. Also contemplated are embodiments in which optical element 30 comprises a dichroic mirror, which reflects photons at one wavelength range and transmits photons at another wavelength range, with the transition wavelength chosen to lie between the two lobes, thereby spatially separating the two photons into reflected and transmitted beams. Further contemplated are embodiments on which optical element 30 is selected from the group consisting of a prism, a grating, a thin film, and the like.

[0073] In some embodiments, optical element 30 is configured for converting a mixed frequencypolarization state of photon pair 12 into a frequency-entangled state. In this configuration, optical element 30 splits the two photons of each pair according to their polarization rather than their frequency, tracing out the polarization degree of freedom and yielding a reduced state that is entangled in frequency. In these embodiments, optical element 30 can comprise a polarizing beam splitter(PBS), which transmits photons of one linear polarization and reflects photons of the other linear polarization, thereby directing the H-polarized and V-polarized photons of each pair into separate output ports and producing a frequency-entangled two-photon state in which the two output modes carry photons at the two distinct frequencies with a well-defined phase relationship.

[0074] Structure 10 and system 20 may find application across a wide range of quantum optical and photonic technologies. In some embodiments of the present invention, structure 10 or system 20 is incorporated into a light emission system, for example as a source of non-classical light for optical experiments or as a component of a photonic device that generates correlated or entangled photon pairs on demand.

[0075] In some embodiments, structure 10 or system 20 is incorporated into a communication system, for example as a source of entangled photon pairs for quantum communication protocols that distribute quantum correlations between spatially separated parties over optical fiber or free- space channels. The entangled photon pairs may serve as the physical carriers of quantum information between nodes of a quantum network. The communication system can comprise a quantum repeater architecture, in which multiple intermediate nodes are connected by entangled photon pair sources, and entanglement swapping operations at the intermediate nodes extend the range of quantum correlations beyond the direct transmission distance of a single optical fiber span. The communication system can comprise a plurality of instances of structure 10 or system 20 operating simultaneously, so as to serve multiple users or multiple channels of a quantum network in parallel.

[0076] In some embodiments, structure 10 or system 20 is incorporated into a quantum teleportation system, in which the polarization-entangled or frequency-entangled photon pairs generated by the present embodiments serve as the entangled resource shared between a sender and a receiver, enabling the transfer of an unknown quantum state from one location to another without physically transmitting the quantum system carrying that state.

[0077] In some embodiments, structure 10 or system 20 is incorporated into a quantum cryptography system, for example as the entangled photon pair source in an Ekert-type quantum key distribution (QKD) protocol, in which the correlations of entangled photon pairs are used to establish a shared secret key between two parties with security guaranteed by the laws of quantum mechanics. Other quantum cryptography protocols are also contemplated. Representative examples include, without limitation, device-independent QKD (DI-QKD) protocols, semi-device-independent QKD protocols, measurement-device-independent QKD (MDI-QKD) protocols, and continuous-variable QKD protocols. The quantum cryptography system can operate over a telecommunication optical fiber or over a free- space optical channel.In some embodiments, structure 10 or system 20 is incorporated into a quantum computer, for example as a source of entangled photon pairs for linear optical quantum computing architectures or photonic quantum processors in which polarization-encoded or frequency-encoded qubits are manipulated by linear optical elements and single-photon detectors. In such a quantum computing system, the photon pairs generated by structure 10 may serve as the physical carriers of quantum information, with each photon of a pair encoding a qubit in its polarization degree of freedom, for example with horizontal polarization H representing the logical state |0) and vertical polarization V representing the logical state 11>, or alternatively in its frequency degree of freedom, with photons at frequency ω1 representing |0⟩ and photons at frequency ω2 2 representing |1⟩. The quantum computer operates according to a linear optical quantum computing architecture, or according to a measurementbased quantum computing architecture, or according to a boson sampling architecture or according to a fusion-based quantum computing architecture, or according to a continuous-variable quantum computing architecture.

[0078] In some embodiments, structure 10 or system 20 is incorporated into a quantum metrology inspection system, for example for quantum-enhanced sensing or imaging applications in which the entangled photon pairs generated by the present embodiments are used to improve measurement precision, or for quantum optical coherence tomography and related techniques.

[0079] In some embodiments, structure 10 or system 20 is incorporated into a quantum simulation system, for example as a source of entangled photons for simulating quantum problems, such as, but not limited to, many-body systems, chemistry problems, or other physical systems whose behavior is encoded in the correlations of multi-photon quantum states.

[0080] Following are example values for parameters suitable for use in structure 10 and system 20, according to some embodiments of the present invention. The numerical values recited below were obtained in a specific experimental demonstration performed according to some embodiments of the present invention. It is to be understood that these numerical values are provided for illustrative purposes only. These values are not to be construed as limiting the scope of the invention. Other combinations of parameters falling within the ranges recited above, or outside those ranges, are also contemplated according to some embodiments of the present invention.

[0081] The poled structure 10 can have a length of from about 2 mm to about 10 mm, for example about 4 mm, and a poling period of from about 30 pm to about 60 pm, for example about 46 pm, along the crystallographic X-axis. The unpoled structure 22 can have a length of from about 1 mm to about 5 mm, for example about 2 mm, corresponding to from about one third to about two thirds of the length of poled structure 10, for example about half the length of poled structure 10. The pump photoncan have a wavelength of from about 700 nm to about 900 nm, for example about 780 nm, and the two peaks of the phase-matching function can be centered at wavelengths of from about 1400 nm to about 1700 nm, for example at about 1548 nm to about 1572 nm, symmetrically displaced about the degenerate wavelength of about 1560 nm. The spectral bandwidth of each of the two peaks, as measured by full width at half maximum (FWHM), can be from about 2 nm to about 20 nm, for example about 6 nm, and the spectral separation between the two peaks can be from about 5 nm to about 100 nm, for example about 24 nm, preferably wherein the spectral separation exceeds the spectral bandwidth of each peak so that the two peaks are spectrally resolved. The relative phase between the two peaks can be from about 0.8K to about 1.2K, for example about K. The pump field can be generated by a pulsed laser having a spectral bandwidth of from about 1 nm to about 20 nm, for example about 7 nm, corresponding to a pulse duration of from about 20 fs to about 500 fs, for example about 90 fs, for a bandwidth- limited pulse, and a pulse repetition rate of from about 10 MHz to about 1 GHz, for example about 76 MHz. The average temporal walk-off between orthogonally polarized photons generated at the center of poled structure 10 can be from about 100 fs to about 2000 fs, for example about 590 fs, prior to compensation by unpoled structure 22, and the residual walk-off difference between the two spectral components of the generated photon pairs after compensation is preferably less than about 10% of the photon coherence time, for example about 1.3 fs. The photon coherence time can be from about 200 fs to about 2000 fs, for example about 617 fs. An optical filter used to suppress the pump photons can have a cut-on wavelength lying between the pump wavelength and the shorter of the two lobe center wavelengths, for example from about 850 nm to about 1100 nm, such as about 950 nm, providing an attenuation of at least about 95% at the pump wavelength and a transmission of at least about 90% at the central wavelength of the generated photon pairs. The structure can be operated at a temperature of from about 15 °C to about 40°C, for example at room temperature of about 23 °C, optionally without active temperature stabilization. The generated photon pairs can exhibit a joint spectral intensity overlap integral of at least about 0.95, for example about 0.998, a single-photon spectral purity of at least about 0.40, for example about 0.496, a two-photon state purity Tr(p2) of at least about 0.85, for example about 0.948, a concurrence of at least about 0.85, for example about 0.948, and a CHSH S-parameter of at least about 2.5, for example about 2.747, with polarization entanglement visibility of at least about 85% in the {H, V} measurement basis, for example about 97%, and at least about 75% in the {D, A} measurement basis, for example about 90%.

[0082] As used herein the term “about” refers to ± 10 %

[0083] The terms "comprises", "comprising", "includes", "including", “having” and their conjugates mean "including but not limited to".The term “consisting of’ means “including and limited to”.

[0084] The term "consisting essentially of" means that the composition, method or structure may include additional ingredients, steps and / or parts, but only if the additional ingredients, steps and / or parts do not materially alter the basic and novel characteristics of the claimed composition, method or structure.

[0085] As used herein, the singular form "a", "an" and "the" include plural references unless the context clearly dictates otherwise. For example, the term "a compound" or "at least one compound" may include a plurality of compounds, including mixtures thereof.

[0086] Throughout this application, various embodiments of this invention may be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range.

[0087] Whenever a numerical range is indicated herein, it is meant to include any cited numeral (fractional or integral) within the indicated range. The phrases “ranging / ranges between” a first indicate number and a second indicate number and “ranging / ranges from” a first indicate number “to” a second indicate number are used herein interchangeably and are meant to include the first and second indicated numbers and all the fractional and integral numerals therebetween.

[0088] It is appreciated that certain features of the invention, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable subcombination or as suitable in any other described embodiment of the invention. Certain features described in the context of various embodiments are not to be considered essential features of those embodiments, unless the embodiment is inoperative without those elements.

[0089] Various embodiments and aspects of the present invention as delineated hereinabove and as claimed in the claims section below find experimental support in the following examples.EXAMPLES

[0090] Reference is now made to the following examples, which together with the above descriptions illustrate some embodiments of the invention in a non limiting fashion.

[0091] Reference is now made to the following examples, which together with the above descriptions illustrate some embodiments of the invention in a non limiting fashion.

[0092] Example 1

[0093] Direct Polarization-Entangled Photon Pair Generation Using Domain-Engineered Nonlinear Crystals

[0094] This Example describes a bi-photon polarization-frequency entangled source which provides polarization or spectral entanglement in a collinear setup based on single-pass SPDC and a dichroic or polarization beam splitter. The described configuration can be implemented outside the lab environment.

[0095] The source described in this Example is a single -pass single-crystal post-selection-free source of polarization Bell states at telecom wavelengths, based on SPDC in a domain-engineered bulk KTiOPO4 (KTP) crystal. Compared to conventional technique the source of the present embodiments enjoys several advantages, including a simple and compact collinear design, requiring only a few optical components. The source of the present embodiments does not require use of interferometers such as Sagnac, Michelson, or Mach-Zender, resulting in improved mechanical stability without the need for active stabilization. The source of the present embodiments can operate under both pulsed and CW pumps. This Example demonstrates operation for a femtosecond pulsed pump, the crystal can be designed to produce a round joint spectral intensity of each process:

[0096]

[0097] ) and

[0098]

[0099] |3making this scheme suitable for quantum repeaters requiring high- visibility interference between two independent sources and therefore pure heralded single photons from each source. The source of the present embodiments can be implemented using nonlinear optical waveguides and optical cavities to enhance the total pair generation rate and spectral brightness. The source of the present embodiments offers simplicity, efficiency, and versatility for various quantum applications.

[0100] SPDC in domain-engineered crystals

[0101] SPDC is a process of interaction between three modes of electromagnetic field in a nonlinear crystal, in which the annihilation of one photon from one mode (pump) is accompanied by the simultaneous creation of two photons into two other modes, traditionally referred to as the signal and idler. This process becomes more efficient when the amplitudes of photon pair creation in different points in time and space (crystal volume) constructively interfere. Constructive interfere can beachieved by ensuring phase-matching conditions that connect the frequencies and wave- vectors of the three interacting fields:

[0102] ωp = ωs + ωi, (1)

[0103]

[0104] kp(ωp) ≈ ks(ωs) + ki(ωp − ωs), (2) where ωl and kl (l = "p," "s," "i") are the frequencies and wave vectors of the pump (p), signal (s), and idler (i) fields, respectively. Here, kl = n(ωl)·ωl / c, where n(ωl) is the refractive index of the crystal at the frequency ωl, and c is the speed of light. This Example describes the case of a collinear type-II SPDC, where EQ. 2 is scalar, with all the wave vectors pointing along the crystallographic X-axis of the nonlinear crystal.

[0105] The state vector describing the generated field can be calculated in the first order of the perturbation theory and is expressed as

[0018] :

[0106] |ψ⟩ = |0⟩ + η∬ dωs dωi f(ωs, ωi) a†H(ωs) a†V(ωi)|0⟩, (3)

[0107]

[0108] where |0) denotes the vacuum state, and a†H(ωs) and a†v(ωi) represent the creation operators for the signal and idler modes, respectively. The function f(ωs, ωi) is the joint spectral amplitude (JSA) of the two-photon field, which describes the amplitude of generating the signal and idler photons at the respective frequencies ωs and ωi. The square of the ISA's absolute value is the joint spectral intensity (JSI). Aside from the central frequencies and spectral bandwidths of the signal and idler photons, the JSA also reveals spectral correlations inherent to photon pairs (or the absence thereof, which is desired for generating pure heralded single photons). As will be shown below, with proper design of the crystal's nonlinear susceptibility / J2’ (and therefore proper shaping of the JSA) these spectral correlations can lead to polarization entanglement between the two photons generated within the crystal. This allows for the formation of an entangled state using only a domain-engineered crystal, without the need for additional lossy manipulation of the generated photons, as in other methods.

[0109] Denoting the pump field amplitude by EP, the crystal length by L, and the frequency-dependent refractive index of the crystal by n(ω), the JSA can be expressed as the product of the spectral amplitude of the pump field, P(ωs, ωi), and the phase-matching function of the crystal (PMF), Φ(Δk(ωs, ωi)), under the low-gain approximation in which K= / (2)EPLo / cn(o) < 1

[0019] :

[0110]

[0111] The PMF in the frequency domain is obtained via the Fourier transform of the crystal's poling pattern

[0020] , which allows for achieving the desired amplitude and phase of the PMF (including analytical solutions), by shaping the crystal's nonlinear susceptibility [21, 22].

[0112] Using this technique, the crystal employed in this Example was engineered so that its PMF in the frequency domain included two lobes with a π-phase difference between them (FIGs. 2A-B). When pumped at a wavelength of about 780 nm, the central wavelengths of the lobes were about 1548 nm and about 1572 nm. The spectral bandwidth (FWHM) of each lobe was about 6 nm. The crystal was 4 mm long and had a poling period of about 46 pm. The poling pattern of the crystal resulted in the following phase-matching function:

[0113] I / / ( A £- _ / i \ / ( A I" 4- z? \ \ = -= exp M - exp, (5)

[0114]

[0115] V27UT \ \ -<r- / \ 2(T- / / where in this example o and a were selected to be about 333 m'1and about 2700 m’1, respectively.

[0116] The state generated at the output of the crystal can be written as follows:

[0117]

[0118] where ω1 and ω2 represent the lower and higher central frequencies of the JSA lobes, the minus sign reflects the π-phase between the PMF (and JSA) lobes, and the 2-1 / 2factor accounts for the equal pair rate generated for each lobe.

[0119] This state can be converted to a polarization-entangled state, for example, by propagating the bi-photon field through a fiber add-drop filter (ADF) or by using a free-space dichroic mirror, with the cut-on frequency ω0 lying between the two lobes, thereby splitting the two created photons into separate paths. After such a transformation, which traces out the frequency degree of freedom, the state becomes:

[0120]

[0121] Also contemplated, is a transmission of the photon pairs in the original state through a polarizing beam splitter (PBS), so as to trace out the polarization degree of freedom, thereby forming a frequency-entangled state:

[0122] 1 / \ \4> Ptis) = — ( |W|H<<>2V) - |fc'2HWtv> )■ (8)

[0123]

[0124] V2 'While the Example describes the polarization-entanglement case, the frequency entanglement case is also contemplated according to some embodiments of the present invention.

[0125] Experimental Results

[0126] Generation of polarization-entangled photon pairs

[0127] The experimental setup is illustrated in FIG. 1. Ti: Sa is a Titanium- sapphire femtosecond laser, HWP is a half-wave plate, L1-L6 are lenses, DE KTP is a domain-engineered KTP crystal, C KTP is a temporal-walk-off compensation crystal, LP is longpass filter, SMF28 is a single-mode optical fiber at 1550 nm, ADF is a fiber add-drop filter, QWP is a quarter-wave plate, Pol is a linear polarizer, PC is a fiber polarization controller, PS is a fiber polarization sorter, Deti, and Det2 is a superconducting nanowire detector, QST is a quantum state tomography part, and JSI is part of the setup intended for the joint spectral intensity measurements based on the time-of-flight spectrometry. The generation of polarization-entangled photon pairs occurs in the top part of FIG. 1, denoted " Source."

[0128] The experimental setup utilized radiation from a pulsed, mode-locked, tunable Ti-Sapphire laser at a wavelength of about 780 nm as the pump source. The laser’s spectral bandwidth was approximately 7 nm, corresponding to a pulse duration of about 90 fs for a bandwidth-limited sech2-shaped pulse, which is typical for this type of lasers. The pulse repetition rate was about 76 MHz. A half-wave plate HWPi was used to align the pump polarization with the crystallographic Y axis of the nonlinear crystal, facilitating type-II SPDC via the corresponding d23 nonlinear coefficient. The pump beam was focused onto the nonlinear crystal using the Ei lens. For the / J2’ nonlinear medium, a domain-engineered KTP (DE KTP) crystal was fabricated according to some embodiments of the present invention with parameters as discussed above. The crystal was operated without an oven at room temperature (about 23 °C).

[0129] Entanglement can be manifested by the indistinguishability of the two corresponding amplitudes: |HV) and |VH). Since the birefringent delay between the H and V photons in the DE KTP (referred to herein as "temporal walk-off") introduces temporal distinguishability, an additional unpoled 2 mm-long KTP crystal was placed immediately after the DE KTP crystal, perpendicularly in the ZY plane of the crystal, so as to compensate for the temporal walk-off. The difference in walk-off between

[0130]

[0131] \H ) and | V <t.jiH ) was found to be 1.3 fs. This difference is significantly smaller than the photon duration (about 617 fs) and was therefore disregarded. Before compensation, the average temporal walk-off between orthogonally polarized photons generated at the center of the 4 mm crystal was approximately 590 fs.After exiting the crystal, the pump was suppressed using three long-pass dichroic mirrors with a cut-on wavelength of about 950 nm. Each filter provided an attenuation of about 99.5 % at the pump wavelength and about 97.8 % transmission at 1560 nm. The collinearly generated biphoton field was then coupled, using the L2 lens, into the single-mode fiber SMF-28, which acted as a spatial filter, ensuring that the collected photons were spatially indistinguishable.

[0132] Spectral Characterization

[0133] Entanglement can be manifested by spectral indistinguishability. The two terms in the generated state correspond to the two lobes of the biphotons' JSA. Spectral indistinguishability is obtained when the JSA of the generated photons satisfies JSA(ω1, ω2) = eiθJSA(ω2, ω1), where 0 is the phase between the two lobes. It is noted that when θ=π, the JSA is antisymmetric under swapping the frequencies of the signal and idler photons and when θ=0 the JSA is symmetric under swapping the frequencies of the signal and idler photons. Spectral indistinguishability was tested by measuring the JSI of the generated photons using time-of-flight spectroscopy, which leverages the natural capability of long and dispersive fibers to perform a frequency-time Fourier transform on incoming light.

[0134] This Example assumes only a π-phase between the two lobes and that the JSA is a real- valued function, disregarding any joint / nonlinear spectral phase dependence. As demonstrated below, the validity of this assumption was confirmed through quantum state tomography. This assumption, combined with the fact that the two lobes do not overlap when projected onto frequency axes, allowed replacing the JSA with the square root of the experimentally measured JSI, where information about the spectral phase of the state is lost, facilitating further symmetry evaluation.

[0135] For these measurements, the generated photons were sent (see FIG. 1 where this corresponds to connecting the output fiber of the source part to the part of the setup dedicated to JSI measurements) to the fiber polarization controller PC followed by a fiber polarization sorter PS that split the photons by polarization into two arms. In each arm, a 10 km long SMF-28 optical fiber (with a dispersion of 18 ps / nm / km at 1550 nm) was utilized to introduce a dispersive delay. Each 10 km fiber was connected to one of the superconducting nano wire detectors Di, D2 (detection efficiency r|det of about 90 % at 1550 nm). Electrical signals from the detectors were registered by a time tagger for counting coincidences. By measuring the number of coincidences between the two arms and a reference clock signal from the laser, the JSI was we reconstructed (FIG. 2A). The overall temporal resolution, determined by the jitter of the detection system, was measured to be approximately 150 ps. This value, along with the spectral delay after the 10 km fibers (180 ps / nm), corresponds to a spectral resolution of 0.83 nm for the reconstructed JSI. For comparison, the calculated JSI based on thecrystal's poling design is shown in FIG. 2B. The overlapping integral between the experiment and the theoretical JSI was 0.99, demonstrating a high degree of similarity between the experimental results and theoretically calculated predictions.

[0136] To quantify the symmetry of the JSI, the overlap integral between JSI(Xs, i) and JSI(Xi, Xs) was used:

[0137] | / JSA (4S, / I;’) JSA (4 / , zls) c / 4s(£4 / j

[0138]

[0139] J (JSA(zl5, / I / )) dlsd-lf J (JSA(zl / ,zl5)) where JSA is the square root of JSI, with JSI being the experimentally measured function.

[0140] The overlap integral takes values between 0 and 1, and is maximized when the JSI is perfectly symmetric or antisymmetric around the degenerate line where Xs= Xi.

[0141] This integral reflects the degree of symmetry in the JSA and directly relates to the ability to generate polarization-entangled states. Specifically, it shows that polarization entanglement can still be achieved under continuous-wave pumping, as long as the JSA remains symmetric, whether the pump is single-mode or comprises multiple non-locked cavity modes. In the latter case, although the pump spectral modes are mutually incoherent, their spectral envelope remains the same as in the locked case, within which the JSA is measured to be symmetric. The values of this integral for the measured and calculated JSIs were 0.998 and 0.992, respectively.

[0142] The overlap integral serves as an upper limit for the degree of polarization entanglement. Denoting the upper-left and lower-right lobes (see FIGs. 2A-B) by / i and / 2, respectively, the state vector can be written as follows:

[0143] p / 7) = Ij ( / i (^0 + / 2(rc>2, ( 10)

[0144]

[0145] The ADF transforms the creation operator for the arm that transmits the wavelengths below ADF cut-on: a^o 1) b^o 1) and similarly for the arm that transmits wavelengths above the cut-on: af(®2) cfa ).

[0146] After passing through the ADF on the quantum state becomes:

[0147] - / / ( fl (< W ■, C92) 1 & 1H} | <4>2 v- > + fl ( ^2 > 1 ) ) | w 1v) ) dl> 1 W2 -

[0148]

[0149] The density matrix is then written as:P ~ |' / / )ADF(^kDP - chi) j dcu-idoj'i dtf-, + h ( CU i, 69; ) 169?,, } I td j, ) | X

[0150] Xs ( fs f j (691, ii>2 ) |w if{) j t<>2vj -.• *— \ — < / ! j|- f f i J V ■ f *(u> '<5C-P ) (<‘X „ IrI + A* (< A, 6: Z ) (t>f I fa ] I ) \A 4“irt *• V ■i■ V' f du){ d(jJ2 I fl (<61, ( 6>1 <62 ) |<61H) k‘92v){t9[HI (<d2 v1+ + / 1 (6-' I, <9? ). A ( O»2, <61 ) i 69 {H) k;->2v} {<6 {v| \6>2H| + + / 2(.6-h - <6] ) / j (<6j56?2.) i69jv) |<67H! + + f2' (6>2, <61 ), A ( <9?, C< J | ) 169 jv) |td2H- X^t v I (w2 u!

[0151]

[0152] where ω1= ω'1 and ω2= ω'2. After rewriting ) {^2# Ias1^1 'K^han^ similar

[0153]

[0154] expressions for all other terms, and tracing out the frequency states, the density matrix in the polarization basis is written as:

[0155] (| / {(ob692)|2|f / )in< H|(V|+ PHV + f. (<6 [. <<>2 ). A* (, <61 ) | / / ) | V ) ( V | ( H | + f? (, <6 j ) ff (<91. (69 ) I y } ( V | +

[0156]

[0157] In matrix notation, pnv has the form:

[0158]

[0159] where the matrix elements are defined from EQ. 13 as JJdoi do2| / i(oi, O2)|2, etc, where 01 and 02 correspond to frequencies below and above the ADF’s cut-off frequency, respectively, and are routed into the two output ports of the ADF. The overlap between the two lobes appears explicitly in EQ.

[0160] 14, as the off-diagonal terms. The predicted values for the non-zero matrix elements, as calculated from the measured spectrum are: f11 = 0.4971, f22 = 0.5028, and f12 = f21 = 0.4978. From these values a bound on the expected quality of the polarization entangled state can be calculated. Notice that the overlap integral of EQ. 9, which is a measure of the symmetry of the spectrum, gives the values of f, and 21 up to a constant. Those in turn are an indication of the purity of the two photon entangled state.Additionally, a Schmidt analysis

[0024] of the JSA that corresponds to FIG. 2A reveals a theoretical single photon spectral purity of about 0.496 for the total two-photon state, indicating that the spectrum consists 2 modes. The presented source can operate equally well under both pulsed and CW pumps, provided the aforementioned condition of the symmetry of the JSA is satisfied. In the present case, a pulsed femtosecond pump allowed each lobe of the JSI to have a round shape and correspondingly high single photon spectral purity of 0.494 under the assumption of | JSA| = JSI, with a 7T phase between the lobes shown in FIG. 2B.

[0161] This high single-lobe spectral purity makes the source of the present embodiments suitable for protocols involving entanglement swapping, where high-visibility interference between polarizationentangled photon pairs emitted from two independent sources requires that the states from each source be pure in all degrees of freedom except polarization. Moreover, utilizing the group velocity matching (GVD) point, which approximately holds for PPKTP at a pump wavelength of about 780 nm and biphoton wavelengths of about 1560 nm, the phase-matching function is positioned diagonally, while the pump function is aligned anti-diagonally in the ωs, ωi space. In this case, the source is characterized by its insensitivity to fluctuations in pump wavelength or crystal temperature.

[0162] Certification Of Polarization Entanglement

[0163] To characterize the quantum properties of the source, particularly the degree of the polarization entanglement, the output of the source part (see FIG. 1) was connected to the section dedicated to quantum state tomography (QST). In the QST setup, the SMF-coupled biphoton field propagated through the ADF, after which the polarization-entangled state generated from the crystal in a single collinear beam was split into the two separate arms of the ADF. This allowed independent projections of each photon of the pair onto a different polarization state. After the ADF, each beam was collimated using the lenses L3 and L4, passed through the quarter-wave plate QWP and the linear polarizer Pol, and was then focused by the lenses L5 and Le onto the SMF28-fiber-coupled superconducting nanowire detectors (Scontel, with detection efficiency η = 90 % at a wavelength of 1550 nm, jitter of 40 ps (FWHM), and dead time is 10 ns).

[0164] Following a 16-measurement QST scheme, the density matrix of the generated biphoton state was experimentally reconstructed. FIGs. 3A-C show the reconstructed density matrix p. Shown are the absolute value (FIG. 3A), the real part (FIG. 3B), and the imaginary part (FIG. 3C) of p. Since the density matrix fully describes the generated polarization state, all other parameters characterizing the quantum state can be derived from it. Specifically, based on the measured density matrix, the Inventors calculated the purity ρ = Tr(ρ2) to be about 0.948 ± 0.003, and the concurrence to be about0.948 ± 0.004. For Bell-type tests, the generated state violates the Clauser-Horne-Shimony-Holt (CHSH) inequality with an S-parameter of about S = 2.747 ± 0.004.

[0165] Polarization visibility measurements were performed by removing the QWPs in both arms of the QST section. The results are shown in FIGs. 4A and 4B, FIG. 4A shows the polarization entanglement visibility, and FIG. 4B shows the polarization entanglement visibility in {H, V} and {D, A} bases as a function of pump power. Each of the curves was measured by setting the polarizer in one arm at 0°, 90°, 45°, and -45° in the laboratory reference frame, corresponding to the H, V, D, and A curves in FIG. 4A, respectively, while rotating the other polarizer. The measure data points are fitted with sine function: a sin2(b0+c)+d, then V = a / (a+2d). VH = 0.94, Vv = 1.00, VD = 0.90, and VA = 0.90. R-square > 0.99 (for all 4 fits). Pump power was about 45 mW. The average visibility was therefore about 97% in the {H, V} basis, and about 90% in the {D, A}.

[0166] Since photon pairs are generated in the crystal in the H / V basis, the visibility measured in this basis remains high even when the photons are not fully polarization-entangled. The visibility on the A / D basis directly reflects the degree of quantum interference and entanglement. The lower visibility in the A / D basis compared to the H / V basis is explained by imperfections in the manufactured crystal and experimental equipment (e.g., collection of multiple spatial Schmidt modes and non-collinearly generated photons, finite extinction ratio of the add-drop filter).

[0167] The above measurements and the derived parameters demonstrate the quantum nature of the generated state.

[0168] The field generated in the SPDC process is a coherent superposition of two-mode Fock states correlated by photon number (two-mode squeezed vacuum). Thus, the biphoton state represented by EQ. 6 is only one term in the complete superposition, with the remaining terms (except for the vacuum state term, which eliminated by the coincidence measurement of the two detectors).

[0169] These multi-photon events cause the generated state to deviate from the ideal two-photon state represented by EQ. 6, gradually reducing the quality of entanglement as the probability of SPDC increases. One contributing factor to the increased SPDC probability is higher pump power. To analyze the effect of pump power on the source of the present embodiments, the visibility in the {H, V} and {D, A} were measured bases as a function of laser pump power (FIG. 4B). The graph demonstrates that even at relatively high pump powers the entanglement visibility remains well above the classical bound of 71%

[0025] . The squeezing parameter η (EQ. 3), corresponding to the visibility at different pump powers, is displayed on the right y-axis of FIG. 4B.Although the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and broad scope of the appended claims.

[0170] It is the intent of the applicant(s) that all publications, patents and patent applications referred to in this specification are to be incorporated in their entirety by reference into the specification, as if each individual publication, patent or patent application was specifically and individually noted when referenced that it is to be incorporated herein by reference. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present invention. To the extent that section headings are used, they should not be construed as necessarily limiting. In addition, any priority document(s) of this application is / are hereby incorporated herein by reference in its / their entirety.REFERENCE

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Claims

WHAT IS CLAIMED IS:

1. A poled nonlinear optical structure for generating pairs of entangled photons from a pump photon, the structure comprising a plurality of domains, and is characterized by a mismatch parameter, wherein a polarization of said domains is periodically reversed to define a periodic poling pattern, and wherein a Fourier transform of said poling pattern as a function of said mismatch parameter is a phase-matching function having two peaks at two different values of said mismatch parameter, and devoid of peaks at other values of said mismatch parameter.

2. The optical structure according to claim 1, wherein said two peaks are in-phase with respect to each other.

3. The optical structure according to claim 1, wherein said two peaks are out of phase with respect to each other.

4. The optical structure according to any of claims 1-3, wherein said two peaks are of substantially equal height in absolute value.

5. The optical structure according to claim 1, wherein said two peaks are of substantially equal width.

6. The optical structure according to any of claims 2-4, wherein said two peaks are of substantially equal width.

7. The optical structure according to claim 1, wherein said poling pattern is characterized by a fixed poling period along a length of the structure.

8. The optical structure according to any of claims 2-6, wherein said poling pattern is characterized by a fixed poling period along a length of the structure.

9. The optical structure according to claim 1, being made of a material selected from the group consisting of potassium titanyl phosphate (KTP), Lithium Niobate (LN), Lithium Tantalate(LT), Stoichiometric Lithium Tantalate (SLT), Potassium Titanyl Arsenate (KTA), Rubidium Titanium Phosphate (RTP), and Rubidium Titanium Arsenate Phosphate (RTA).

10. The optical structure according to any of claims 2-8, being made of a material selected from the group consisting of potassium titanyl phosphate (KTP), Lithium Niobate (LN), Lithium Tantalate (LT), Stoichiometric Lithium Tantalate (SLT), Potassium Titanyl Arsenate (KTA), Rubidium Titanium Phosphate (RTP), and Rubidium Titanium Arsenate Phosphate (RTA).

11. The optical structure according to claim 1, wherein said phase-matching function is selected to ensure type II spontaneous parametric down-conversion (SPDC).

12. The optical structure according to any of claims 2-10, wherein said phase-matching function is selected to ensure type II spontaneous parametric down-conversion (SPDC).

13. The optical structure according to claim 1, being a crystal.

14. The optical structure according to any of claims 2-12, being a crystal.

15. The optical structure according to claim 1, being a waveguide.

16. The optical structure according to any of claims 2-12, being a waveguide.

17. A method of generating pairs of entangled photons, comprising directing a beam of pump photons onto the poled nonlinear optical structure according to claim 1.

18. A method of generating pairs of entangled photons, comprising directing a beam of pump photons onto the poled nonlinear optical structure according to any of claims 2-16.

19. The method according to claim 17, wherein said directing said beam is executed to ensure a single pass of said beam though the optical structure.

20. The method according to claim 18, wherein said directing said beam is executed to ensure a single pass of said beam though the optical structure.

21. A system for generating pairs of entangled photons, the system comprises the poled nonlinear optical structure according to claim 1, and an unpoled optical structure, the poled and unpoled structures being arranged along an axis in a manner that pairs of entangled photons exiting the poled structure enter said unpoled structure.

22. A system for generating pairs of entangled photons, the system comprises the poled nonlinear optical structure according to any of claims 2-16, and an unpoled optical structure, the poled and unpoled structures being arranged along an axis in a manner that pairs of entangled photons exiting the poled structure enter said unpoled structure.

23. The system according to claim 21, wherein the poled nonlinear optical structure is a poled nonlinear optical crystal, and said unpoled optical structure is an unpoled optical crystal.

24. The system according to claim 22, wherein the poled nonlinear optical structure is a poled nonlinear optical crystal, and said unpoled optical structure is an unpoled optical crystal.

25. The system according to claim 23, wherein said unpoled crystal is rotated by about 90° relative to the poled crystal, so as to compensate for group velocity walk off of said pairs of entangled photons.

26. The system according to claim 24, wherein said unpoled crystal is rotated by about 90° relative to the poled crystal, so as to compensate for group velocity walk off of said pairs of entangled photons.

27. The system according to claim 21, wherein the poled nonlinear optical structure is a poled waveguide, and said unpoled optical structure is an unpoled waveguide.

28. The system according to claim 22, wherein the poled nonlinear optical structure is a poled waveguide, and said unpoled optical structure is an unpoled waveguide.

29. The system according to claim 27, wherein said unpoled waveguide is selected to support propagation of photons at a polarization state that is rotated by about 90° relative to a polarization state of said pairs of entangled photons upon exiting said poled waveguide.

30. The system according to claim 28, wherein said unpoled waveguide is selected to support propagation of photons at a polarization state that is rotated by about 90° relative to a polarization state of said pairs of entangled photons upon exiting said poled waveguide.

31. The system according to claim 29, comprising a polarization rotating optical element between the poled and said unpoled waveguides.

32. The system according to claim 30, comprising a polarization rotating optical element between the poled and said unpoled waveguides.

33. The system according to claim 21, comprising an optical element constituted to split each pair of entangled photons into separate optical paths.

34. The system according to any of claims 22-32, comprising an optical element constituted to split each pair of entangled photons into separate optical paths.

35. The system according to claim 33, wherein said optical element is configured for converting a mixed frequency-polarization state of said pair of entangled photons into a polarization-entangled state.

36. The system according to claim 34, wherein said optical element is configured for converting a mixed frequency-polarization state of said pair of entangled photons into a polarization-entangled state.

37. The system according to claim 35, wherein said optical element comprises a fiber add-drop filter (ADF).

38. The system according to claim 36, wherein said optical element comprises a fiber add-drop filter (ADF).

39. The system according to claim 35, wherein said optical element comprises a dichroic mirror.

40. The system according to any of claims 36-38, wherein said optical element comprises a dichroic mirror.

41. The system according to claim 33, wherein said optical element is configured for converting a mixed frequency-polarization state of said pair of entangled photons into a frequency-entangled state.

42. The system according to claim 34, wherein said optical element is configured for converting a mixed frequency-polarization state of said pair of entangled photons into a frequency-entangled state.

43. The system according to claim 41, wherein said optical element comprises polarizing beam splitter.

44. The system according to claim 42, wherein said optical element comprises polarizing beam splitter.

45. The system according to claim 21, comprising an optical cavity characterized by a resonance frequency matching a frequency of said pump photon.

46. The system according to any of claims 22-44, comprising an optical cavity characterized by a resonance frequency matching a frequency of said pump photon.

47. The system according to claim 45, wherein said optical cavity is arranged to allow said pump photon to propagate therein unidirectionally.

48. The system according to claim 46, wherein said optical cavity is arranged to allow said pump photon to propagate therein unidirectionally.

49. The system according to claim 45, wherein said optical cavity is configured to ensure a single pass of said pairs of entangled photons through the optical structure.

50. The system according to any of claims 46-48, wherein said optical cavity is configured to ensure a single pass of said pairs of entangled photons through the optical structure.

51. A light emission system comprising the optical structure or system according to any of claims 1-50.

52. A communication system comprising the optical structure or system according to any of claims 1-50.

53. A quantum teleportation system comprising the optical structure or system according to any of claims 1-50.

54. A quantum cryptography system comprising the optical structure or system according to any of claims 1-50.

55. A quantum computer comprising the optical structure or system according to any of claims 1-50.

56. A quantum metrology inspection system, comprising the optical structure or system according to any of claims 1-50.

57. A quantum simulation system, comprising the optical structure or system according to any of claims 1-50.

Images