Method for Generating Non-Classical Light from Classical Light

Abstract

Non-classical light is generated from classical light by providing a non-classical light generation stage with at least one waveguide; inputting classical light into the non-classical light generation stage; and converting at least part of the classical light into non-classical light. The classical light is in a non-fundamental propagation mode of a waveguide of the non-classical light generation stage, and the non-classical light is in a fundamental propagation mode a waveguide of the non-classical light generation stage. The converting does not involve quasi-phase-matching. An input adaptation stage obtains classical light for input into the non-classical light generation stage. In the input adaptation stage, classical light is converted into classical light of a different waveguide propagation mode. A system has a non-classical light generation stage for converting classical light at least partly into non-classical light, and an optical switch and/or an optical phase shifter, arranged on a single optical chip.

Claims

1. A method for generating non-classical light from classical light, the method comprising the steps of: providing a non-classical light generation stage comprising at least one waveguide, inputting classical light into the non-classical light generation stage, and converting in the non-classical light generation stage at least part of the classical light into non-classical light, wherein the classical light is in a non-fundamental propagation mode of a waveguide of the non-classical light generation stage and the non-classical light is in a fundamental propagation mode of a waveguide of the non-classical light generation stage.

2. A method for generating non-classical light from classical light, the method comprising the steps of: providing a non-classical light generation stage comprising at least one waveguide, inputting classical light into the non-classical light generation stage, and converting in the non-classical light generation stage at least part of the classical light into non-classical light, wherein the converting of at least part of the classical light into non-classical light in the non-classical light generation stage does not involve quasi-phase-matching.

3. The method of claim 1, wherein in the non-classical light generation waveguide, the classical light is of a first wavelength and the non-classical light is of a second wavelength different from the first wavelength.

4. The method of claim 1, wherein the non-classical light generation waveguide's effective refractive index for the classical light injected into the non-classical light generation waveguide is identical to the non-classical light generation waveguide's effective refractive index for the non-classical light.

5. A method for generating non-classical light from classical light, the method comprising the steps of: providing a non-classical light generation stage, inputting classical light into the non-classical light generation stage, and converting in the non-classical light generation stage at least part of the classical light into non-classical light, wherein the method further comprises the step of providing an input adaptation stage for obtaining the classical light to be input into the non-classical light generation stage, wherein in the input adaptation stage classical light is converted into classical light of a different waveguide propagation mode.

6. The method of claim 5, wherein the input adaptation stage and the non-classical light generation stage are combined.

7. The method of claim 5, wherein that it comprises the step of separating non-classical light exiting the non-classical light generation stage from classical light also exiting the non-classical light generation stage.

8. The method of claim 5, wherein that a waveguide of the non-classical light generation stage is of a nonlinear optical material.

9. The method of claim 8, wherein a waveguide in the non-classical light generation stage is of LiNbO.sub.3.

10. The method of claim 1, wherein a waveguide of the non-classical light generation stage has a thickness of between 300 and 500 nm.

11. An apparatus for generating non-classical light from classical light, the apparatus comprising a non-classical light generation stage for converting classical light at least partly into non-classical light, wherein a waveguide of the non-classical light generation stage is of a non-doped optical material.

12. An apparatus for generating non-classical light from classical light, the apparatus comprising a non-classical light generation stage for converting classical light at least partly into non-classical light, wherein the non-classical light generation stage does not comprise a periodically poled structure for the light to pass through periods of such periodically poled structure.

13. An apparatus for generating non-classical light from classical light, the apparatus comprising a non-classical light generation stage for converting classical light at least partly into non-classical light, wherein the apparatus comprises an input adaptation stage for converting classical light into classical light of a different waveguide propagation mode, the input adaptation stage being arranged upstream of the non-classical light generation stage such that the converted light obtained in the input adaptation stage can be input into the non-classical light generation stage for converting it at least partly into non-classical light.

14. A system comprising a non-classical light generation stage for converting classical light at least partly into non-classical light, and an optical switch and/or an optical phase shifter, the non-classical light generation stage and the optical switch and/or optical phase shifter being arranged on a single optical chip.

15. A device for performing the method according to claim 1.

16. A device for performing the method according to claim 2.

17. A device for performing the method according to claim 5.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In the following, further preferred embodiments of invention are illustrated by means of examples. The invention is not limited to these examples, however.

[0084] The drawings schematically show:

[0085] FIG. 1A scheme for the generation of squeezed light in the inventors' non-doped, MPM-based LNOI nanophotonic waveguides;

[0086] FIG. 2A scheme of the three stages of our MPM single mode squeezed vacuum source in LNOI;

[0087] FIG. 3A top view and cross section of the proposed device in Example 1 below. The layer stack, ie the thickness of the different materials, is shown in FIG. 4.

[0088] FIG. 4A cross sectional view of a straight waveguide, highlighting the different degrees of freedom of the LNOI platform;

[0089] FIG. 5A detailed design drawing of the pump mode conversion stage;

[0090] FIG. 6A flowchart describing the method to design the asymmetric directional coupler;

[0091] FIG. 7 An outline of the TE.sub.20 pump mode in the waveguide with 810 nm top width; this is the input pump mode required in the non-classical light generation stage;

[0092] FIG. 8A graph indicating the dependence of the effective refractive index n.sub.eff of the input TE.sub.00 mode and the output TE.sub.20 mode, for different waveguide widths;

[0093] FIG. 9 An outline of the TE.sub.00 input pump mode in the 145 nm-wide waveguide;

[0094] FIG. 10A graph indicating the optimal power transfer from the TE.sub.00 mode to the TE.sub.20 mode. Optimal coupling is observed for an inter-waveguide distance d=900 nm and a coupling length of 34 m;

[0095] FIG. 11A graph indication the dependence of the optimal power transfer between the TE.sub.00 and TE.sub.20 as the wavelength of the pump field is varied;

[0096] FIG. 12 An outline of the TE.sub.00 mode at 1 550 nm in the waveguide with 810 nm top width;

[0097] FIG. 13A top view and cross section of the straight waveguide providing MPM for the generation of single mode squeezed vacuum;

[0098] FIG. 14: A flowchart describing the method to design the geometry of the modal phase matched waveguide;

[0099] FIG. 15A graph indicating the variation of the central down converted wavelength, as a function of the waveguide width;

[0100] FIG. 16A cross sectional view of the straight waveguide used for squeezed light generation and two metallic electrodes used for electro-optic tuning;

[0101] FIG. 17A scheme of the symmetric directional coupler;

[0102] FIG. 18A sketch of a tapered asymmetric directional coupler as disclosed in Ding et al;

[0103] FIG. 19A sketch of a tapered asymmetric directional coupler as disclosed by Dai et al;

[0104] FIG. 20A A drawing of a single-pass waveguide generating squeezed vacuum light;

[0105] FIG. 20B A drawing of a multi-pass waveguide (or ring resonator) generating squeezed vacuum light;

[0106] FIG. 21A A drawing of a non-classical light generation stage with multiple interconnected straight waveguides;

[0107] FIG. 21A A view of the non-classical light generation stage with multiple interconnected straight waveguides;

[0108] FIG. 21B A drawing of a spiral-shaped non-classical light generation stage;

[0109] FIG. 22A drawing of an optical chip for near-term photonic quantum computing. It includes the apparatus of Example 1 and a 44 optical interferometer with tuneable phase shifters;

[0110] FIG. 23A drawing of an optical chip for the generation of multiplexed heralded single photon states; and

[0111] FIG. 24 A drawing of a circuit employing the optical chip in FIG. 23 for the generation of multiplexed deterministic single photon states; the outputs of the optical chips are edge coupled to eight optical fibres; four of these fibres are routed to off-chip single photon detectors. The remaining four fibres are routed to delay lines and then to a network of switches, whose state is controlled by the output of the single photon.

DETAILED DESCRIPTION OF AN EMBODIMENT OF THE INVENTION

[0112] In the following description of preferred embodiments of the invention, identical reference numerals refer to identical or similar components.

Stages of Non-Classical Light Generation

[0113] A method for generating squeezed vacuum in a nanophotonic .sup.(2) waveguide is shown in FIG. 1. All stages of this method are present on the same optical chip of non-doped LNOI: [0114] 1. Input light 1, coming from either an off- or on-chip source, is injected into an input adaptation stage 2. This adaptation stage 2 has the function of modifying the properties of the input light 1 to match it to the type of input required for the proper functioning of the second stage, the non-classical light generation stage 3. [0115] 2. In the non-classical light generation stage 3, the adapted input light 4 undergoes spontaneous parametric downconversion and generates squeezed light 5. In this stage 3, photons belonging to the input light field 4 are converted into light at longer wavelengths using modal phase matching. To this aim, a waveguide of the non-classical light generation stage 3 is dimensioned so to achieve modal phase matching between the input light 4 and the generated field 5. [0116] 3. The residual input light 6 and the generated light 5 then enter the final stage, the separation stage 7, also referred to as pump filtering stage. In this stage, the residual input light 6 is physically separated from the generated light 5. The generated light can then be used for photonic quantum computing 8.

[0117] The three different sections 2, 3 and 7 can be designed to have different waveguide cross sectionseg to avoid unwanted nonlinear light generation in the first and third stage. In this case, to connect these sections, intermediate transition regions can be present in between the main three stages, where the waveguide dimensions are adapted by means of adiabatic tapers.

Example 1: System for Generating Single Mode Squeezed Vacuum in a Non-Doped Single Pass LNOI Nanophotonic Waveguide

General Considerations

[0118] We designed a system in non-doped, non-poled LNOI that can generate squeezed vacuum at a wavelength of 1 550 nm using the aforementioned method for generating squeezed vacuum in a .sup.(2) nanophotonic waveguide without the need of periodic poling. The current example is designed for X-cut non-doped LNOI substrates. It is possible to apply the current invention to other types of LNOI substrates-such as Z-cut LNOI or doped LNOIas well as other types of .sup.(2) substrates. However, the specific design will need to be adapted, depending on the refractive index of the chosen substrate. The schematic of the system is shown in the following FIG. 2. The device works as follows: [0119] 1. Classical input light (also referred to as the pump field) 1 at 775 nm is injected into an input port of the system into the fundamental TE.sub.00 mode. The pump field 1 may come from a different section of the optical chip or may be injected on the chip using suitable edge or grating couplers. The specific design of these couplers is not essential to this invention. [0120] 2. The pump field 1 then enters the input adaptation stage 2. The function of this stage is to convert classical pump light from the input mode to the mode required by the non-classical light generation stage 3. In our design, the input adaptation stage 2 consists of an asymmetric directional coupler. The pump light enters the coupler in one 9 of the two input arms, and it is evanescently coupled into the opposite output arm 10. The input adaptation stage 2 is not restricted to be an asymmetric directional coupler, but it can also be an adiabatic taper 11. [0121] 3. The pump light, now converted into the correct non-fundamental spatial mode, then enters the non-classical light generation stage 3. The function of this stage is to generate the squeezed light, using SPDC of the input pump light. The cross section of the waveguide in this stage is designed such that the 775 nm field in the non-fundamental mode is phase matched with the 1 550 nm field in the fundamental mode, as discussed below. This allows the generation of single-mode squeezed vacuum at 1 550 nm. [0122] 4. The residual input light and the generated single-mode squeezed light finally enter the separation stage 7. The function of this stage is to spatially separate the strong pump light 6 and the much weaker non-classical light 5, in order transmit only the non-classical light 5 to the subsequent systems. In our design, this stage consists in a symmetrical directional coupler, where both fields (at 775 nm and at 1 550 nm) enter one of the two input ports of the directional coupler, and the generated single-mode squeezed vacuum is coupled into the opposite output port via evanescent coupling.

[0123] The detailed top view and cross section of the device is shown in FIG. 3.

[0124] The design of the individual sections can vary, depending on the fabrication equipment and on the substrate used. In the following, we will provide a set of fabrication parameters for each component, given the usage of a specific substrate, namely non-doped X-cut LNOI. The device has been designed in agreement with the fabrication method detailed by Zihan Li et al in the section Fabrication process with DLC hard mask, pages 3 to 4 of Tightly confining lithium niobate photonic integrated circuits and lasers, arXiv: 2208.05556 (2022). This disclosure of the fabrication process in this document is incorporated into the present disclosure by reference.

[0125] Common properties of the geometry of the system discussed in this Example 1

[0126] The layer stack, ie the thickness and order of the layers that compose the material platform before etching, can be seen in FIG. 4. The system comprising [0127] A lithium niobate (LN) thin film 12 [0128] A substrate layer 13 [0129] a handle 14

[0130] is provided as-is by the LNOI supplier. For the scope of the current invention, the handle 14 can be made of lithium niobate, silicon or sapphire, and its thickness 15 is irrelevant; yet, for reasons of convenient handling it, the thickness 15 is typically greater than 1 m. The substrate layer 13 is made of silicon dioxide (SiO.sub.2) and its thickness 16 is greater than 2 m.

[0131] The LN thin film 12 is non-doped X-cut LN. The propagation direction is the crystallographic Y-axis, ie the waveguides need to be parallel to the crystallographic Y-axis. The simulations, discussed below, revealed that thicknesses t between 300 nm and 500 nm yield suitable MPM conditions. Therefore, in the design of Example 1 considers a film thickness t=400100 nm. From here onwards, all physical dimensions relative to Example 1 are calculated assuming a film thickness of 400 nm. For a different film thickness, the specified quantities will need to be slightly changed, to account for the different film thickness. The method for calculating the new quantities is specified below. The etching depth h of the LN film needs to be at least 75% of the film thickness, according to the simulation method discussed below. The sidewall angle indicated in FIG. 4 is set to be 103, due to the fabrication parameters discussed by Zihan Li et al in the section regarding the fabrication process on pages 3 to 4 of the above-mentioned publication. The waveguide top width w.sub.top is a free parameter and will be different in each section of the device.

[0132] The cladding layer 17 is deposited on top of the waveguides, after the fabrication of the device. The deposition method is described Cheng Wang et al in the section 3, 3 Device fabrication, of the above-mentioned publication Second harmonic generation in nano-structured thin-film lithium niobate waveguides, Opt. Express 25, 6963-6973 (2017). Any thickness 22 that is greater than 1 m is sufficient.

[0133] In this example design, we considered generation of squeezed light at 1 550 nm. The design methods and fabrication can be adapted to address other wavelengths. However, for different target wavelengths, the fabrication parameters will vary.

[0134] For the non-doped X-cut LNOI substrate discussed in this Example 1, simulations show that the critical parameters are the film thickness t and the etching depth. For a film thickness t between 300 and 500 nm, it is always possible to achieve MPM by varying the waveguide width and/or the sidewall angle. Regarding the etching depth, our simulations show that a film etched by at least 75% entails geometries that led themselves to MPM. The sidewall angle is defined by the etching process, and varying the sidewall angle requires adapting the waveguide width to ensure MPM. However, we found no practical restrictions for the admissible sidewall angles . Similarly, we found that the presence of a cladding layer 17 on top of the LN film is not required to obtain MPM. However, it is commonly present, to protect the waveguides and the electrodes.

Design of the Input Adaptation Stage

Introductory Notes

[0135] We start describing the design of the input adaptation stage 2. In the design process, one must first design the non-classical light generation stage 3, which is the more critical one. The design of the non-classical light generation stage 3 provides the design constraints for the input adaptation stage 2, namely the waveguide width w.sub.top and the necessary non-fundamental mode 18in this case the TE.sub.20 mode. For this reason, in this section we assume known the results of the design of the non-classical light generation stage 3, namely the target waveguide top width w.sub.top=810 nm and the shape of the non-fundamental mode 18 shown in FIG. 7. Operatively, one needs to start with the design of the non-classical light generation stage 3 and then carry on with the design of the input adaptation stage 2 and the separation stage 7, which are independent.

Design Principles and Properties

[0136] The input adaptation stage 2 is an integrated component used to efficiently convert single mode 775 nm pump light 1 from the fundamental TE.sub.00 mode of the input waveguide into the TE.sub.20 mode in a different output waveguide. It means that, ideally, 100% of the light in the TE.sub.00 mode is converted into the TE.sub.20 mode.

[0137] The input adaptation stage 2 consists of an asymmetrical directional coupler. The device has two inputs, two outputs and three sections: the input section 19, the coupling section 20 and the output section 21. The scheme of the device is shown in FIG. 5. In the input section, two waveguides 9, 10, characterised by different widths, are slowly brought close together using bent waveguides. Bends with a wide variety of designs can be used here, ie they can be Euler bends, cosine bends, splines. Their functionality is limited to bringing the waveguides 9, 10 close together without losing light from bending too abruptly. If necessary, the waveguide widths can be varied throughout the bends, to obtain the designed waveguide widths in the coupling section 20. In the coupling section 20, the waveguides 9, 10 have well-defined width, gap and length, in order to achieve modal conversion from one waveguide to the other. These quantities are specified hereafter and are dependent on the layer stack chosen and described above.

[0138] The design of the asymmetric directional coupler proceeds as detailed in the following ALGORITHM 1, a procedure described in FIG. 6: [0139] 1. From the design of non-classical light generation stage 3, the target output waveguide top width w.sub.out, the non-fundamental TE.sub.20 mode of the pump light at 775 nm and the effective refractive index of the mode n.sub.pump,out.sup.TE20 are known. [0140] 2. Using a suitable eigenmode solver, one calculates the properties (mode shape and effective refractive index) of the fundamental TE.sub.00 mode of the waveguide at 775 nm for different waveguide widths. The aim of these calculations is to find the correct width w.sub.in of the input waveguide. The correct condition for the input waveguide 9 width is the one that ensures that the fundamental TE.sub.00 mode of the 775 nm pump light in the input waveguide (w.sub.in) has the same effective refractive index as the non-fundamental TE.sub.20 mode of the 775 nm pump light in the output waveguide (w.sub.out), ie n.sub.pump, in.sup.TE00=n.sub.pump,out.sup.TE20. [0141] 3. With input and the output waveguide widths w.sub.in and w.sub.out fixed, one uses a suitable electromagnetic field propagation solver, such as an eigenmode expansion (EME) solver, a beam propagation (BPM) solver or a finite difference time domain (FDTD) solver to study the optimal length of the coupling region and the optimal distance between the two parallel waveguides 9, 10 in the coupling region. One launches the input TE.sub.00 mode in the narrower input waveguide 9 and simulates how much light is coupled to the output wider waveguide 9 in the target mode, while varying the distance between the two parallel waveguides and the length of the coupling region. In this way, one studies what is the correct length of the coupler and the correct distance between the two waveguides 9, 10 which maximises the power transfer from the input 9 to the output waveguide 10.

Design Specifications

[0142] For the layer stack discussed above, the design of the non-classical light generation stage 3 requires a waveguide top with w.sub.top=810 nm, corresponding to the target TE.sub.20 mode 18 shown in FIG. 7.

[0143] We carried out the simulation detailed in step 2 of ALGORITHM 1 using the FDE solver contained in ModeSolution in Ansys Lumerical, and obtained the plot in FIG. 8, which shows that, for an input waveguide width of w.sub.in=145 nm, the input TE.sub.00 mode 24, shown in FIG. 9, and the output TE.sub.20 mode 18, shown in FIG. 7, have the same effective refractive index.

[0144] After determining the properties of the input mode, we proceeded with the step 3 of ALGORITHM 1 to determine the optimal inter-waveguide distance d.sub.a and coupling length L.sub.a. To this aim, we employed the eigenmode expansion (EME) solver in ModeSolution of the Ansys Lumerical. We injected the TE.sub.00 mode in the narrower waveguide and varied the parameters d.sub.a and L.sub.a to maximise the power transferred to the TE.sub.20 mode. The results of this procedure are shown in FIG. 10. It indicates the converted power as a function of propagation, ie, coupling length at a coupler gap of 0.9 m (full line) and 1.1 m (dotted line).

[0145] Using the EME solver in Ansys Lumerical, it is possible to estimate the wavelength acceptance bandwidth of this device. The simulations show that >90% mode conversion is possible in the range between 758 nm and 795 nm, as shown in FIG. 11.

Design of Non-Classical Light Generation Stage

Design Principles and Properties

[0146] The non-classical light generation stage 3 is an integrated component able to split one pump photon at 775 nm into one photon pair at 1 550 nm. This process is called spontaneous parametric downconversion (SPDC). In the present example, the component is a straight waveguide 25 that uses a type 0 process, where one pump photon at 775 nm in the TE.sub.20 mode 18 (FIG. 7) is converted into two photons at 1 550 nm in the TE.sub.00 mode 26 (FIG. 12) by means of three-wave mixing. The top view and cross section of this component are shown in FIG. 13.

[0147] The design of the non-classical light generation stage 3 consists in finding the correct waveguide top width w.sub.top, such that the effective refractive index of the TE.sub.20 pump mode is the same as the effective refractive index of the TE.sub.00 mode at 1 550 nm, if possible. The procedure to find the correct waveguide top width w.sub.top is described in the following ALGORITHM 2 outlined in FIG. 14: [0148] 1. Select a non-fundamental mode at 775 nm that will be used as a pump for the process. This selection is not entirely up to the designer. The designer needs to consider the material restrictioneg the crystallographic structure of LN only allows interaction between well define polarisations, as well as symmetry restrictionsthe pump mode needs to share the same spatial symmetry as the fundamental SPDC mode. [0149] 2. Using a suitable eigenmode solver for the electromagnetic field, one varies the waveguide top width w.sub.top, while monitoring the effective refractive index of the fundamental TE.sub.00 mode at 1 550 nm and the chosen non-fundamental modes at 775 nm, to find the waveguide top width w.sub.top Where they coincide. [0150] 3. The waveguide length 27 is arbitrary and depends only on material availability and fabrication performance. The impact of fabrication performance on phase matched processes is discussed in detail by Matteo Santandrea et al in New J. Phys. 21 033038 (2019).

Design Specification

[0151] Following the procedure of ALGORITHM 2, we identified that it is possible to perform MPM between the fundamental TE.sub.00 mode at 1 550 nm and the non-fundamental TE.sub.20 mode at 775 nm in a waveguide with a top width w.sub.top of around 82020 nm. By varying this width w.sub.top, it is possible to down convert photons into the whole telecom C-band (1 530 nm to 1 570 nm), as shown in FIG. 15. Simulations show that the phase matching wavelength decreases by about 20 nm when moving to cryogenic temperatures (range 1 510 nm to 1 550 nm), as seen in FIG. 15.

[0152] The waveguide length 27 is arbitrarythe longer the waveguide 25, the higher the efficiency. The normalised conversion efficiency is about 60%/Wcm.sup.2, according to the above-mentioned publication by Cheng Wang et al Second harmonic generation in nano-structured thin-film lithium niobate waveguides, Opt. Express 25, 6963-6973 (2017), which has a comparable design.

Tunability of the MPM Process

[0153] The structure can be tuned by employing electrodes 28 on the side of the waveguide 25, as shown in FIG. 16.

[0154] The modulator design considered here was studied on the 400 nm-thick LNOI waveguide. Design of the modulator can be performed using the following ALGORITHM 3 [0155] 1. Design the target waveguide using ALGORITHM 2. [0156] 2. Using a suitable solver, simulate the distribution of the electric field inside the waveguide 25, for a given choice of electrodes 28 metal, thickness, distance and position, relative to the waveguide. [0157] 3. For each computed electric field, calculate the overlap integral .sub.pump between the electric field and the pump mode, and the overlap integral .sub.SPDC between the electric field and the SPDC mode. The overlap integral between the electric field E.sub.RF generated by the electrodes and the electric field E.sub.opt.field of the optical mode is given by

[00003]$=\frac{E_{RF}\left(x,y\right)E_{\mathrm{opt}.\mathrm{field}}\left(x,y\right)\mathrm{dx}\mathrm{dy}}{{.Math.E_{RF}\left(x,y\right).Math.}^{2}dxdy{.Math.E_{\mathrm{opt}.\mathrm{field}}\left(x,y\right).Math.}^{2}dxdy}.$ [0158] 4. Update the effective refractive indices seen by the modes at 775 nm and 1 550 nm, using the relation

[00004]$n^{}=n-\frac{n^3}{2}{r}_{eo}\frac{V}{d},$

where r.sub.eo is the relevant electrooptic coefficient, V is the voltage between the electrodes 28 and d is the distance between the electrodes 28. The choice of r.sub.eo depends on the polarisations of the optical mode and of the modulator. For the system considered here, it is the r.sub.33 of lithium niobate, which is equal to 31 pm/V. [0159] 5. With the updated refractive indices, calculate the new wavelengths where the modified effective refractive indices of the 775 nm and the 1 550 nm modes are identical.

[0160] In our design, we found that the optimal structure consists in a modulator with gold (Au) electrodes 28 with a thickness of 100 nm. The bottom side of the electrode 28 is located 200 nm above the base of the waveguide, to align with the vertical centre of the waveguide. The distance between the two electrodes is 2 m. With these electrode parameters, the overlap integral between the RF field and the TE.sub.20 pump mode at 775 nm is .sub.pump=0.637, while the overlap integral between the RF field and the TE.sub.00 SPDC mode at 1 550 nm is .sub.SPDC=0.587. With these values, the estimated phase matching shift due to the electro-optic effect is 2 to 6 pm/V, depending on the exact position of the electrodes with respect to the waveguide.

[0161] Using numerical simulations, we also calculated the effect of a temperature variation to the refractive indices of the guided modes at 1 550 nm and at 775 nm, to calculate the phase matching shift due to temperature. In the range 20 to 50 C., the phase matched wavelength changes by 20 pm/K, as shown in FIG. 15. To perform these numerical simulations, it is sufficient to use ALGORITHM 2 to calculate the phase matching point in a range of wavelength around 1 550, while providing the correct refractive index model that takes into consideration the desired operating temperature.

Design of the Separation Stage

Design Principles and Properties

[0162] The separation stage 7 is an integrated component to remove the 775 nm pump light from the waveguide 25 where the down converted non-classical 1 550 nm light is generated. In this example, we designed a symmetrical directional coupler that separates the TE.sub.00 SPDC mode at 1 550 nm into a new waveguide 29 as shown in FIG. 17. The directional coupler is a standard component in integrated optical circuits and can be designed according to the discussion presented by Amnon Yariv and Pochi Yeh in section 13.3 of their above-mentioned publication Photonics: Optical Electronics in Modern Communications, Oxford Series in Electrical and Computer Engineering. Oxford University Press, Oxford.

Design Specification

[0163] The specific design for the circuitry developed in this invention consists in a system analogous to the asymmetrical directional coupler of the exemplary input adaptation stage 2 discussed above. The main difference is that the coupler is now symmetrical, meaning that the two waveguides have the same widths. Using the design principles discussed by Amnon Yariv and Pochi Yeh in section 13.3 of their before-mentioned publication, considering two waveguides with top widths w.sub.1=w.sub.2=810 nm, it is found using step 3 of ALGORITHM 1 that the optimal inter-waveguide distance is d.sub.s1.2 m and optimal coupling length L.sub.s=37.91.5 m. These parameters allow transfer of more than 99.5% of the light (23 dB of extinction ratio).

Alternative Designs of the Input Adaptation Stage 2

Variation 1Tapered Asymmetric Directional Coupler Resilient to Fabrication Errors

[0164] In this variation, the output, wider waveguide 10 is tapered to compensate for the fabrication errors present on the narrower waveguide 9, as discussed by Yunhong Dinget al in On-chip two-mode division multiplexing using tapered directional coupler-based mode multiplexer and demultiplexer, Opt. Express 21, 10376-10382 (2013) and Z Zhang et al in their previously mentioned publication On-chip optical mode exchange using tapered directional coupler, Sci Rep 5, 16072 (2015), the relevant parts of which publications are incorporated into the present disclosure by reference. FIG. 18, based on the above-cited publication by Ding et al, shows the sketch of the device. The wider waveguide is tapered on the side that is opposite to the coupling region, such that the coupling properties change along the coupling region. This ensures that small fabrication inaccuracies of the narrower waveguide 9 do not disrupt the coupling behaviour.

Variation 2Tapered Mode Converter

[0165] In this variant, mode conversion is performed using a tapered waveguide 30, as discussed by Daoxin Dai et al in their previously mentioned publication Mode conversion in tapered submicron silicon ridge optical waveguides, Opt. Express 20, 13425-13439 (2012). The principle behind this device is that a slow transition between two waveguide widths can allow a smooth transition between two light fields with different spatial distribution. An example of this is shown in FIG. 19.

Alternative Designs of the Non-Classical Light Generation Stage 3

[0166] Regardless of the type of material chosen, there are two different types of structures that can be used to generate squeezed light, namely single-pass waveguides 31 as shown in FIG. 20A, and multi-pass waveguides (also referred to as resonators or resonating structures) 32 as shown in FIG. 20B. In the single-pass waveguide 31, light propagates along the structure only once and then both the input (or pump) light and the generated light is extracted from the device. In the multi-pass waveguide 32, one or more fields travel multiple times across the region where the generation happens.

[0167] The non-classical light generation stage can also consist of multiple straight waveguides 33, with propagation along the crystallographic Y-axis, connected by suitable straight and/or bent junctions as shown in FIG. 21A.

[0168] The non-classical light generation stage can employ a type II process, with input photons in the TM polarisation, and output photons in the TE and TM polarisation.

[0169] For Z-cut LNOI, the non-classical light generation stage could be a spiral 34 as shown in FIG. 21B to reduce the footprint while increasing the source efficiency.

Alternative Designs for the Separation Stage 7

[0170] There are several possible filtering options for the separation stage 7. One possible way is the use of Bragg grating filters in reflection and/or transmission. In these systems, the refractive index of the 775 nm mode is modulated by means of eg doping or waveguide cross section variation. A second possible option is the usage of filtering cavities. These comprise ring resonators, integrated Fabry Perot cavities, photonic crystal cavities, or similar. A third possible option is the usage of a cascade of the components above (including directional couplers).

Example 2: Gaussian Boson Sampling with On-Chip Single-Mode Squeezed Vacuum Sources

[0171] An example of how to use the apparatus of Example 1 is detailed in FIG. 22. The Figure shows a detailed example of a four-mode Gaussian Boson Sampling (GBS) apparatus 35 in X-cut LNOI. A GBS apparatus on n modes involves the generation of n single-mode squeezed light states, which are made to interfere on a linear optical interferometer and detected after interference on photon-number resolving detectors. Details of the GBS procedure are disclosed Craig S Hamilton et al in the section Gaussian Boson sampling with squeezed states on page 2, column II and page 3 Column I of their publication in Phys. Rev. Lett. 119, 170501 (2017), the relevant parts of which are incorporated into the present disclosure by reference.

[0172] By way of example, we consider a GBS device acting on n=4 modes. The first section of the chip for implementing GBS is based on a device design described in Example 1. Input pump light at 775 nm is injected via edge-coupling into a single mode waveguide, having a top width of 145 nm. This waveguide is used to route the pump light. A cascade of two Y splitters is used to split the input pump into four different waveguides. Each of these waveguides is then used as input for the four single mode squeezed vacuum sources with a design as described above in Example 1. We recall that they consist of an asymmetric directional coupler, which converts the fundamental pump mode (TE.sub.00) into the non-fundamental (TE.sub.20) mode, in a waveguide with 810 nm top width. This mode is the correct pump mode for the generation of single-mode squeezed vacuum (SMSV) in the straight waveguide section.

[0173] This first section is followed by a symmetric directional coupler for the separation of the generated SMSV and the leftover of the pump light. The leftover pump radiation is sent to grating couplers 36 for efficient extraction. Suitable grating couplers can be designed via a process similar to those described by I Krasnokutska et al in section II of their publication High coupling efficiency grating couplers on lithium niobate on insulator, Opt. Express 27 (13), 17681-17685 (2019), but instead using X-cut LNOI; the relevant parts of the publication by I Krasnokutska is incorporated into the present disclosure by reference. The generated SMSV is then used as input of the four-mode optical interferometer. The four-mode optical interferometer consists of a cascade of 6 beam splitters 37 and twelve electro optical phase shifters 38, arranged as in FIG. 22.

[0174] Each beam splitter 37 in turn consists of a symmetric directional coupler. The waveguides with 810 nm top width are coupled at a distance d=1.2 m and for an optimal coupling length of L=17.51.0 m. The phase shifters consist of electro optical phase shifters, which can be fabricated as described in the previously-mentioned publication by Zihan Li et al Tightly confining lithium niobate photonic integrated circuits and lasers, arXiv: 2208.05556 (2022), in the section Fabrication process with DLC hard mask on pages 3 and 4. Such an interferometer, consisting of tuneable beam splitters 37 and phase shifters 38 can be used to realise an arbitrary linear optics transformation, which allows performing arbitrary GBS computations. Photon-number resolving detection is performed on the output light. The detection could be performed either using superconducting nanowire single-photon detectors or using transition edge sensors. These detectors can be integrated on the waveguides in the photonic chip itself or be present off-chip.

[0175] The input of the GBS computation is the settings of the chip that describe the squeezing amounts and the settings of the interferometer including the beam splitter 37 and phase shifter 38 settings. The output of the GBS computation is the set of photon numbers measured on the different detectors.

[0176] The present invention enables the realisation of a GBS apparatus on a single photonic chip made of non-doped LNOI. Such a chip could include the sources, switches and potentially also the detectors on one platform, thus offering unmatched scalability and ease of fabrication.

Example 3: Deterministic Heralded Single Photon Source for Universal Photonic Quantum Computing

[0177] An example of the usage of the apparatus of Example 1 as a source of heralded single photons is shown in FIGS. 23 and 24. In FIG. 23, the details of an optical chip 39 containing the sources are shown.

[0178] The first section of the chip is based on an apparatus of Example 1. Input pump light at 775. nm is injected via edge-coupling into a single mode waveguide, having a top width of 145 nm. This waveguide is used to route the pump light. A cascade of two Y splitters is used to split the input pump into four different waveguides. Each of these waveguides is then used as input for the four single mode squeezed vacuum sources of Example 1. They consist of an asymmetric directional coupler 2, which converts the fundamental pump mode (TE.sub.00) into the non-fundamental (TE.sub.20) mode, in a waveguide with 810 nm top width. This mode is the correct pump mode for the generation of SMSV in the straight waveguide section 25. This section is followed by a symmetric directional coupler 7 for the separation of the generated SMSV and the leftover of the pump light. For efficient extraction, the leftover pump radiation is sent to grating couplers 36 as described by I Krasnokutska et al in section II of their above-mentioned publication High coupling efficiency grating couplers on lithium niobate on insulator, Opt. Express 27 (13), pages 17681-17685 (2019). The generated SMSV needs to be manipulated, in order to separate the two photons that, probabilistically, populate the state. This can be performed using a frequency-selective beam splitter 40, in order to separate the photons according to their wavelength. Photons with a wavelength shorter than 1 550 nm are coupled out of the waveguide, into a different output. These photons will be routed to single photon detectors 41, as shown in FIG. 24, in order to provide the heralding signals, which allows one to infer the presence of the sibling photon.

[0179] The frequency-dependent beam splitters 40 can be designed using the technique presented by E S Magden et al in Transmissive silicon photonic dichroic filters with spectrally selective waveguides, Nat Commun 9, 3009 (2018).

[0180] After separation, the photons that have a wavelength smaller than 1 550 nm are coupled off-chip to external single photon detectors 41 that detect the number of photons impinging on them. Only the detection events constituted by one single photon are considered successful detection events. These successful detection events herald the presence of the sibling photon, ie, a photon with wavelength greater than 1 550 nm.

[0181] The photons with wavelength greater than 1 550 nm are guided to a delay network 42, which could be either on chip or off-chip in optical fibre. Such a network needs to impart a delay sufficient to wait for the successful detection of the single photons and the analysis of the detection event. Therefore, these delays will need to provide delays of between approximately 100 ns and 1 s. The delayed signals are then injected into a network consisting of electro optic switches 43, as seen in FIG. 24. These switches are controlled according to the detection events measured by the external single photon detectors 41. The switches 43 are used to redirect the heralded single photons to the output of the network.

[0182] Deterministic heralded single photons are a crucial resource for universal photonic quantum computing. While a single SMSV source along with a single-photon detector functions as a non-deterministic single-photon source, many such non-deterministic sources as described above can function as a deterministic or near-deterministic single-photon source. The present invention opens the possibility of fabricating several such SMSV generators and fast optical switches on a single chip, thus enhancing the prospects of fabricating deterministic single-photon sources for universal photonic quantum computing.