Source for generating squeezed states for Gaussian boson sampling

Abstract

The invention relates to a source (1) for generating squeezed states for Gaussian boson sampling, comprising a laser (2), an optical component (3) and a waveguide (4), wherein the laser (2) is optically connected to the optical component (3) for transmitting the laser beam emitted by the laser, the optical component (3) is optically connected to the waveguide (4) for transmitting the laser beam, wherein the optical component (3) is configured to couple the laser beam into the waveguide (4) such that a spatial mode of order ≥ 1 is excited in the waveguide (4), and the waveguide (4) has a nonlinear medium, such that a squeezed signal-idler state having signal and idler beams is generated in the waveguide (4) with the spatial mode.In this way, a source for generating squeezed states for Gaussian boson sampling with improved spectral purity and brightness is provided.

Description

[0001] The invention relates to a source for generating squeezed states for Gaussian boson sampling, comprising a laser, an optical component and a waveguide, wherein the laser is optically connected to the optical component for transmitting the laser beam emitted by the laser, and the optical component is optically connected to the waveguide for transmitting the laser beam.

[0002] Uncorrelated and indistinguishable quantum photonic states of pulsed light are important in quantum information processing, quantum networks, quantum communication, and quantum computing. In these areas, correlated and distinguishable quantum states can lead to unwanted noise and limitations in the manipulation of quantum information. Particularly in boson sampling applications, it is crucial that photon pair sources generate uncorrelated and indistinguishable photons.

[0003] Unlike traditional boson sampling, which uses single photons, Gaussian boson sampling utilizes squeezed states of light. A squeezed state is a quantum-optical state of light in which quantum uncertainty is reduced in one variable while correspondingly increasing in another. Gaussian boson sampling is a quantum computing method that uses the interference of squeezed states to solve complex problems. A widely used technique for generating squeezed states at telecommunications wavelengths, i.e., wavelengths around 1550 nm, is parametric two-photon fluorescence in nonlinear media such as single crystals or optical waveguides.A prerequisite for achieving indistinguishable, uncorrelated photonic states using single crystals or waveguides is phase matching, where a common spectral amplitude exhibits a precise phase-match angle of 45°. This condition ensures that an energy conservation function fixed at -45° is orthogonal to the phase-match function. The common spectral amplitude describes the spectral properties and correlations of photon pairs generated by parametric two-photon fluorescence in nonlinear media. The common spectral amplitude is a product of a pump envelope function and the phase-match function, which together describe the energy and momentum conservation conditions of parametric two-photon fluorescence.Parametric two-photon fluorescence is highly sensitive and varies depending on the dispersion properties of the nonlinear medium used and the wavelength of the photons. Consequently, the phase adjustment angle varies according to the specific requirements of the respective process.

[0004] In an experimental demonstration by Zhon et al. (ZHONG, Han-Sen [et al.]: Experimental Gaussian Boson sampling. In: Science Bulletin, Vol. 64, 2019, No. 8, pp. 511-515. ISSN 2095-9281) on the development of entangled quantum sources, the evolution of the joint spectral amplitude of entangled photon-pair sources with and without filters was investigated in both single crystals and waveguides. Both single crystals and waveguides are suitable for generating uncorrelated photonic states. However, generating pulsed uncorrelated and indistinguishable photon pairs, i.e., changing the phase-matching angle towards a phase-matching angle of 45°, is a challenge.

[0005] US patent 2023 / 0221616 A1 describes a photonic integrated circuit (PIC) that utilizes a first microresonator which, in a nonlinear medium, generates a pair of entangled signal and idler photons from two pump photons via spontaneous four-wave mixing. The remaining, unconverted pump light is then coupled into a leakage waveguide by a second microresonator tuned only to the pump frequency – acting as an integrated notch filter. This results in only a slight increase in the path length of the squeezed states.

[0006] US Patent 2019 / 0187380 A1 describes a device for quantum computing that includes an optically integrated on-chip generation of photon pairs as building blocks for creating entangled photon states, which are recognized as necessary for quantum information processing. It includes a frequency-selective optical coupling device that controls the transmission of light by varying the relative dimensions of otherwise symmetrical linear optical waveguides tangentially to an annular optical waveguide, thereby controlling the coupling of light between the linear waveguides and the annular waveguide. The dimensional change of the optical waveguides is achieved by a heated medium in the vicinity of the waveguides and under electronic control.

[0007] In waveguides, the phase matching angle is limited to approximately 60° due to the properties of the nonlinear medium. This limitation impairs the correlation and distinguishability—that is, the spectral purity—of a generated photonic state, posing a challenge for maintaining high-quality quantum states. In single crystals, on the other hand, efficiency problems arise due to the continuous distribution of the emission directions of the generated photon pairs, resulting in a lower number of generated photon pairs and reduced brightness. Spectral purity is a measure of the quality of a specific parametric two-photon fluorescence generation process for network applications. Spectral purity is influenced by the number of spectral modes present in the generated state or, equivalently, by the degree of correlation between the generated signal and idler fields.Formally, spectral purity is a measure of how pure one of the generated fields is when all information about the second field is removed. In practice, spectral purity is a measure of how well a particular source of squeezed light is suited for network applications, since high spectral purity leads to good interference between fields generated by multiple sources, which is a crucial factor in such systems. Additionally, spectral filtering after parametric two-photon fluorescence is often necessary to select the generated photon pairs within a specific wavelength range and minimize spectral correlations.

[0008] Based on this, the object of the present invention is to provide a source for generating squeezed states for Gaussian boson sampling with improved spectral purity and brightness.

[0009] This problem is solved by the subject matter of the independent claim. Preferred embodiments of the invention are described in the dependent claims.

[0010] According to the invention, a source for generating squeezed states for Gaussian boson sampling is thus provided, comprising a laser, an optical component and a waveguide, wherein the laser is optically connected to the optical component for transmitting the laser beam emitted by the laser, the optical component is optically connected to the waveguide for transmitting the laser beam, wherein the optical component is configured to couple the laser beam into the waveguide such that a spatial mode of order ≥ 1 is excited in the waveguide, and the waveguide has a nonlinear medium, such that a squeezed signal-idler state having signal and idler beams is generated in the waveguide with the spatial mode.

[0011] According to the invention, the laser beam is emitted by the laser in such a way that it strikes the optical component. The optical component is understood to be a component that modulates, directs, and / or focuses the laser beam in a specific manner and therefore enables coupling into the waveguide, so that the spatial mode of order ≥ 1 can be excited in the waveguide.

[0012] In this context, an optical connection is defined as a connection that enables the transmission of the laser beam emitted by the laser, and subsequently, the signal and idler beams. This can be achieved, for example, through transmission in a gas mixture such as air or in a vacuum, or through fiber optic connections suitable for transmitting light of an appropriate optical bandwidth. Alternatively, the respective components, such as the laser, the optical component, and the waveguide, can be arranged side by side in such a way that they are directly adjacent to one another.

[0013] The essential aspect of the invention is that the optical component is designed to couple the laser beam into the waveguide in such a way that a spatial mode of order ≥1 is excited in the waveguide. Spatial modes of a laser or waveguide refer to the distribution of the light intensity and phase of the laser beam or electric field across the beam's cross-section. Each spatial mode, a transverse electromagnetic mode (TEM mode), has a specific intensity and phase distribution. A fundamental mode, also known as TEM 0,0 The -mode, known as λ-mode, has a Gaussian intensity distribution, with the highest intensity in the center of the laser beam or electric field and the intensity decreasing towards the edges. The phase is constant across the entire beam cross-section. Higher-order modes are known as TEM. m,n-Modes have more complex intensity distributions, described by indices m and n. One first-order mode, the TEM, is... 0,1 The -mode exhibits an intensity distribution with two main maxima and a node in the middle. These modes can take various shapes, including rectangular or ring-shaped patterns.

[0014] The nonlinear medium is a material that enables nonlinear interactions between electric fields, leading to the generation of squeezed states. Using the nonlinear medium within the waveguide, a squeezed signal idler state is generated by an excited laser beam of spatial mode order ≥ 1. This is a squeezed two-mode signal idler state. In any case, it is characterized by the fact that the signal and idler beams contained within the squeezed signal idler state exhibit significantly improved uncorrelatedness and indistinguishability.

[0015] Due to modal dispersion, spatial modes of order ≥ 1 exhibit a different group velocity than the fundamental mode. This reduces or optimizes the phase matching angle in the waveguide from 59°, thereby improving the spectral purity of the squeezed states while maintaining the same improved brightness of the waveguide. In this context, the squeezed states are uncorrelated and indistinguishable at phase matching angles less than 59°. Modal dispersion refers to the different propagation rates of spatial modes in the waveguide due to their varying propagation times. Each mode has a specific group propagation time that depends on the geometric and optical properties of the waveguide. The differences in mode propagation times result from their different group velocities and the effective length they travel in the waveguide.

[0016] With the source according to the invention for generating squeezed states for Gaussian boson sampling, squeezed states with high brightness can therefore be efficiently generated with simultaneously improved uncorrelatedness and indistinguishability. In contrast, the phase-matching angle in single crystals cannot be adjusted by changing the excited spatial mode.

[0017] A further advantage is that spectral filtering is unnecessary, since the precise excitation using specific spatial modes results in high spectral purity and uncorrelatedness of the generated squeezed states. The optical component that couples the laser beam into the waveguide enables the generated states to already exhibit high spectral purity at the time of generation. Here, spectral filtering is understood as a method in which light of different wavelengths is selectively transmitted or blocked to isolate specific spectral components of a light beam. The source according to the invention thus leads to a significant reduction in spectral correlations and improves the indistinguishability of the photon pairs without requiring subsequent spectral filtering.Another advantage lies in the simplification of the source, as no additional filter components are required, which reduces complexity and losses.

[0018] In principle, the optical component can be designed in various ways. However, according to a preferred embodiment of the invention, the optical component comprises a mirror and a lens, and the laser beam is coupled into the waveguide at a predetermined angle, thus exciting the spatial mode in the waveguide. The mirror enables the laser beam to be coupled into the waveguide at the predetermined angle. This arrangement allows for precise control of the predetermined angle and focus of the laser beam, enabling efficient coupling into the waveguide and the excitation of higher spatial modes. Various mirrors and lenses can be used. However, according to a preferred embodiment of the invention, the lens is an aspherical lens and the mirror is a dichroic mirror.The dichroic mirror prevents unwanted wavelengths of the laser beam emitted by the laser from being coupled into the waveguide. The aspherical lens avoids imaging errors, thus improving the coupling of the laser beam into the waveguide. In a further development of the invention, the predetermined angle is 90° and the laser beam strikes the waveguide parallel to a longitudinal axis.

[0019] An alternative embodiment of the invention provides that the optical component has a concave mirror. This would also allow the predetermined angle of the laser beam to be manipulated. A further alternative embodiment of the invention provides that the optical component is configured to shape the laser beam spatially in order to excite the spatial modes in the waveguide. In this context, a further development of the invention provides that the optical component includes a wire inserted into the laser beam, a spatial light modulator, or an optical resonator.

[0020] In principle, it is possible to design the source for generating squeezed states in various ways. However, according to a preferred embodiment of the invention, the source is designed with a beam splitter, wherein the waveguide is optically connected to the beam splitter for transmitting the squeezed signal idler state, and the squeezed signal idler state interferes in the beam splitter, so that the squeezed signal idler state is converted into two mutually uncorrelated and indistinguishable squeezed single-mode states. The present beam splitter allows the signal and idler beams of the squeezed signal idler state to interfere with each other. A squeezed two-mode state is initially generated by the waveguide. By connecting the beam splitter downstream, the squeezed two-mode signal idler state is converted into two mutually uncorrelated and indistinguishable squeezed single-mode states.The squeezed two-mode state is a state consisting of two modes exhibiting phase and amplitude correlations. According to a preferred embodiment of the invention, the source for generating squeezed states comprises an additional lens, the additional lens being arranged between the waveguide and the beam splitter. The additional lens allows the signal beam and the idler beam to be coupled out of the waveguide and focused. According to a particularly preferred embodiment of the invention, the lens is an aspherical lens, enabling precise focusing and minimal aberrations.

[0021] It is possible that different spatial modes of order ≥ 1 are excited in the waveguide. However, according to a preferred embodiment of the invention, the excited spatial mode is a first-order spatial mode. The first-order spatial mode has a specific intensity distribution with a node in its mode profile. The first-order mode reduces the phase matching angle of the squeezed two-mode state, thereby improving the spectral purity of the squeezed states. Thus, after interference in the beam splitter, the first-order mode results in the squeezed state TE. 0,0 and the further squeezed state TM, which is uncorrelated and indistinguishable from the squeezed state 0,0 generated. The respective squeezed single-mode states are therefore in the fundamental mode.

[0022] In principle, various lasers and laser beam wavelengths can be used. However, according to a preferred embodiment of the invention, the laser is configured to emit the laser beam in a wavelength range between 750 nm and 800 nm, particularly between 760 nm and 780 nm. A laser beam in this wavelength range is particularly suitable for parametric two-photon fluorescence in nonlinear media to generate squeezed states at the telecommunications wavelength of 1550 nm.

[0023] According to a preferred embodiment of the invention, the nonlinear medium of the waveguide is potassium titanyl phosphate. Potassium titanyl phosphate is a nonlinear medium used in the present parametric two-photon fluorescence. Potassium titanyl phosphate is characterized by a positive phase-match angle. Furthermore, it exhibits a high nonlinear coefficient, which enhances brightness. The nonlinear coefficient of the medium is a measure of its ability to modify the frequency of light through nonlinear optical processes. Potassium titanyl phosphate also has a wide transparency range, enabling the use of various wavelength ranges and thus providing flexibility in applications.Another advantage of potassium titanyl phosphate is its high thermal stability and low tendency to photorefractive damage, which makes it robust against intense laser irradiation and ensures long-term reliability.

[0024] In principle, the waveguide can be formed in various ways. However, according to a preferred embodiment of the invention, rubidium ions are diffused into the waveguide, thus forming a conduction region. The rubidium ions do not replace the nonlinear medium of the waveguide, but rather integrate into it through diffusion, thereby forming the conduction region. Depending on the number of diffused rubidium ions, the refractive index can be increased to a predetermined value. This improves the guidance of the excited spatial mode ≥ 1. This arrangement enables optimized phase matching, which is advantageous for the efficiency of parametric two-photon fluorescence.

[0025] In principle, the conduction area can have different dimensions. According to a preferred embodiment of the invention, the conduction area is arranged at an entry point of the laser beam in the waveguide and extends through the waveguide to an exit point of the squeezed signal idler state from the waveguide. This arrangement ensures that the entire area of ​​the waveguide in which the nonlinear processes take place is configured for the generation of squeezed states. According to a preferred embodiment of the invention, the waveguide, and thus also the conduction area, has a length of 3 mm to 5 mm, in particular a length of 3.9 mm, running parallel to the laser beam.

[0026] In a further embodiment of the invention, the rubidium ions diffuse into the waveguide with a concentration gradient perpendicular to a longitudinal axis of the waveguide. The optical component directs the laser beam accordingly to the entry point, which then exhibits a rubidium ion concentration corresponding to the excitation of the spatial mode ≥ 1. In the case where the predetermined angle is 90°, the longitudinal axis runs parallel to the laser beam.

[0027] According to a further preferred embodiment, the highest rubidium ion concentration is located directly at the surface of the waveguide. This determines the orientation of the concentration gradient of the conduction region within the waveguide. Concentration gradient here means that the concentration decreases from the surface of the waveguide to a certain depth within the waveguide. Accordingly, within a cross-sectional area cut parallel to the inlet or the inlet surface containing the inlet, the conduction region exhibits different rubidium ion concentrations. Conversely, in a cross-sectional area parallel to the surface, the conduction region exhibits the same rubidium ion concentration.

[0028] A further embodiment of the invention provides that the concentration gradient exhibits a complementary error function. Because the concentration gradient has this profile, the entry point can be selectively positioned at a rubidium ion concentration corresponding to excitation of the spatial mode ≥ 1 with the optical component.

[0029] In a further development of the invention, it is intended that the conduction area formed with the rubidium ions extends from the surface to a depth of between 7 µm and 9 µm, in particular 7.39 µm and 8.1 µm in the waveguide, and has a width of 1.5 µm to 4.5 µm, in particular 2.7 µm, in a cross-sectional area perpendicular to the longitudinal axis of the waveguide and perpendicular to the depth.

[0030] In principle, the waveguide can have different polarization periods. However, according to a preferred embodiment of the invention, the waveguide is periodically polarized along its longitudinal axis and has a polarization period between 120 µm and 160 µm, in particular a polarization period of 146 µm. Periodic polarization for establishing a polarization period in the waveguide is a technique in which the waveguide is regularly reversed to optimize phase matching and ensure momentum conservation, so that both the signal beam and the idler beam are squeezed in the telecommunications wavelength range. In particular, periodically polarized potassium-titanyl phosphate waveguides with diffused rubidium ions in the conduction region generate squeezed states at the optimized phase matching angle in the telecommunications wavelength range around 1550 nm.

[0031] According to a preferred embodiment of the invention, the source is designed as an integrated circuit. An integrated circuit is a compact and scalable arrangement of optical components on a single substrate. An advantage of this arrangement is the miniaturization and integration of the entire source, which leads to increased stability when generating squeezed states.

[0032] The invention is described in more detail below with reference to the drawings and preferred embodiments.

[0033] The drawings show Fig. 1 schematically a source for generating squeezed states for Gaussian boson sampling according to a preferred embodiment of the invention, Fig. 2a graphically represents a phase adjustment angle for a spatial fundamental mode in a waveguide and a phase adjustment angle for a spatial first-order mode in the waveguide according to a preferred embodiment of the invention, and Fig. 2b graphically a cross-sectional profile of the spatial mode of the first order according to a preferred embodiment of the invention.

[0034] Out of Fig. Figure 1 is a source 1 for generating squeezed states for Gaussian boson sampling, comprising a laser 2, an optical component 3, and a waveguide 4. The laser 2 is configured to emit a laser beam with a wavelength of 779.90 ± 0.39 nm, which is optically transmitted to the optical component 3. The optical component 3 has a mirror 5 and a lens 6 and optically transmits the laser beam to the waveguide 4. The mirror 5 is oriented such that the laser beam strikes an entry point 10 on the waveguide 4 at a predetermined angle. The lens 6 couples the laser beam into the waveguide 4 with virtually no loss, thus exciting a first-order spatial mode in the waveguide 4.To excite the spatial first-order mode, the angle of the beam must be varied very slightly in the angle corresponding to a direction in which the two principal maxima of the first-order modes are discernible, which are in . Fig. Figure 2b illustrates this. Specifically, the predetermined angle is determined by slightly varying the angle by 90°. The 90° angle is parallel to a longitudinal axis 14 of the waveguide 4. If the angle of the laser beam is changed so that the point moves towards higher or lower rubidium ion concentrations, the first-order mode can be excited more effectively.

[0035] The waveguide 4 is provided with a periodically polarized nonlinear medium, a potassium titanyl phosphate crystal. The polarization period is 146 µm. A conduction region 9 with diffused rubidium ions, exhibiting a refractive index of 1.7, is formed within the waveguide 4. The conduction region 9 itself exhibits a concentration gradient of the diffused rubidium ions. This concentration gradient extends perpendicular to the longitudinal axis 14 of the waveguide from a highest concentration at the surface 15 of the waveguide 4 to a depth of 8.1 µm and follows a complementary error function. In a cross-sectional area perpendicular to the longitudinal axis, or parallel to the inlet surface containing the inlet 10, the conduction region 9 thus extends from the surface 15 to the aforementioned depth. This conductor area 9 also has a width of 2.7 µm in the cross-section specified above.The excited first-order spatial mode generates a squeezed signal idler state in the transmission line section 9 of the waveguide 4. This squeezed signal idler state is a squeezed two-mode state. The signal beam and the idler beam exit the waveguide through exit point 11 in this state and are coupled out without loss by the further lens 8. A beam splitter 7 following the further lens 8 causes the signal and idler beams to interfere with each other, converting the squeezed two-mode signal idler state, which has a phase matching angle of 52° and is coupled out of the waveguide 4, into a squeezed partial-order state. 0,0 condition and a squashed TM 0,0 state, i.e., two mutually uncorrelated and indistinguishable squeezed single-mode states, each in the range of a telecommunications wavelength around 1550 nm.

[0036] Out of Fig. Figure 2a shows a graph in which a phase adjustment angle of 59° for a spatial fundamental mode in waveguide 4 and a phase adjustment angle of 52° for the spatial first-order mode in waveguide 4 are shown. A y-axis 12 shows the wavelengths λ idler of the crushed state TM 0,0 of the idler beam and an x-axis 13 shows the wavelengths λ signal of the crushed state TE 0,0 of the signal beam. A cross-sectional profile of the first-order spatial mode is made up of Fig. 2b is shown. Reference symbol list 1 Source 2 lasers 3 optical components 4 waveguides 5 mirrors 6 lens 7 beam splitters 8 more lenses 9 Management area 10 Entry Point 11 Exit point 12 y-axis 13 x-axis 14 Longitudinal axis 15 surface

Claims

[1] Source (1) for generating squeezed states for Gaussian boson sampling, comprising a laser (2), an optical component (3) and a waveguide (4), wherein the laser (2) is optically connected to the optical component (3) for the transmission of the laser beam emitted by the laser, the optical component (3) is optically connected to the waveguide (4) for the transmission of the laser beam, wherein the optical component (3) is designed to couple the laser beam into the waveguide (4) in such a way that a spatial mode of order ≥ 1 is excited in the waveguide (4), and the waveguide (4) has a nonlinear medium, so that a squeezed signal-idler state with signal and idler rays is generated in the waveguide (4) with the spatial mode. [2] Source (1) according to claim 1, wherein the optical component (3) comprises a mirror (5) and a lens (6) and the laser beam is coupled into the waveguide (4) at a predetermined angle, so that the spatial mode is excited in the waveguide (4). [3] Source (1) according to one of claims 1 or 2 with a beam splitter (7), wherein the waveguide (4) is optically connected to the beam splitter (7) for the transmission of the squeezed signal idler state, and the squeezed signal idler state interferes in the beam splitter (7) so that the squeezed signal idler state is converted into two mutually uncorrelated and indistinguishable squeezed single-mode states. [4] Source (1) according to claim 3 with a further lens (8), wherein the further lens (8) is arranged between the waveguide (4) and the beam splitter (7). [5] Source (1) according to any of the preceding claims, wherein the excited spatial mode is a first-order spatial mode. [6] Source (1) according to one of the preceding claims, wherein the laser (2) is configured to emit the laser beam in a wavelength range between 750 nm and 800 nm, in particular between 760 nm and 780 nm. [7] Source (1) according to any of the preceding claims, wherein the nonlinear medium of the waveguide (4) is a potassium titanyl phosphate. [8] Source (1) according to one of the preceding claims, wherein rubidium ions have diffused into the waveguide (4) so ​​that a conduction area (9) is formed. [9] Source (1) according to claim 8, wherein the conduction area (9) is arranged at an entry point (10) of the laser beam in the waveguide (4) and extends through the waveguide (4) to an exit point (11) of the squeezed signal idler state from the waveguide (4). [10] Source (1) according to one of claims 8 or 9, wherein the rubidium ions have diffused into the waveguide (4) with a concentration gradient perpendicular to a longitudinal axis (14) of the waveguide. [11] Source (1) according to claim 10, wherein a highest rubidium ion concentration is formed directly on the surface (15) of the waveguide (4). [12] Source (1) according to one of claims 10 or 11, wherein the concentration gradient has a complementary error function. [13] Source (1) according to one of claims 8 to 12, wherein the conduction area (9) formed with the rubidium ions extends from the surface (15) to a depth between 7 µm and 9 µm, in particular 7.39 µm and 8.1 µm, in the waveguide (4) and has a width of 1.5 µm to 4.5 µm, in particular 2.7 µm, in a cross-sectional area perpendicular to the longitudinal axis (14) of the waveguide (4) and perpendicular to the depth. [14] Source (1) according to one of the preceding claims, wherein the waveguide (4) is periodically polarized along the longitudinal axis (14) and has a polarization period between 120 µm and 160 μm, in particular a polarization period of 146 μm. [15] Source (1) according to any of the preceding claims, wherein the source (1) is designed as an integrated circuit.

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