Quantum transducer with embedded optical resonator

Abstract

Techniques related to quantum transducers are provided. For example, one or more embodiments described herein may include a device that may include a superconducting microwave resonator having a microstrip architecture that includes a dielectric layer disposed between a superconducting waveguide and a ground plane. The device may also include an optical resonator disposed within the dielectric layer.

Description

Technical Field

[0001] The present disclosure relates to one or more quantum transducers having a microstrip, coplanar, and / or twin-strip architecture, and more specifically to a quantum transducer architecture including one or more optical resonators disposed adjacent to and / or within a dielectric substrate of one or more superconducting microwave resonators.

Summary of the Invention

[0002] A summary is presented below to provide a basic understanding of one or more embodiments of the present invention. This summary is not intended to identify key or essential elements nor to delineate any scope of particular embodiments or any scope of the claims. Its sole purpose is to present concepts in a simplified form as an introduction to the more detailed description that follows. In one or more embodiments described herein, apparatuses, systems, devices, and / or methods related to quantum transducers are described.

[0003] According to one embodiment, an apparatus is provided. The apparatus can include a superconducting microwave resonator having a microstrip architecture including a dielectric substrate disposed between a superconducting waveguide and a ground plane. The apparatus can also include an optical resonator disposed within the dielectric layer.

[0004] According to another embodiment, an apparatus is provided. The apparatus can include a superconducting microwave resonator having a twin-strip architecture including a dielectric layer disposed between a first superconducting waveguide and a second superconducting waveguide. The apparatus can also include an optical resonator disposed within the dielectric substrate.

[0005] According to one embodiment, a method is provided. This method may include the step of forming an optical resonator on a dielectric substrate. The method may also include the step of expanding the dielectric substrate by depositing a dielectric cladding layer on the dielectric substrate and the optical resonator. Furthermore, the method may include the step of forming a superconducting waveguide by depositing a first superconducting material on the dielectric substrate. At least a portion of the dielectric substrate may be placed between the superconducting waveguide and the optical resonator. [Brief explanation of the drawing]

[0006] [Figure 1A] This specification shows illustrative and non-limiting top views of one or more embodiments of quantum transducers described herein.

[0007] [Figure 1B] This specification shows illustrative, non-limiting graphs of optical and / or microwave transitions that may characterize the operation of one or more quantum transducers according to one or more embodiments described herein.

[0008] [Figure 2] The following are illustrative and non-limiting cross-sectional diagrams of one or more quantum transducers having a microstrip architecture according to one or more embodiments described herein.

[0009] [Figure 3] This specification includes illustrative and non-limiting simulation figures showing magnetic and / or electric fields that may characterize the operation of one or more quantum transducers according to one or more embodiments described herein.

[0010] [Figure 4A] The following are illustrative and non-limiting cross-sectional diagrams of one or more quantum transducers having a coplanar waveguide architecture according to one or more embodiments described herein. [Figure 4B]The following are illustrative and non-limiting cross-sectional diagrams of one or more quantum transducers having a coplanar waveguide architecture according to one or more embodiments described herein.

[0011] [Figure 5] The following are illustrative and non-limiting cross-sectional diagrams of one or more quantum transducers having a twin-strip architecture according to one or more embodiments described herein.

[0012] [Figure 6] This specification includes illustrative and non-limiting simulation figures showing magnetic and / or electric fields that may characterize the operation of one or more quantum transducers according to one or more embodiments described herein.

[0013] [Figure 7] The following are illustrative and non-limiting table figures that can demonstrate the effectiveness of one or more quantum transducers according to one or more embodiments described herein.

[0014] [Figure 8] This specification shows illustrative and non-limiting step-by-step diagrams for fabricating one or more quantum transducers according to one or more embodiments described herein.

[0015] [Figure 9] This specification shows illustrative and non-limiting step-by-step diagrams for fabricating one or more quantum transducers according to one or more embodiments described herein.

[0016] [Figure 10] This specification shows a flowchart of an exemplary, non-limiting method for fabricating one or more quantum transducers according to one or more embodiments described herein. [Modes for carrying out the invention]

[0017] The following detailed description is merely illustrative and is not intended to limit the embodiments and / or the application or use of the embodiments. Further, it is not intended to be constrained by any explicit or implied information presented in the foregoing background art or summary of the invention or the form for carrying out the invention.

[0018] Here, one or more embodiments will be described with reference to the drawings. Throughout, like reference numerals are used to refer to like elements. In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a more thorough understanding of one or more embodiments. However, in various instances, it will be apparent that one or more embodiments can be practiced without these specific details.

[0019] For long-distance networks of superconducting quantum computers, quantum transducers that convert single photons from microwave frequencies to the infrared telecommunication domain may be required. The energy of microwave photons is smaller than the thermal background energy at room temperature; thus, quantum information links at room temperature in the microwave frequency can be extremely difficult. However, in optical fibers, infrared photons can travel long distances without attenuation or interference. Subsequently, a quantum transducer connected to other superconducting quantum processors can convert the photons back from infrared to the microwave domain.

[0020] There are multiple approaches to this problem. One is to use a mechanical resonator as a mediating degree of freedom between the microwave and optical domains. The other utilizes atomic or solid defect centers, or optical or spin transitions in magnon states. Optical resonators and microwave resonators are X (2) or X (3)When coupled through a nonlinear optical medium, microwave and optical resonators can directly exchange energy without the need for mediating degrees of freedom. However, a challenge in electro-optic quantum transformation is confining the microwave field sufficiently to improve the efficiency of the quantum transformation. The transformation efficiency is proportional to the square of the coupling strength of the microwave-optical single photon, which is inversely proportional to the square root of the microwave field mode volume. Therefore, by minimizing the microwave mode volume, a highly efficient quantum transducer can be realized.

[0021] Various embodiments described herein may include apparatus, devices, systems, and / or methods relating to one or more quantum transducers that may rely on electro-optic coupling between one or more microwave resonator architectures and one or more optical resonators. In one or more embodiments, one or more microwave resonator architectures can confine microwave modes to a substrate of quantum transducers, resulting in a peak field at the center of the substrate. In one or more embodiments, one or more optical resonators may be located inside a dielectric substrate and beneath one or more superconducting waveguides. One or more superconducting waveguides may further be included in microstrip, coplanar, and / or twinstrip microwave resonator architectures.

[0022] In this specification, the terms “deposition process” and / or “multiple deposition processes” can refer to any process of growing, coating, depositing, and / or otherwise transferring one or more first materials onto one or more second materials. Exemplary deposition processes include, but are not limited to, physical vapor deposition ("PVD"), chemical vapor deposition ("CVD"), electrochemical deposition ("ECD"), atomic layer deposition ("ALD"), reduced-pressure chemical vapor deposition ("LPCVD"), plasma-excited chemical vapor deposition ("PECVD"), high-density plasma chemical vapor deposition ("HDPCVD"), semi-atmospheric pressure chemical vapor deposition ("SACVD"), rapid thermochemical vapor deposition ("RTCVD"), in-situ radical-assisted deposition, and high-temperature acid Examples include ion-based deposition ("HTO"), low-temperature oxide deposition ("LTO"), rate-limiting reaction-based CVD ("LRPCVD"), ultra-high vacuum chemical vapor deposition ("UHVCVD"), metal-organic chemical vapor deposition ("MOCVD"), physical vapor deposition ("PVD"), chemical oxidation, sputtering, plating, vapor deposition, spin-on coating, ion beam deposition, electron beam deposition, laser-assisted deposition, chemical solution deposition, and / or combinations thereof.

[0023] Where herein it is used, the terms “epitaxial growth process” and / or “multiple epitaxial growth processes” can refer to any process for growing an epitaxial material (e.g., a crystalline semiconductor material) onto the deposition surface of another semiconductor material, wherein the grown epitaxial material has substantially the same crystalline properties as the semiconductor material on the deposition surface. In an epitaxial deposition process, the chemical reactants supplied by the source gas (e.g., a gas containing silicon and / or germanium) and / or source liquid can be controlled, and system parameters can be set so that the deposited atoms have sufficient energy to reach the deposition surface, move around on its surface, and orient themselves to the crystalline arrangement of atoms on the deposition surface. Therefore, the grown epitaxial material has substantially the same crystalline properties as the deposition surface on which the epitaxial material was formed. For example, <100> Epitaxially grown semiconductor material deposited on a crystal plane oriented in a certain direction, <100> Orientation can be achieved. Exemplary epitaxial growth processes include, but are not limited to, gas-phase epitaxy ("VPE"), molecular beam epitaxy ("MBE"), liquid-phase epitaxy ("LPE"), and / or combinations thereof.

[0024] As used herein, the terms “etching process,” “multiple etching processes,” “removal process,” and / or “multiple removal processes” may refer to any process for removing one or more first materials from one or more second materials. Examples of etching and / or removal processes include, but are not limited to, wet etching, dry etching (e.g., reactive ion etching ("RIE")), chemical mechanical planarization ("CMP"), and / or combinations thereof.

[0025] In this specification, the terms “lithography process” and / or “multiple lithography processes” may refer to the formation of a three-dimensional relief image or pattern on a semiconductor substrate, with the aim of subsequent pattern transfer to the substrate. In semiconductor lithography, patterns can be formed using a photosensitive polymer called a photoresist. To create the complex structures that form semiconductor devices and the many wires that connect the various features of the circuit, the lithography process and / or etching pattern transfer step may be repeated multiple times. Each pattern to be printed on the wafer can be aligned with previously formed patterns, gradually forming the target features (e.g., conductors, insulators, and / or selectively doped areas) to form the final device.

[0026] As used herein, the term “superconducting” may characterize materials that exhibit superconducting properties at or below their superconducting critical temperature, such as aluminum (e.g., a superconducting critical temperature of 1.2 Kelvin) or niobium (e.g., a superconducting critical temperature of 9.3 Kelvin). Furthermore, those skilled in the art will recognize that other superconducting materials (e.g., hydride superconductors such as lithium / magnesium hydride alloys) may be used in the various embodiments described herein.

[0027] As used herein, the term “microstrip” may refer to a microwave waveguide that includes metal tracks and a ground plane separated by dielectric spacers. The term “twin strip” may refer to a microwave waveguide that includes two parallel metal tracks instead of a ground plane. The term “coplanar” may refer to a microwave waveguide that includes metal tracks and two ground planes in the same plane as the waveguide.

[0028] Figure 1A shows an exemplary, non-limiting top view of an exemplary quantum transducer 100 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. In various embodiments, the quantum transducer 100 may include one or more microwave transmission lines 102 and / or one or more optical waveguides 104. One or more microwave transmission lines 102 may extend, for example, from a microwave input section, e.g., a single microwave photon input section 106, to a microwave output section, e.g., a single microwave photon output section 108. Similarly, one or more optical waveguides 104 may extend, for example, from an optical input section, e.g., a single optical photon input section 110 (e.g., coupled to an excitation laser input section), to an optical output section, e.g., a single optical photon output section 112.

[0029] In one or more embodiments, one or more microwave transmission lines 102 may include one or more types of superconducting materials. Exemplary superconducting materials that may be included in one or more microwave transmission lines 102 include, but are not limited to, niobium, niobium nitride, titanium nitride, and / or combinations thereof. The thickness of one or more microwave transmission lines 102 (for example, along the "Y" axis shown in Figure 1A) can be, for example, greater than or equal to 5 micrometers (μm) and less than or equal to 20 μm. In various embodiments, one or more microwave transmission lines 102 may be arranged on a dielectric substrate 114. In one or more embodiments, one or more optical waveguides 104 may include one or more types of transparent materials and / or substantially transparent materials. Exemplary materials that may be included in one or more optical waveguides 104 include, but are not limited to, silicon germanium, lithium niobate, aluminum nitride, and / or combinations thereof. The thickness of one or more optical waveguides 104 (for example, along the "Y" axis shown in Figure 1A) can be, for example, greater than or equal to 1 μm and less than or equal to 10 μm. In various embodiments, one or more optical waveguides 104 may be located inside the dielectric substrate 114.

[0030] The dielectric substrate 114 can be crystalline, semicrystalline, microcrystalline, or amorphous. The dielectric substrate 114 may essentially consist of a single element (e.g., silicon or germanium) and / or compounds (e.g., aluminum oxide, silicon dioxide, gallium arsenide, silicon carbide, silicon germanium, and / or combinations thereof) (excluding, for example, contaminants). The dielectric substrate 114 may also have multiple material layers, for example, but not limited to, a semiconductor-on-insulator substrate ("SeOI"), a silicon-on-insulator substrate ("SOI"), a germanium-on-insulator substrate ("GeOI"), a silicon germanium-on-insulator substrate ("SGOI"), and / or combinations thereof. Furthermore, the dielectric substrate 114 may also have other layers, for example, high-dielectric constant oxides ("high-K oxides") and / or nitrides. In one or more embodiments, the dielectric substrate 114 may be a silicon wafer. In various embodiments, the dielectric substrate 114 may include single-crystal silicon (Si), silicon germanium (e.g., characterized by the chemical formula SiGe), a wafer or surface / active layer of a III-V semiconductor, sapphire, garnet, and / or a combination thereof.

[0031] As shown in Figure 1A, one or more microwave resonators 116 may be positioned adjacent to one or more microwave transmission lines 102 and / or between a single microwave photon input section 106 and a single microwave photon output section 108. In one or more embodiments, one or more microwave resonators 116 may comprise one or more superconducting waveguides 118. One or more superconducting waveguides 118 may comprise one or more superconducting materials. Exemplary superconducting materials that may comprise one or more superconducting waveguides 118 include, but are not limited to, niobium, niobium nitride, titanium nitride, and / or combinations thereof. In various embodiments, one or more superconducting waveguides 118 may be positioned on a dielectric substrate 114. In one or more embodiments, one or more superconducting waveguides 118 may be positioned at a distance of at least a first distance D1, which is, for example, greater than or equal to 1 μm and less than or equal to 100 μm, from one or more microwave transmission lines 102.

[0032] Furthermore, in one or more embodiments, one or more microwave resonators 116 may further include one or more ground planes positioned beneath the dielectric substrate 114. For clarity, one or more ground planes are not shown in Figure 1A, but are shown in the cross-sectional views of the quantum transducer 100 shown in Figures 2, 4A-5, and 8-9.

[0033] As shown in Figure 1A, one or more optical resonators 120 may be positioned adjacent to one or more optical waveguides 104 and / or between a single optical photon input section 110 and a single optical photon output section 112. In one or more embodiments, one or more optical resonators 120 may include one or more transparent materials and / or substantially transparent materials. Exemplary materials that may be included in one or more optical resonators 120 include, but are not limited to, silicon germanium, lithium niobate, aluminum nitride, and / or combinations thereof. In various embodiments, one or more optical resonators 120 may be positioned inside a dielectric substrate 114. Furthermore, one or more optical resonators 120 may be positioned at a distance of at least a second distance D2, which is, for example, greater than or equal to 100 nanometers (nm) and less than or equal to 2 μm, from one or more optical waveguides 104.

[0034] Figure 1A shows one or more superconducting waveguides 118 and / or optical resonators 120 having a circular shape, but the architecture of the quantum transducer 100 is not limited in this way. For example, embodiments in which one or more superconducting waveguides 118 and / or optical resonators 120 have alternative shapes (e.g., elliptical or polygonal shapes) are also envisioned. Furthermore, Figure 1A shows one or more superconducting waveguides 118 and optical resonators 120 that are misaligned relative to each other, but the architecture of the quantum transducer 100 is not limited in this way. For example, embodiments in which one or more superconducting waveguides 118 and optical resonators 120 are aligned relative to each other (e.g., as described later in this specification) are also envisioned.

[0035] Figure 1B shows an exemplary and non-limiting Graph 124 that can illustrate optical transitions and / or microwave transitions that one or more quantum transducers 100 may encounter in one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. Graph 124 can illustrate optical transitions that the quantum transducer 100 may encounter as the energy states of one or more microwave resonators 116 and / or optical resonators 120 increase (e.g., indicated by the "OT" arrow). Graph 124 can also illustrate microwave transitions that the quantum transducer 100 may encounter as the energy states of one or more microwave resonators 116 and / or optical resonators 120 increase (e.g., indicated by the "MT" arrow). a The first optical mode of the optical resonator 120 can be represented by "ω b The second optical mode of the optical resonator 120 can be represented by "ω c The microwave mode of the microwave resonator 116 can be represented by this.

[0036] Figure 2 shows an exemplary, non-limiting cross-sectional view of a quantum transducer 100 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. Figure 2 can show a cross-section of the quantum transducer 100 along the AA' plane shown in Figure 1A. As shown in Figure 2, one or more microwave resonators 116 may include one or more superconducting waveguides 118 and superconducting ground planes 202 separated from each other by a dielectric substrate 114. Thus, one or more microwave resonators 116 may have a microstrip architecture (as shown, for example, in Figure 2).

[0037] In one or more embodiments, the superconducting ground plane 202 may comprise one or more superconducting materials. Examples of superconducting materials that may be incorporated into the superconducting ground plane 202 include, but are not limited to, niobium, niobium nitride, titanium nitride, and / or combinations thereof. For example, one or more superconducting waveguides 118 and superconducting ground planes 202 may have the same or substantially the same composition. Furthermore, the thickness of the superconducting ground plane 202 (for example, along the "Z" axis shown in Figure 2) may be in the range of, for example, greater than or equal to 50 nm and less than or equal to 5 μm.

[0038] In various embodiments, one or more superconducting waveguides 118 may be arranged on a dielectric substrate 114, and one or more optical resonators 120 may be arranged inside the dielectric substrate 114. This allows one or more superconducting waveguides 118 to be arranged on one or more optical resonators 120 (for example, along the "Z" axis shown in Figure 2). For example, the positions of one or more superconducting waveguides 118 may overlap the positions of one or more optical resonators 120 along a vertical plane (for example, along the "Z" axis shown in Figure 2). As shown in Figure 2, the dielectric substrate 114 can accommodate one or more optical resonators 120. One or more superconducting waveguides 118 may be arranged on a first surface 204 of the dielectric substrate 114, and a superconducting ground plane 202 may be arranged on a second surface 206 of the dielectric substrate 114. Furthermore, the first surface 204 and the second surface 206 may be on opposite sides of the dielectric substrate 114.

[0039] In one or more embodiments, the width of one or more superconducting waveguides 118 (for example, along the "X" axis as shown in Figure 2) may be greater than the width of one or more optical resonators 120 (for example, along the "X" axis as shown in Figure 2). In one or more embodiments, the widths of one or more superconducting waveguides 118 and / or optical resonators 120 may be equal. The width of one or more superconducting waveguides 118 (for example, along the "X" axis as shown in Figure 2) may be, for example, greater than or equal to 3 μm and less than or equal to 20 μm (e.g., 4 micrometers (μm)). The width of one or more optical resonators 120 (for example, along the "X" axis as shown in Figure 2) may be, for example, greater than or equal to 1 μm and less than or equal to 10 μm (e.g., 3 μm).

[0040] In one or more embodiments, the thickness of one or more superconducting waveguides 118 (for example, along the "Z" axis as shown in Figure 2) may be greater than the thickness of one or more optical resonators 120 (for example, along the "Z" axis as shown in Figure 2). In one or more embodiments, the widths of one or more superconducting waveguides 118 and / or optical resonators 120 may be equal (for example, as shown in Figure 2). The thickness of one or more superconducting waveguides 118 (for example, along the "Z" axis as shown in Figure 2) may be, for example, greater than or equal to 50 nm and less than or equal to 5 μm. The thickness of one or more optical resonators 120 (for example, along the "Z" axis as shown in Figure 2) may be, for example, greater than or equal to 100 nm and less than or equal to 1 μm (for example, 0.5 μm).

[0041] In various embodiments, one or more optical resonators 120 may be located inside the dielectric substrate 114 at a height H1 that is, for example, greater than or equal to 1 μm and less than or equal to 10 μm (e.g., 10 μm) from the superconducting ground plane 202. Furthermore, one or more optical resonators 120 may be located perpendicularly (for example, along the "Z" axis shown in Figure 2) from one or more superconducting waveguides 118 by a third distance D3 that is, for example, greater than or equal to 1 and less than or equal to 10 μm (e.g., 9.5 μm).

[0042] Figure 3 shows illustrative and non-limiting simulations 302 and / or 304 illustrating the magnetic and / or electric fields that may be produced by one or more quantum transducers 100 having one or more microwave resonators 116 with a microstrip architecture, according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. Simulation 302 can evaluate the magnetic field that may be produced by one or more quantum transducers 100 having one or more microwave resonators 116 with a microstrip architecture, and / or simulation 304 can evaluate the electric field that may be produced by one or more quantum transducers 100 having one or more microwave resonators 116 with a microstrip architecture. Simulations 302 and / or 304 can be generated using a two-dimensional finite difference element ("FDE") solver. The input here can be the width (e.g., along the "X" axis as shown in Figure 2) of one or more superconducting waveguides 118; the thickness (e.g., along the "Z" axis as shown in Figure 2) of the dielectric substrate 114; and / or the width (e.g., along the "X" axis as shown in Figure 2) of one or more optical resonators 120. The solver output can be the spatial distribution of the electric and / or magnetic fields of the modes, and the effective mode index. In various embodiments described herein, the width (e.g., along the "X" axis as shown in Figure 2) of one or more superconducting waveguides 118 that can produce the highest electric field in the optical field overlap region can be used (e.g., the effective index of the optimal width of one or more superconducting waveguides 118 can be 2.744).

[0043] Figures 4A to 4B show exemplary and non-limiting cross-sectional views of a quantum transducer 100 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. Figures 4A to 4B can show a cross-section of the quantum transducer 100 along the AA' plane shown in Figure 1A. As shown in Figures 4A to 4B, one or more microwave resonators 116 may include one or more superconducting waveguides 118, a superconducting ground plane 202, and / or one or more second superconducting ground planes 402. One or more superconducting waveguides 118 and the second superconducting ground plane 402 may be isolated from the superconducting ground plane 202 by a dielectric substrate 114. Thus, one or more microwave resonators 116 may have a coplanar waveguide ("CPW") architecture (as shown, for example, in Figures 4A and 4B).

[0044] In one or more embodiments, one or more second superconducting ground planes 402 may comprise one or more types of superconducting materials. Exemplary superconducting materials that may comprise one or more second superconducting ground planes 402 include, but are not limited to, niobium, niobium nitride, aluminum nitride, and / or combinations thereof. For example, one or more superconducting waveguides 118, superconducting ground planes 202, and one or more second superconducting ground planes 402 may have the same or substantially the same composition. Furthermore, the thickness of one or more second superconducting ground planes 402 (for example, along the "Z" axis shown in Figures 4A and 4B) may be in the range of, for example, greater than or equal to 50 nm and less than or equal to 5 μm.

[0045] As shown in Figures 4A and 4B, one or more second superconducting ground planes 402 may be positioned on the dielectric substrate 114 adjacent to one or more superconducting waveguides 118. Alternatively, one or more second superconducting ground planes 402 may be positioned horizontally (for example, along the "X" axis shown in Figures 4A and 4B) from one or more superconducting waveguides 118 by a distance, for example, greater than or equal to 2 μm and less than or equal to 20 μm. In Figure 4A, the quantum transducer 100 may have a grounded coplanar waveguide ("CPWG") transverse electric field ("TE") mode configuration. As shown in Figure 4A, one or more optical resonators 120 may be positioned directly beneath one or more superconducting waveguides 118 (for example, one or more optical resonators 120 may be aligned perpendicular to one or more superconducting waveguides 118 along the "Z" axis). In Figure 4B, the quantum transducer 100 may have a CPWG transverse field ("TM") mode configuration. As shown in Figure 4B, one or more optical resonators 120 may be positioned offset from one or more superconducting waveguides 118 along a vertical plane (for example, along the "Z" axis shown in Figure 4B).

[0046] Figure 5 shows an exemplary and non-limiting cross-sectional view of a quantum transducer 100 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. Figure 5 can show a cross-section of the quantum transducer 100 along the AA' plane shown in Figure 1A. As shown in Figure 5, one or more microwave resonators 116 may include one or more superconducting waveguides 118 and one or more second superconducting waveguides 502 separated from each other by a dielectric substrate 114. Thus, one or more microwave resonators 116 may have a twin-strip architecture (as shown, for example, in Figure 5).

[0047] For example, using a twin-strip architecture, one or more second superconducting waveguides 502 can replace the superconducting ground plane in a microstrip architecture. For example, one or more second superconducting waveguides 502 may be located on the second surface 206 of the dielectric substrate. One or more second superconducting waveguides 502 may include one or more types of superconducting materials. Examples of superconducting materials that may be included in one or more second superconducting waveguides 502 include, but are not limited to, niobium, niobium nitride, titanium nitride, and / or combinations thereof. The thickness of one or more second superconducting waveguides 502 (for example, along the "Z" axis shown in Figure 5) can be, for example, greater than or equal to 50 nm and less than or equal to 5 μm. The width of one or more second superconducting waveguides 502 (for example, along the "X" axis shown in Figure 5) can be, for example, greater than or equal to 3 μm and less than or equal to 20 μm (for example, 4 μm). In one or more embodiments, one or more second superconducting waveguides 502 may have the same or substantially the same composition and / or dimensions as one or more superconducting waveguides 118.

[0048] As shown in Figure 5, one or more superconducting waveguides 118 and / or a second superconducting waveguide 502 can be aligned with each other in a vertical plane (for example, along the "Z" axis shown in Figure 5). In one or more embodiments, one or more optical resonators 120 can be directly positioned between one or more superconducting waveguides 118 and a second superconducting waveguide 502 (for example, as shown in Figure 5).

[0049] Figure 6 shows illustrative and non-limiting simulations 602 and / or 604 illustrating the magnetic and / or electric fields that may be produced by one or more quantum transducers 100 having one or more microwave resonators 116 with a twin-strip architecture, according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. Simulation 602 can evaluate the magnetic field that may be produced by one or more quantum transducers 100 having one or more microwave resonators 116 with a twin-strip architecture, and / or simulation 604 can evaluate the electric field that may be produced by one or more quantum transducers 100 having one or more microwave resonators 116 with a twin-strip architecture. Simulations 602 and / or 604 can be generated using a two-dimensional FDE solver. The input here can be the width of one or more superconducting waveguides 118 (e.g., along the "X" axis as shown in Figure 5); the thickness of a dielectric substrate 114 (e.g., along the "Z" axis as shown in Figure 5); the width of one or more optical resonators 120 (e.g., along the "X" axis as shown in Figure 5); and / or the width of one or more second superconducting waveguides 502 (e.g., along the "X" axis as shown in Figure 5). The solver output can be the spatial distribution of the electric and / or magnetic fields of the modes, and the effective mode index. In various embodiments described herein, the width of one or more superconducting waveguides 118 and / or second superconducting waveguides 502 (e.g., along the "X" axis as shown in Figure 5) that can produce the highest electric field in the optical field overlap region can be used (e.g., the effective index of the optimal width of one or more superconducting waveguides 118 and / or second superconducting waveguides 502 can be 2.82).

[0050] Figure 7 shows an exemplary and non-limiting diagram of Table 700 that can illustrate the effect of varying the first height H1 of one or more optical resonators 120 according to various embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. Table 700 shows the results of several simulations performed using a two-dimensional FDE solver, e.g., simulations 302, 304, 602, and / or 604 shown in Figure 3 and / or Figure 6. The first column 702 of Table 700 can define the architecture of the microwave resonator 116 used in each simulation (e.g., microstrip architecture, CPWG TE architecture, CPWG TM architecture, twinstrip architecture, and / or coplanar waveguide ("CPW") architecture (e.g., CPWG structure without superconducting ground plane)). The second column 704 of Table 700 can define the height H1 of one or more optical resonators 120. The third column 706 of Table 700 allows you to specify the single-photon microwave ("SP MW") field in volts per meter (V / m). The fourth column 708 of Table 700 can be the effective exponent associated with the relevant parameters.

[0051] Figure 8 shows exemplary and non-limiting cross-sectional views of the quantum transducer 100 at several stages of a fabrication process 800 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. Figure 8 can show cross-sections of the quantum transducer 100 along the AA' plane shown in Figure 1A at various fabrication stages. The fabrication stages shown in Figure 8 may be carried out to fabricate various embodiments of the quantum transducer 100 described herein. For example, the fabrication stages shown in Figure 8 may be carried out to fabricate a quantum transducer 100 including one or more microwave resonators 116 having a microstrip architecture, a CPWG TE architecture, a CPWG TM architecture, and / or a twinstrip architecture.

[0052] In the first stage 802 of the fabrication process 800, an SOI wafer may be provided. For example, the SOI wafer may comprise a handle layer 804, a buried oxide layer 806, and / or a device layer 808. For example, the buried oxide layer 806 may contain a metal oxide. Also, the handle layer 804 and / or the device layer 808 may contain the same or substantially the same material as the dielectric substrate 114 (for example, silicon and / or sapphire). In various embodiments, the device layer 808 may be at least a portion of the dielectric substrate 114. In the second stage 810 of the fabrication process 800, one or more optical resonators 120 may be deposited and / or patterned on the device layer 808. For example, one or more optical resonators 120 may be grown on the device layer 808 by one or more epitaxial growth processes, and the epitaxial growth may be further patterned by one or more lithography processes to achieve desired dimensions of the optical resonators 120. For example, one or more optical resonators 120 are grown on a device layer 808 and patterned by one or more lithography processes using silicon germanium (e.g., Si 1-x Ge x This may include (crystalline alloys of silicon and germanium). In one or more embodiments, one or more optical resonators 120 and / or optical waveguides 104 can be formed by epitaxial growth lithography patterning (e.g., silicon germanium patterning).

[0053] In the third stage 812 of the fabrication process 800, one or more cladding layers 814 can be deposited on one or more optical resonators 120 and / or optical waveguides 104 to form a dielectric substrate 114. In one or more embodiments, one or more cladding layers 814 may have the same or substantially the same composition as the dielectric substrate 114 and / or may be grown on the device layer 808, one or more optical resonators 120, and / or one or more optical waveguides 104 (e.g., by one or more epitaxial growth processes). For example, one or more cladding layers 814 may be one or more grown silicon layers. In Figure 8, the third stage 812 is indicated by a dashed line to define the positions of the device layer 808 and the cladding layers 814; this illustrates the formation of the dielectric substrate 114. Furthermore, in the third stage 812, one or more cladding layers 814 may be polished (e.g., by CMP) to form a second surface 206 of the dielectric substrate 114.

[0054] Figure 9 shows exemplary and non-limiting cross-sectional views of the quantum transducer 100 at multiple stages of the fabrication process 800 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. Figure 9 can show cross-sections of the quantum transducer 100 along the AA' plane shown in Figure 1A at various fabrication stages. In various embodiments, the fabrication stages shown in Figure 9 can continue the fabrication process 800 shown in Figure 9.

[0055] In the fourth stage 902 of the fabrication process 800, a superconducting material can be deposited on the second surface 206 of the dielectric substrate 114 by one or more deposition processes (e.g., by one or more deposition processes) to form a superconducting ground plane 202. In one or more embodiments where the fabrication process 800 is the fabrication of a microwave resonator 116 having a twin-strip architecture, instead of the superconducting ground plane 202, one or more second superconducting waveguides 502 can be deposited (e.g., by one or more deposition processes) and / or patterned (e.g., by one or more lithography processes) on the second surface 206 of the dielectric substrate 114. In the fifth stage 904 of the fabrication process 800, a wafer (e.g., a silicon wafer) can be bonded to the superconducting ground plane 202 to form a second handle layer 906.

[0056] In the sixth stage 908 of the fabrication process 800, the quantum transducer 100 can be inverted, and the handle layer 804 and the embedded oxide layer 806 can be removed by one or more etching and / or polishing processes (e.g., CMP) to form the first surface 204 of the dielectric substrate 114. In the seventh stage 910 of the fabrication process 800, a superconducting material can be deposited (e.g., by one or more deposition processes) and / or patterned (e.g., by one or more lithography processes) on the first surface 204 of the dielectric substrate 114 to form one or more superconducting waveguides 118 and / or microwave transmission lines 102. In one or more embodiments, the tenth step 708 of the initial fabrication process 600 may also include a step of depositing and / or patterning (e.g., by a deposition process) one or more second superconducting ground planes 402 on the first surface 204 of the dielectric substrate 114 (e.g., by a deposition process) and / or (e.g., by a lithography process) to realize a microwave resonator 116 with a CPWG architecture. Furthermore, the second handle layer 906 can be removed by one or more etching processes to realize the structure of the quantum transducer 100 illustrated in Figures 1A-2 and / or Figures 4A-5.

[0057] Figure 10 shows a flowchart of an exemplary and non-limiting method 1000 that may facilitate the fabrication of one or more quantum transducers 100 by one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity.

[0058] In 1002, method 1000 may include the step of forming one or more optical resonators 120 on a dielectric substrate 114. For example, the step of forming one or more optical resonators in 1002 may be carried out according to the first step 802 and / or second step 810 of the fabrication process 800. For example, an SOI wafer may be provided, where one or more optical resonators 120 can be deposited on the device layer 808 of the SOI wafer (for example, by one or more deposition processes and / or epitaxial growth processes).

[0059] In 1004, method 1000 may include a step of extending the dielectric substrate 114 by depositing one or more dielectric cladding layers 814 on the dielectric substrate and / or one or more optical resonators 120. For example, the step of extending the dielectric substrate 114 in 1004 may be carried out according to the third step 812 of the fabrication process 800. In 1006, method 1000 may include a step of forming one or more superconducting waveguides 118 by depositing a first superconducting material (e.g., niobium, niobium nitride, and / or titanium nitride) on the dielectric substrate 114. Here, at least a portion of the dielectric substrate 114 may be placed between one or more superconducting waveguides 118 and one or more optical resonators 120. For example, the step of forming one or more superconducting waveguides 118 may be carried out according to the fourth step 902, fifth step 904, sixth step 908, and / or seventh step 910 of the fabrication process 800. In various embodiments, Method 1000 may further comprise the step of forming a superconducting ground plane 202 or one or more second superconducting waveguides 502 on a dielectric substrate 114. For example, Method 1000 can facilitate the fabrication of a quantum transducer 100 including one or more microwave resonators 116 having a microstrip, twinstrip, and / or CWPG architecture, according to various embodiments described herein.

[0060] Furthermore, the term “or” is intended to mean an inclusive “or,” not an exclusive “or.” That is, unless otherwise specified or it is clear from the context, “X uses A or B” is intended to mean either of the natural inclusive substitutions. That is, “X uses A or B” is satisfied in any of the aforementioned cases: when X uses A; when X uses B; or when X uses both A and B. Furthermore, the articles “a” and “an” used herein and in the accompanying drawings should generally be interpreted as meaning “one or plural,” unless otherwise specified or it is clear from the context that they refer to a singular noun. Where used herein, the terms “example” and / or “exemplary” are used to mean serving as an example, instance, or illustration. To avoid doubt, the subject matter disclosed herein is not limited to such examples. Furthermore, any aspect or design described herein as “example” and / or “exemplary” is not necessarily construed as being preferable or more advantageous than other aspects or designs, nor does it mean that equivalent exemplary structures and techniques known to those skilled in the art are excluded.

[0061] Naturally, it is impossible to describe all possible combinations of components, products, and / or methods in order to illustrate this disclosure, but those skilled in the art will recognize that many further combinations and substitutions of this disclosure are possible. Furthermore, to the extent that terms such as “includes,” “has,” and “possesse” are used in the detailed description, claims, appendices, and drawings, such terms are intended to be comprehensive in the same way that “comprising” is interpreted when used as a transitional clause in a claim. The descriptions of various embodiments have been presented for illustrative purposes, but are not intended to be exhaustive or to limit oneself to the disclosed embodiments. Those skilled in the art will see many changes and modifications without departing from the scope and spirit of the described embodiments. The terminology used herein has been selected to best describe the principles of the embodiments, the practical applications of the technology found in the market or technical improvements thereto, or to enable those skilled in the art to understand the embodiments disclosed herein.

Claims

1. A superconducting microwave resonator having a microstrip architecture including a dielectric substrate placed between a superconducting waveguide and a ground plane; and Optical resonator disposed inside the dielectric substrate A device equipped with the following features.

2. The apparatus according to claim 1, wherein the superconducting waveguide and the ground plane include at least one element selected from the group consisting of niobium, niobium nitride, and titanium nitride.

3. The apparatus according to claim 2, wherein the dielectric substrate comprises at least one element selected from the group consisting of silicon, sapphire, and garnet.

4. The apparatus according to claim 3, wherein the optical resonator includes an optical waveguide comprising at least one material selected from the group consisting of silicon germanium, lithium niobate, and aluminum nitride.

5. The apparatus according to any one of claims 1 to 4, wherein the dielectric substrate is disposed between the superconducting waveguide and the optical resonator, and the dielectric substrate is further disposed between the ground plane and the optical resonator.

6. The apparatus according to any one of claims 1 to 5, further comprising a second ground plane that is coplanar with the superconducting waveguide and disposed on the dielectric substrate.

7. The apparatus according to claim 6, wherein the second ground plane comprises at least one element selected from the group consisting of niobium, niobium nitride, and titanium nitride.

8. The apparatus according to claim 6 or 7, wherein the dielectric substrate extends from the ground plane to the superconducting waveguide along a certain direction, and the position of the optical resonator inside the dielectric substrate is offset along the direction from the position of the superconducting waveguide on the dielectric substrate.

9. A superconducting microwave resonator having a twin-strip architecture including a dielectric substrate positioned between a first superconducting waveguide and a second superconducting waveguide; and Optical resonator disposed inside the dielectric substrate A device equipped with the following features.

10. The apparatus according to claim 9, wherein the first superconducting waveguide and the second superconducting waveguide each contain at least one element selected from the group consisting of niobium, niobium nitride, and titanium nitride.

11. The apparatus according to claim 10, wherein the dielectric substrate comprises at least one element selected from the group consisting of silicon, sapphire, and garnet.

12. The apparatus according to claim 11, wherein the optical resonator has an optical waveguide comprising at least one material selected from the group consisting of silicon germanium, lithium niobate, and aluminum nitride.

13. The apparatus according to claim 12, wherein the dielectric substrate is disposed between the first superconducting waveguide and the optical resonator, and between the second superconducting waveguide and the optical resonator.

14. The step of forming an optical resonator on a dielectric substrate; A step of expanding the dielectric substrate by depositing a dielectric cladding layer on the dielectric substrate and the optical resonator; and A step of forming a superconducting waveguide by depositing a first superconducting material on the dielectric substrate, wherein at least a portion of the dielectric substrate is placed between the superconducting waveguide and the optical resonator. A method for providing this.

15. A step of depositing a second superconducting material on the dielectric substrate, wherein the deposit step forms a member selected from the group consisting of a ground plane and a second superconducting waveguide. The method according to claim 14, further comprising:

16. The dielectric substrate is the device layer of a silicon-on-insulator wafer, which includes a first silicon handle layer, an insulating layer, and a device layer, and the method is Step of forming a second silicon handle layer on the second superconducting material. The method according to claim 15, further comprising:

17. The step of removing the first silicon handle layer and the insulating layer from the dielectric substrate after depositing the second superconducting material and before forming the superconducting waveguide. The method according to claim 16, further comprising:

18. This step involves depositing a third superconducting material on the dielectric substrate to form a second ground plane that lies in the same plane as the superconducting waveguide. The method according to claim 17, further comprising:

19. The method according to claim 18, wherein the first superconducting material, the second superconducting material, and the third superconducting material each contain at least one element selected from the group consisting of niobium, niobium nitride, and titanium nitride.

20. The method according to claim 19, wherein the step of forming the optical resonator includes a step of growing metal tracks on the dielectric substrate by an epitaxial growth process before depositing the dielectric cladding layer.

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