Method and device for manufacturing nanofiber cavity for quantum computing

Abstract

To provide a method for manufacturing a polarization-degenerate fiber Bragg grating nanofiber cavity for quantum computing or quantum relay.SOLUTION: A manufacturing method comprises transmitting electromagnetic radiation characterized by a wavelength of 150 nm to 400 nm or more through a pattern in a phase shift mask and diffracting the electromagnetic radiation to form an interference pattern. The pattern is radiated to a core at a first end of a fiber optic cable region. In one example, the method forms a fiber Bragg grating on the core of the fiber optic cable region by using the electromagnetic radiation to change a refractive index of the core of the fiber optic cable region while rotating the fiber optic cable around an axis defined along a length of the fiber optic cable region.SELECTED DRAWING: Figure 1

Description

[Background technology]

[0001] Various techniques have been developed to create quantum computers. Superconducting qubits have been implemented using superconducting circuits that can exhibit quantum behavior. Such superconducting circuits are typically made using thin films of superconducting materials and require extremely low temperatures (close to absolute zero) to operate. Superconducting qubits exhibit relatively long coherence times, enabling complex calculations. They can be fabricated using existing semiconductor fabrication techniques. Unfortunately, they are more difficult to operate due to the required low temperature operation and the need for complex cooling systems. Also, the coherence of qubits is susceptible to environmental noise, limiting their scalability.

[0002] Another approach is the trapped ion qubit, which uses individual ions trapped in electromagnetic fields to store and manipulate quantum information.

[0003] Ions are manipulated using laser beams to create the fundamental operation of qubits. Trapped ion qubits have shown exceptional coherence properties and demonstrated long qubit lifetimes. They can also be individually controlled with high precision. However, the complexity of manipulating individual ions has made it difficult to scale up trapped ion systems. Furthermore, the need for high-quality vacuum systems and precise laser control makes them complex and costly to implement.

[0004] Yet another technology, topological qubits, rely on the manipulation of quasiparticles called 'anyons', which appear in exotic states of matter such as topological superconductors.

[0005] Anyons store and process quantum information in a topologically protected manner, making them less susceptible to errors caused by environmental noise. Topological qubits are robust against certain types of errors and may be useful for error-resistant quantum computing. However, there are drawbacks: topological qubits are still in the early stages of development, and practical applications face challenges in generating and controlling topological states. The exotic materials and stable conditions required are technically challenging to achieve.

[0006] Additionally, photonic qubits are being researched. Such photonic qubits use photons (i.e. particles of light) to encode and manipulate quantum information. Quantum gates are implemented using optical elements such as beam splitters, wave plates, and detectors. Photonic qubits can be easily manipulated with existing optical techniques. Photonic qubits are inherently immune to certain types of noise and can be transmitted over long distances. Unfortunately, photonic qubits struggle with efficient qubit-photon interactions and are difficult to create, store, and measure on demand. Integrating large numbers of qubits is currently difficult.

[0007] Each of the aforementioned approaches has its advantages and challenges, and the field of quantum computing is actively exploring these techniques. Unfortunately, these techniques have their drawbacks, including difficulties with scalability, reliability, and qubit coherence. Summary of the Invention

[0008] According to the present invention, techniques related to quantum computing and quantum repeaters in general are provided. In particular, the present invention provides a method for fabricating a nanofiber-based quantum computing system and the resulting device, which includes an optical cavity composed of a pair of Bragg gratings. By way of example only, the present invention can be applied to a variety of applications such as cryptography, drug discovery, optimization, machine learning and artificial intelligence, finance, weather forecasting, chemistry, mechanics, electricity, civil engineering, nuclear fusion and fission, economics, materials, and any other complex human or non-human matter.

[0009] In one example, the present invention provides a method for fabricating a polarization-degenerate fiber Bragg grating nanofiber cavity for quantum computing or quantum repeaters. The method includes transmitting electromagnetic radiation characterized by a wavelength of 150 nm to 400 nm or more through a pattern of a phase shift mask to diffract the electromagnetic radiation to form an interference pattern. The pattern is illuminated onto a core at a first end of a fiber optic cable region. In one example, the method includes forming a first fiber Bragg grating on the core of the fiber optic cable region by varying the refractive index of the core of the fiber optic cable region with the electromagnetic radiation while rotating the fiber optic cable about an axis defined along the length of the fiber optic cable region, forming a first fiber Bragg grating around the core of the fiber optic cable, the first fiber Bragg grating being comprised of a plurality of azimuthally symmetric patterns of a plurality of refractive index modulations at angles of 360 degrees along a longitudinal region perpendicular to a cross section of the fiber optic cable region. The method includes forming a second fiber Bragg grating at a second end of the fiber optic cable region, the second fiber Bragg grating configured to have a plurality of azimuthally symmetric patterns of a plurality of refractive index modulations around a core of the fiber optic cable, the plurality of refractive index modulations being 360 degrees in an angle. In one example, the second fiber Bragg grating is formed using similar radiation through a phase shifting mask.

[0010] In yet another example, the invention provides related systems and other methods that include forming a first fiber Bragg grating in one spatial region of a fiber optic cable and rotating the cable a predetermined amount to form a second fiber Bragg grating.

[0011] In one example, the present invention can achieve one or more of these benefits and / or advantages. In one example, the present invention provides an efficient quantum computing system based on a novel nanofiber-based optical cavity. That is, the present invention provides a quantum computing device that uses a nanofiber region configured with a pair of reflectors to form a cavity for quantum computing and a repeater. In one example, the device uses conventional optical technology and is compact and efficient. In one example, the present invention provides the advantage of producing a reliable, efficient, manufacturable optical cavity. These benefits and / or advantages are realizable by the present device and associated methods. Details of these benefits and / or advantages are described throughout this specification and in further detail below. [Brief description of the drawings]

[0012] [Figure 1] FIG. 2 is a simplified diagram illustrating a method for fabricating an azimuthally symmetric fiber Bragg grating along the fiber axis in one example of the present invention. [Diagram 2] FIG. 1 is a simplified diagram showing how a fiber Bragg grating cavity with arbitrary polarization for each cavity mode can be fabricated by rotating the fiber about the fiber axis during fabrication of the fiber Bragg grating in one example of the present invention. [Diagram 3] FIG. 11 is a simplified diagram illustrating another method of fabricating a fiber Bragg grating cavity with arbitrary polarization for each cavity mode, also by forming sequential fiber Bragg gratings at 90 degree offset angles along the fiber axis in an example of the present invention. [Figure 4]FIG. 1 is a simplified diagram showing how polarization of cavity modes can be controlled and characterized by monitoring scattering from nanofiber regions in one example of the present invention. [Diagram 5] FIG. 13 is an exemplary diagram showing an application of circularly polarized cavity modes for atom-photon entanglement and non-destructive imaging via polarization rotation in one example of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0013] The present invention provides technology generally related to quantum computing and manufacturing methods. In particular, the present invention provides manufacturing methods and resulting devices for nanofiber-based quantum computing systems that include an optical cavity composed of a pair of Bragg gratings. By way of example, the present invention can be applied to a variety of applications, such as cryptography, drug discovery, optimization, machine learning and artificial intelligence, finance, weather forecasting, chemistry, mechanics, electricity, civil engineering, nuclear fusion and fission, economics, materials, and other complex human or non-human problems. In one example, the present invention provides a method for manufacturing a polarization-degenerate cavity for quantum computing.

[0014] By way of background, a polarization degenerate cavity is an optical cavity that can support light of any polarization state without introducing different resonant frequencies or other property differences. That is, the cavity has a structure that allows light waves with different electric field orientations to resonate at the same frequency. By way of background, conventional optical cavities are designed to preferentially support a particular polarization state or to necessarily support only one particular polarization state because of factors that result in polarization dependence, such as anisotropic stress due to material impurities or surrounding structures. However, in this example, it is beneficial that the cavity can support any polarization state without distinguishing between polarization states. In a polarization degenerate cavity, light waves of different polarization states (e.g., horizontally and vertically polarized, or right-handed and left-handed circularly polarized) can resonate at the same frequency with the same efficiency. A polarization degenerate cavity ensures that changes in polarization state do not adversely affect the performance of the optical system, for example by introducing differences in the resonant frequencies of different polarization states.

[0015] Polarization-degenerate cavities are important in many fields, especially in optics and photonics, due to their ability to simultaneously support any polarization state. In lasers, polarization-degenerate cavities can improve output power and stability. The ability to support any polarization is beneficial in achieving higher efficiency and more stable laser operation. In fiber optic communications, the ability to manipulate the polarization state of light is crucial. Polarization-degenerate cavities can be used in devices such as modulators that can control the polarization of light to encode information. By utilizing different polarization states, it is possible to increase the capacity of a communication channel. This is achieved by multiplexing signals with different polarization states, allowing more data to be transmitted over the same medium without increasing the bandwidth. In optical sensors, the ability to support and analyze different polarization states can improve the sensitivity and specificity of the sensor. For example, by examining the change in the polarization state, changes in the physical or chemical properties of a substance being analyzed can be detected. Polarization-degenerate cavities can be used to study the properties of materials with spectroscopy and microscopy. By examining how a material affects the polarization state of light, insights into its structure and composition can be gained.

[0016] Polarization-degenerate cavities are often compact structures, making them ideal for integration into small photonic devices. This is especially important in light of the growing demand for miniaturization and integration in modern electronics and photonics. Polarization-degenerate cavities are often more robust against external disturbances that can cause drift in the polarization state. This makes them suitable for applications where stability and reliability are important. In quantum technology, polarization-degenerate cavities are desirable for the manipulation and storage of quantum information. They are also useful for entanglement of atoms and photons and the generation of entangled photon pairs, which are essential for quantum communication and quantum computing. Degenerate cavities are therefore important building blocks in modern optics, photonics, and quantum technology, as their ability to handle arbitrary polarization states makes them desirable for improving the performance, capacity, and functionality of a variety of systems and devices.

[0017] However, creating a polarization-degenerate high-finesse fiber Bragg grating cavity is challenging because of several factors that must be carefully controlled to ensure both high finesse and polarization degeneracy. Some of the reasons why this is difficult are listed below. Birefringence: Most optical materials are naturally birefringent to some degree, in the sense that they have different refractive indices for light of different polarizations. Even slight birefringence can create cavities with different resonant frequencies depending on the degree of polarization, which is the exact opposite of what is needed for polarization degeneracy. Fiber Bragg Grating (FBG) mirrors: Low-loss FBG-based mirrors in the cavity are important to achieve high finesse. However, with standard manufacturing procedures, the reflectivity of the FBG can also be polarization dependent. Fabricating highly reflective and polarization-independent FBGs is challenging. Stress-induced birefringence: Mechanical stress due to fiber mounting or bedding can induce birefringence in the FBG. This stress-induced birefringence causes different polarizations of light to resonate at different frequencies. Complexity of design and manufacturing: Achieving polarization degeneracy requires a high degree of control over material properties, FBG fabrication, and proper fiber attachment. This complexity in design and manufacturing makes polarization-degenerate high-finesse cavities difficult and costly to achieve.

[0018] Due to these challenges, creating polarization-degenerate, high-finesse cavities often requires careful design, precision manufacturing, and meticulous alignment and stabilization.

[0019] As further described below, these and other challenges are overcome by the present methods and systems.

[0020] The fiber-based cavity consists of two fiber Bragg gratings (FBGs) that act as high reflectors to form the cavity modes. FBGs are passive optical components used to filter and reflect light of specific wavelengths. FBGs are created by introducing periodic variations in the refractive index within a small section of optical fiber. Optical fibers consist of a core and a cladding, both made of dielectric materials, but each with a slightly different refractive index. In the case of fiber Bragg gratings, a series of periodic refractive index variations are created within the core of the fiber. Various methods are available to change the refractive index of the core, such as exposing the fiber core to an interference pattern of ultraviolet light. As light travels through an optical fiber, most wavelengths pass through unaffected. However, certain wavelengths that satisfy the Bragg condition are reflected. The Bragg condition is satisfied when twice the period of the refractive index variations in the fiber is equal to the wavelength of the light. Mathematically, it is given by λ_B=2*n*Λ, where λ_B is the Bragg wavelength, n is the effective refractive index of the core, and Λ is the period of the grating. All other wavelengths that do not satisfy the Bragg condition continue to propagate in the fiber.

[0021] FIG. 1 is a simplified diagram showing a method for fabricating a polarization-degenerate fiber Bragg grating (FBG) in one example of the present invention. One common technique for fabricating FBGs is the phase mask method. A phase mask has a binary pattern of alternating transparent and opaque regions and is designed to maximally diffract light equally into positive and negative first diffraction orders. Self-interference between these two diffraction orders creates an interference pattern with half the phase mask period required for grating formation. An ultraviolet (UV) laser beam passes through the phase mask and the resulting interference pattern is imprinted into the fiber core. The core of a fiber optic cable is generally made of a UV-sensitive material that is used for photosensitivity and UV irradiation of FBGs, and germanium-doped silica glass is used for FBGs. Germanium-doped fibers have enhanced photosensitivity compared to standard optical fibers and hydrogen-loaded fibers (hydrogen loading is a process frequently used to increase the photosensitivity of optical fibers), making them suitable for fabricating optical fibers. Germanium-doped silica and hydrogen-loaded fibers can have a controllable change in refractive index when exposed to ultraviolet light. An ultraviolet laser is used to expose germanium-doped silica fiber, creating a periodic change in the refractive index to form a Bragg grating structure. This structure reflects light of a specific wavelength, known as the Bragg wavelength.

[0022] Conventional UV light is focused onto the fiber optic cable from one fixed direction such that the intensity distribution in the cross section of the fiber is azimuthally asymmetric along the fiber axis. As a result, the inscribed refractive index modulation in the cross section of the fiber optic cable is not azimuthally symmetric. Therefore, the Bragg wavelength depends on the polarization of the light in the fiber optic cable. This is because the refractive index modulation for light polarized parallel to the UV exposure direction is different from that for light polarized perpendicular to the UV exposure direction, which induces birefringence for light polarized parallel and perpendicular to the UV light propagation direction.

[0023] In the present invention, the average intensity of the UV exposure is made uniform in the azimuth direction across the cross section of the optical fiber cable by rotating the optical fiber cable along the fiber axis during UV exposure. In one example, the UV exposure time is from tens of seconds to 10 minutes or more.

[0024] In one example, the rotation period is much shorter than the UV exposure time, e.g., much shorter than half the exposure time. The high speed rotation during UV exposure creates a uniform refractive index modulation in the azimuth direction at the cross section of the fiber optic cable, creating a polarization-independent FBG whose Bragg wavelength is independent of polarization.

[0025] FIG. 2 is a simplified diagram showing a method for fabricating a polarization-degenerate FBG cavity in which two orthogonal optical polarization modes are degenerate in frequency by continuously rotating a fiber around the fiber axis in the fabrication of an FBG in one embodiment of the present invention. Two FBGs are fabricated sequentially by scanning a UV light source along the fiber axis. After fabricating the first FBG, the UV light source is blocked by a mechanical shutter, an acousto-optic modulator, an electro-optic modulator, and / or other types of intensity modulators. The UV light source is then illuminated again on the fiber to fabricate the second FBG. The blocking time of the UV light source and the scanning speed determine the cavity length with a frequency approaching the MHz level. This scanning method for cavity fabrication allows the fabrication of two FBGs that are nearly identical in terms of Bragg wavelength, peak reflectivity, and reflection bandwidth, which are essential for creating an azimuthally symmetric FBG fabrication as well as a birefringence-free cavity. Due to the lack of birefringence in each FBG, the resonant frequencies of the two cavity modes with the two orthogonal polarizations are identical. Here, the two orthogonal polarized lights are, for example, two linearly polarized lights in the horizontal and vertical directions, or two circularly polarized lights in the right-handed and left-handed directions, or any other pair of orthogonal polarized lights.

[0026] FIG. 3 is a simplified diagram illustrating an alternative method of fabricating a polarization-degenerate FBG cavity in which two orthogonal optical polarization modes are degenerate in frequency by forming sequential fiber Bragg gratings at 90 degree offset angles along the fiber axis in one example of the present invention. In this method, a first FBG is fabricated without rotating the fiber during UV exposure, resulting in a birefringent FBG whose refractive index modulation depends on the polarization state. Before fabricating a second FBG, the fiber is rotated by 90 degrees and then exposed to UV light without rotating the fiber, which also rotates the birefringence of the second FBG by 90 degrees. Thus, the birefringence of the first and second FBGs cancel each other out, and the cavity formed by the first and second FBGs supports two orthogonal polarizations at the same resonant frequency.

[0027] 4 is a simplified diagram showing how, in one example of the invention, the polarization state of a cavity mode in a nanofiber region can be characterized and controlled by monitoring scattering from the nanofiber region to determine whether the polarization state is linear, circular, or elliptical.

[0028] Information about the polarization state of the cavity modes is extracted from the polarization state of the scattered light in the nanofiber region. This scattering from optical nanofibers refers to the phenomenon where light guided in the nanofiber interacts with the fiber material and structure and is redirected in a different direction instead of being guided along the fiber. In nanofibers, this scattering occurs when the size of impurities and / or defects is much smaller than the wavelength of light, and the polarization state of the scattered light represents the local polarization of the cavity modes. The polarization state of the scattered light can therefore be characterized by a polarimeter, usually consisting of a pair of waveplates and polarizers, to measure the Stokes parameters that fully characterize the polarization state. To create the desired input polarization state that is coupled into the cavity, polarizers, waveplates, and other types of polarization-sensitive optical components are used, and the scattered light is evaluated by the polarimeter.

[0029] Referring to the figures, in one example, the invention also includes a quantum computer and repeater cell system. As shown, the system includes a fiber optic cable region having a first end region and a second end region. The first end region has a first end and the second end region has a second end. In one example, the fiber optic cable region includes a silicon dioxide material with a dopant material entity within a core region. The system includes a first fiber Bragg grating with a plurality of first patterns on the first end region, configured 360 degrees around a periphery of the first end region and extending laterally along a length of the first end region, and a second fiber Bragg grating with a plurality of second patterns on the second end region, configured 360 degrees around a periphery of the second end region and extending laterally along a length of the second end region.

[0030] In one example, the system comprises a central portion of a fiber optic cable having a nanofiber region coupled between a first end region and a second end region. The nanofiber region has a transmittance of 95% or greater. The nanofiber region has a diameter ranging from 300 nanometers to 1.5 micrometers. The length of the nanofiber region is, such as, from 10 micrometers to 10 centimeters. The system comprises a first tapered region comprising a first portion of the nanofiber region in the vicinity of a first fiber Bragg grating and a second tapered region comprising a second portion of the nanofiber region in the vicinity of a second fiber Bragg grating.

[0031] In one example, the system has a cavity including a tapered region and a nanofiber region formed between a first fiber Bragg grating and a second fiber Bragg grating. A plurality of atoms, including alkali metal atoms, alkaline earth metal, alkaline earth-like atoms, or other laser-coolable atoms, are evanescently coupled to the nanofiber region between the first fiber Bragg grating and the second fiber Bragg grating such that the number of atoms ranges from 1 to 100,000. Details of the system and related methods are described in more detail throughout this specification and below.

[0032] 5 is an exemplary diagram illustrating the application of a polarization-degenerate cavity for atom-photon entanglement and non-destructive imaging by polarization rotation in one example of the present invention. The creation of atom-photon entanglement typically involves a process of atom-photon interaction in which the quantum states of the atom and photon become correlated or entangled. In this example, the atom-photon interaction is facilitated by strong coupling of the atomic transition to one or more cavity modes, such that an emitted single photon efficiently couples to the cavity mode and is then extracted from the cavity for atom-photon entanglement distribution.

[0033] A schematic diagram of atom-photon entanglement generation is as follows. First, a single atom is initialized to a well-defined quantum state, typically the ground state or a specific excited state. This can be achieved using laser cooling and optical pumping techniques, and / or other suitable methods. Next, in one example of an entanglement generation protocol, a single atom is coupled to an optical cavity mode and illuminated with a laser to transition from the initial state to the excited state. The excited atom then preferentially emits a single photon into the cavity mode with both orthogonal circular polarizations with right-handed and left-handed rotations. As a result, the internal state of the single atom and the polarization state of the single photon are entangled, and the photon is efficiently extracted from the cavity for subsequent applications, including entanglement-based long-distance communication. This entanglement generation protocol requires a cavity mode that supports right-handed and left-handed circular polarizations at the same resonant frequency, which can be achieved by the present invention described above.

[0034] The second application is the engineering of spin-spin interactions between multiple atoms, generating Faraday interactions. Faraday interactions with double lambda systems refer to the interaction of light with quantum systems that exhibit a particular energy level structure known as the double lambda configuration. This configuration consists of two sets of closely spaced energy levels that resemble the Greek letter "lambda". In double lambda systems, there are typically two ground states, e.g. |g1〉 and |g2〉, and two excited states, |e1〉 and |e2〉, as shown in Figure 5.

[0035] When a magnetic field is applied perpendicular to the direction of light propagation, the energy levels of the double lambda system undergo Zeeman splitting due to the interaction of the magnetic field with the atomic magnetic moments. This splitting results in a difference in the transition frequencies of right- and left-handed circularly polarized light. The Faraday effect occurs when a double lambda system is illuminated with linearly polarized control light in the presence of a magnetic field. The magnetic field induces a phase difference between the two orthogonal components of the linearly polarized light due to their difference in frequency due to Zeeman splitting. This phase difference results in a rotation of the plane of polarization of the transmitted or reflected light.

[0036] By analyzing the rotation of the plane of polarization, information about the magnetic field strength or other relevant properties of the system can be extracted. The Faraday interaction in double-lambda systems is widely used in applications such as magnetic measurements, optical isolators, and quantum information processing.

[0037] Furthermore, the Faraday interaction can be applied to engineer effective spin-spin interactions that provide a tool for the manipulation and control of quantum systems, enabling the implementation of various quantum technologies. The spin-exchange interaction is generated by the exchange of virtual photons between atoms dispersively coupled to the cavity modes. The basis of this construction is the Raman process, where an atom changes its internal state by absorbing a photon from the control field and emitting it into the cavity mode. If the control field is misaligned (detuned) from the Raman resonance, the virtual emission into the cavity triggers a spin "flip-flop" process, where a second atom absorbs a virtual photon in the cavity mode and flips its spin by rescattering a real photon into the mode of the control field.

[0038] In one example, the present invention provides a method for fabricating a polarization degenerate fiber Bragg grating nanofiber cavity for quantum computing or quantum repeaters. The method includes transmitting electromagnetic radiation characterized by a wavelength of 150 nm to 400 nm or more through a pattern of a phase shift mask to diffract the electromagnetic radiation to form an interference pattern. The pattern is illuminated onto a core at a first end of a fiber optic cable region. The first end is opposite a second end, and a nanofiber cavity region is defined between the first end and the second end.

[0039] In one example, the method includes forming a first fiber Bragg grating on a core of the fiber optic cable region by varying the refractive index of the core of the fiber optic cable region using electromagnetic radiation while rotating the fiber optic cable about an axis defined along the length of the fiber optic cable. The first fiber Bragg grating is formed along a longitudinal region perpendicular to a cross section of the fiber optic cable region, 360 degrees around a central axis of the fiber optic cable, the first fiber Bragg grating being comprised of a plurality of azimuthally symmetric patterns of a plurality of refractive index modulations. The method includes forming a second fiber Bragg grating at a second end of the fiber optic cable region, the second fiber Bragg grating being comprised of a plurality of azimuthally symmetric patterns of a plurality of refractive index modulations arranged at an angle of 360 degrees around the core of the fiber optic cable. In one example, the second fiber Bragg grating is formed using similar radiation through a phase shift mask.

[0040] In one example, the nanofiber cavity comprised of the first Bragg grating and the second Bragg grating is characterized by a polarization-degenerate cavity mode that accommodates any polarization state of light without generating one or more distinct resonant frequencies. In one example, the nanofiber cavity is characterized as a polarization-degenerate fiber Bragg grating nanofiber cavity, such that light of any polarization state is not subject to distinct resonant frequencies. In one example, the nanofiber cavity ranges from 100 micrometers to 1 centimeter or more.

[0041] In one example, the first or second fiber Bragg grating characterized by an azimuthally symmetric pattern of refractive index modulation is configured with a modulation period along the fiber axis ranging in size from 200 nm to 1 micron. In one example, the first or second fiber Bragg grating characterized by an azimuthally symmetric pattern of refractive index modulation has a cross-section ranging in size from 1 micron to 10 microns or more. In one example, the first or second fiber Bragg grating has a length ranging from 50 microns to 10 centimeters or more.

[0042] In one example, the electromagnetic radiation is characterized by an exposure time of 10 seconds to 100 minutes. In a preferred example, the exposure time is controlled by monitoring in real time the peak reflectivity of either the first fiber Bragg grating or the second fiber Bragg grating, where the power of the electromagnetic radiation is 10 mW to 1 W and the diameter of the electromagnetic radiation is in the range of 30 microns to 1 mm.

[0043] In one example, the first fiber Bragg grating and the second fiber Bragg grating are spatially positioned on the fiber optic cable with a spatial distance between the first fiber Bragg grating and the second fiber Bragg grating being 100 microns to 10 cm or more. In one example, the first fiber Bragg grating and the second fiber Bragg grating are configured on opposite sides of a tapered region coupled to a nanofiber region. In one example, the first fiber Bragg grating and the second fiber Bragg grating are characterized by a plurality of patterns imprinted into a silicon dioxide material of the fiber optic cable region.

[0044] In one example, the rotation of the fiber along the fiber axis is characterized by a rotation rate that is faster than the inverse of the UV exposure time, causing the formation of an azimuthally symmetric pattern of refractive index modulation such that the transverse anisotropic pattern of refractive index modulation is averaged across the azimuth direction.

[0045] In another example, the invention provides a method for fabricating a polarization-degenerate fiber Bragg grating nanofiber cavity for quantum computing or quantum repeaters. In one example, the method includes providing a fiber optic cable having a first end, a second end, and a nanofiber region between the first end and the second end. The method includes transmitting electromagnetic radiation having a wavelength of 150 nm to 400 nm and greater through a phase shift mask and diffracting the electromagnetic radiation to form an interference pattern onto a core of the first end of the fiber optic cable.

[0046] In one example, the method includes forming a first fiber Bragg grating on a core at a first end of the fiber optic cable region by varying a refractive index of a core of the fiber optic cable region using electromagnetic radiation without rotating the fiber to generate an additional spatial region of the fiber optic cable region such that the first fiber Bragg grating has a plurality of azimuthal anisotropic patterns of a plurality of refractive index modulations around the core of the fiber optic cable region and along a longitudinal region perpendicular to a cross-section of the fiber optic cable region.

[0047] In one example, the method includes rotating the fiber optic cable (or the light source) by 90 degrees or other angle about an axis defined along the length of the fiber optic cable. The method includes forming a second fiber Bragg grating on a core at a second end of the fiber optic cable without rotating the fiber, such that the first fiber Bragg grating and the second fiber Bragg grating are characterized by respective transverse anisotropies of refractive index modulation that are angularly shifted by 90 degrees, and a polarization-degenerate cavity is created due to cancellation of the transverse anisotropies.

[0048] In one example, the nanofiber region comprised of the first and second Bragg gratings form a polarization-degenerate fiber Bragg grating nanofiber cavity such that light of any polarization state does not induce different resonant frequencies. In one example, the nanofiber region is 100 micrometers to 1 centimeter or more. In one example, the nanofiber region is characterized by polarization-degenerate cavity modes adapted to support light of any polarization state without inducing different resonant frequencies or other property differences. In one example, the first fiber Bragg grating is characterized by birefringence and the second fiber Bragg grating is configured at a 90 degree offset angle along the axis such that the birefringence of the first fiber Bragg grating and the second fiber Bragg grating cancel each other out, thereby making one or more cavity modes formed by the first fiber Bragg grating and the second fiber Bragg grating polarization degenerate.

[0049] Although the above is a detailed description of a particular example, various modifications, alternative constructions, and equivalents can be used. In one example, the device can include any combination of the elements described above, as well as elements outside the scope of this specification. Furthermore, the terms "first", "second", "third", and "final" do not imply any order in one or more of the examples. As used herein, the terms "back" and / or "front" do not imply a particular arrangement, but are merely used to refer to other elements within the scope of the claims. Thus, the above description and figures should not be construed as limiting the scope of the present invention, which is defined by the appended claims. [Prior art documents] [Non-patent literature]

[0050] [Non-Patent Document 1] S. Kato and T. Aoki, "Single-frequency fiber Fabry-Perot-Brillouin laser," Opt.Lett47,5000 (2022) [Non-Patent Document 2] Maxime Joos, Alberto Bramati, and Quentin Glorie, "Perfect polarization control of nanofiber waveguides using scattering properties," Opt. Lett. 27, 18818 (2019)

Claims

1. 1. A method for fabricating a polarization-degenerate fiber Bragg grating nanofiber cavity for quantum computing or quantum repeaters, comprising: transmitting electromagnetic radiation characterized by a wavelength of 150 nm to 400 nm or more through a pattern of a phase shift mask to diffract the electromagnetic radiation to form an interference pattern and illuminate a core at a first end of a fiber optic cable region having a first end opposite a second end, the first end defining a nanofiber cavity region between the first end and the second end; forming a first fiber Bragg grating on a core of the fiber optic cable region using the electromagnetic radiation to vary a refractive index of the core of the fiber optic cable region while rotating the fiber optic cable region about an axis defined along a length of the fiber optic cable region, forming the first fiber Bragg grating having a plurality of azimuthally symmetric patterns of a plurality of refractive index modulations around a 360 degree angle around the core of the fiber optic cable region and along a longitudinal region perpendicular to a cross-section of the fiber optic cable region; and forming a second fiber Bragg grating at a second end of the fiber optic cable region, the second fiber Bragg grating being formed to define a plurality of azimuthally symmetric patterns of a plurality of refractive index modulations at an angle of 360 degrees around a core of the fiber optic cable region.

2. 2. The method of claim 1, wherein the nanofiber cavity region comprised of the first Bragg grating and the second Bragg grating is characterized by polarization-degenerate cavity modes that accommodate any polarization state of light without generating one or more distinct resonant frequencies.

3. 10. The method of claim 1, wherein the nanofiber cavity region is characterized as a polarization-degenerate fiber Bragg grating nanofiber cavity in which light of any polarization state does not induce distinct resonant frequencies.

4. 2. The method of claim 1, wherein the first fiber Bragg grating or the second fiber Bragg grating characterized by the azimuthally symmetric pattern of refractive index modulation is configured with a modulation period along the fiber axis spanning dimensions from 200 nm to 1 micron.

5. 2. The method of claim 1, wherein the first fiber Bragg grating or the second fiber Bragg grating characterized by the azimuthally symmetric pattern of refractive index modulation has a cross-section with a dimension from 1 micrometer to 10 micrometers or more.

6. 2. The method of claim 1, wherein the electromagnetic radiation is characterized by an exposure time of 10 seconds to 100 minutes, and the exposure time is controlled by real-time monitoring of the peak reflectivity of either the first fiber Bragg grating or the second fiber Bragg grating for a power of the electromagnetic radiation of 10 mW to 1 W and a diameter of the electromagnetic radiation in the range of 3 micrometers to 1 mm.

7. 2. The method of claim 1, wherein the first fiber Bragg grating and the second fiber Bragg grating are each spatially positioned on the fiber optic cable region, and a spatial distance between the first fiber Bragg grating and the second fiber Bragg grating ranges from 100 micrometers to 10 centimeters or more.

8. The method of claim 1 , wherein the first fiber Bragg grating and the second fiber Bragg grating are configured on opposite sides of a tapered region coupled to a nanofiber region.

9. The method of claim 1 , wherein the first fiber Bragg grating and the second fiber Bragg grating are characterized by a plurality of patterns imprinted into a silicon dioxide material of the fiber optic cable region.

10. 2. The method of claim 1, wherein rotation of the fiber along the fiber axis is characterized by a rotation rate that causes formation of an azimuthally symmetric pattern of the refractive index modulation, the rotation rate being faster than the inverse of a UV exposure time such that the laterally anisotropic pattern of the refractive index modulation is azimuthally averaged.

11. 1. A method for fabricating a polarization-degenerate fiber Bragg grating nanofiber cavity for quantum computing, comprising: providing a fiber optic cable section comprising a first end, a second end, and a nanofiber section between the first end and the second end; transmitting electromagnetic radiation characterized by a wavelength of 150 nm to 400 nm or more through a phase shift mask and diffracting the electromagnetic radiation to form an interference pattern and illuminating a core at a first end of the optical fiber cable region; forming a first fiber Bragg grating on the core at the first end of the fiber optic cable region by varying the refractive index of the core of the fiber optic cable region using electromagnetic radiation without rotating the fiber, creating an additional spatial region of the fiber optic cable region such that the fiber Bragg grating has a plurality of azimuthal anisotropic patterns of refractive index modulations around the core of the fiber optic cable region and along a longitudinal region perpendicular to a cross-section of the fiber optic cable region; rotating the fiber optic cable section through an angle of 90 degrees about an axis defined along a length of the fiber optic cable section; forming a second fiber Bragg grating on a core at a second end of the optical fiber cable region without rotating the fiber, the first fiber Bragg grating and the second fiber Bragg grating each characterized by transverse anisotropy of refractive index modulation that is offset by 90 degrees, causing a polarization degenerate cavity due to cancellation of the transverse anisotropy.

12. 12. The method of claim 11 , wherein the nanofiber region comprised of the first Bragg grating and the second Bragg grating forms a polarization-degenerate fiber Bragg grating nanofiber cavity such that light of any polarization state does not induce different resonant frequencies.

13. 12. The method of claim 11, wherein the nanofiber region is characterized by polarization-degenerate cavity modes adapted to support light of any polarization state without inducing different resonant frequencies or other different properties.

14. 12. The method of claim 11 , wherein the first fiber Bragg grating is characterized by birefringence and the second fiber Bragg grating is configured at a 90 degree offset angle along an axis, and one or more cavity modes formed by the first fiber Bragg grating and the second fiber Bragg grating are configured to be polarization degenerate due to birefringence cancellation of the first fiber Bragg grating and the second fiber Bragg grating.

15. 1. A quantum computer and repeater cell system, comprising: an optical fiber cable region having a first end region and a second end region, the first end region having a first end and the second end region having a second end, the optical fiber cable region including a silicon dioxide material having a dopant material component distributed within a core region; a first fiber Bragg grating configured 360 degrees around the first end region and having a plurality of first patterns extending laterally along a length of the first end region; a second fiber Bragg grating configured 360 degrees around the second end region and having a second plurality of patterns extending laterally along a length of the second end region; a nanofiber region comprised of a central portion of the fiber optic cable and bonded between the first end region and the second end region, the nanofiber region having a transmittance of 95% or greater, a diameter of 300 nanometers to 1.5 micrometers, and a length of 10 micrometers to 10 centimeters; a first tapered region comprising a first portion of the nanofiber region proximate the first fiber Bragg grating; a second tapered region comprising a second portion of the nanofiber region proximate the second fiber Bragg grating; a cavity formed between the first fiber Bragg grating and the second fiber Bragg grating, the cavity including the tapered region and the nanofiber region; a plurality of atoms comprising alkali metal atoms, alkaline earth metal, alkaline earth-like atoms, or other laser-coolable atoms, the number of atoms being greater than or equal to 1 and less than or equal to 100,000, the plurality of atoms being evanescently coupled to the nanofiber region between the first fiber Bragg grating and the second fiber Bragg grating.

16. 16. The system of claim 15, wherein each of the first and second plurality of patterns is characterized by a linewidth having a dimension between 200 nm and 1 micrometer.

17. 16. The system of claim 15, wherein each of the first and second plurality of patterns is characterized by a length between 100 micrometers and 10 centimeters in length.

18. 16. The system of claim 15, wherein each of the first fiber Bragg grating and the second fiber Bragg grating is imprinted with the plurality of patterns on a core of the fiber optic cable region.

19. 16. The system of claim 15, wherein the first fiber Bragg grating and the second fiber Bragg grating form a polarization-degenerate cavity that supports any polarization state of light without inducing different resonant frequencies.

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