A spin qubit system having a quantum dot

Abstract

The present disclosure relates to a spin qubit system comprising a quantum dot unit comprising a planar nanophotonic waveguide comprising a grating coupler, and a nano beam waveguide section for guiding photons and a photonic bandgap waveguide section, the quantum dot unit further comprises a quantum dot configured to interact with the planar photonic bandgap waveguide, and an electrode for applying a DC electric field to the quantum dot. The spin qubit system further comprises a quarter wavelength resonator in a coplanar waveguide configuration comprising an open input end having three input electrodes, and a closed resonator end wherein the three input electrodes are shorted at the closed resonator end by a conducting material.

Description

[0001] A spin qubit system having a quantum dot

[0002] The present disclosure relates to a spin qubit system comprising a quantum dot equipped with a novel microwave resonator setup for controlling the quantum dot to induce transitions in the spin qubit system.

[0003] Background

[0004] The state of the art in qubit devices comprises a plethora of geometries that are used in the pursuit of realising quantum computing platforms. One of such geometries involve the generation of deterministic single-photon sources by utilizing semiconducting quantum dots, embedded in photonic nanostructures with the aim of realizing quantuminformation processing applications. Typically, such applications involve a semiconducting quantum dot formed in a lll-V semiconductor substrate and a nanophotonic waveguide or cavity that is used to collect the single photons emitted from the quantum dot. A laser can provide the energy to excite an unpaired electron in the quantum dot to an excited state, emitting a single photon in the process. The mode of such a photon, can be used as the building block of photonic quantum computers. For example a photon in one optical mode (e.g. propagation direction, polarization, or emission time) can be treated as “0”, while a photon in a different optical mode can be treated as “1”.

[0005] Two standard techniques are performed in such applications, the excitation of the quantum dot to perform transitions, by exciting an electron to a higher energy level, and the use of a laser to control the spin state of the quantum dot, and eventually perform quantum-information processes.

[0006] However, the state of the art involves controlling the spin state of the quantum dot with a laser, a technique which has certain limitations, as it can cause incoherent spin transitions in the quantum dot. In addition, such a method may be a source of noise for the system.

[0007] In order to tackle the above challenges, attempts have been made by researchers to utilize radio-frequency (RF) coils or microwave antennas to manipulate qubit devices. However, such tools have significant drawbacks, such as high parasitic inductance when utilizing RF coils, or field inhomogeneity and high heat-load when using microwave antennas.

[0008] Therefore, the need of a novel approach is required in order to advance the progress of photonic-based spin qubit systems by preventing incoherent spin transitions in the spin qubit system.

[0009] Summary

[0010] One of the objectives of the present disclosure is to provide a more effective way of inducing transitions in a spin qubit system. The present inventors have realized that this can be provided by employing a resonator, preferably a quarter wavelength resonator, in a coplanar waveguide configuration. A resonator may be used to create either an electric field or a magnetic field on the quantum dot system, with the aim of inducing transitions in the quantum dot.

[0011] One embodiment of the present disclosure relates to a spin qubit system comprising a quantum dot unit and a quarter wavelength resonator. The quantum dot unit typically accommodates a planar nanophotonic waveguide that for example comprises: 1) a grating coupler, and preferably also 2) a nano beam waveguide section and optionally a photonic bandgap waveguide. The quantum dot unit may further comprise a quantum dot configured to interact with the planar nanophotonic waveguide, and preferably an electrode for applying a DC electric field to the quantum dot.

[0012] In an embodiment, the resonator (preferably a quarter wavelength resonator, for example in a coplanar waveguide configuration) comprises an open input end having three input electrodes, and a closed resonator end. The resonator may be configured to generate an electric field, with the purpose controlling the quantum dot to induce transitions in the spin qubit system. Specifically, when the resonator is tuned at resonance frequency, the open input end of the resonator acts as an antinode for electric field. Therefore, a spin qubit system can be positioned at the open end of the resonator, allowing the electric field to control the quantum dot and induce transitions in the spin qubit system.

[0013] Moreover, when the resonator is tuned at resonance frequency, the closed resonator end acts as an antinode for magnetic field. Specifically, two of the three input electrodes may form a parallel slit extending along at least part of the planar nanophotonic waveguide. The quarter wavelength resonator may advantageously be configured to generate a magnetic field in the slit for controlling the quantum dot to induce transitions in the spin qubit system. This can for example be provided if the third input electrode is separated from the slit.

[0014] An advantage of the presently disclosed approach is that it is possible to tune the state of the quantum dot by maintaining as low noise in the environment as possible. State of the art methods involve shining a laser on a quantum dot in order to induce spin rotations, but such an approach can cause problems such as incoherent spin-flips. Therefore, the presently disclosed approach allows an alternative way of inducing quantum dot spin transitions. For instance, considering a quantum dot with one unpaired electron; the ground state of the quantum dot would be a doublet state, as the electron can be either spin-up or spin-down. When no external magnetic field is applied, the two states are degenerate, being at the same energy. Applying an external magnetic field, the spin qubit system lifts the degeneracy, and the two states have an energy difference equal to the Zeeman energy. As a result, by applying a radiofrequency current on the coplanar waveguide resonator, it is possible to form a localized radio-frequency magnetic field perpendicular to an external static magnetic field, in the vicinity of the quantum dot that can be positioned above the parallel slit, and induce transitions from the spin-up state to the spin-down state and vice versa, effectively controlling the quantum dot system. This is a major achievement.

[0015] In an embodiment, the frequency of the microwave magnetic field generated by the quarter wavelength resonator can be tuned, such that said frequency matches with the frequency corresponding to the energy difference of the Zeeman splitting. Further if the quarter wavelength resonator is designed to have a resonance frequency near the Zeeman splitting energy, this would maximize the effectiveness of the magnetic field on the quantum dot and produce a low heat load compared to state of the art solutions involving resonators, an important requirement for spin qubit experiments that are typically held at cryogenic temperatures. In an embodiment, the localized radiofrequency magnetic field is perpendicular to the static magnetic field. When the frequency of microwave magnetic field transmitted by the quarter wavelength resonator matches the frequency corresponding to the energy difference of the Zeeman splitting of the quantum dot, it is possible to execute Sxand Sygates, which can be used to implement a TT / 2 or TT gate. If the two aforementioned frequencies do not match, that would also lead to a Szgate, changing the phase of the spin qubit system, an outcome which is not desired. Further details regarding the magnetic field are disclosed in the next sections of the detailed description.

[0016] Advantageously, the spin qubit system can be configured such that the first, second and third input electrodes of the quarter wavelength resonator are shorted at one end by a conducting material. Having the three electrodes shorted while the other end of the resonator is open can be beneficial, as it can maximize the inductive coupling of the resonator, a feature which can be important for maximizing the localized magnetic field created by the coplanar waveguide resonator. Moreover, as described above, the open end of the resonator can be utilized to generate an electric field, said electric field can be used to induce transitions in the spin qubit system.

[0017] In an embodiment, the spin qubit system can be further configured such that the quarter wavelength resonator generates magnetic fields perpendicular to the plane of the quarter wavelength resonator of at least 30 mT.

[0018] The present disclosure further relates to a method for operating a spin qubit system having a quantum dot, in particular the presently disclosed spin qubit system. The preferred embodiment of the method comprises the steps of: applying an external static magnetic field to Zeeman-split the degenerate levels of the ground state of an unpaired electron in the quantum dot; applying a microwave electrical signal on the quarter wavelength resonator to drive transitions in the quantum dot; and irradiating with a laser the planar nanophotonic waveguide to excite the quantum dot and generate a photon.

[0019] The present disclosure in a further aspect relates to a quarter wavelength resonator in itself, for example the quarter wavelength resonator disclosed herein. In the preferred embodiment the quarter wavelength resonator in a coplanar waveguide configuration comprises an open input end having three input electrodes, and a closed resonator end wherein two of the three input electrodes form a parallel slit, preferably of a width between 50-300 nm. The slit may extend along at least part of the planar nanophotonic waveguide. The third input electrode is preferably separated from the slit, for example by at least 10 m, such that the quarter wavelength resonator is configured to generate a magnetic field in the vicinity of the slit, for example for controlling a quantum dot to induce transitions in a surrounding spin qubit system. Further features of the quarter wavelength resonator can be found in the description below.

[0020] Description of the drawings

[0021] Various embodiments are described hereinafter with reference to the drawings. The drawings are examples of embodiments and are intended to illustrate some of the features of the presently disclosed spin qubit system, and are not limiting to the presently disclosed system and method.

[0022] Fig. 1 shows a schematic view of a planar nanophotonic waveguide.

[0023] Fig. 2 shows a schematic view of a quarter wavelength resonator.

[0024] Fig. 3 shows an optical image of the closed end of a quarter wavelength resonator.

[0025] Fig. 4 shows a schematic of the open end of a quarter wavelength resonator.

[0026] Fig. 5A, B shows a simulation of the generated magnetic field caused by the quarter wavelength resonator.

[0027] Fig. 6 shows a schematic cross section of a substrate with a quarter wavelength resonator and a quantum dot.

[0028] Fig. 7 shows the steps of a method for realizing a spin qubit system.

[0029] Fig. 8 shows a design example of a spin qubit system.

[0030] Fig. 9 shows a simulation of the generated electric field at the open end of a quarter wavelength resonator.

[0031] Fig. 10 shows a spin qubit system positioned on the open end of a quarter wavelength resonator.

[0032] Detailed description

[0033] As presented above, the present disclosure relates to a spin qubit system comprising a quantum dot unit comprising a) a planar nanophotonic waveguide. In the preferred embodiment the planar nanophotonic waveguide is comprising i) a grating coupler, ii) and a nano beam waveguide section and a photonic bandgap waveguide section. The quantum dot unit preferably further comprises b) a quantum dot configured to interact with the planar nanophotonic waveguide, and c) an electrode configured for applying a DC electric field to the quantum dot. The spin qubit system may also comprise a quarter wavelength resonator in a coplanar waveguide configuration comprising an open input end having three input electrodes, and a closed resonator end. Two of the three input electrodes may advantageously form a parallel slit extending along at least part of the planar nanophotonic waveguide. The third input electrode may be separated from the slit, such that the quarter wavelength resonator can be configured to generate a magnetic field in the slit, for example for controlling the quantum dot to induce transitions in the spin qubit system.

[0034] As used herein the nano beam waveguide in general can be seen as a sub-micron- sized optical waveguide that confines, guides and directs light at nanoscale. For example the nano beam waveguide can have a thickness and / or a width in the range

[0035] 100 nm to 250 nm.The small width and thickness of the waveguide allows for strong light-matter interactions and efficient integration with other nanophotonic devices. Hence, the presently disclosed nano beam waveguide has the function of efficiently coupling the grating coupler with the photonic bandgap waveguide.

[0036] The spin qubit system can be any two-level system hosting a spin state that can be manipulated between the two levels, using an external probe such as a microwave magnetic or electric field to tune the spin qubit. Preferably, the spin qubit system can be configured such that the quantum dot is a lll-V semiconductor quantum dot, such as GaAs, InAs, GaSb, InSb, InP or lll-V semiconductor alloys embedded in a wider bandgap material. Such materials can be used for spin qubits and as single photon emitters given their small electronic band gap. An example of semiconductor alloys that that can host a quantum dot can be a stack comprising an n-doped GaAs layer, followed by a GaAs layer, followed by a layer of AlAs, followed by a GaAs layer, followed by an AIGaAs layer, followed by a p-doped GaAs layer. In this example, the quantum dot can be hosted in the AlAs layer, and a bias voltage can be applied between the p-doped GaAs and the n-doped GaAs layers.

[0037] The quantum dot unit comprises several elements that enable the interaction of light with matter, by guiding a light source towards the quantum dot via the use of a planar nanophotonic waveguide. An embodiment of a planar nanophotonic waveguide can be seen in Fig. 1. The use of the planar nanophotonic waveguide 100 allows a user to guide a light source such as a laser, through the input section of the grating coupler

[0038] 101 towards a nano beam waveguide section 102, and by filtering the light source in the photonic bandgap waveguide section 103 the light source can finally interact with a quantum dot that can be placed in close proximity to the photonic bandgap waveguide section. An alternative option is to excite the quantum dot with a laser beam applied vertically in order to couple directly to the quantum dot through weakly coupled radiation modes as opposed to through the waveguide.

[0039] The light source can act as an excitation on the quantum dot, creating deterministic single photons when interacting with the quantum dot. In one embodiment, the microwave source can potentially be utilized to perform dispersive read-out of the state of the quantum dot. The quantum dot can comprise unpaired electrons that can be manipulated by the spin qubit system, or alternatively it can comprise unpaired holes.

[0040] In order to tune the number of electrons or holes of the quantum dot, it can be advantageous to have an electrode, also known as a gate, which can apply a DC electric field, shifting the Fermi energy in the quantum dot. That process can effectively add or remove electrons or holes from the quantum dot. Such an electrode can be important, as it allows a user to control the number of electrons on the quantum dot, effectively changing the ground state of it. When a quantum dot has even number of electrons, then the ground state is a singlet state, while when a quantum dot has odd number of electrons, then the ground state is a doublet state. Therefore, having the capability of controlling the number of electrons in the quantum dot can add further functionality and capabilities on the spin qubit system.

[0041] Moreover, the spin qubit system can be configured, such that the grating coupler comprises a single grating section that can act as an input and / or output section. That geometry can be advantageous on one-side waveguides that comprise a single grating. In an embodiment, the spin qubit system can be configured, such that the grating coupler comprises a plurality of sections that can act as input or output sections. The number of gratings in the planar nanophotonic waveguide can be adjusted depending on the needs of each experiment, having different gratings to be used as input sections and other gratings to be used as output sections.

[0042] Moreover, the spin qubit system can be further configured such that the photonic bandgap waveguide section optionally comprises an array of periodic holes displayed in a periodic structure. The array of periodic holes in the photonic bandgap waveguide can be beneficial as they can allow certain electromagnetic modes to propagate through the waveguide, while they can prevent others from propagating. In an embodiment, it is possible to tune the array of periodic holes of the photonic bandgap waveguide in order to modify the photonic bandgap of the planar nanophotonic waveguide. Hence, modifying the bandgap of the planar nanophotonic waveguide can be a useful tool, as that can determine the wavelength of light that the waveguide can support. Depending on the type of experiment, different type of periodic holes can be designed. For example, depending on the energy difference between two states of the quantum dot, a specific laser frequency can be used to excite an electron in the quantum dot and emit a single photon. Therefore, it can be beneficial to tune the bandgap of the planar nanophotonic waveguide depending on the specifications of the quantum dot.

[0043] In addition, the spin qubit system can be further configured such that the nano beam waveguide is a rectangular cross-section slab configured to guide the photons generated by the quantum dot to a second structure. An embodiment of a nano beam waveguide can be seen in Fig. 1 (102), comprising two parallel wires interrupted by a thin slit. The nano beam waveguide can have thickness and / or width in the range 10 nm to 1000 nm, preferably 100 nm to 250 nm.

[0044] Furthermore, the spin qubit system can be further configured such that the photonic bandgap waveguide section is a photonic crystal waveguide. As described above, the photonic bandgap waveguide may comprise an array of periodic holes, which can act as a periodic modulation of the refractive index of the material. That can lead to a Bragg scattering of light, resulting in a photonic bandgap, effectively preventing light from propagating through the photonic crystal. It is possible to remove a section of the holes, creating a path for the light to propagate. Therefore, a photonic crystal can be used to assist the quantum dot unit into guiding coherent single photons through the planar nanophotonic waveguide. In another embodiment, the photonic crystal waveguide can be employed as a backward reflector for single photons to maximize the coupling efficiency of single photons of the quantum dot unit. Additionally, the quantum dot can be positioned on the photonic crystal waveguide, allowing a laser excitation to be guided to the quantum dot. In an embodiment, the periodic membrane structure of the photonic crystal waveguide can be a one-dimensional photonic crystal comprising an array of circular air holes with a radius of 70 nm to 100 nm and a hole- to-hole spacing of 210 nm to 250 nm.

[0045] Moreover, the spin qubit system can be further configured such that the electrode configured for applying a DC electric field to the quantum dot can control the number of electrons or holes in the quantum dot. In one embodiment, a dielectric layer can be deposited on the quantum dot followed by a deposition of a metallic electrode. The metallic electrode can be positioned on top of the quantum dot, as a top-gate configuration, or in close proximity to the quantum dot, as a side-gate configuration. By close proximity we refer to distances between 50-300 nm. The dielectric layer and the electrode can be fabricated by means of electron beam lithography or ultraviolet lithography processes. By having a dielectric layer between the electrode and the quantum dot, it is possible to apply a voltage to the electrode without having any current flow through the quantum dot. Therefore, an electric field can be induced, which can tune the Fermi energy of the quantum dot, effectively adding or removing electrons from the quantum dot. Depending on the type of the quantum dot and its doping, the quantum dot charge carriers can be holes instead of electrons. In that case, holes can be added or removed from the quantum dot by inducing an electric field from the electrode.

[0046] Quarter wavelength resonator

[0047] As used herein the quarter wavelength resonator can in general be seen as a transmission line having a coupling capacitor at one end while the other end is shorted to ground. These boundary conditions lead to a standing wave of a quarter of the wavelength A, with a current node and a voltage anti-node on the side of the capacitor, and a current anti-node and a voltage node on the end shorted to ground. As described in the summary section above, these properties of the quarter wavelength resonator can be used to generate an electric field at the open end (capacitor) of the resonator, and / or to generate a magnetic field at the closed end of the resonator (shorted end). The harmonics of the quarter wavelength resonator are (2n+1)A / 4.

[0048] The quarter wavelength resonator can be utilized to interact with the quantum dot of the spin qubit system. Specifically, the quarter wavelength resonator can be configured in a coplanar waveguide configuration, such that the quarter wavelength resonator comprises three electrodes. A quarter wavelength resonator has an open input end, where one of the electrodes is capacitively connected to a power source. An embodiment of a quarter wavelength resonator can be seen in Fig 2. The three electrodes 200, 201 , 202 are separated by insulating gaps 203. The insulating gaps can be for example air or any insulating material. An example of the open input end can be visualized 204. More information about the open input of the quarter wavelength resonator are disclosed in the following parts of the detailed description. The second end of the quarter wavelength resonator is closed 205, for example by having the three electrodes shorted. An embodiment of the closed end of a quarter wavelength resonator can be seen in Fig 3, wherein the first and second electrodes 300, 301 are forming a thin slit, and the third electrode 302 is positioned further away from the other two. The benefit of having such a resonator is that the inductive coupling is maximized. Such a feature can be useful, as when a power source is connected to the second electrode of the resonator, magnetic fields are formed which are maximized between the gaps of the resonator electrodes. As a result, increasing the inductive coupling can increase the resulting magnetic field caused by the quarter wavelength resonator. By separating an electrode from the two other electrodes, the magnetic field between the other two electrodes can be maximized, which can be the area of interest as the quantum dot can be positioned on the slit. As a result, the created localized magnetic field can interact with the quantum dot and induce transitions in the spin qubit system, or possibly be used to read-out the state of the quantum dot.

[0049] Importantly, the presently disclosed quarter wavelength resonator has the advantage of being versatile, as the quarter wavelength resonator can be used to either induce transitions in a spin qubit system by using a magnetic field or by using an electric field.

[0050] For example, a spin qubit system may be positioned at the open resonator end 204, and as the open resonator end may act as an antinode for electric field, it is possible to use the electric field to control the quantum dot, thereby inducing transitions in the spin qubit system.

[0051] Alternatively, a spin qubit system may be positioned at the closed resonator end 205. At the closed resonator end the three input electrodes are shorted, forming a antinode for magnetic field. Therefore, it is possible to use the magnetic field to control the quantum dot, thereby inducing transitions in the spin qubit system. In an embodiment, the spin qubit system can be configured, such that the widths of the three input electrodes are progressively becoming thinner towards the closed end of the quarter wavelength resonator. For example, the widths of the three input electrodes at the closed end of the quarter wavelength resonator can be less than 10 pm, more preferably less than 5 pm, most preferably less than 1.5 pm, such as approximately 1 pm. The purpose of thinner input electrodes is that the current density increases locally, therefore increasing the generated localized magnetic field. For example, an embodiment of the three input electrodes at the closed end of a quarter wavelength resonator can be seen in Fig. 3, where the three input electrodes 300, 301 , 302 have a width of 1.2 pm.

[0052] Geometry of the spin qubit system

[0053] The spin qubit system can be configured such that the slit width is preferably less than 300 nm, more preferably less than 200 nm, even more preferably less than 100 nm, most preferably around 50 nm. In addition, the spin qubit system can be further configured such that the separation width of the third input electrode to the slit is preferably larger than 10 pm, more preferably larger than 20 pm, even more preferably larger than 25 pm, most preferably around 30 pm. It can be beneficial for the spin qubit system to have a small width of the slit, as that can enhance the generated magnetic field in the slit. At the same time, by keeping the third electrode at a distance from the slit increases the magnitude of the magnetic field in the slit. An embodiment of the closed end of the quarter wavelength resonator can be seen in Fig. 3. In this example, the three electrodes are parallel and are shorted by a conducting wire perpendicular to the three electrodes.

[0054] Moreover, the spin qubit system can be further configured such that the parallel slit is positioned below at least part of the planar nanophotonic waveguide. Typically, fabricating the spin qubit system can involve first designing and producing the quarter wavelength resonator, followed by the deposition of the quantum dot unit that comprises the quantum dot and the planar nanophotonic waveguide. It is important for the system to have the quantum dot positioned on the planar nanophotonic waveguide, preferably in the photonic bandgap waveguide section. In order to maximize the applied magnetic field on the quantum dot, it is beneficial to position the parallel slit below the planar nanophotonic waveguide, preferably below the photonic bandgap waveguide section that the quantum dot is also positioned. It is also possible to position the parallel slit below other parts of the planar nanophotonic waveguide, depending on the needs of each experiment.

[0055] Moreover, the spin qubit system can be further configured such that an input section of the grating coupler is positioned at one end of the planar nanophotonic waveguide, and wherein an output section of the grating coupler is positioned at the other end of the nanophotonic waveguide. Depending on the experiment where the spin qubit system is used, a light excitation can be applied to the planar nanophotonic waveguide from any direction, therefore the input section and the output section of the grating coupler can be interchangeable.

[0056] The spin qubit can be configured such that the first, second and third input electrodes of the quarter wavelength resonator are shorted at one end by a conducting material. In an embodiment, the conducting material can be a conducting wire that is perpendicular to at least a part of the three electrodes of the quarter wavelength resonator. As described in the sections above, it can be beneficial for the spin qubit system to comprise a resonator in a quarter wavelength setup. A quarter wavelength resonator consists of a transmission line having a coupling capacitor at one end while the other end is shorted to the ground. These boundary conditions lead to a standing wave of a quarter of the wavelength, with a current node and a voltage anti-node on the side of the capacitor, and a current anti-node and a voltage node on the end shorted to ground. Therefore, it is possible to short the three input electrodes on one end of the resonator to achieve the quarter wavelength requirements. Additionally, the spin qubit system can be configured such that the first and the third input electrodes are grounded. Moreover, the first and the third input electrodes can be shorted with the second electrode on the one end of the quarter wavelength resonator. In that configuration, a signal can be fed on the second input electrode, which acts as the current source that can generate the localized magnetic field. For example, an embodiment showing the closed end of a quarter wavelength resonator where the three input electrodes 300, 301 , 302 are shorted is shown in Fig. 3. In this example, a conducting material in a line-shape 303 is used to short the three input electrodes.

[0057] Furthermore, the spin qubit system can be further configured such that the second input electrode of the quarter wavelength resonator comprises gaps at the open input, forming a capacitive structure in the input second electrode. That feature can be beneficial, in order to create a current node and a voltage anti-node on the open end of the resonator, by creating the boundary conditions that can lead to a standing wave of a quarter of the wavelength. An embodiment of the open end of a quarter wavelength resonator can be seen in Fig. 4, wherein the second input electrode 400 forms a capacitive structure. Advantageously, the open end of the quarter wavelength resonator may be utilized to generate an electric field for controlling the quantum dot to induce transitions in the spin qubit system.

[0058] In an embodiment, the spin qubit system can be configured, such that the second input electrode of the quarter wavelength resonator comprises gaps at the open input end, forming a capacitive structure in the second input electrode, thereby configured to generate an electric field for controlling the quantum dot to induce transitions in the spin qubit system. The spin qubit system can be configured, such that a plurality of finger capacitors are utilized to form the gaps at the open input end of the quarter wavelength resonator.

[0059] For example, as seen in Fig. 9, at resonance frequency, the open end of the quarter wavelength resonator 900 acts as an antinode for electric field, generating average Exyelectric fields along the lines in the order of approximately 1 mV / nm, by utilizing the plurality of finger capacitors 901. Such an electric field can be utilized to induce transitions in the spin qubit system.

[0060] Larger electric fields may be also be generated, by tuning the characteristics of the open end of the quarter wavelength resonator, such as the number of the finger capacitors or the width and length of the finger capacitors. The aforementioned geometry is beneficial, as the quantum dot can be positioned at the minima of local ohmic density, leading to a significant decrease of the heat load for the system. An example of the geometry where a quantum dot 1000 is positioned on the open end of the quarter wavelength resonator is shown in Fig. 10.

[0061] In an embodiment, the number of finger capacitors may be larger than 5, more preferably larger than 10, even more preferably larger than 15, most preferably larger than 20. Depending on the type of application, different designs with custom number of finger capacitors can be designed. For example, using a larger number of finger capacitors may be used to incorporate more than one spin qubit system in the same resonator configuration.

[0062] Moreover, the length of the finger capacitors, the width of the finger capacitors and the spacing between adjacent finger capacitors may also be customized. As the generated electric field is dependent on the capacitance between the finger capacitors, tuning the length of the finger capacitors, the width of the finger capacitors and spacing between finger capacitors may influence the generated electric field. In an embodiment, the length of at least one finger capacitor is preferably larger than 1 pm, more preferably larger than 10 pm, even more preferably larger than 25 pm, most preferably larger than 50 pm. For example, the length of at least one finger capacitor may be around 100 pm. An embodiment of a finger capacitor 401 having a length of 100 pm can be seen in figure 4. As a reference, a scale bar is provided 402 having a length of 6 pm.

[0063] The width of at least one finger capacitor is preferably less than 10 pm, more preferably less than 7.5 pm, even more preferably less than 5 pm, most preferably less than 3.5 pm, for example 1.7 pm. A finger capacitor 401 shown in figure 4 has a width of 1.7 pm.

[0064] The spacing between adjacent finger capacitors is preferably less than 15 pm, more preferably less than 10 pm, even more preferably less than 7.5 pm, most preferably less than 5.5 pm, such as 3.5 pm. As shown in figure 4, the spacing 403 between adjacent finger capacitors is 3.3 pm.

[0065] The finger capacitors may also be designed to have varying length, width and / or spacing. Furthermore, the finger capacitors on the same open end of a resonator may also be designed to have varying dimensions, such as length, width and / or spacing between finger capacitors.

[0066] Properties of the spin qubit system

[0067] The spin qubit system can be configured such that the input section of the grating coupler is configured to couple incoming light from a laser into the planar nanophotonic waveguide. For example, the input section of the grating coupler may comprise a first- order or second-order Bragg grating with respect to the signal wavelength of the incoming laser. As seen in Fig. 1, the input grating coupler 101 may comprise a series of individual grooves, wherein the grooves are adapted to provide efficient coupling of the incoming light from the laser to the planar nanophotonic waveguide.

[0068] Additionally, the spin qubit system can be configured such that the output section of the grating coupler is configured to transmit out of the nanophotonic waveguide part of the light from the laser to the exterior of the nanophotonic waveguide and to reflect a part of the light from the laser into the planar nanophotonic waveguide. For example, the output section of the grating coupler can be positioned after the quantum dot, and it can improve the efficiency with which single photons generated by the quantum dot are coupled out of the planar nanophotonic waveguide, for instance to an optical fiber or another waveguide. The spin qubit system can be further configured such that the quantum dot is configured to emit single photons. As described in the sections above, a light excitation can be guided through the planar nanophotonic waveguide, inducing a transition in the quantum dot. Such a transition which can for example be an electron being moving to an excited state, can emit single photons.

[0069] The spin qubit system can be configured such that the quarter wavelength resonator generates magnetic fields perpendicular to the plane of the quarter wavelength resonator of at least 30 mT. An illustration showing a simulation of the generated magnetic field near the slit of the quarter wavelength resonator is shown in Fig. 5A. The color bar represents the magnitude of the magnetic field in units of Tesla. Fig. 5B shows a zoomed-in region of simulated magnetic field in the area of interest, where the slit is positioned between the two input electrodes of the quarter wavelength resonator. In an embodiment, point B 501 is positioned in the slit, where a simulated magnetic field of approximately 30 mT is recorded. In the embodiments shown in Fig. 5A, B, the resonance frequency of the resonator is 20.6 GHz, and the input power 0.02 W. As the quarter wavelength resonator has a coplanar waveguide configuration, the input current that is provided on the second electrode can generate a magnetic field, which can be perpendicular to the plane of the quarter wavelength resonator. That magnetic field can be utilized to control or potentially read out the state of the quantum dot.

[0070] Additionally, the spin qubit system can be further configured such that said magnetic fields are localized in the parallel slit of the quarter wavelength resonator. For example, by maintaining the slit width to a minimum, it is possible to maximize the magnetic field inside the slit, by maximizing the current in the area surrounding the slit. As a result, the magnetic field can be localized in the slit, and by positioning a quantum dot on the slit, it is possible to take advantage of the enhanced magnetic field in order to manipulate the quantum dot.

[0071] The spin qubit system can be further configured such that the quarter wavelength resonator is used for coherent spin-flip operations of the state of the quantum dot. For example, as described above, it is possible to use the quarter wavelength resonator to induce transitions in the quantum dot system. This for instance can be done, by also including an external magnetic field that splits the degenerate doublet states of an unpaired electron in the quantum dot.

[0072] Furthermore, the spin qubit system can be configured such that the second input electrode of the quarter wavelength resonator is arranged in a zig-zag pattern that produces half-circles with radius of at least 25 pm. This zig-zag pattern can relate on the section of the quarter wavelength resonator between the open end and the closed end. In that section, the geometrical parameters such as thickness of electrodes, length / width of electrodes play a role in the properties of the resonator, such as its inductance and capacitance , as those parameters can affect the resonance frequency and quality factor of the resonator. As a result, certain zig-zag patterns can be designed in order to manipulate the parameters of the quarter wavelength resonator depending on the application that it is used.

[0073] Quarter wavelength resonator parameters

[0074] In another embodiment, the spin qubit system can be configured such that the bandwidth of the quarter wavelength resonator is between 10 MHz to 200 MHz. Bandwidth refers to the range of frequencies over which the quarter wavelength resonator can resonate or respond to external signals. The bandwidth is referenced around the resonance frequency of the resonator. Changing the bandwidth of the quarter wavelength resonator would require to modify the shape or size of the resonator. It can be beneficial to have a large bandwidth as that allows the application of different frequency signals that can be transmitted through the resonator to the quantum dot unit.

[0075] The spin qubit system can be further configured such that the resonance frequency of the quarter wavelength resonator is between 10 GHz to 20 GHz. The resonance frequency can be an important feature of the quarter wavelength resonator, as it dictates the frequency on which the resonator responds more potently to external signals. The resonance frequency is affected by the resonator’s properties as described above, and it can be calculated by the following formula fres= — 2Tt jLC where L is the inductance of the resonator, and C is the capacitance of the resonator. As described in the sections above, one end of the quarter wavelength resonator is open. That open end, as it can be seen in an embodiment in Fig. 4, can comprise several finger capacitors. The larger the number of finger capacitors 401, the stronger the coupling capacitance becomes, resulting in a reduced resonance frequency and an increased bandwidth of the resonator. As a result, different designs of finger capacitors can be utilized in order to tune the bandwidth of the magnetic field interacting with the quantum dot.

[0076] As described earlier in the summary of the invention, the resonance frequency of the quarter wavelength resonator can be tuned, such that the said frequency matches the frequency of the Zeeman splitting, maximizing the effectiveness of the magnetic field on the quantum dot.

[0077] The spin qubit system can be further configured such that the Q factor of the quarter wavelength resonator is at least 100. The Q factor describes the efficiency and selectivity of a resonator in response to a certain frequency. The Q factor can be defined as the ratio between the resonance frequency of the resonator, divided by its bandwidth. A larger Q factor is linked to a small bandwidth. It is possible to tune the Q factor of a quarter wavelength resonator depending on the needs of each experiment, by fabricating resonators with different inductance and / or capacitance values.

[0078] Moreover, the spin qubit system can be configured such that the input power of the quarter wavelength resonator is 0.02 W. Having such low input powers can be an important advantage of the present disclosure over state of the art solutions, as the present quarter wavelength resonator can produce strong enough magnetic fields, while maintaining the heat load on the chip to a minimum. A low input power is linked to lower heat generated by the resonator. As most of spin qubit experiments are conducted at cryogenic temperatures below 1 Kelvin, it can be important to minimize any heat sources, as they can disturb the temperature of the experiment. Additionally, having a low heat load allows the scalability of the present disclosure to implement a plurality of spin qubit systems.

[0079] Fabrication process of the spin qubit system

[0080] The spin qubit system can be further configured such that the quarter wavelength resonator is made of Cu, Al, Ag, Au, Mo, alloy, compound or any other conducting material. The choice of material that the quarter wavelength resonator is fabricated from can be important, as it can affect the resonance frequency of the resonator, as well as its resistance.

[0081] In addition, the spin qubit system can be configured such that the quantum dot structure is elevated preferably by 0.5 pm, more preferably 0.75 pm above the plane of the quarter wavelength resonator. The quarter wavelength resonator can be at a different height compared to the quantum dot in order to minimize any possible heat transfer from the resonator to the quantum dot. Increasing the temperature of the quantum dot may result to higher noise in the system and it might affect negatively the process of single photon emission.

[0082] The spin qubit system can be configured such that the spin qubit system is fabricated on a sapphire, intrinsic silicon, quartz, alumina, SiN, PTFE or any other substrate with low microwave losses. By low microwave losses we refer to loss tangent values of less than 0.001. The material that the substrate is made of can be important, as the resonance frequency and the Q factor of the quarter wavelength resonator can be affected by the physical properties of the substrate. Additionally, the choice of material can affect the microwave losses of the system, therefore it can be important to choose the correct type of material.

[0083] The fabrication process of the spin qubit system comprises a number of steps. Starting from a substrate, standard lithography processes are used. A layer of resist can be spin-coated on the substrate, which can be exposed using an electron beam lithography or ultraviolet lithography system. The substrate can subsequently be submerged in a developer chemical, which can dissolve the exposed resist and create a cast with the desired design. An electron beam evaporation system can be then utilized to deposit metal on the substrate. A final step of removing the excess resist layer is performed, by submerging the substrate in a chemical that can fully dissolve the resist layer. After removing the excess resist layer, the final design of the quarter wavelength resonator has been shaped on the substrate. A layer of epoxy can be spin- coated in order to create an insulating layer above the resonator, protecting the quantum dot that can be deposited on top from leakage from the resonator. Figure 6 shows a cross section schematic example of a substrate 600 with a quarter wavelength resonator 601, an epoxy layer 602 and a quantum dot 603 positioned in the slit between two of the three electrodes of the quarter wavelength resonator.

[0084] The present disclosure further relates to a method for operating a spin qubit system, comprising the steps of: a) providing: a quantum dot unit comprising: 1) a planar nanophotonic waveguide comprising; i) a grating, and ii) a nano beam waveguide section and a photonic bandgap waveguide section , 2) a quantum dot configured to interact with the planar nanophotonic waveguide, and 3) an electrode for applying a DC electric field to the quantum dot. The method further provides: a quarter wavelength resonator in a coplanar waveguide configuration comprising: an open input end having three input electrodes, and a closed resonator end wherein two of the three input electrodes form a parallel slit extending along at least part of the planar nanophotonic waveguide, and wherein the third input electrode is separated from the slit, such that the quarter wavelength resonator is configured to generate a magnetic field in the slit for controlling the quantum dot to induce transitions in the spin qubit system. The following steps of the method are: b) applying a static external magnetic field to Zeeman-split the degenerate levels of the ground state of an unpaired electron in the quantum dot; c) applying an electrical signal on the quarter wavelength resonator to drive transitions in the quantum dot; and d) irradiating with a laser the planar nanophotonic waveguide to excite the quantum dot and generate a photon. A figure illustrating the steps of the above method is shown in Fig. 7.

[0085] The present disclosure further relates to a quarter wavelength resonator in a coplanar waveguide configuration comprising an open input end having three input electrodes, and a closed resonator end wherein two of the three input electrodes form a parallel slit of a width between 50-300 nm, the slit extending along at least part of the planar nanophotonic waveguide and wherein the third input electrode is separated from the slit by at least 10 pm, such that the quarter wavelength resonator is configured to generate a magnetic field in the slit for controlling the quantum dot to induce transitions in the spin qubit system. Moreover, the present disclosure relates to a quarter wavelength resonator in a coplanar waveguide configuration comprising an open input end having three input electrodes, and a closed resonator end wherein the three input electrodes are shorted, wherein the open input end is configured to generate an electric field for controlling the quantum dot to induce transitions in the spin qubit system. The open input end may utilize a plurality of finger capacitors in order to generate an electric field.

[0086] The quarter wavelength resonator may be configured according to any one of the embodiments of the present disclosure.

[0087] Examples

[0088] Fig. 8 shows an example of a design where a quantum dot 800 is positioned on the closed end of a quarter wavelength resonator, above the slit 803 between the first electrode 801 and the second electrode 802. The quantum dot is also aligned accordingly, in order to be positioned in the photonic bandgap waveguide section 804 of the planar nanophotonic waveguide. In this example, an input current would be fed on the second electrode 802, generating a localized magnetic field in the slit 803 between the first and the second electrodes 801, 802. The localized magnetic field can induce transitions in the quantum dot 800, where the quantum dot 800 can emit a single photon in the process. That photon can be guided through the planar nanophotonic waveguide.

[0089] Items

[0090] 1. A spin qubit system comprising a quantum dot unit, the quantum dot unit comprising a planar nanophotonic waveguide comprising o a grating coupler, o a nano beam waveguide section for guiding photons and a photonic bandgap waveguide section, a quantum dot configured to interact with the planar nanophotonic waveguide, an electrode for applying a DC electric field to the quantum dot, a quarter wavelength resonator in a coplanar waveguide configuration comprising o an open input end having three input electrodes, and o a closed resonator end, wherein the three input electrodes are shorted at the closed resonator end by a conducting material.

[0091] 2. The spin qubit system according to item 1, wherein the quantum dot is a lll-V semiconductor quantum dot, such as GaAs, InAs, GaSb, InSb, InP or lll-V semiconductor alloys embedded in a wider bandgap material.

[0092] 3. The spin qubit system according to any one of the preceding items, wherein the grating coupler comprises a single grating section that can act as an input and / or output section.

[0093] 4. The spin qubit system according to any one of the preceding items, wherein the grating coupler comprises a plurality of sections that can act as input or output sections.

[0094] 5. The spin qubit system according to any one of the preceding items, wherein the open input end is configured to generate an electric field for controlling the quantum dot to induce transitions in the spin qubit system.

[0095] 6. The spin qubit system according to any one of the preceding items, wherein the photonic bandgap waveguide section optionally comprises an array of periodic holes displayed in a periodic structure.

[0096] 7. The spin qubit system according to item 1, wherein the nano beam waveguide is a rectangular cross-section slab configured to guide the photons generated by the quantum dot to a second structure.

[0097] 8. The spin qubit system according to any one of the preceding items, wherein the photonic bandgap waveguide section is a photonic crystal waveguide.

[0098] 9. The spin qubit system according to any one of the preceding items, wherein the electrode configured for applying a DC electric field to the quantum dot can control the number of electrons or holes in the quantum dot. The spin qubit system according to any one of the preceding items, wherein two of the three input electrodes form a parallel slit extending along at least part of the planar nanophotonic waveguide, and wherein the third input electrode is separated from the slit, such that the quarter wavelength resonator is configured to generate a magnetic field in the slit for controlling the quantum dot to induce transitions in the spin qubit system. The spin qubit system according to item 10, wherein the slit width is preferably less than 300 nm, more preferably less than 200 nm, even more preferably less than 100 nm, most preferably around 50 nm. The spin qubit system according to any one of the items 10-11 , wherein the separation width of the third input electrode to the slit is preferably larger than 10 pm, more preferably larger than 20 pm, even more preferably larger than 25 pm, most preferably around 30 pm. The spin qubit system according to any one of the items 10-12, wherein the parallel slit is positioned below at least part of the planar nanophotonic waveguide. The spin qubit system according to any one of the preceding items, wherein the first and the third input electrodes are grounded. The spin qubit system according to any one of the preceding items 3-14, wherein an input section of the grating coupler is positioned at one end of the planar nanophotonic waveguide, and wherein an output section of the grating coupler is positioned at the other end of the planar nanophotonic waveguide. The spin qubit system according to any one of the preceding items, wherein the first, second and third input electrodes of the quarter wavelength resonator are shorted at one end by a conducting material. 17. The spin qubit system according to any one of the preceding items, wherein the quantum dot is configured to emit single photons.

[0099] 18. The spin qubit system according to any one of the preceding items, wherein the input section of the grating coupler is configured to couple incoming light from a laser into the planar nanophotonic waveguide.

[0100] 19. The spin qubit system according to any one of the preceding items, wherein the output section of the grating coupler is configured to transmit out of the nanophotonic waveguide part of the light from the laser to the exterior of the nanophotonic waveguide and to reflect a part of the light from the laser into the planar nanophotonic waveguide.

[0101] 20. The spin qubit system according to any one of the preceding items, wherein the quarter wavelength resonator is configured to generate magnetic fields perpendicular to the plane of the quarter wavelength resonator of at least 30 mT.

[0102] 21. The spin qubit system according to any one of the preceding items, wherein said magnetic fields are localized in the parallel slit of the quarter wavelength resonator.

[0103] 22. The spin qubit system according to any one of the preceding items, wherein the quarter wavelength resonator is used for coherent spin-flip operations, of the state of the quantum dot.

[0104] 23. The spin qubit system according to any one of the preceding items, configured such that the bandwidth of the quarter wavelength resonator is between 10 MHz to 200 MHz.

[0105] 24. The spin qubit system according to any one of the preceding items, configured such that the resonance frequency of the quarter wavelength resonator is between 10 GHz to 20 GHz.

[0106] 25. The spin qubit system according to any one of the preceding items, wherein the Q factor of the quarter wavelength resonator is at least 100. 26. The spin qubit system according to any one of the preceding items, wherein the input power of the quarter wavelength resonator is 0.02 W.

[0107] 27. The spin qubit system according to any one of the preceding items, wherein the second input electrode of the quarter wavelength resonator comprises gaps at the open input, forming a capacitive structure in the input second electrode.

[0108] 28. The spin qubit system according to any one of the preceding items, wherein the quarter wavelength resonator is made of Cu, Al, Ag, Au, Mo, alloy, compound or any other conducting material.

[0109] 29. The spin qubit system according to any one of the preceding items, wherein the quantum dot structure is elevated, preferably by 0.5 pm, more preferably 0.75 pm, above the plane of the quarter wavelength resonator.

[0110] 30. The spin qubit system according to any one of the preceding items, wherein the spin qubit system is fabricated on a sapphire, intrinsic silicon, quartz, alumina, SiN, PTFE or any other substrate with low microwave losses.

[0111] 31. A method for operating the spin qubit system of any of the preceding items, the method comprising the steps of: applying an external magnetic field to Zeeman-split the degenerate levels of the ground state of an unpaired electron in the quantum dot; applying an electrical signal on the quarter wavelength resonator to drive transitions in the quantum dot; and irradiating with a laser the planar nanophotonic waveguide to excite the quantum dot and generate a photon.

[0112] 32. The method of item 31, wherein the steps of the method are according to any one of the items 1-30.

[0113] 33. A quarter wavelength resonator in a coplanar waveguide configuration comprising an open input end having three input electrodes, and a closed resonator end wherein two of the three input electrodes form a parallel slit of a width between 50-300 nm, the slit extending along at least part of the planar nanophotonic waveguide, wherein the third input electrode is separated from the slit by at least 10 pm, such that the quarter wavelength resonator is configured to generate a magnetic field in the slit.

[0114] 34. A quarter wavelength resonator in a coplanar waveguide configuration comprising - an open input end having three input electrodes, and a closed resonator end wherein the three input electrodes are shorted, wherein the open input end is configured to generate an electric field for controlling the quantum dot to induce transitions in the spin qubit system. 35. The quarter wavelength resonator according to any one of the items 33-34, comprising any one of the features of the quarter wavelength waveguide according to any one of the preceding items 1-30.

Claims

Claims1. A spin qubit system comprising a quantum dot unit, the quantum dot unit comprising a planar nanophotonic waveguide comprising o a grating coupler, o a nano beam waveguide section for guiding photons and a photonic bandgap waveguide section, a quantum dot configured to interact with the planar nanophotonic waveguide, an electrode for applying a DC electric field to the quantum dot, a quarter wavelength resonator in a coplanar waveguide configuration comprising o an open input end having three input electrodes, and o a closed resonator end, wherein the three input electrodes are shorted at the closed resonator end by a conducting material.

2. The spin qubit system according to claim 1 , wherein the quantum dot is a lll-V semiconductor quantum dot, such as GaAs, InAs, GaSb, InSb, InP or lll-V semiconductor alloys embedded in a wider bandgap material.

3. The spin qubit system according to any one of the preceding claims, wherein the second input electrode of the quarter wavelength resonator comprises gaps at the open input end, forming a capacitive structure in the second input electrode.

4. The spin qubit system according to claim 3, wherein the quarter wavelength resonator is configured to generate an electric field for controlling the quantum dot to induce transitions in the spin qubit system.

5. The spin qubit system according to claim 3, wherein the quarter wavelength resonator is configured to generate an electric field of at least 0.75 mV / nm for controlling the quantum dot to induce transitions in the spin qubit system.

6. The spin qubit system according to any one of the claims 3-5, wherein a plurality of finger capacitors are utilized to form the gaps at the open input end of the quarter wavelength resonator.

7. The spin qubit system according to any one of the preceding claims, wherein the grating coupler comprises a single grating section that can act as an input and / or output section.

8. The spin qubit system according to any one of the preceding claims, wherein the grating coupler comprises a plurality of sections that can act as input or output sections.

9. The spin qubit system according to any one of the preceding claims, wherein the photonic bandgap waveguide section comprises an array of periodic holes displayed in a periodic structure.

10. The spin qubit system according to any one of the preceding claims, wherein two of the three input electrodes form a parallel slit extending along at least part of the planar nanophotonic waveguide, and wherein the third input electrode is separated from the slit.

11. The spin qubit system according to claim 10, that the quarter wavelength resonator is configured to generate a magnetic field in the slit for controlling the quantum dot to induce transitions in the spin qubit system.

12. The spin qubit system according to any one of the claims 10-11, wherein the slit width is less than 100 nm.

13. The spin qubit system according to any one of the claims 10-12, wherein the separation width of the third input electrode to the slit is 30 pm.

14. The spin qubit system according to any one of the claims 10-13, wherein the parallel slit is positioned below at least part of the planar nanophotonic waveguide.

15. The spin qubit system according to any one of the preceding claims, wherein the first, second and third input electrodes of the quarter wavelength resonator are shorted at one end by a conducting material.

16. The spin qubit system according to any one of the preceding claims, wherein the quarter wavelength resonator is configured to generate magnetic fields perpendicular to the plane of the quarter wavelength resonator of at least 30 mT.

17. The spin qubit system according to any one of the preceding claims, wherein the quantum dot structure is elevated by 0.75 pm above the plane of the quarter wavelength resonator.

18. The spin qubit system according to any one of the preceding claims, wherein the spin qubit system is fabricated on a sapphire, intrinsic silicon, quartz, alumina, Si N , PTFE or any other substrate with low microwave losses.

19. A method for operating the spin qubit system of any of the preceding claims, the method comprising the steps of: applying an external magnetic field to Zeeman-split the degenerate levels of the ground state of an unpaired electron in the quantum dot; applying an electrical signal on the quarter wavelength resonator to drive transitions in the quantum dot; and irradiating with a laser the planar nanophotonic waveguide to excite the quantum dot and generate a photon.

20. A quarter wavelength resonator in a coplanar waveguide configuration comprising an open input end having three input electrodes, and a closed resonator end wherein two of the three input electrodes form a parallel slit of a width between 50-300 nm, the slit extending along at least part of the planar nanophotonic waveguide, wherein the third input electrode is separated from the slit by at least 10 pm, such that the quarter wavelength resonator is configured to generate a magnetic field in the slit.

21. A quarter wavelength resonator in a coplanar waveguide configuration comprising an open input end having three input electrodes, and a closed resonator end wherein the three input electrodes are shorted, wherein the open input end is configured to generate an electric field for controlling the quantum dot to induce transitions in the spin qubit system.

22. The quarter wavelength resonator according to any one of the claims 20-21 , comprising any one of the features of the quarter wavelength waveguide according to any one of the preceding claims 1-18.

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