Optical technique to produce quantum devices in semiconductors using structured light

Abstract

A method for creating arrays of quantum dots, the method comprising the steps of: providing a semiconductor comprising a quantum well, subsurface regions of photosensitive dopants and a plurality of conducting gates deposited on a surface of the semiconductor; generating light from a source; directing the light onto a transmission diffractive optical element to generate a periodic interference pattern; creating an elongated quantum dot or a plurality of elongated quantum dots inside the semiconductor by applying voltages to a first plurality of the conducting gates or by means of mesa etching; irradiating the semiconductor with the interference pattern generated by the transmission diffractive optical element to periodically change the charge state of the photosensitive dopants, thereby inducing a periodic electrostatic potential near the plurality of elongated quantum dots and thus partitioning the elongated quantum dots into smaller quantum dots defined by the light-induced periodic electrostatic potential.

Description

OPTICAL TECHNIQUE TO PRODUCE QUANTUM DEVICES IN SEMICONDUCTORS USING STRUCTURED LIGHTFIELD

[0001] This invention relates generally to a method and apparatus for inducing periodic electrostatic potentials inside semiconductors using structured light generated by diffractive optical elements.BACKGROUND

[0002] The spin degree of freedom of an electron provides a natural two-state system that can be used for the realization of qubits. In 1998, Loss and DiVincenzo proposed to use the spin degree of freedom of individual electrons confined in semiconductor quantum dots (QDs) for quantum computing f1]. Since then, QD-based electron spin qubits have been produced in semiconductors such as gallium arsenide (GaAs) [2],[3] and silicon (Si) [4], Additionally, hole spin qubits were also demonstrated in double quantum QDs fabricated from germanium (Ge) hut wires [5] and in double quantum QDs in planar Ge [6], In each of the above cases spin qubits were implemented by means of electrostatic potentials applied to conducting surface gates.

[0003] Generally, electron (or hole) spin qubits in semiconductor QDs hold promise in terms of practical large-scale quantum processing because of their small size, low quantum decoherence (i.e., long quantum coherence times) if the spin is well isolated from the environment, and compatibility with modem semiconductor fabrication processes [7],[8]. Several quantum components utilizing high-quality QD-based spin qubits, such as on-chip quantum communication links between quantum modules and spares qubit arrays, have been demonstrated and tested [7],[9],

[10] . However, only small arrays of operational QD-based spin qubits (i.e., arrays consisting of just 9 qubits |1 11) have been produced so far, mainly because of the challenging wiring problems in the currently pursued designs wherein each qubit requires multiple conducting surface gates to form, initialize (i.e., tune to the single-spin regime), control, and readout the spin states [9],

[12] .

[0004] The practical implementation of quantum computing based on the solid-state semiconductor platform critically depends on (i) the quality and reproducibility of spin qubits based on single quantum dots (QDs), spin qubit registers based on QD arrays and coherent links between such qubit registers and (ii) the availability of new technologies that would allow decreasing the number of gates, which are currently used to create and operate the qubit circuits by means of electric signals. The fulfilment of the above two requirements is necessary (i) to reduce the quantum decoherence of the qubits constituting a quantum circuit, whichdeteriorates the qubits’ quantum states and leads to errors, e.g., in the stored quantum information and processing thereof and (ii) to facilitate interfacing a quantum circuit with classical electronics that is used to form, manipulate, and readout the qubits.

[0005] Currently, laterally modulated microscale electrostatic potentials in semiconductors for-quantum circuits are induced by using conducting surface gates, which are fabricated either on the semiconductor surface (Schottky gates) or on an intermediate dielectric layer deposited on the semiconductor surface. Electrostatic potentials produced by the surface gates can create pockets of electrons or holes in a nearby quantum well (QW) containing a two-dimensional electron gas (2DEG) or a two-dimensional hole gas (2DHG), respectively, and thus create single QDs or arrays of QDs [7],

[13] ,

[14] ,

[15] .

[0006] In the surface-gates approach, the QW to be affected by the conducting gates must be placed very close to the surface, which considerably reduces the quality of the resultant quantum structures because of (i) unavoidable imperfections in the semiconductor crystal structure caused by the close proximity to the surface (e.g., non-uniform strains originating from the surface inhomogeneity caused by the deposition of gates, dielectric fdms and etching) and (ii) the presence of unavoidable surface and interface charges which cause harmful fluctuations of the electrostatic potentials imposed by the conducting surface gates.

[0007] If the QW containing the 2DEG (or 2DHG) is positioned deeper below the semiconductor surface (e.g., more than 1 micrometre below the surface) to minimize the above effects, the surface gates can produce only very large multi-electron (or multi-hole) QDs with the characteristic size of more than 1 micrometre. Such QDs cannot be made identical at the single-spin level because the electrostatic potential produced by surface gates is not reproducible at large depths. Also, every gate unavoidably introduces additional sources of electric noise (e.g., shot noise and random switching noise)

[16] ,

[17] . Additionally, because in the surface-gates approach QD-based spin qubits are created by means of gates, the implementation of large-scale quantum circuits can simply become impossible because of the wiring and thermal management issues

[12] ,

[18] . Finally, the fabrication of fine and densely spaced surface gates requires sophisticated and expensive manufacturing facilities, i.e., clean rooms and equipment for photolithography, metal deposition, etching, surface passivation / oxidation, annealing, etc.

[0008] In the late 1980s and early 1990s, an all-optical approach to induce a periodically modulated microscale electrostatic potential in a GaAs / AlGaAs heterostructure was demonstrated by Weiss et al. in

[19] ,

[20] ,

[21] . In the studies by Weiss et al., an interference pattern was generated by a free-space two-beam interferometer and the interference patternwas then used to create a periodically modulated microscale electrostatic potential near the 2DEGin the GaAs-AlGaAs-heterojunction. The potential was induced by changing the charge state of the Si-dopant which was contained within the thin modulation-doped AlGaAs layer deposited on the GaAs epitaxial layer. Similar to the surface-gates approach, the light-induced electrostatic potential generated line-shaped pockets of electrons in the 2DEG, which lead to the creation of a lateral superlattice. In the studies by Weiss et al.

[19] ,

[20] ,

[21] ,

[22] , the 2DEG was located less than 100 nanometres (nm) from the semiconductor surface and, as a consequence, the resultant superlattice was influenced by the surface effects (i.e., strain fields, surface contaminations, surface charges, etc.).

[0009] The main limitations of the aforementioned all-optical approach are associated with the accommodation and alignment of a free-space interferometer inside a cryostat at liquid helium temperatures. The interference pattern used in this approach drifts along the sample surface because of mechanical instability of the free-standing optical setup and vibrations inside a cryostat, which, in turn, quickly erases modulations in the induced electrostatic potential. Consequently, the exposure times in

[19] ,

[22] are limited to milliseconds. To compensate for such short exposure times, the light intensity needs to be increased accordingly. However, the formation of an electrostatic potential under illumination, which is caused by interband absorption in the semiconductor and the subsequent diffusion of the photo-excited charge carriers, is generally a nonlinear process at high illumination intensities. This immediately puts restrictions on the intensity range that is suitable for different types of dopants and dopant concentrations. Moreover, illumination times on a millisecond scale disallow the use of multi-exposure / multi-wavelength procedures, which often require hours in order to optimize the quantum structures performance by adjusting the modulation amplitude of the light-induced electrostatic potential. Such procedures are absolutely critical in the R&D phase. Another disadvantage of free-space interferometers in the above context is that their use is essentially restricted to monochromatic illumination light. Light monochromaticity is required to ensure that the interfering light beams have a sufficiently large coherence length to compensate for the optical path difference in the interferometer’s arms. Also, in order to avoid the speckle effect at the sample surface in monochromatic light, the optical components of the interferometer should meet stringent cleanliness requirements. On the other hand, the use of polychromatic light would necessitate balancing the optical path difference in the interferometer’s arms to a few micrometres, which is very difficult to achieve in the confined geometry of cryostats and large temperature gradients experienced by the interferometer. Yet another major disadvantage of this approach is that a two-beam interferometer can only createa one-dimensional light pattern, i.e., straight interference fringes. The above arguments may explain why the approach of Weiss et al. has not been adopted by other laboratories after its first demonstration more than thirty years ago. Weiss et al. never considered / discussed the possibility of creating arrays of QDs using light.SUMMARY

[0010] In one aspect, there is provided a method for creating arrays of quantum dots, the method comprising the steps of: providing a semiconductor comprising a quantum well, engineered subsurface regions of photosensitive dopants and a plurality of conducting gates deposited on a surface of the semiconductor; generating light from a source, wherein the light comprises a wavelength capable of photo-exciting and changing a charge state of the photosensitive dopants; directing the light onto a transmission diffractive optical element, installed adjacent to the semiconductor at a predetermined distance, to generate a periodic interference pattern; creating a plurality of elongated quantum dots inside the semiconductor by at least one of applying voltages to a first plurality of the conducting gates and by means of mesa etching; irradiating the semiconductor with the interference pattern generated by the transmission diffractive optical element, wherein the interference pattern has a light intensity and light fluence that are sufficiently high to periodically change the charge state of the photosensitive dopants, thereby inducing a periodic electrostatic potential near the plurality of elongated quantum dots and dividing the plurality of elongated quantum dots into arrays of smaller quantum dots.

[0011] In another aspect, a method for creating a spin-based coherent quantum link between a first quantum computing module and a second quantum module in a semiconductor, wherein the semiconductor can be partially light-transmitting or lightabsorbing, and wherein the semiconductor comprises a quantum well, engineered subsurface regions of photosensitive dopants and a plurality of conducting gates deposited on a surface of the semiconductor, the method comprising the steps of: directing light onto a transmission diffractive optical element, installed adjacent to the semiconductor at a predetermined distance, to generate a periodic interference pattern; creating an elongated quantum dot or a plurality of elongated quantum dots inside the semiconductor by applying voltages to a first plurality of the conducting gates;irradiating the semiconductor with the interference pattern generated by the transmission diffractive optical element to periodically change the charge state of the photosensitive dopants, thereby inducing a periodic electrostatic potential near the plurality of elongated quantum dots, and dividing the plurality of elongated quantum dots into at least one array of smaller quantum dots; wherein a charge carrier with a certain spin state can be transported by successively adjusting the electrochemical potentials of the constituting quantum dots by applying alternating phase-shifted voltages to a second plurality of conducting gates and thus the spin- encoded quantum information can be exchanged between a first spin qubit in the first quantum module, adjacent to an input quantum dot in the at least one array, and a second spin qubit in the second quantum module, adjacent to an output quantum dot in the at least one array.

[0012] In one aspect, a method for creating a spin-based coherent quantum link between a first quantum computing module and a second quantum computing module in a semiconductor, wherein the semiconductor is partially light-transmitting or light-absorbing, and wherein the semiconductor comprises a quantum well, engineered subsurface regions of photosensitive dopants, a plurality of conducting gates deposited on a surface of the semiconductor, a global transparent or semi-transparent conducting gate deposited on the semiconductor, the method comprising the steps of: directing light onto a transmission diffractive optical element, installed adjacent to the semiconductor at a predetermined distance, to generate a periodic interference pattern; creating an elongated quantum dot or a plurality of elongated quantum dots inside the semiconductor by applying voltages to a first plurality of the conducting gates and the global transparent or semi-transparent conducting gate; irradiating the semiconductor with the interference pattern generated by the transmission diffractive optical element to periodically change the charge state of the photosensitive dopants, thereby inducing a periodic electrostatic potential near the plurality of elongated quantum dots, and dividing the plurality of elongated quantum dots into at least one array of smaller quantum dots; wherein a charge carrier with a certain spin state can be transported by successively adjusting the electrochemical potentials of the constituting quantum dots by applying alternating phase- shifted voltages to a second plurality of conducting gates and thus the spin-encoded quantum information can be exchanged between a spin qubit in the first quantum module, adjacent tothe input quantum dot in the at least one array, and a spin qubit in the second quantum module, adjacent to the output quantum dot in the at least one array.

[0013] In one aspect, a smaller quantum dots can be transformed into one-dimensional ID arrays of single-spin qubits by applying a predetermined constant voltage to the first plurality of conducting gates, in order to adjust the height of the potential energy barrier of the quantum well, and by applying predetermined alternating phase-shifted voltages to the second plurality of conducting gates, adjacent to the smaller quantum dots, in order to adjust the number of free charge carriers in the smaller quantum dots.

[0014] In another aspect, a method for creating two-dimensional arrays of quantum dots inside a partially light-transmitting or light-absorbing semiconductor, comprising the steps of: providing the partially light transmitting or absorbing semiconductor that contains a quantum well, engineered subsurface regions of photosensitive dopants and a global transparent or semi-transparent conducting gate deposited on the surface of the semiconductor; providing a source of light; providing a two-dimensional transmission diffractive optical element, installed adjacent to the partially light transmitting or absorbing semiconductor at a predetermined distance, that when illuminated by the light creates a periodic two-dimensional interference pattern behind a back surface of the transmission diffractive optical element; irradiating the semiconductor with the interference pattern generated by the two- dimensional transmission diffractive optical element, with the light intensity and the light fluence in the two-dimensional interference pattern being sufficiently high to periodically change the charge state of the photosensitive dopants, thus inducing a two-dimensional periodic electrostatic potential near the quantum well and consequently a two-dimensional array of quantum dots, wherein the number of free charge carriers inside the quantum dots can be simultaneously adjusted by applying a constant voltage to the global conducting gate.

[0015] In an aspect, a method for creating a spin-based coherent quantum link between two quantum modules in a semiconductor by means of periodic electrostatic potentials induced inside the semiconductor substrate using structured light generated by a diffractive optical element, comprising the steps of: providing a semiconductor containing a quantum well, embedded regions of photosensitive dopants and two or more distinct pluralities of transparent, semi-transparent or opaque conducting gates deposited on the semiconductor surface;providing a source of monochromatic or polychromatic tight, wherein the source of light is a continuous-wave or pulsed one, and wherein the wavelength of the light has a characteristic wavelength to photo-excite the dopants in the wavelength range from 180 nanometers to 3500 nanometers; providing a transmission diffractive optical element that when illuminated by the light creates an interference pattern behind its back surface; creating a plurality of elongated quantum dots inside the semiconductor by applying constant voltage to the first plurality of conducting gates or by means of mesa etching; irradiating the semiconductor substrate with the interference pattern generated by the diffractive optical element, with i) the interference fringes in the interference pattern being oriented perpendicularly or at a smaller angle to the first plurality of conducting gates or the grooves etched in the mesa and ii) with the light intensity in the interference pattern being sufficiently high to periodically change the charge state of the photosensitive dopants thus inducing a ID periodic electrostatic potential near the plurality of elongated quantum dots and dividing the plurality of elongated quantum dots into ID arrays of smaller quantum dots; adjusting a constant voltage applied to the first plurality of conducting gates and adjusting alternating phase-shifted voltages applied to the second plurality of conducting gates, adjacent to the smaller quantum dots, so that each smaller QD in the ID arrays contains zero free charge carriers and cannot contain more than one free charge carrier.

[0016] When a charge carrier with a certain spin state is placed into a ID array of quantum dots without free charge carriers and predetermined alternating phase-shifted voltages are applied to neighbouring quantum dots in the ID array by means of adjacent conducting gates, the electrochemical potentials of the neighbouring quantum dots can be successively adjusted in such a way that the charge carrier with a certain spin state is conveyed along the ID array from the sending quantum module to the receiving quantum module. Thus, an exchange of quantum information encoded in the spin state of a charge carrier is performed between a spin qubit in the sending quantum module, adjacent to the input quantum dot in the ID array, and a spin qubit in the receiving quantum module, adjacent to the output QD in the ID array.

[0017] In another aspect, the method further comprises a step of applying voltage to a semiconductor substrate that contains light-induced arrays of quantum dots in order to restore the charge state of the photosensitive dopants and thus erase the quantum dots.

[0018] In another aspect, the restoration of the charge state of the photosensitive dopants is achieved by local heating of the semiconductor substrate.

[0019] In another aspect, the restoration of the charge state of the photosensitive dopants is achieved by irradiating the semiconductor using light whose wavelength is different from the wavelength of the structured light.

[0020] In another aspect, a method for creating two-dimensional arrays of quantum dots inside a partially light-transmitting or light-absorbing semiconductor, comprising the steps of: providing the partially light transmitting or absorbing semiconductor that contains a quantum well, engineered subsurface regions of photosensitive dopants and a global transparent or semi-transparent conducting gate deposited on the surface of the semiconductor; providing a source of light; providing a two-dimensional transmission diffractive optical element, installed adjacent to the partially light transmitting or absorbing semiconductor at a predetermined distance, that when illuminated by the light creates a periodic two-dimensional interference pattern behind a back surface of the transmission diffractive optical element; irradiating the semiconductor with the interference pattern generated by the two- dimensional transmission diffractive optical element, with the light intensity and the light fluence in the two-dimensional interference pattern being sufficiently high to periodically change the charge state of the photosensitive dopants, thus inducing a two-dimensional periodic electrostatic potential near the quantum well and consequently a two-dimensional array of quantum dots, wherein the number of free charge carriers can be simultaneously adjusted by applying a constant voltage to the global conducting gate.

[0021] Advantageously, the quantum decoherence in a semiconductor quantum circuit can be improved by (i) placing its components as deep as possible inside a high quality host material in order to decrease the influence of the surface (e.g., strain fields originating from the surface inhomogeneity caused by the deposition of gates, surface contaminations, unavoidable surface charges, fluctuating traps, etc.) and (ii) decreasing the number of control gates in order to reduce noise associated with them. The ability to decrease the number of gates in a quantum circuit also determines whether its architecture can be made practical in terms of (i) delivering the control signals to and the read-out signals from a large number of qubits (i.e., spin qubits in QDs), which is predicted to be in the 106- 108range [9] for solving computational problems that are intractable for classical computers, and (ii) handling the large thermal load caused by heat transfer through the numerous signal transmission lines.

[0022] The methods described herein overcome the limitations of the prior art methods for creation of QDs inside semiconductors by means of periodic electrostatic / electric potentials.Specifically, there is provided a method and apparatus to produce regular arrays of identical high-quality QDs in different semiconductors using structured light generated by a diffractive optical element. When each of the QDs contains a single electron spin or a single hole spin, the QDs can be used as an array of QD-based spin qubits.

[0023] In this disclosure, a “superlattice” is referred to the combination of the light-induced periodic electrostatic potential and the semiconductor lattice potential which together determine the energy spectrum and transport characteristics of charge carriers.

[0024] In one aspect, there is provided a method and apparatus for inducing periodic electrostatic potentials inside semiconductors using low-intensity structured light in order to produce regular arrays of quantum dots. Furthermore, the arrays of quantum dots can be transformed into arrays of spin qubits by tuning the height of the light -induced electrostatic potential by means of adjusting the intensity and accumulated fluence of the structured light. A periodic electrostatic potential in a semiconductor is induced by the interference pattern generated by a transmission diffractive optical element. In the present application, references to transmission diffractive optical elements refer more specifically to transmission phase diffraction gratings (PDGs) which are also known as phase masks

[46] . PDGs are designed to periodically change the phase of an electromagnetic wave passing through it as a function of position. A PDG is characterized by its phase modulation function which determines the difference in the phase of the incident wave immediately in front of the PDG and the phase of the transmitted wave immediately behind the PDG at exactly the same xv-location. The changes in the phase are achieved by introducing variation of the real part of the refractive index of the PDG either in one dimension (ID) or two dimensions (2D). Transmission phase diffraction gratings can be made of any material that is transparent to the range of wavelengths used to induce electrostatic potentials inside semiconductors, for instance, optical quality fused silica, borosilicate glass and soda-lime glass.

[0025] The approach based on using high-intensity structured light generated by a transmission PDG to change properties of glass is well-known. Specifically, a method of photo imprinting Bragg gratings in optical fibers and other types of waveguides is taught by Hill et al. in U.S. Pat. No. 5,367,588 where a structured light pattern (i.e., an interference pattern) is generated by impinging a single ultraviolet (UV) laser beam onto a PDG. The fiber to be processed is placed behind the PDG and exposed to the generated interference pattern, which leads to the formation of the Bragg grating structure inside the fiber core. In this case, the required light intensity lies in the range from 103W / cm2to 1010W / cm2The fabrication of fiber Bragg gratings using infrared (IR) femtosecond laser pulses and a PDG is taught by Mihailovet al. in U.S. Pat. No. 6,993,221. In this case, the required light intensity is much higher and lies in the range from IO13W / cm2to 1014W / cm2The high light intensities in the above two fabrication processes are needed to induce permanent refractive index changes in the fiber core by means of creating periodic regions with color centers, densification and optical damage in the form of micro-voids or nano-gratings. The respective accumulated fluences, which strongly depend on the illumination wavelength and pulse duration, also he in a very wide range e.g. from approximately 0.1 J / cm2to 108J / cm2

[0026] In the present disclosure, the following are defined as follows:A “quantum dot” is a quantum semiconductor structure that can confine charge carriers (i.e., electrons or holes) in three dimensions (3D) by means of an electric potential.A “quantum well” is a nanometer-thin layer inside a semiconductor which can confine charge carriers (electrons or holes) in the dimension perpendicular to the semiconductor surface, whereas the movement in the other two dimensions is not restricted.A “spin qubit” is a charge carrier with a non-zero spin confined inside a quantum dot. By applying microwaves and magnetic fields to quantum dots, quantum-dot-based spin qubits can exhibit superposition and entanglement.A “coherent quantum link” is a linear quantum device (i.e., a ID array of quantum dots) capable of transmitting quantum information encoded in the spin state of a charge carrier (electron or hole).A “quantum module,” for example, can stand for a quantum register (i.e., a set of qubits that holds all possible configurations of input data at the same time) within a quantum processing unit.“Accumulated fluence” is the total optical energy delivered per unit area.“Mesa etching” is a technique commonly used for electrical and optical device isolation in monolithic integration, wherein a “mesa” is an area on a semiconductor wafer where the semiconductor has not been etched away.DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 shows a simplified diagram of a one-dimensional phase diffraction grating that redirects the normally incident light into a plurality of diffraction orders denoted by the diffraction angles 6m

[0028] Figure 2a shows a simplified diagram of a one-dimensional phase diffraction grating that redirects the normally incident light into ±1 diffraction orders denoted by thediffraction angles 0±1, respectively; in one example the period of the generated two-beam interference pattern in the y-plane is A / 2;

[0029] Figure 2b is an expanded view of the one-dimensional phase diffraction grating in Figure 2a and the two-beam interference pattern produced behind it;

[0030] Figure 3a shows a simplified diagram of a one-dimensional phase diffraction grating that redirects the normally incident light into 0 and ±1 diffraction orders denoted by the diffraction angles 0Oand 0±1, respectively, in which the period of the generated three-beam interference pattern in the y-plane is either A / 2 or A depending on the distance from the onedimensional phase diffraction grating;

[0031] Figure 3b is an expanded view of a one-dimensional phase diffraction grating in Figure 3a and the three-beam interference pattern produced behind it;

[0032] Figure 4a depicts a situation where a one-dimensional phase diffraction grating generates ±1 diffraction orders and the produced two-beam interference pattern penetrates through a semiconductor;

[0033] Figure 4b is an expanded view of the one-dimensional phase diffraction grating in Figure 4a, the semiconductor and the two-beam interference pattern penetrating into the semiconductor;

[0034] Figure 5a shows a simplified diagram of a two-dimensional phase diffraction grating that redirects the normally incident light into four diffraction orders, in which the two ±1 diffraction orders in the xz-plane are denoted by 0±1and the two ±1 diffraction orders in the vz-plane are denoted by i±1;

[0035] Figure 5b is a schematic visualization of the intensity distribution in the four-beam interference pattern generated by the two-dimensional phase diffraction grating in Figure 5a;

[0036] Figure 6 shows the semiconductor structure inside which periodic electrostatic potentials were induced using structured light generated by a one-dimensional phase diffraction grating;

[0037] Figure 7 shows an optical microscopy image of the Hall bar fabricated by photolithography on the semiconductor structure shown in Figure 6;

[0038] Figure 8 depicts how a spatially modulated flux of photons generated by a onedimensional phase diffraction grating is used to photoionize deep-level complexes inside the semiconductor structure in Figure 6 and create two subsurface layers with a quasi-sinusoidal distribution of positive charges (+) near the quantum well;

[0039] Figure 9a shows magnetoresistivity pxxB plots depicting how the structured light with = 780 nm generated by the one-dimensional phase diffraction grating affects the magnetoresistivity pxxB) of the Hall bar, in which the magnetoresistivity plots are obtained at different accumulated fluences F, with plots marked with larger numbers corresponding to higher Fs;

[0040] Figure 9b shows how the structured light with= 780 nm generated by the onedimensional phase diffraction grating affects the electron sheet electron nsof the Hall bar, in which the nsis plotted as a function of accumulated fluence F and the magnetoresistivity plots are obtained at different accumulated fluences F and the data point numbering corresponds to the trace numbering in Figure 9a;

[0041] Figure 10a shows how the structured light with A2= 637 nm generated by the onedimensional phase diffraction grating affects the magnetoresistivity pxxB) of the Hall bar; and the magnetoresistivity plots are obtained at different accumulated fluences F. Plots marked with larger numbers correspond to higher Fs;

[0042] Figure 10b shows magnetoresistivity plots depicting how the structured light with 22= 637 nm generated by the one-dimensional phase diffraction grating affects the electron sheet electron nsof the Hall bar; in which the nsis plotted as a function of accumulated fluence F and the magnetoresistivity plots are obtained at different accumulated fluences F, with the data point numbering corresponding to the trace numbering in Figure 10a;

[0043] Figure I la shows a one-dimensional array of quantum dots created by means of structured light generated by a one-dimensional phase diffraction grating, where the gate voltage VG1is such that each QD in the array confines a plurality of electrons (-);

[0044] Figure 11b shows a one-dimensional array of quantum dots created by means of structured light generated by a one-dimensional phase diffraction grating, where the gate voltages VG2, V°, V2, P3° and V are such that each quantum dot in the array contains zero electrons and a coherent quantum link is thus prepared;

[0045] Figure 12a represents a scenario where an electron with a certain spin state is placed into the input quantum dot of the coherent quantum link in Figure 1 lb;

[0046] Figure 12b depicts the transfer of one bit of quantum information in the coherent quantum link in Figure 11b from the input quantum dot to the neighbouring quantum dot by successively adjusting the electrochemical potentials of the quantum dots using four alternating phase-shifted voltages Vr, V2, ^3ar|d4; and

[0047] Figure 12c depicts the transfer of one bit of quantum information along the coherent quantum link in Figure 11b.DETAILED DESCRIPTION OF THE INVENTION

[0048] Referring to Figure 1, there is shown a simplified diagram of a one-dimensional (ID) phase diffraction grating (PDG) 10 that redirects incident light 11 into a plurality of diffraction orders 12. The diffraction orders 12 are defined by the respective diffraction angles 6m. In one example, when the ID PDG 10 is placed in vacuum and the light falls onto the ID PDG 10 normally, i.e., it propagates along the z-axis, the magnitude of 6mmeasured with respect to the z-axis will be given by sin-1(mA0 / A), where Aois the wavelength of the incident light in vacuum, A is the ID PDG 10’s period and m is an integer satisfying the condition |ml0 / A| < 1. In one example, |m| < 1, i.e., the ID PDG can generate only 0 and ±1 diffraction orders.

[0049] Referring now to Figure 2a, there is shown a simplified diagram of a ID PDG 20 that forms a two-beam interference pattern 21. The two-beam interference 21 behind the ID PDG 20 is formed by the ±1 diffraction orders 22, whereas the O-diffraction order is suppressed, i.e., the power in the 0-diffraction order is much lower than that in the ±1 diffraction orders. The two-beam interference pattern 21 does not change with the distance from the ID PDG 20 along the z-axis provided that the illumination light 23 is collimated, quasi-monochromatic and spatially coherent. The period of the two-beam interference pattern 21 along the x-axis is given by Ao / [2 sin(0±1)] = A / 2

[23] both for vacuum and any transparent medium. Figure 2b is an expanded view of the PDG 20 and the two-beam interference pattern 21 generated behind it. The grooves of the ID PDG 20 in Figure 2a and 2b are aligned along the y-axis, and the light propagates along the z-axis and falls onto the ID PDG 20 normally . In Figure 2b, the ID PDG 20’s period A is denoted by 24 and the period of the interference pattern (i.e., A / 2) 21 is denoted by 25. In Figure 2 and hereinafter, brighter regions 26 in the visualizations of interference patterns 21 generated by PDGs 20 represent regions in the interference patterns 21 where the light intensity is higher.

[0050] Referring to Figure 3a, a ID PDG 30 generates a sufficiently strong 0 diffraction order 31 in addition to the ±1 diffraction orders 32 and a three-beam interference pattern 33 is formed behind the ID PDG 30. The spatial structure of the three-beam interference pattern periodically changes as the distance from the ID PDG 30 and the observation point along the z-axis increases (Figure 3b). If the PDG 30 is illuminated with collimated, quasi-monochromatic and spatially coherent light, the intensity distribution in the xv-plane will be replicated when this distance is changed by a distance 8 35 that can be approximated by [24,25]

[0052] Therefore, an interference pattern 33 with a period of either A / 2 or A can be seen in the y-plane when the observation point is moved along the z-axis by approximately 8 / 4, as it is depicted in Figure 3b. These two distinct periods will be observed in both vacuum and any transparent material. Examples of experimentally obtained multi-beam interference patterns (i.e., Talbot patterns) can be found in [24, 25,26].

[0053] Figures 4a and 4b depict a situation when a ID PDG 40 generates a two-beam interference pattern 41 and the two-beam interference pattern 41 penetrates into a semiconductor 42. Importantly, the period of the two-beam interference pattern 41 in vacuum and inside the semiconductor 42 remains the same. Indeed, the period of the two-beam interference pattern 41 inside the semiconductor 42 is given by As / [2 sin(<p±1)], whereis the wavelength of the incident light inside the semiconductor 42 and <p±1is the angle at which the ±1 diffraction orders propagate in the semiconductor 42 with respect to the z-axis. The wavelength is given by A0 / n and the diffraction angles sin(<p±1) are given by sin(0±1) / n, where n is the refractive index of the semiconductor 42. Hence, As / [2 sin(<p±1)] = 2.0 / [2 sin(0±1)] = A / 2 regardless of whether the pattern is formed in vacuum or a transparent medium. If i) the illumination light 43 is collimated, quasi-monochromatic and spatially coherent, and ii) the semiconductor 42 is sufficiently transparent at the wavelength of the illumination light, the two-beam interference pattern 41 with a constant period of A / 2 can be nominally observed at any depth below the semiconductor 42 surface. Additionally, the period of the two-beam interference pattern 41 does not depend on the distance D 44 between the ID PDG 40 and the semiconductor 42 surface, i.e., in the region where the ±1 diffraction orders overlap the period will always be A / 2. Even though the distance D does not affect the period of the two-beam interference pattern 41 under the above conditions, for practical reasons it can be adjusted, for example, by inserting a spacer 45 with a predetermined thickness between the ID PDG 40 and the semiconductor 42.

[0054] In the case of a three-beam interference pattern produced due to the interference of the 0 and ±1 diffraction orders, the spacing (i.e., either A or A / 2) between the interference fringes at the semiconductor 42 surface, i.e., either A or A / 2, will depend on D. If the illumination light is collimated, quasi-monochromatic and spatially coherent, these two distinctperiods will be observed at the semiconductor 42 surface when D is changed by approximately 8 / 4, as it is depicted in Figure 3b.

[0055] In one aspect pertinent to the case of three-beam interference pattern, the spacing between the interference fringes at the semiconductor 42 surface at a fixed D can be changed by tuning the wavelength of the quasi-monochromatic illumination light because, according to Formula 1, the distance 8 depends on the wavelength Ao.

[0056] In another aspect, the uncertainty in the spacing between the interference fringes at the semiconductor 42 surface can be removed by using polychromatic light sources. For instance, if a collimated and spatially coherent light source with the full spectral width at halfmaximum (FWHM) exceeding 20 nm is used, the three-beam interference pattern transforms into a two-beam interference pattern 41 with a stable period of A / 2 for D exceeding one hundred micrometers (pm). Analytically, distance D at which this transformation occurs can be estimated based on the coherence length of the polychromatic light source and the walk-off effect of the diffraction orders, as taught by [47, 48].

[0057] The distance D between the ID PDG and the semiconductor 42 surface can be adjusted by means of a spacer, as it is depicted in Figs. 4a and 4b. The suitability of ID PDGs for operation with polychromatic light sources, specifically high-intensity broadband femtosecond lasers in order to fabricate fiber Bragg gratings, is well known and described in detail in U.S. Pat. No. 6,993,221, and

[31] ,

[0058] In yet another aspect, the low-intensity structured light generated by a 2D PDG is used for inducing a 2D periodic electrostatic potential embedded inside a semiconductor 42. In this case, 2D arrays of quantum dots can be produced. The 2D arrays of quantum dots can be further transformed into 2D arrays of identical spin qubits by tuning the height / magnitude of the 2D light-induced electrostatic potential by means of adjusting the intensity and accumulated fluence of the structured light. A global transparent or semi-transparent conducting gate deposited on the semiconductor 42 can be used to simultaneously tune the optically created QDs into the spin-qubit regime wherein the individual QDs comprises one or more spins. An additional plurality of transparent, semi-transparent or opaque conducting gates deposited on the semiconductor 42 can be used to transform the 2D array of QDs, for example, into a network of coherent quantum links to transfer quantum information encoded in spin states between quantum modules accommodated in the semiconductor 42.

[0059] Schematics of a 2D PDG 50 and 2D interference light pattern formed behind it are depicted in Figures 5a and 5b. Referring to Figure 5a, a simplified diagram of a 2D PDG 50that forms a four-beam interference pattern is shown. The 2D PDG 50 splits the incident beam 51 into four diffraction orders: ±1 diffraction orders in the xz-plane 52, which are denoted by 0±1, and ±1 diffraction orders in theyz-plane 53, which are denoted by i±1. The four-beam interference pattern will not change with the distance from the 2D PDG 50 along the z-axis provided that the illumination light is collimated, quasi-monochromatic and spatially coherent. The characteristic period of the four-beam interference pattern is the same both for vacuum and any transparent medium. The intensity distribution in the four-beam interference pattern in the y-observation plane 54 in Figure 5a is schematically visualized in Figure 5b.

[0060] If a 2D PDG 50 generates a sufficiently strong 0 diffraction order in addition to the four ±1 diffraction orders, a five-beam interference pattern is formed behind the 2D PDG 50. The spatial structure of the five-beam interference pattern periodically changes as the distance from the 2D PDG 50 and the observation point along the z-axis increases. In one example, the 2D PDG 50 is patterned in such a way that the normally incident beam is split into more than five diffraction orders or the 2D PDG 50 is illuminated at the Bragg angle, similar to the well-known principle of 0 / -1 order ID PDGs. A 2D PDG 50 can also be designed in such a way that the 2D light pattern has different periods along the x-axis and y- axis.

[0061] A wide variety of alternatives are envisioned, for example, other aspects may feature a ID or 2D amplitude diffraction grating (ADG) instead of a ID PDG or 2D PDG. An ADG is characterized by its transmittance pattern where transmittance is defined as the ratio of the electric field amplitudes immediately behind and immediately in front of the ADG at exactly the same xv-location

[46] . The changes in the electric field amplitudes can be achieved, for instance, by introducing variation of the imaginary part of the refractive index of the ADG either in one dimension (ID) or two dimensions (2D). In this disclosure, PDGs are preferred to ADGs because i) the diffraction efficiency of PDGs can be made substantially higher than that of APDs and ii) optical power in the O-diffraction order of PDGs can be made substantially lower than that of APDs

[0045] , Herein, diffraction efficiency determines how much optical power is diffracted into designated diffraction orders compared with the power incident onto the diffractive optical element.

[0062] Figure 6 schematically depicts a semiconductor sample 69 in which periodic electrostatic potentials were induced using structured light generated by a ID PDG, in experiments. The GaAs / AlGaAs quantum well (QW) structure 60 inside the sample was grown by molecular beam epitaxy. The QW 60 was sandwiched between two 5-doping layers 61which were deposited in order to achieve an ultrahigh-mobility (~1.1 x 107cm2 / Vs) of the 2DEG confined in the QW 60. The center of the QW 60 was ~500 nm below the sample 69 surface. In Figure 6, the AlxGai-xAs barrier layers with different x and the GaAs substrate are denoted by 63, 64 and 65, respectively. The variable x in the above expression for AlxGai-xAs can take on values from 0 and 1, which translates into an arbitrary alloy between GaAs and Al As. A Hall bar shown in Figure 7 was then fabricated by photolithography on the semiconductor sample 69.

[0063] A ID PDG with a 1400 nm period (i.e., A = 1400 nm) was attached to the Hall bar, as it is schematically shown in Figure 4a. At the wavelengths in one demonstration, the ID PDG generated 0 and ±1 diffraction orders only. Also, the inventors tested the ID PDG at A-L = 780 nm and A2= 637 nm and observed that a substantial portion of the laser power was contained in the O-diffraction order. As a result, a three-beam interference patterns was produced by the 0 and the ±1 diffraction orders behind the ID PDG, as it is schematically shown in Figs. 3a and 3b.

[0064] The assembly consisting of the Hall bar and the ID PDG was placed in a helium-3 cryostat equipped with a split-coil superconducting solenoid with the magnetic field B directed perpendicular to the y-plane. During the two demonstrations described further below the Hall bar was kept at temperatures in the range of 260-280 mK.

[0065] Single mode optical fibers were used to deliver light to the sample compartment of the helium-3 refrigerator in order to illuminate the ID PDG. Referring to Figure 7, the measurements of the magnetoresistivity pxxB) = wVxx / L I) and the Hall resistivitywereperformed using a low-frequency lock-in amplifier. In the above expressions, Vxxis the longitudinal voltage, Vxyis the Hall voltage, w is the width of the Hall bar, L is the distance between neighboring potential contacts of the Hall bar, and I is the current passing through the Hall bar. By observing changes in the magnetoresistivity and the Hall resistivity caused by illumination of the Hall bar with the structured light at= 780 nm and A2= 637 nm, the inventors were able to demonstrate the creation of a ID periodic electrostatic potential near the QW and also the ability to change the modulation amplitude of the potential.

[0066] The inventors found that depending on the illumination wavelength there were two different mechanisms by means of which the structured light generated by the ID PDG induced periodic electrostatic potentials near a high-mobility 2DEG gas confined in the QW. The high mobility 2DEG served as a sensor of the periodic potential. In the futures there can be other means to detect modulation including optical and quantum transport methods.

[0067] In the first demonstration, the inventors used near-infrared light with= 780 nm. The photon energy Ephof the light is lower than the band gap energy of the AlxGai-xAS structure shown in Figure 6 and the light can thus reach silicon (Si) donors in the two 5-doping layers lying above and below the QW, as it is depicted in Figure 8. It is known that Si as well as other impurities in AlxGai-xAs can produce deep-level complexes, e.g., complexes containing a donor atom and a vacancy

[27] which are often referred to as DX-centers

[28] . Thermal ionization of deep-level complexes requires temperatures above 100 Kelvin (100 K)

[27] and, therefore, at cryogenic temperatures below 77 K (i.e., the boiling point of liquid nitrogen) the excited levels of these centers are very stable (often referred to as metastable).

[0068] Figure 8 shows a scenario where a periodically modulated flux 80 of the nearinfrared photons is realized by the interference of two plane waves at the surface of the Hall bar. Herein, the photon flux is defined as the number of photons traversing unit area per unit time. The near-infrared photons photoionize the Si-based deep-level complexes (Figure 6) and create two subsurface layers with a quasi-sinusoidal distribution of positive charges 81. The weak absorption within the QW is not expected to play an important role in this process because the photo-generated electron-hole pairs quickly recombine (withing nanoseconds) and cannot change the charge state of the Si-based deep-level complexes in the 5-doped regions. As a result, the 2DEG in the QW moves under the influence of a periodic electrostatic potential originating from the two layers with immobile positive charges and regularly spaced regions with higher concentration of electrons 82 are thus created in the 2DEG. The depth 83 at which the QW and the 5-doping layers can be positioned below the surface can be as large as several micrometers because the light pattern does not change with depth and light absorption in the AlxGai-xAs layers surrounding the QW is very weak. The quality of the resultant quantum structures is high as the extent to which they will be influenced by surface charges and strain fields originating from surface gates and other surface imperfections is significantly reduced due to the large depth bellow the surface. Any photo-sensitive dopants can be employed in described above process, often referred as “photo-doping”

[29] .

[0069] In the first demonstration, the light intensity at the sample surface was increased between consecutive illuminations but the exposure time was fixed at dt = 10 s for each illumination step. The intensity at the Hall bar did not exceed 500^ W / cm2. The magnetoresistivity pxx(B) of the Hall bar and the Hall resistivity pxy(B) as a function of applied magnetic field B were recorded after each illumination step and used to calculate theelectron sheet concentration ns= B / [epxy(B)J and the Hall mobility pH= pxyB) / Bp0~). In the above expressions, e is the electron charge and p0is the zero-field resistivity at B = 0.

[0070] Figure 9a and 9b show how the magnetoresistivity pxxB) and the respective nschange with the accumulated fluence F. Commensurability Weiss oscillations are clearly seen on the pxxB) plots 90, which undoubtedly indicates that a high-quality electrostatic potential has been induced near the 2DEG contained in the QW. Thirty separate illuminations at different intensities were performed in the first demonstration over 11 hours. This result demonstrates the remarkable stability of the PDG-based optical setup and its suitability for practical applications.

[0071] In Figure 9b, the electron sheet concentration nsis plotted on a semi -logarithmic scale as a function of accumulated fluence F. Photoionization of Si-based deep-level complexes in the 5-doped layers is approximated by a linear function fl 91. The generation efficiency of electrons is such that ~ 5 x 104photons produce one additional electron in the QW. This process clearly follows a linear dependence up to the saturation point occurring around F « 1 mJ. Such linear dynamics are expected only when one type of dopants is involved in the photoionization process. In this demonstration, it is Si-dopants localized in the thin 5- doping layers on both sides of the QW. The mechanism described above is similar to the one employed in photo-doped 2D materials

[29] ,

[30] . In the latter case, charge carriers are also selectively generated in the photo-doped regions and then tunnel to the 2D conducting layer.

[0072] After processing the pxxB) -traces in Figure 9a according to the procedure described in

[31] , the period of the ID light-induced electrostatic potential was found to be approximately 1420 nm. This result indicates that the distance D between the PDG and the Hall bar in the first demonstration was such that the period of the three-beam interference pattern at the sample surface was A, as it is depicted in Figure 3.

[0073] In a second demonstration, the inventors used visible light with A2= 637 nm. The visible radiation with A2= 637 nm is strongly absorbed in the sample as its photon energy Ephis considerably larger than the band gap energy of AlxGai-xAs. The light intensity at the sample surface was increased between consecutive illuminations but the exposure time was fixed at dt = 1 s for each illumination step.

[0074] The respective magnetoresistivity pxx(B)-plots 101 for different F and ns-values 102 as a function of F are presented in Figure 10a and Figure 10b, respectively. The observed growth of nsas a function of F can be described as follows: (i) the visible light with A2= 637 nm is strongly absorbed in the AlxGai-xAs barrier layers and produces electron-hole pairs nearthe 6-doping layers containing Si-based deep-level complexes; (ii) some of the photo-generated holes are captured by the Si-based deep-level complexes, change their charge states and consequently create a ID periodic distribution of immobile positive charges in the 5-doping layers with a spatial distribution that follows the light pattern; (iii) the unpaired free electrons drift towards and are eventually captured by the QW, thus increasing nsof the 2DEG. The generation efficiency of electrons of this process is high. Specifically, ~10 photons produce one additional electron in the QW. This mechanism can be employed in photon-to-spin devices if photo-active layers of different nature are introduced at the tunneling distance from the quantum-dot structure designed to store and process quantum information

[32] ,

[33] .

[0075] After processing the pxx(B)-plots in Figure 10a according to the procedure described in

[31] , the period of the light-induced electrostatic potential was found to be approximately 710 nm. This result indicates that the distance D between the ID PDG and the Hall bar in the second demonstration was such that the period of the three-beam interference pattern at the Hall bar’s surface was A / 2, as it is depicted in Figure 3.

[0076] Following the formalism presented in

[31] , the inventors also determined the dimensionless modulation potential of the lateral superlattice formed in the semiconductor sample after illuminating it with structured light produced by the ID PDG. Herein, the dimensionless modulation potential is given by r / = eV0 / EF, where Fois the modulation amplitude of the light-induced electrostatic potential and EFis the Fermi energy of the 2DEG. The maximum value for the dimensionless potential r / for the illumination at= 780 nm and A2= 637 nm was found to be 2.2% and 0.6%, respectively. The corresponding Fermi energies were found to be 8.71 meV and 7.72 meV based on the magnetoresistivity plots in Figure 10a (i.e., for A-L = 780 nm) and Figure 10b (i.e., for A2= 637 nm). For the illumination at= 780 nm and A2= 637 nm Fotranslated into is 0.19 mV and 0.046 mV, respectively. It should be noted that the modulation amplitude in this demonstration is very strongly screened by the free carriers. In QD structures the produced potential modulation will be much stronger, fully sufficient to form uniform arrays of quantum dots for spin qubit application as is described below.

[0077] The modulation amplitude Vo of the light-induced electrostatic potential in the first and second demonstrations is sufficiently high to form an array of QDs in AlxGai-xAs and other semiconductors, as it is schematically depicted in Figure 11. Referring to Figure Ila, i) the ID PDG generates a two-beam interference pattern 110 that penetrates into the semiconductor and creates a periodic electrostatic potential near the QW by photo-ionizing deep-level complexesconfined in the doping layers (Figs. 4 and 8); ii) the QW confines electrons along the z-axis, which allows the formation of a 2DEG inside the QW; iii) electrons in the 2DEG are periodically confined along the x-axis by the light-induced periodic electrostatic potential (Figure 8); iv) electrons in the 2DEG are confined along the v-axis by applying voltage VG1to two electric surface gates 111. Thus, a ID array of QDs 112 is formed. In Figure Ila, the voltage VG1is such that each QD in the ID array contains many free electrons. After the illumination with structured light has been stopped, the number of free electrons in the resultant QDs can be changed by adjusting the constant voltage applied to the surface gates 111 and the phase-shifted voltages, which are denoted by 7°, F2°, k3° and F4°, applied to the surface gates 113. Specifically, the removal of electrons from the QDs in the ID array require special protocols based on periodically changing the potential energy barriers of neighbouring QDs in the ID array, which is achieved by means of the phase-shifted voltages 7°, F2°, k3° and F4°, in order to convey the electrons from the QDs to an ohmic contact which terminates the ID array and serves as a reservoir for electrons

[34] . Referring to Figure 11b, the gate voltages VG2, V°, V°, F3° and F4° are such that each QD in the ID array contains zero free electrons. Without loss of generality, each QDs in the ID array can be populated with only one free electron if the voltages applied to the surface gates are tuned accordingly. In this case, a ID array of QD- based spin qubits is produced.

[0078] Referring to Figure 12a, there is shown another example in which a spin-based coherent quantum link between two quantum computing modules on a semiconductor chip is created by means of structured light generated by a ID PDG and two systems of electric surface gates. Coherent quantum links are required to transfer quantum information encoded in spin states of spin qubits. The exchange of quantum information between the spin qubits can be implemented by means of the spin of a single electron wherein the electron is transported through a ID array of QDs by successively adjusting their electrochemical potentials using electric signals. It is also known that four phase-shifted sine wave electric signals applied to neighboring QDs in the ID array by means of gates are sufficient to move an electron with a defined spin state along the QD-based quantum link

[18] ,

[34] . In Figure 12, the four phase- shifted alternating voltages, which are denoted by Vr, V2, V3and F4, are applied to the first system of surface gates 120, the constant voltage VG2is applied to the other (second) system of surface gates 121, and an electron is launched into the QD with coordinate xrat time tr. At time t2, as it is depicted in Figure 12b, the phases of the alternating voltages are such that the electrochemical potential of the QD with coordinate x2is lower than the electrochemicalpotential of the neighbouring QDs with coordinates xiand %3. Thus, it is energetically favourable for the electron to move from the QD with coordinate xrto the QD with coordinate x2. As a result, one bit of quantum information encoded in electron spin has been transferred by one step along the quantum coherent link. As the alternating voltages applied to the first system of gates changes, the electron moves along the coherent link, with the electron’s coordinate being x3at time t3, x4at time t4and x5at time t5, as it is schematically presented in Figure 12c. The inventors found that i) the conducting gates 111 and 120 can be transparent, semi-transparent or opaque to the structured light and ii) the conducting gates 111 and 120 are insulated from each other and the semiconductor by means of thin dielectric films. Also, a transparent or semi-transparent global conducting gate can be deposited on the semiconductor, in addition to the gates 111, in order to facilitate the tuning of optically created QDs into different regimes wherein the individual QDs can contain zero spins, a single spin or more than one spin. The inventors also found that the ID interference fringes of the interference pattern 110 and the spin / charge-conveying gates 120 can be misaligned along the x-axis.

[0079] One advantage of the described coherent quantum link over electrically produced spin-based coherent quantum links is the dramatic reduction of the number of electric surface gates and electrodes required to form (produce) the ID array of individually controlled QDs. Indeed, creating and controlling one QD by voltages requires four surface gates bonded to four separate electrodes, whereas the described coherent quantum link, which can consist of tens or hundreds of QDs, may be implemented using only six electrodes for its operation. Wiring issues, electric noise and Joule heating in a spin-based coherent quantum link created by structured light are thus dramatically reduced.

[0080] Another advantage of the disclosed coherent quantum link over electrostatically produced spin-based coherent quantum links is the high quality and uniformity of the constituting QDs. This can be accomplished because in optically produced coherent quantum links i) the strain fields, which are caused by the deposition of gates and etching, are reduced and ii) the influence of surface charges can be significantly mitigated by placing the QDs more than 1 pm below the surface. Additionally, the characteristic lateral pitch between the high- quality individual QDs can be ~0.5 pm, which allows the production of coherent links between qubit function circuits separated by tens of micrometers. The latter aspect is important as the minimum length of a coherent link for realistic quantum computing architectures is -100 pm to create space for classical on-chip control electronics between spin-qubit arrays and facilitate scalability of quantum computing architectures in general. Current attempts to construct spin-based quantum links in Si by means of electric surface gates reveal that the constituting QDs and the distance between them needs to be small due to the large effective mass of the electrons and strong fluctuations of the electrostatic potential. Hence, to electrically create individual QDs in a 100 pm -long coherent link in the Si-based architecture would require thousands of gates and electrodes, which is impractical, if not impossible.

[0081] Beneficially, arrays of QDs or QD-based spin qubits may be repeatedly created and erased on demand. The individual QDs are defined by means of a persistent periodic electrostatic potential created by periodic regions of photo-ionized deep-level complexes. There is a broad variety of dopants, e.g., Cr, O, Fe, Sn, Te, Si

[35] , that can form deep-level complexes in semiconductors and therefore be employed in the methods and apparatus described herein. The kind of dopants to be used will depend on the semiconductor structure engineered for a particular application. In the two aforementioned demonstrations, the stability of the light-induced electrostatic potential is substantially improved compared with the situation when deep-center complexes are uniformly distributed inside the semiconductor. This happens because the recharging of the photoionized Si-based deep-level complexes used in the demonstrations is strongly supressed as the complexes and the photo-exited electrons are spatially separated and the recombination thereof thus requires tunneling of electrons from the QW to the <5-doping layers through a high and wide potential energy barrier. As a consequence, the periodic spatial distribution of photo-charged deep-level complexes can survive at liquid helium temperatures indefinitely. Nonetheless, the deep-level complexes can be returned to their original neutral-charge state using at least three methods.

[0082] In another aspect, the restoration of the charge state of the photo-dopants is achieved by heating the semiconductor above a certain critical temperature to thermally re-charge the photo-sensitive dopants, fully or partially. The critical temperature depends on the photoactive dopants and the surrounding potential barriers associated with the QW-structure. For instance, Si-based deep-level complexes used in the proof-of-principle demonstrations are optically charged at liquid helium temperatures and remain in the meta-stable excited charge state for a very long time, i.e. days and weeks. In order to return the complexes to their equilibrium neutral charge state, they need to be heated above 150 K - the higher is the annealing temperature, the faster are the relaxation and erasure processes. The temperature can be raised by introducing a small local heater that is thermally connected to the semiconductor chip carrier. However, the write-erase cycle in this method takes hundreds of seconds as the semiconductor chip after heating to above 100 K needs to be cooled down to a few Kelvin andreach thermal equilibrium with the thermal bath. The described method is similar to a full reset operation of a computer by powering it off.

[0083] In another aspect, a method to erase optically induced QDs is based on applying a pulsed voltage to a transparent gate deposited on the semiconductor that contains the QDs. The magnitude and polarity of the pulsed voltage depend on the design of the semiconductor material and the kind of photo-sensitive dopants embedded therein. Surface gates / electrodes to which the pulsed voltage is applied can be made of transparent to light conducting oxides, for example, indium-tin-oxide (ITO) or ZnO. Surface gates can also be made of semi-transparent thin metal fdms, with a thickness of about 60-100 Angstroms (A) to ensure that the fdms are sufficiently transparent to the structured light and sufficiently conductive. A similar approach to recharge deep-level impurity centers is commonly used in deep-level transient spectroscopy (DLTS) techniques

[27] ,

[35] ,

[36] . Specifically, DLTS is used for measuring concentration and activation energy of charge carrier traps in semiconductor materials. In the DLTS technique, a capacitor structure consisting of the semiconductor under study, a surface capacitor gate and a grounded back capacitor gate is fabricated. Electric pulses are then applied to the surface capacitor gate to drive the energy levels of the charge carrier traps below the Fermi level of the back capacitor gate. This initiates the process of electron (hole) tunneling to the traps, which quickly returns them to the initial neutral charge state. A variation of the DLTS technique can be applied to a semiconductor QW structure to partially or fully restore the charge state of the photo-sensitive dopants near the QW structure and thus prepare it for the subsequent inscription of QDs using structured light. In order to implement the aforesaid write-erase approach, a transparent conducting gate is deposited on the top surface of the QW structure and an electric pulse is applied between the surface gate and the semiconductor wafer whereon the QW structure has been grown. The write-erase cycle in this method can be performed on a millisecond timescale.

[0084] In another aspect, a method to erase optically induced QDs is a purely optical one, wherein the restoration of the charge state of the photo-dopants is achieved by irradiating the semiconductor using light whose wavelength is different from the wavelength of the structured light that was used to create the QDs. This method is applicable for both deep-level donor complexes, which are used for the creation of electron QDs, and deep-level acceptor complexes, which are used for the creation of hole QDs. For example, deep-level donor complexes that became positively charged due to the photoionization by the structured light need to recombine with electrons, which would change the charge state of the donors to neutral and thus erase the spatially modulated electrostatic potential. It is known that suchrecombination processes are possible by photo-exciting electrons from the fully occupied valence band to the positively charged donor states

[36] . The wavelength and intensity of the light used for the erasure / recharging depends on the photo-dopant and the semiconductor structure wherein QDs and QD-based quantum components will be created.

[0085] In another aspect, structured light generated by diffractive optical elements can be used to fabricate regular arrays of QDs and QD-based spin qubits in a wide variety of semiconducting materials. In fact, any semiconductor platform can be used including indirect band gap semiconductors, such as semiconductor-foundry compatible Group-IV materials, e.g., Si, germanium (Ge) and combinations thereof including high-quality strained Ge (s-Ge) on Si

[37] .

[0086] In another aspect, any photo-sensitive dopants, i.e. donors or acceptors, can be used, as they are not required to form Si-based deep-level complexes. The main requirement is that the photo-doping regions and the QDs created by structured light are spatially separated so that the photo-generated charge carriers (electrons or holes) cannot be recaptured by the photoionized dopants.

[0087] In another aspect, the techniques described herein may be used to create hole QDs and hole spin qubits in the QDs. Generally, hole spin qubits exhibit weak hyperfine coupling to nuclear spins, which allows for longer quantum coherence times, and inherently strong spinorbit coupling, which allows for rapid processing of quantum information [7],

[15] ,

[38] . The most promising are semiconductors wherein the effective mass of holes is small, e.g., s-Ge on Si- structures

[37] . The small effective mass allows increasing the size of QDs and positioning them deep under the semiconductor surface in order to reduce the influence of surface charges and micro-strains caused by surface imperfections.

[0088] In another aspect, the techniques described herein are not limited to single-spin qubits, and may be employed to fabricate regular arrays consisting of charge qubits

[39] , hybrid charge-spin qubits

[40] , two-spin singlet-triplet qubits

[41] ,

[42] , three-spin qubits and various modifications thereof

[43] ,

[44] .

[0089] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any invention or on the scope of what may be claimed, but rather as descriptions of features that may be specific to particular implementations of particular inventions. Certain features that are described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementationsseparately or in any suitable sub-combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.

[0090] Accordingly, the above description of example implementations does not define or constrain this disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of this disclosure.

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Claims

CLAIMS1. A method for creating arrays of quantum dots, the method comprising the steps of: providing a semiconductor comprising a quantum well, engineered subsurface regions of photosensitive dopants and a plurality of conducting gates deposited on a surface of the semiconductor; generating light from a source, wherein the light comprises a wavelength capable of photo-exciting and changing a charge state of the photosensitive dopants; directing the light onto a transmission diffractive optical element, installed adjacent to the semiconductor at a predetermined distance, to generate a periodic interference pattern; creating a plurality of elongated quantum dots inside the semiconductor by at least one of applying voltages to a first plurality of the conducting gates and by means of mesa etching; irradiating the semiconductor with the interference pattern generated by the transmission diffractive optical element, wherein the interference pattern has a light intensity and light fluence that are sufficiently high to periodically change the charge state of the photosensitive dopants, thereby inducing a periodic electrostatic potential near the plurality of elongated quantum dots and dividing the plurality of elongated quantum dots into arrays of smaller quantum dots.

2. The method of claim 1, wherein the semiconductor is partially light transmitting or absorbing and comprises transparent, semi-transparent or opaque conducting gates.

3. The method of claim 1, wherein the light is monochromatic or polychromatic, and wherein the source of light is a continuous -wave or a pulsed wave.

4. The method of claim 3, wherein the light has a wavelength ranging from 180 nanometers to 3500 nanometers.

5. The method of any one of claims 1 to 4, wherein the transmission diffractive optical element is one-dimensional, and generates a one-dimensional periodic interference pattern.

6. The method of claim 1, wherein the interference pattern comprises interference fringes oriented perpendicularly or at a smaller angle to the first plurality of the conducting gates or grooves etched in a mesa of the semiconductor.

7. The method of claim 6, wherein the transmission diffractive optical element is a onedimensional transmission phase diffraction grating.

8. The method of claim 6, wherein the transmission diffractive optical element is a onedimensional transmission amplitude diffraction grating.

9. The method of claim 5, wherein the induced periodic electrostatic potential is onedimensional, and the arrays of smaller quantum dots are one-dimensional.

10. The method of any one of claims 1 to 9, wherein the quantum dots are at least one of electron quantum dots and hole quantum dots.

11. The method of claim 1, wherein the quantum dots comprise zero free charge carriers.

12. The method of claim 11, wherein the quantum dots with zero free charge carriers are generated comprising the steps of: applying a predetermined constant voltage to the first plurality of conducting gates and predetermined alternating phase-shifted voltages to a second plurality of conducting gates, adjacent to the smaller quantum dots, in order to ensure that the number of free charge carriers in the smaller quantum dots is zero but cannot exceed one.

13. The method of claim 11, wherein the quantum dots with zero free charge carriers are generated comprising the steps of: applying a predetermined constant voltage to the first plurality of conducting gates, applying a predetermined constant voltage to a global transparent or semi-transparent conducting gate deposited on the semiconductor, andapplying predetermined alternating phase-shifted voltages to a second plurality of conducting gates, adjacent to the smaller quantum dots, in order to ensure that the number of free charge carriers in the smaller quantum dots is zero but cannot exceed one.

14. The method of claim 12 or 13, comprising a further step of transforming the smaller quantum dots into single-spin qubits that confine one free charge carrier.

15. A method for creating a spin-based coherent quantum link between a first quantum computing module and a second quantum module in a semiconductor, wherein the semiconductor can be partially light-transmitting or light-absorbing, and wherein the semiconductor comprises a quantum well, engineered subsurface regions of photosensitive dopants and a plurality of conducting gates deposited on a surface of the semiconductor, the method comprising the steps of: directing light onto a transmission diffractive optical element, installed adjacent to the semiconductor at a predetermined distance, to generate a periodic interference pattern; creating an elongated quantum dot or a plurality of elongated quantum dots inside the semiconductor by applying voltages to a first plurality of the conducting gates; irradiating the semiconductor with the interference pattern generated by the transmission diffractive optical element to periodically change the charge state of the photosensitive dopants, thereby inducing a periodic electrostatic potential near the plurality of elongated quantum dots, and dividing the plurality of elongated quantum dots into at least one array of smaller quantum dots; wherein a charge carrier with a certain spin state can be transported by successively adjusting the electrochemical potentials of the constituting quantum dots by applying alternating phase-shifted voltages to a second plurality of conducting gates and thus the spin- encoded quantum information can be exchanged between a first spin qubit in the first quantum module, adjacent to an input quantum dot in the at least one array, and a second spin qubit in the second quantum module, adjacent to an output quantum dot in the at least one array.

16. The method of claim 15, wherein the quantum dots contain zero free charge carriers and are at least one of electron quantum dots and hole quantum dots.

17. The method of claim 15, wherein the light is monochromatic or polychromatic.

18. The method of claim 17, wherein the source of light is a continuous-wave or a pulsed wave.

19. The method of claim 18, wherein the light has a wavelength ranging from 180 nanometers to 3500 nanometers.

20. A method for creating a spin-based coherent quantum link between a first quantum computing module and a second quantum computing module in a semiconductor, wherein the semiconductor is partially light-transmitting or light-absorbing, and wherein the semiconductor comprises a quantum well, engineered subsurface regions of photosensitive dopants, a plurality of conducting gates deposited on a surface of the semiconductor, a global transparent or semitransparent conducting gate deposited on the semiconductor, the method comprising the steps of: directing light onto a transmission diffractive optical element, installed adjacent to the semiconductor at a predetermined distance, to generate a periodic interference pattern; creating an elongated quantum dot or a plurality of elongated quantum dots inside the semiconductor by applying voltages to a first plurality of the conducting gates and the global transparent or semi-transparent conducting gate; irradiating the semiconductor with the interference pattern generated by the transmission diffractive optical element to periodically change the charge state of the photosensitive dopants, thereby inducing a periodic electrostatic potential near the plurality of elongated quantum dots, and dividing the plurality of elongated quantum dots into at least one array of smaller quantum dots; wherein a charge carrier with a certain spin state can be transported by successively adjusting the electrochemical potentials of the constituting quantum dots by applying alternating phase- shifted voltages to a second plurality of conducting gates and thus the spin-encoded quantum information can be exchanged between a spin qubit in the first quantum module, adjacent to the input quantum dot in the at least one array, and a spin qubit in the second quantum module, adjacent to the output quantum dot in the at least one array.

21. The method of claim 20, wherein the quantum dots contain zero free charge carriers and are at least one of electron quantum dots and hole quantum dots.

22. The method of claim 20 or claim 21, wherein the quantum dots contain one free charge carrier and are at least one of electron spin qubits and hole spin quantum dots.

23. The method of claim 20, wherein the light is monochromatic or polychromatic.

24. The method of claim 23, wherein the source of light is a continuous-wave or a pulsed wave.

25. The method of claim 24, wherein the light has a wavelength ranging from 180 nanometers to 3500 nanometers.

26. A method for creating two-dimensional arrays of quantum dots inside a partially lighttransmitting or light-absorbing semiconductor, comprising the steps of: providing the partially light transmitting or absorbing semiconductor that contains a quantum well, engineered subsurface regions of photosensitive dopants and a global transparent or semi-transparent conducting gate deposited on the surface of the semiconductor; providing a source of light; providing a two-dimensional transmission diffractive optical element, installed adjacent to the partially light transmitting or absorbing semiconductor at a predetermined distance, that when illuminated by the light creates a periodic two-dimensional interference pattern behind a back surface of the transmission diffractive optical element; irradiating the semiconductor with the interference pattern generated by the two- dimensional transmission diffractive optical element, with the light intensity and the light fluence in the two-dimensional interference pattern being sufficiently high to periodically change the charge state of the photosensitive dopants, thus inducing a two-dimensional periodic electrostatic potential near the quantum well and consequently a two-dimensional array ofquantum dots, wherein the number of free charge carriers inside the quantum dots can be simultaneously adjusted by applying a constant voltage to the global conducting gate.

27. The method of claim 26, wherein the light is at least one of monochromatic light and polychromatic light, wherein the light is a continuous -wave or a pulsed wave.

28. The method of claim 26, wherein the light has a wavelength ranging from 180 nanometers to 3500 nanometers in order to photo-excite and change the charge state of the photosensitive dopants.

29. The method of any one of claims 26 to 28, wherein the two-dimensional transmission diffractive optical element is a two-dimensional transmission phase diffraction grating.

30. The method of any one of claims 26 to 29, wherein the two-dimensional transmission diffractive optical element is a two-dimensional transmission amplitude diffraction grating.

31. The method of any one of claims 23 to 29, wherein the transmission diffractive optical element is two-dimensional, and generates a two-dimensional periodic interference pattern.

32. The method of claim 30, wherein the transmission diffractive optical element is a two- dimensional transmission amplitude diffraction grating.

33. The method of claim 30, wherein the induced periodic electrostatic potential is two- dimensional, and the arrays of smaller quantum dots are two-dimensional.

34. The method of any one of claims 1, 15, 20 and 26, comprising a further step of erasing the light-induced quantum dots comprising a step of applying voltage to the semiconductor in order to restore the charge state of the photosensitive dopants and thus erase the light-induced quantum dots.

35. The method of any one of claims 1, 15, 20, and 26 comprising a further step of erasing the light-induced quantum dots comprising a step of locally heating the semiconductor in order to restore the charge state of the photosensitive dopants and thus erase the light-induced quantum dots.

36. The method of any one of claims 1, 15, 20, and 26, comprising a further step of erasing the light-induced quantum dots comprising a step of illuminating the semiconductor in order to restore the charge state of the photosensitive dopants and thus erase the light-induced quantum dots, and wherein the wavelength of the light used for the erasure is different from the wavelength of the light in the interference pattern that was used to create the light-induced quantum dots.

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