Quantum microwave-to-optical transducer and associated methods

Abstract

A quantum transducer includes a back gate having a doped semiconductor layer, a tunnel barrier located above the doped semiconductor layer, a quantum dot contacting a top surface of the tunnel barrier, a cap layer located above the tunnel barrier and covering the quantum dot, a surface acoustic wave (SAW) resonator located above the cap layer, a SAW transducer coupled to the SAW resonator, and a top gate located above the SAW resonator. The SAW resonator is mechanically coupled to the quantum dot. The depth and electrical conductivity of the doped semiconductor layer may be selected such that SAW attenuation is not the dominant contributor to the total phonon loss rate of the SAW resonator. The depth and electrical conductivity may also be selected such that the SAW transducer has a piezoelectric coupling constant of 0.055% or higher.

Description

QUANTUM MICROWAVE-TO-OPTICAL TRANSDUCERAND ASSOCIATED METHODSRELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 608,848, filed December 12, 2023, the entirety of which is incorporated herein by reference.STATEMENT REGARDING FEDERALLYSPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under grant number 70NANB23H027, awarded by the National Institute of Standards and Technology (NIST). The government has certain rights in the invention.BACKGROUND

[0003] Microwave-to-optical quantum transducers may be used to unlock the potential of quantum networks by leveraging the unique strengths of diverse quantum systems [1, 2], These quantum transducers bridge the gap between microwave frequencies, which are characteristic of superconducting [3, 4] and spin-based [5,6] quantum processors, and optical frequencies that are preferable for transmitting quantum information over long distances [7, 8], These transducers therefore allow the exchange of quantum information between quantum nodes over distances that would otherwise be infeasible.SUMMARY

[0004] An ideal microwave-to-optical transducer converts a microwave signal to an optical signal (and vice versa) with 100% efficiency and no added noise. However, a five-order- of-magnitude energy gap between microwave and optical frequencies makes it challenging to build such a transducer with high efficiency. In quantum information processing and quantum communication, heralding protocols may be used to largely bypass this obstacle, improving fidelity at the expense of communication rate. However, minimizing added noise remains an important challenge for the design and fabrication of such a transducer [9],

[0005] One approach to quantum microwave-to-optical transduction uses hybrid systems based on mechanical resonators (i.e., confined phonons)

[0010] , These electro-optomechanical systems take advantage of the slower speed of phonons compared to photons,resulting in phonons at gigahertz frequencies with wavelengths comparable to optical photons. This is key for mediating interactions across the energy gap. Phonons interact well with various types of quantum systems

[0011] , For example, phonons piezoelectrically interact with superconducting qubits

[0012] and parametrically modulate various optical systems, such as optical cavities

[0013] and single photon emitters (SPEs) in two-dimensional (2D) materials [14— 16], defect centers [17-19], and semiconductor quantum dots (QDs) [20-24],

[0006] Integrating two standalone electromechanical and optomechanical systems is challenging due to the added system complexity and possible incompatibility

[0025] , The present embodiments overcome this integration challenge with an electro-opto-mechanical system that uses gated self-assembled QDs that are mechanically coupled to a surface acoustic wave (SAW) resonator. The present embodiments may also incorporate microwave and DC electronics, optics, and mechanical elements in a single structure. Advantageously, the present embodiments can fully realize the advantages of QDs as optical two-level systems for optomechanics, including single-phonon generation

[0026] and acousto-optic preparation of exciton or biexciton states

[0027] , which have so far been only theoretically proposed. In addition, interactions between acoustics and other types of SPEs (e.g., diamond vacancies) have recently been studied [28-30], The present embodiments advance QD technology, with its many advantages, to the same level of development as these other systems. When combined with superconducting qubits [31, 32], the present embodiments may be used for low-noise and efficient conversion of quantum information between the microwave and optical domains.

[0007] In some of the present embodiments, a quantum transducer includes a back gate having a doped semiconductor layer, a tunnel barrier located above the doped semiconductor layer, a quantum dot contacting a top surface of the tunnel barrier, a cap layer located above the tunnel barrier and the quantum dot, a surface acoustic wave (SAW) resonator located above the cap layer, a SAW transducer coupled to the SAW resonator, and a top gate located above the SAW resonator. The SAW resonator is mechanically coupled to the quantum dot.BRIEF DESCRIPTION OF THE FIGURES

[0008] FIG. 1A is a top view of a quantum microwave-to-optical transducer 100, in embodiments. FIG. IB is a side sectional view of the quantum transducer of FIG. 1A, taken along the cutting plane line labeled “IB” in FIG. 1A. FIG. 1C is a side sectional view of the quantum transducer of FIG. 1A, taken along the cutting plane line labeled “1C” in FIG. 1A. FIG. ID is a scanning electron microscope (SEM) image showing fingers of an interdigital transducer (IDT). FIG. IE is an SEM image of an etched surface acoustic wave (SAW)distributed Bragg reflector (DBR).

[0009] FIGS. 2A and 2B show a reflection spectrum and a transmission spectrum, respectively, measured with SAW delay lines. FIG. 2C is a plot of peak transmitted SAW signal versus delay-line gap between the IDTs of the SAW delay lines. FIG. 2D shows reflection spectra of SAW resonators with the same design parameters, fabricated on substrates with (bottom panel) and without (top panel) a doped layer.

[0010] FIG. 3A shows a photoluminescence spectrum of a gated quantum dot, as measured with a spectrometer and charge-coupled device (CCD) camera. FIG. 3B shows the resonance fluorescence signal of the gated quantum dot, as measured with a superconducting nanowire single photon detector (SNSPD). FIG. 3C shows a photoluminescence spectrum of the gated quantum dot with SAW modulation at a fixed frequency of 3.53388 GHz, as measured with a Fabry-Perot filter and the SNSPD. FIG. 3D shows the photoluminescence spectrum of the gated quantum dot at a fixed gate bias with varying microwave drive frequency and constant microwave power, as measured with the Fabry-Perot filter and SNSPD.

[0011] FIG. 4A is a plot of calculated phonon loss rate versus conductivity <J for SAWs propagating along the

[0110] direction of a free GaAs surface located above a uniform conductive thin layer. FIG. 4B is a plot of piezoelectric coupling constant k2versus doped layer depth for SAWs propagating along the

[0110] direction of the free GaAs surface located above the uniform conductive thin layer.DETAILED DESCRIPTIONIntroduction

[0012] Self-assembled quantum dots (QDs) are a type of single-photon emitter (SPE) that offers many benefits over other types of SPEs, such as trapped ions, color centers, vacancies, and defects. For example, self-assembled indium arsenide (InAs) QDs have been used to demonstrate state-of-the-art end-to-end photon collection efficiencies as high as 57%

[0033] , two-photon interference visibilities as high as 99%

[0034] , and repetition rates up to 1 GHz

[0033] , Furthermore, self-assembled QDs are embedded in semiconductor materials and are compatible with various fabricated photonic structures for efficient photon extraction [35-38], Another advantage of self-assembled QDs is that their electrostatic environment and charge state can be controlled by a simple gate structure

[0039] , With deterministic trapping of a single charge or hole, self-assembled QDs enable spin-photon entanglement

[0040] and remote spin-spin entanglement

[0041] , as needed for quantum information processing applications. Finally, manytypes of self-assembled QDs (e.g., InAs QDs embedded in GaAs) exhibit a relatively simple energy level structure that approximates a two-level system, allowing for deterministic excitation with straightforward optical pumping schemes. These features and advantages provide a promising route toward the generation of single phonons for phononic-based quantum technologies

[0026] , In contrast, atoms and ions require active trapping mechanisms and complex optical pumping schemes for cooling and state preparation

[0042] , Atoms and ions also suffer from poor photon collection efficiencies into fiber

[0043] , While color centers, vacancies, and defects have some promising properties, they suffer from non-unity quantum efficiencies and often fast phonon-assisted emission pathways

[0044] ,

[0013] Self-assembled InAs QDs embedded in GaAs are particularly promising for optomechanical devices as they are sensitive to local strain fields

[0045] due to the large deformation potential of GaAs (~1014- 1015Hz)

[0022] , This sensitivity is exemplified by large optomechanical single-phonon coupling rates on the order of a few megahertz [46, 47], exceeding state-of-the-art systems based on optomechanical crystals [1, 48], Moreover, with gigahertz -frequency phonon modes, mechanical motion can be passively cooled to the ground state while the QD scatters photons at gigahertz rates under extremely low optical pump powers (~100 pW)

[0049] , suggesting the possibility for low-noise operation

[0047] ,

[0014] While these results are promising, they were all obtained using ungated QDs. The lack of gating limited the optomechanical performance of these devices in two ways: (i) a reduced interaction duty cycle between the QD and the resonant pump laser as the QD randomly hops between different charge states and (ii) inhomogeneous broadening of the QD linewidth due to moving charges nearby. Both of these detrimental effects lower optomechanical cooperativity and transduction efficiency.

[0015] A gate structure for InAs QDs typically includes (i) a back gate formed from a thin n-doped GaAs: Si layer that is located just below the QDs and (ii) a top gate that is formed from either a layer of metal (Schottky structure) or a p-doped GaAs layer (p-i-n structure) that is located above the QDs

[0039] , By applying an electric potential across these two gates, the net charge of the QD may be controlled via the Coulomb blockade and the charge noise is significantly reduced as excess charges get depleted. The importance of integrating charge- controlled (i.e., gated) QDs with state-of-the-art surface acoustic wave (SAW) resonators cannot be overstated, with evidence in the years of research that led to QD-based devices surpassing the performance of down-conversion sources for pure and indistinguishable singlephoton generation [49, 50],

[0016] One challenge with integrating a SAW resonator with a gated QD is the impactof the doped semiconductor layer (i.e., the back gate) on the creation and propagation of SAWs. In particular, the present embodiments overcome three systematic effects that can adversely affects quantum-transduction efficiency. The first systematic effect is piezoelectric coupling of the SAW-resonator material to the electrical dissipation of the doped semiconductor layer, which increases the phonon loss rate of the SAW resonator. The second systematic effect is screening of the piezoelectric transducer (e.g., a interdigital transducer) by to the electrical conductivity of the doped semiconductor layer. This second systematic effect reduces the piezoelectric coupling used to electrically excite the SAW resonator. The third systematic effect is a change in the impedance of adjacent microwave-circuit elements (e.g., a planar transmission line) due to the electrical conductivity of the doped semiconductor layer. This third systematic effect further reduces the piezoelectric coupling by reflecting most of the microwave electrical power used to excite the SAW resonator.

[0017] The present embodiments include quantum transducers that are configured to overcome these three adverse effects, both individually and in combination. The present embodiments also include corresponding methods for microwave-to-optical transduction that are based on operation of the quantum transducers. Furthermore, while the quantum transducers of the present embodiments are described herein as performing microwave-to-optical transduction, it should be understood that these quantum transducers may also be operated in reverse to perform quantum opti cal -to-micro wave transduction. Thus, the present embodiments also include methods for opti cal -to-microwave transduction that are similarly based on operation of these quantum transducers.Device Embodiments

[0018] FIG. 1A is a top view of a quantum microwave-to-optical transducer 100, in accordance with some of the present embodiments. FIG. IB is a side sectional view of the quantum transducer 100, taken along the cutting plane line labeled “IB” in FIG. 1A. FIG. 1C is a side sectional view of the quantum transducer 100, taken along the cutting plane line labeled “1C” in FIG. 1A. With regards to FIGS. 1A, IB, and 1C, all directions and dimensions are identified relative to a right-handed Cartesian coordinate system 120. For clarity, the views shown in FIGS. 1A, IB, and 1C are not necessarily drawn to scale. FIGS. 1A, IB, and 1C are best viewed together with the following description.

[0019] As shown in FIGS. IB and 1C, the quantum transducer 100 includes a stack of layers. Specifically, the quantum transducer 100 includes a substrate 102 on which the other layers are grown, etched, deposited, or otherwise fabricated. The quantum transducer 100 alsoincludes a back gate 106 located above (i.e., the +z direction) the substrate 102, a tunnel barrier 108 located above the back gate 106, a wetting layer 110 located above the tunnel barrier 108, one or more quantum dots 136 extending upward (i.e., the +z direction) from the wetting layer 110, a cap layer 112 located above the wetting layer 110 and covering the one or more quantum dots 136, and a SAW layer 116 located above the cap layer 112.

[0020] The back gate 106 is composed of a doped semiconductor material that is electrically conductive. For example, the doped semiconductor material may be n-type silicon- doped gallium arsenide (GaAs:Si) or aluminum gallium arsenide (AlGaAs). In the experimental prototype described below (see section titled “Demonstration”), the doped semiconductor material was GaAs:Si with a doping concentration of 2* 1018cm’3and an electrical conductivity <JXXof 105S / m. However, the doped semiconductor material may have a different doping concentration, electrical conductivity, or both, without departing from the scope hereof.

[0021] As shown in FIGS. IB and 1C, the top of the back gate 106 is located a depth d below (i.e., in the -z direction) a top surface 182 of the SAW layer 116. The back gate 106 has a thickness t, as measured along z. For the experimental prototype described below, the thickness t was 47 nm and the depth d was 360 nm. However, the thickness t may alternatively be greater than 47 nm or less than 47 nm. Similarly, the depth d may alternatively be greater than 360 nm or less than 360 nm (e.g., see FIG. 4B and the corresponding text).

[0022] As shown in FIG. IB, the one or more quantum dots 136 are located beneath (i.e., in the -z direction) a SAW resonator 180 formed in the SAW layer 116. In general, the quantum dots 136 may be composed of any semiconductor material used in the art for fabricating quantum dots. In the example of FIGS. 1A, IB, and 1C, the quantum dots 136 are self-assembled. In this case, the quantum dots 136 may be composed, for example, of indium arsenide (InAs) or indium gallium arsenide (InGaAs). These self-assembled quantum dots 136 may be buried in a material that is not lattice-matched to the semiconductor material of the quantum dots 136. For example, when the quantum dots 136 are composed of InAs or InGaAs, the tunnel barrier 108 and cap layer 112 may be composed of gallium arsenide (GaAs). Other materials that may be used for the tunnel barrier 108 and cap layer 112 include, but are not limited to, indium gallium phosphide (InGaP), aluminum arsenide (AlAs), and alloys thereof.

[0023] The SAW resonator 180 includes a first SAW mirror 122(1) and a second SAW mirror 122(2) that face each other to define an acoustic axis 125 that lies parallel to the x axis and coincides with the transverse (i.e., perpendicular to the acoustic axis 125) centers of the SAW mirrors 122(1) and 122(2). The SAW resonator 180 also includes an inter-mirror region186 located between the SAW mirrors 122(1) and 122(2). As shown in FIG. IB, each of the SAW mirrors 122(1) and 122(2) may be a distributed Bragg reflector (DBR) mirror formed from a series of trenches 188 that are formed downward (i.e., in the -z direction) from the top surface 182 of the SAW layer 116. In this case, the top surface 182 of the SAW layer 116 coincides with the top surface of the SAW resonator 180. One or both of the SAW mirrors 122(1) and 122(2) may be another type of acoustic mirror or reflector known in the art.

[0024] The quantum transducer 100 also includes a SAW transducer 124 that is located on the top surface 182 and in the inter-mirror region 186 of the SAW resonator 180, as shown in FIG. IB. When the SAW layer 116 is composed of a piezoelectric material, an oscillating voltage applied to the SAW transducer 124 induces an oscillating strain within the SAW layer 116. This oscillating strain, in turn, excites a SAW resonance of the SAW resonator 180 when the frequency of the oscillating voltage matches the resonant frequency of the SAW resonance. Piezoelectric materials that may be used for the SAW layer 116 include, but are not limited to, InGaP, GaAs, AlAs, and alloys thereof.

[0025] In the embodiment shown in FIGS. 1 A and IB, the SAW transducer 124 is an interdigital transducer (IDT) formed from first and second series of IDT fingers that are interlocking. FIGS. IB and 1C show a first finger 154(1) that is a member of the first series of IDT fingers and a second finger 154(2) that is a member of the second series of IDT fingers. The SAW transducer 124 may be composed of metal deposited (e.g., via evaporation) directly onto the top surface 182. For example, in the experimental prototype described below, the IDT was formed from a 20-nm layer of aluminum (Al) or gold (Au). The IDT may be thin enough (along z) that it is partially optically transparent. The IDT may be formed from one or more other types of metal without departing from the scope hereof. The SAW transducer 124 may be another type of electrode or transducer known in the art.

[0026] As shown in FIG. 1 A, the SAW transducer 124 may be driven by a microwave signal 145, i.e., an electromagnetic signal whose frequency f lies in the microwave regime of the electromagnetic spectrum (e.g., 300 MHz to 300 GHz). The microwave signal 145 excites a SAW resonance whose resonant frequency is also f . To drive the SAW transducer 124, some embodiments of the quantum transducer 100 further include a microwave circuit 130 whose output is electrically connected to the SAW transducer 124. This microwave circuit 130 may be fabricated with the other layers of the quantum transducer 100 such that the microwave circuit 130 is fully integrated with the SAW resonator 180 and SAW transducer 124. Examples of this microwave circuit 130 include, but are not limited to, a microwave transmission line (e.g., coaxial cable, twisted pair, etc.), an electromagnetic microwave resonator, and logiccircuitry (e.g., superconducting logic).

[0027] In the example of FIG. 1A, the microwave circuit 130 is a coplanar waveguide (CPW) having a main line 194 and adjacent return conductors 192 that are coplanar (in the x- y plane) with the main line 194. The microwave signal 145 propagates along the main line 194 toward the IDT. One end of the main line 194 is electrically connected to the first series of IDT fingers, including the first finger 154(1) (see FIG. 1C). Also in the example of FIG. 1A, the microwave circuit 130 includes a ground pad 196 that is electrically connected to the second series of IDT fingers, including the second finger 154(2) (see FIG. 1C). The ground pad 196 may be electrically connected to an external ground that is outside the quantum transducer 100. As shown in FIG. 1C, the ground pad 196 may be fabricated (e.g., by depositing metal into the vias 190) so that it is shorted to the ohmic contacts 138 and therefore the back-gate pad 134. Alternatively, the ground pad 196 may be electrically isolated from the ohmic contacts 138 (and therefore the back-gate pad 134). The CPW may be replaced with another type of planar transmission line known in the art (e.g., microstrip, stripline, slotline, finline, etc.).

[0028] The quantum transducer 100 also includes a top gate 126 located on the top surface 182 and in the inter-mirror region 186 of the SAW resonator 180. The top gate 126 is an electrode composed of an electrically conductive material located on the top surface 182. The top gate 126 may have a thickness along z that is small enough that the top gate 126 is partially optically transparent. The electrically conductive material may be metal, in which case the top gate 126 cooperates with the underlying semiconductor material of the SAW layer 116 to create a Schottky barrier. Thus, for this choice of materials, the top gate 126 is also known as a “Schottky gate.” For example, in the experimental prototype described below (see section titled “Demonstration”), the top gate 126 was a Schottky gate formed from a 3-nm layer of titanium (Ti) capped by a 7-nm layer of gold (Au). However, the top gate 126 may be formed of other metals without departing from the scope hereof.

[0029] To facilitate wirebonding, some embodiments of the quantum transducer 100 further include a top-gate pad 132 that is electrically connected to the top gate 126. The top gate 126 and top-gate pad 132 may be composed, either entirely or in part, of the same electrically conductive material. Alternatively, the top gate 126 and top-gate pad 132 may be composed of different electrically conductive materials (e.g., different types of metal). The top-gate pad 132 lies outside of the SAW resonator 180, where optical transparency is not needed. Thus, the topgate pad 132 may be thicker than the top gate 126. For example, in the experimental prototype described below, the top-gate pad 132 was formed from a 10-nm layer of titanium capped by a 250-nm layer of gold. Like the top gate 126, the top-gate pad 132 may be formed of other metalswithout departing from the scope hereof.

[0030] To facilitate an electrical connection to the back gate 106, some embodiments of the quantum transducer 100 further include one or more ohmic contacts 138 that extend downward (i.e., in the -z direction) toward the back gate 106. The ohmic contacts 138 may be composed, for example, of metal deposited into one or more vias 190 or trenches that are etched downward from the top surface 182 of the SAW layer 116. This metal may be deposited, for example, via electron-beam evaporation or another metal-deposition technique known in the art. When the back gate 106 is composed of a semiconductor material (e.g., GaAs), the deposited metal and back gate 106 cooperate to form a Schottky barrier. For example, in the experimental prototype described below, the deposited metal was a combination of nickel (Ni), gold germanium (AuGe), and gold (Au) that was thermally annealed. However, the ohmic contacts 138 may be formed of other types of metal without departing from the scope hereof.

[0031] To prevent acoustic loss, the vias 190 are located transversely (i.e., parallel to the x-y plane) outside of the SAW resonator 180. Similarly, the back-gate pad 134 is also located transversely outside of the SAW resonator 180. As described in more detail below, the bottoms of the vias 190 (in the -z direction) need not reach or contact the back gate 106. For example, FIGS. IB and 1C show the bottoms of the vias 190 coinciding with the cap layer 112.

[0032] To facilitate wirebonding, some embodiments of the quantum transducer 100 further include a back-gate pad 134 that is electrically connected to the ohmic contacts 138 (see FIG. 1 A). The back-gate pad 134 may be composed of an electrically conductive material, such as metal. This metal may be deposited into the vias 190 (e.g., via evaporation) such that it directly contacts the ohmic contacts 138. The back-gate pad 134 and ohmic contacts 138 may be composed, either partially or entirely, of the same metal or metals. Alternatively, the back- gate pad 134 and ohmic contacts 138 may be composed of different metals.

[0033] In some embodiments, the quantum transducer 100 further includes a DBR optical mirror 140 located above the substrate 102 and beneath the back gate 106. The DBR optical mirror 140 is configured to reflect downward-propagating photons into upward- propagating photons. Thus, the DBR optical mirror 140 may be used to improve the photon collection efficiency of photons emitted by the quantum dots 136. The DBR optical mirror 140 is a sequence of layers that alternate between a low refractive-index material 162 and a high refractive-index material 160. For example, the low refractive-index material 162 may be AlAs (n « 2.94 at 1 pm) and the high refractive-index material 160 may be GaAs (n « 3.47 at 1 pm). However, each of the materials 160 and 162 may be another material used for fabricating DBR optical mirrors without departing from the scope hereof.

[0034] In some embodiments, the quantum transducer 100 also includes a current barrier 114 that is located above the cap layer 112 and beneath the SAW layer 116. Also known as a “blocking barrier,” the current barrier 114 prevents current flow to the top surface 182.Systematic Effects

[0035] One aspect of the present embodiments is the realization that there are three systematic effects that may adversely reduce the microwave-to-optical transduction efficiency. As described in more detail in this section, these three systematic effects are all related to the back gate 106. This section also describes how the present embodiments overcome these systematic effects to achieve or maintain a relatively high transduction efficiency.

[0036] The first systematic effect is SAW propagation loss in the SAW layer 116 due to the presence of the back gate 106. This systematic effect is represented in FIG. IB as an attenuation coefficient K. The SAW layer 116 is composed of a piezoelectric material that piezoelectrically couples to the back gate 106. Due to this piezoelectric coupling, the acoustic properties of the SAW layer 116 are affected by the electrical properties of the back gate 106. Specifically, the finite electrical conductivity of the doped semiconductor material forming the back gate 106 introduces dissipation that affects SAW propagation, including the attenuation coefficient K. If this dissipation is sufficiently large, it can adversely reduce the phonon lifetime (or, equivalently, increase the phonon loss rate) of the SAW resonator 180. This reduction in phonon lifetime (and increase in phonon loss rate) reduces the Q factor of the SAW resonator 180, which in turn reduces the transduction efficiency.

[0037] Mathematically, the SAW layer 116 and back gate 106 can be modeled as a thin piezoelectric slab and an electrically conductive medium, respectively. The electrically conductive medium is shaped as a sheet that is perpendicularly displaced from the slab by a depth d (e.g., see the depth d in FIGS. IB and 1C). A SAW propagating along the slab will have a velocity shift AV and attenuation coefficient K given bywhere <JXXis the longitudinal electrical conductivity of the electrically conductive medium, q is the wavevector of the SAW, and a2and amare system-specific coefficients [51, 52], The coefficient a2depends on (i.e., is a function of) one or more components of the piezoelectric tensor of the material forming the slab; it is assumed that these tensor components are fixed for a given slab material. Both of the coefficients a2and omdepend on the depth d.

[0038] In the present embodiments, the quantum transducer 100 of FIGS. 1A, IB, and1C operates in what is referred to herein as the “low SAW -loss regime.” In this regime, SAW attenuation, as quantified by the attenuation coefficient K, is not the dominant contributor to the total phonon loss rate of the SAW resonator 180. For example, the total phonon loss rate for state-of-the-art gigahertz SAW resonators is approximately 100 kHz. Thus, for this class of SAW resonator, the quantum transducer 100 is configured such that SAW attenuation contributes less than 100 kHz to the total phonon loss rate of the SAW resonator 180.

[0039] Another aspect of the present embodiments is the realization that the attenuation coefficient K can be reduced by increasing the electrical conductivity oxx. Specifically, Eqn. 1 shows that negligible SAW attenuation occurs when oxx» am. Thus, the low SAW-loss regime can be accessed by increasing the doping concentration of the doped semiconductor layer forming the back gate 106, which in turn increases the electrical conductivity axx.

[0040] Another aspect of the present embodiments is the realization that the attenuation coefficient K can be reduced by increasing the depth d. As shown in Fig. 2 of Ref.

[0051] , increasing the depth d reduces the coefficient a2while the coefficient amapproaches a constant. From Eqn. 1, this reduction in a2also reduces the attenuation constant K, even for relatively low values of the electrical conductivity axx. Thus, the low SAW-loss regime may also be accessed by increasing the depth d. However, there is a limit to how much the depth d can be increased, as discussed below.

[0041] In some embodiments, the doped semiconductor layer forming the back gate 106 has an electrical conductivity axxand a depth d such that the quantum transducer 100 operates in the low SAW-loss regime. In some embodiments, the doped semiconductor layer is composed of an n-type semiconductor material with a doping concentration such that the n- type semiconductor material has an electrical conductivity axxof 103S / m or more. In other embodiments, the doped semiconductor layer has a depth d of 100 nm or more.

[0042] The second systematic effect is poor piezoelectric coupling between the SAW transducer 124 and the SAW resonator 180. Here, the doped semiconductor layer forming the back gate 106 suppresses the launching of SAWs (i.e., exciting a resonance of the SAW resonator 180) by screening the microwave field (see the microwave signal 145 in FIG. 1A) applied to the SAW transducer 124 [53, 54], This effect will decrease with increasing depth d of the doped semiconductor layer. However, there is a limit to how large the depth d can be since (i) the doped semiconductor layer should be sufficiently close to the quantum dots 136 to optimize depletion of excess charges and (ii) the quantum dots 136 should be located near the top surface 182 where the strain field is largest. In some embodiments, the doped semiconductorlayer has an electrical conductivity oxxand a depth d such that the SAW transducer 124 has a piezoelectric coupling constant of 0.055% or higher.

[0043] The third systematic effect is an impedance mismatch between the CPW and the source of the microwave signal 145. Due to this impedance mismatch, some of the microwave signal 145 is reflected back to the source. Due to the proximity (typically several hundred nanometers) of the doped semiconductor layer to the CPW, the microwave mode in the CPW is modified, thereby reducing the characteristic transmission-line impedance from a nominal value of 50 Q to only 3 Q. Due to this drop in impedance, 88% of the power of the microwave signal 145 will be reflected, thereby reducing the SAW launching efficiency.

[0044] To avoid this third systematic effect, the doped semiconductor layer is removed from underneath the microwave circuit 130. For example, in FIG. 1 A the doped semiconductor layer is removed from underneath the main line 194 and return conductors 192 of the CPW so that the CPW recovers its nominal transmission-line impedance of 50 Q. As shown in FIG. 1 A, the doped semiconductor layer only exists within the region outlined by the dashed line 144. The doped semiconductor layer is etched away everywhere outside of this region.Demonstration

[0045] An experimental prototype of the quantum transducer 100 of FIGS. 1 A, IB, and 1C was fabricated and tested. For this prototype, the doped semiconductor layer forming the back gate 106 was composed of n-type GaAs:Si with a doping concentration of 2* 1018cm’3. The thickness t of the doped semiconductor layer was 47 nm. From Hall measurements, the doped semiconductor layer had an electrical conductivity oxxof 105S / m. The value of amwas estimated to be 10 S / m

[0010] , Therefore, the prototype operated in the low SAW-loss regime. Numerical and analytical calculations further show that these values of axxand omcorrespond to a phonon loss rate on the order of 100 Hz (see “Supplementary Information”). In comparison, current state-of-the-art gigahertz SAW resonators have phonon loss rates on the order of 100 kHz, mostly due to bulk scattering losses.

[0046] The impact of the depth d on SAW launching efficiency was evaluated numerically (see “Supplementary Information” below). The conductivity oxxand thickness t of the doped semiconductor layer were fixed to experimentally derived values. The coupling constant k2begins to drop dramatically when the doped semiconductor layer is within approximately 400 nm of the IDT. Considering constraints on the depth of the quantum dots 136, a depth d of 360 nm was chosen, which provides good coupling while retaining 80% of the coupling constant compared to that of bulk semi-insulating GaAs substrates.

[0047] Microwave Measurements Characterizing the SAW Resonator

[0048] To experimentally verify the solutions described above, acoustic delay lines were first fabricated from two IDTs separated by a gap of approximately 400 pm on a “chargecontrol substrate” (i.e., with the doped semiconductor layer). The delay lines’ performance was compared to identical devices fabricated on mechanical -grade semi-insulating GaAs substrates without the doped semiconductor layer. The microwave reflection and transmission of the acoustic delay lines were measured with a vector network analyzer (VNA) in a probe station at room temperature. As shown in FIG. 2A, similarity in the reflection-spectrum (IS^ |2in dB vs. frequency in GHz) dip sizes between identical devices on the two substrates indicates negligible reduction in piezoelectric coupling between IDTs and SAWs. SAW generation and attenuation were analyzed by looking at peak transmitted signals in the transmission spectrum (|S2112in dB versus frequency in GHz; see FIG. 2B) with different delay line gaps (see FIG. 2C). Variations in the peak transmitted power with propagation length directly reveal phonon loss rates. The error bars in FIG. 2C represent the noise in the transmission spectra as a result of beating between the acoustic signal and electrical crosstalk. Due to the doped semiconductor layer, this electrical crosstalk is larger in the “charge-control substrate,” leading to slightly higher noise level. However, similar transmission peak power and loss per unit length show that (1) microwave power is delivered equally well to the IDTs in both systems and (2) propagation loss introduced by the doped semiconductor layer is not evident above the measurement uncertainty. To further verify this, planar SAW resonators on charge-control substrates were fabricated, cooled to 1.7 K, and measured to characterize losses and external coupling rates. By fitting the microwave reflection spectra (see “Supplementary Information”), an internal (external) quality factor Qt(Qe) of approximately 28,000 (112,500) was extracted (see FIG. 2D, lower panel). Both internal losses (as characterized by the internal quality factor Qi) and electromechanical coupling (as characterized by the external quality factor Qe) are comparable to similar devices fabricated on a semi-insulating GaAs substrate (see FIG. 2D, upper panel). In addition, the internal quality factor Qtis comparable with the state-of-the-art SAW cavities fabricated on a variety of materials at gigahertz frequencies [55-60], This demonstrates that the doped semiconductor layer can be integrated with the SAW resonator 180 without degrading electromechanical performance. By comparing these results with previous results in the literature

[0046] , it is clear that losses are dominated by features unrelated to the doped semiconductor layer, but rather to bulk scattering from the mirrors 122(1) and 122(2) and the IDT. In particular, the higher values of Qi and better coupling demonstrated herein, as compared to Ref.

[0046] , are related to the lighter IDT metal (aluminum, compared to niobium orgold; see “Supplementary Information”).

[0049] Optical Characterization of the Hybrid Device

[0050] In the prototype, the top gate 126 was a thin semi-transparent layer of Ti / Au inside the SAW resonator 180, forming a Schottky-diode structure. Optical measurements were performed on the quantum dots 136 located directly below this top gate 126. The top gate 126 was connected to a thick Ti / Au layer (see the top-gate pad 132 in FIG. 1A) outside the SAW resonator 180 for wirebonding. The metal surrounding the SAW resonator 180 provides ohmic contact to the doped semiconductor layer and ensures a uniform electric potential across the doped semiconductor layer.

[0051] The fabricated device was cooled in a 5-K optical cryostat. Optical and microwave measurements were performed to characterize the optomechanical performance of the prototype. To determine the behavior of the gated quantum dots, photoluminescence of a single quantum dot was measured while varying the bias voltage V applied to the Schottky diode (see bias voltage V applied to the top-gate pad 132 in FIG. 1A). The quantum dot was excited with a non-resonant pump at 632 nm and photoluminescence was measured with a spectrometer and a charge-coupled device (CCD) detector. FIG. 3 A shows two charge plateaus when sweeping the bias voltage V, which is a signature of gated quantum dots: the emission energy changes abruptly as a result of adding or removing charge. The following experiments were conducted on the state around 0 V.

[0052] Resonance fluorescence is a sensitive probe of both a quantum dot’s linewidth and additional noise sources in the quantum dot’s environment [33, 61], While the bias voltage V was fixed at one of the charge plateaus, the quantum dots were resonantly pumped and reflected pump photons were rejected with a cross-polarization scheme. The experimental setup was similar to that described in Ref.

[0021] , FIG. 3B shows an exemplary resonance fluorescence spectrum of the unmodulated quantum dot. The measured optical linewidth is approximately 643.6 MHz, comparable to the state-of-the-art performance described in Ref.

[0033] , This narrow linewidth is a result of the reduced charge-noise of the gated quantum dots, compared to a typical linewidth of approximately 1.7 GHz without a gate structure.

[0053] The gated quantum dots also interact with SAW resonators optomechanically. While the SAW resonator 180 of the prototype was resonantly driven with an external microwave source, the photoluminescence of the quantum dot was measured as a function of the bias voltage V. The photoluminescence spectrum was measured with a tunable Fabry-Perot filter having a 600-MHz linewidth. As shown in FIG. 3C, the quantum dot is phase-modulated by the SAW field, resulting in a series of optical sidebands. The entire phase-modulatedspectrum is Stark-shifted by varying the bias voltage V , with a rate of approximately 0.13 GHz / mV, verifying that both the quantum-dot charge control and SAW resonator 180 operate simultaneously.

[0054] The modulated quantum-dot spectrum depends on the SAW field amplitude and can act as a probe to measure the acoustic Q factor of the fully integrated device under optical pumping

[0046] , The acoustic Q factor sampled by the quantum dot includes both internal and external loss channels. The quantum dot photoluminescence spectrum was measured by fixing the bias voltage V and the microwave drive power while sweeping the microwave drive frequency around the SAW-resonator mode. The modulation index 6 was then extracted by fitting the phase-modulated photoluminescence spectrum as a function of the microwave drive frequency. A Lorentzian fit to 62shows a clear acoustic resonance with a linewidth of approximately 232 kHz, corresponding to a Q factor of approximately 15,000. Microwave reflection measurement of the same cavity mode shows a total Q of approximately 17,800 (Q(- « 18,500; see “Supplementary Information”). This small discrepancy may be due to local heating or additional charges in the cavity introduced by the pump laser, which can be avoided when pumping the quantum dots 136 resonantly. This suboptimal internal quality factor of 18,500, compared to value of 28,000 shown in FIG. 2D, is likely due to design imperfections in the resonators when introducing the thin Ti / Au layer. These design issues may be solved by more carefully compensating for SAW phase-velocity changes under the Ti / Au layer. In addition, it is estimated that the single-phonon coupling rate g0is approximately 42 kHz for this prototype (see “Supplementary Information”). Compared to the best value of g0achieved in previous work

[0046] , this smaller value of g0is a result of a larger cavity-mode volume, which was used for easier characterization. The design principle described in this work may be immediately applied to the tightly focusing cavities studied in Ref.

[0046] to achieve values of g0larger than 1 MHz. Therefore, gated quantum dots and SAW resonators may be integrated without sacrificing the performance of the individual components.Supplementary Information

[0055] Sample Structure and Fabrication Process

[0056] With the exception of the top metal layers, all components of the prototype were grown by molecular beam epitaxy (MBE). The structure includes a distributed Bragg reflector (DBR) below, formed by 22 pairs of AlAs / GaAs layers, for improved photon collection efficiency. The doped GaAs (GaAs:Si) layer was 46-nm thick and located 360 nm below the surface. The InAs quantum dots were located 30 nm above the n-doped GaAs, at the antinodeof the field in the weak cavity formed by the DBR and the thin Au film on top. A 40-nm-thick layer of an AlAs / GaAs superlattice was located near the surface to block current flow between the two gates of the Schottky diode (see current barrier 114 in FIGS. IB and 1C).

[0057] The MBE-grown wafer was then processed. First, the SAW DBR mirror trenches (see trenches 188 in FIG. IB) were defined by electron beam lithography (EBL) and etched by reactive-ion etching (RLE). Then, ohmic contacts to the n-doped GaAs layer (see ohmic contacts 138 in FIGS. IB and 1C) were made by first etching vias around the SAW resonator down to approximately 100 nm above the GaAs: Si layer and then depositing approximately 400 nm of Ni / AuGe / Ni / Au by electron-beam evaporation. The metals were thermally annealed in forming gas (95% argon (Ar) and 5% hydrogen gas (Ek)) at 420°C for one minute to optimize contact resistance. To finish the Schottky -di ode structure, a thin layer of Ti / Au (3 nm / 7 nm) was evaporated inside the acoustic resonator region (i.e., the inter-mirror region 186 of FIG. IB) along with a thick layer of Ti / Au (10 nm / 250 nm) outside the resonator region to connect to large wirebond pads (see top-gate pad 132 and back-gate pad 134 in FIG. 1A). In the next step, the n-doped layer was etched away everywhere outside the SAW resonator region so that the on-chip microwave CPW and wirebond pads were unaffected by the doped layer. The CPW traces (see main line 194 and return conductors 192 in FIG. 1A) were then defined by photolithography and lifted-off with 450 nm of Ti / Au. The thickness of the CPW metal was chosen to be thicker than the etched depth so that it connect across the step. Finally, 20 nm of gold (Au) or aluminum (Al) were deposited to fabricate the IDTs (see the SAW transducer 124 of FIGS. 1A and IB). The IDT structure was defined by EBL and then formed using a lift-off process. Gold IDTs were used for the measurements shown in FIGS. 2 A, 2B, and 2C while aluminum IDTs were used for the measurements shown in all other figures.

[0058] Estimates for SAW Propagation Losses and Electromechanical Coupling

[0059] A highly n-doped thin epitaxial layer below the GaAs surface was used as the bottom gate of the Schottky-diode structure, which is used to control the electrostatic environment of the quantum dots 136. This conductive layer may affect device performance in two ways. First, it may change the propagation length of a SAW by introducing new dielectric losses which interact with the electrical component of the piezomechanical wave. Second, it creates new electrostatic boundary conditions that may affect the ability of the IDT to generate piezomechanical waves in the substrate. These two effects were studied numerically using commercially available multiphysics software. FIGS. 4A and 4B summarize the results. In all calculations, SAWs propagate along the

[0110] crystal direction on the (001) surface of GaAs and the conductive layer is 40-nm thick with uniform conductivity.

[0060] FIG. 4A shows calculated SAW propagation loss rates (circles) as a function of the thin layer’s conductivity <J (at a constant layer depth of 360 nm). These values were derived from the complex eigenfrequencies for SAW modes calculated in a two-dimensional (2D) unit cell with periodic boundary conditions; the loss rate is the imaginary part of the complex eigenfrequency. Two distinct regimes are apparent. For <J < 1 S / m, the thin layer acts as a low- loss dielectric. For <J > 103S / m, the layer acts as a conductive metal. The loss rate reaches a maximum between these two regimes. These numerical results are in excellent agreement with analytical results calculated from Ref. 1 (see dashed curve). At 1.7 K, the n-doped layers have characteristic conductivity of <5 ~ 105S / m, measured with typical Hall bar structure. These conductivities are expected to contribute approximately 100 Hz to SAW propagation losses (indicated by the dashed ellipse in FIG. 4A). For comparison, SAW resonators fabricated on insulating substrates already exhibit total loss rates of approximately 100 kHz (indicated by the dashed circle in FIG. 4A). The measured losses are dominated by diffraction, impurity scattering, and bulk scattering from mirrors, other structures, and possibly surface roughness. The doped layer is thus expected to negligibly contribute to SAW losses in the prototype.

[0061] FIG. 4B shows the calculated piezoelectric coupling constant k2as a function of the conductive layer’s depth below the surface (constant conductivity a = 106S / m). The values of k2were calculated with the relation k2= 2 v / v, where v is the difference in SAW phase velocity between systems with electrically shorted and insulating surface boundary conditions, according to Ref. [2], When the depth d is less than approximately 100 nm, the conductive layer effectively screens the IDT’s driving potential and strongly reduces its ability to generate SAWs. The coupling constant k2approaches the well-established value for insulating GaAs (fc20.07%) for depths greater than approximately 500 nm [2], For the prototype studied herein (360 nm, indicated by the gray dashed line), the effective coupling constant k2— 0.055%, approximately 80% its value for insulating GaAs.

[0062] Micro wave Reflection Model

[0063] The microwave reflection and transmission measurements shown in FIGS. 2A- 2D were performed with a commercial vector network analyzer. The internal quality factor Qtand external quality factor Qecan then be extracted by fitting the reflection spectra according to Eqn. 1 in Ref. [3]:The size of the dip in a l^i l2reflection spectrum provides an upper bound on theelectromechanical coupling efficiency, which can be improved by impedance matching with, for example, a tunable superconducting microwave cavity [4],

[0064] Optical Measurement Setup

[0065] The optical measurements shown in FIGS. 3A, 3B, 3C, and 3D were performed with a conventional confocal microscope, with details described in Ref. [5], The microwave power used for the measurements in FIGS. 3C and 3D are -29 dBm and -26 dBm, respectively. For the cavity mode studied in FIG. 3D, the microwave reflection measurement results in an internal quality factor Qtof 18,396 and an external quality factor Qeof 548,077, corresponding to a total Q of approximately 17,798. Using the techniques described in Appendix D of Ref. [6], the single-phonon coupling rate g0is estimated to be approximately 42 kHz.Method Embodiments

[0066] The present embodiments also include methods for microwave-to-optical transduction. These methods may be implemented or performed using the quantum transducer 100 of FIGS. 1A, IB, and 1C. Thus, in some of the present embodiments, a method for microwave-to-optical transduction includes electrically driving the SAW resonator 180 of the quantum transducer 100 to excite a standing-wave resonance of the SAW resonator 180. The method also includes applying a bias voltage V across the back gate 106 of the quantum transducer 100 and the top gate 126 of the quantum transducer 100 to place the quantum dot 136 of the quantum transducer 100 into a charge state. The method also includes optically pumping the quantum dot 136 while the quantum dot 136 is in the charge state. In some embodiments, the method denoted further includes detecting photoluminescence or resonance fluorescence emitted by the quantum dot 136 in response to the optically pumping.

[0067] For microwave-to-optical transduction, the optical pump is red-detuned from the QD resonance by the (microwave) resonant frequency of the SAW resonator 180. In this case, optical excitation of the QD is assisted by one phonon from the SAW resonance, i.e., the energy of the one phonon adds to the energy of the red-detuned pump photon such that the sum equals the transition energy of the QD resonance.

[0068] The present embodiments also include methods for opti cal -to-micro wave transduction. These methods may also be implemented or performed using the quantum transducer 100 of FIGS. 1A, IB, and 1C. In this case, when the optical pump is blue-detuned from the QD resonance by the (microwave) resonant frequency of the SAW resonator 180, excitation of the QD generates a phonon that is resonant with the SAW resonator 180. This phonon may then be piezoelectrically coupled (via the SAW transducer 124) out of the SAWresonator 180 as a microwave photon.Figure Captions

[0069] FIGS. 1A-1E: Illustration of the integrated device. FIG. 1A is based on an optical micrograph taken of a prototype of the quantum transducer 100. FIG. IB is a cross- sectional view of the quantum transducer 100 of FIG. 1A corresponding to the horizontal dashed line labeled “IB” in FIG. 1A. FIG. 1C is a cross-sectional view of the quantum transducer 100 of FIG. 1A corresponding to the vertical dashed line labeled “1C” in FIG. 1A. As shown in FIGS. 1A and IB, the doped semiconductor layer was etched away outside the region defined by the dashed line 144. Removing the doped semiconductor layer in these areas reduces reflections caused by the microwave transmission line. A thin film of Ti / Au evaporated inside the SAW resonator forms the top gate of the Schottky structure. An ohmic contact is made to the n-doped GaAs layer by Ni and AuGe, serving as the back gate. FIG. ID is a scanning electron microscope (SEM) image of aluminum (Al) IDT fingers. FIG. IE is an SEM image of the etched SAW DBR mirror. As shown in FIG. IE, a slight curvature was added to reduce phonon diffraction loss.

[0070] FIGS. 2A-2D: Microwave characterization of the SAW delay lines and resonators. FIGS. 2A and 2B show reflection and transmission spectra, respectively, of SAW delay lines with a 400-pm gap. The similar peak transmission on substrates with buried n-doped GaAs, as compared to the same device on bulk GaAs, shows that the loss introduced by SAW launching and propagation is negligible with the proper choice of the depth and doping concentration of the n-doped GaAs layer. FIG. 2C is a plot of peak transmitted SAW signal (|S2112in dB) versus delay-line gap (in pm) between the IDTs of the delay lines, for the two substrates. The similar slope indicates that the propagation loss introduced by the n-doped GaAs layer is negligible. The error bars represent the noise in the transmission spectra as a result of beating between the acoustic signal and electrical crosstalk. FIG. 2D shows reflection spectra of SAW resonators with the same design parameters, fabricated on substrates with (bottom panel) and without (top panel) the buried doped layer, showing similar internal quality factors of Qt « 28,000. Circles: data. Solid line: fit according to the model described in the “Supplementary Information.”

[0071] FIGS. 3A-3D: Optical characterization of the hybrid device. FIG. 3A shows the photoluminescence spectrum of the gated quantum dot, as measured with a spectrometer and CCD camera. Two charge plateaus are visible when varying the bias voltage applied to the gate. FIG. 3B shows the resonance fluorescence signal of the gated quantum dot, as measured witha superconducting nanowire single photon detector (SNSPD). A near-transform-limited linewidth is observed, which is a result of reduced charge noise by the gate structure. FIG. 3C shows a photoluminescence spectrum of the gated quantum dot with SAW modulation at a fixed frequency of 3.53388 GHz, as measured with a Fabry -Perot filter and SNSPD. Both the quantum dot’s resonant peak and sideband peaks are shifted by the Stark effect, with a rate of approximately 0.13 GHz / mV. FIG. 3D shows the photoluminescence spectrum of the gated quantum dot at a fixed gate bias with varying microwave drive frequency and constant microwave power, as measured with a Fabry-Perot filter and SNSPD. A Lorentzian fit to the square of the modulation index (<52) shows an acoustic resonance linewidth of approximately 232 kHz, corresponding to a quality factor of approximately 15,000.

[0072] FIG. 4A is a plot of calculated phonon loss rate (in Hz) versus conductivity <J (in S / m) for SAWs propagating along the

[0110] direction of a free GaAs surface located above a uniform conductive thin layer (40 nm thick). The layer was held at 360 nm below the surface while the conductivity <J was varied. Circles: numerical calculations. Dashed line: analytical calculation. Dashed ellipse: approximate loss rate expected from room-temperature conductivity measurements. Dashed Circle: approximate total loss rates measured from typical SAW resonator at 3.5 GHz.

[0073] FIG. 4B is a plot of piezoelectric coupling constant k2(in %) versus doped layer depth (nm) for SAWs propagating along the

[0110] direction of a free GaAs surface located above a uniform conductive thin layer (40 nm thick). The conductivity was held at (J = 106S / m while the layer depth (vertical axis) was varied. Dashed line: the 360-nm depth of the doped layer used in the prototype described herein.References[1] X. Han et al, Optica 8, 1050-1064 (2021).[2] M. Mirhosseini, A. Sipahigil, M. Kalaee, and O. Painter, Nature 588, 599-603 (2020).[3] F. Arute et al., Nature 574, 505-510 (2019).[4] Y. Kim et al., Nature 618, 500-505 (2023).[5] M. A. Eriksson et al., Quantum Inf. Process. 3, 133-146 (2004).[6] C. Kloeffel and D. Loss, Annu. Rev. Condens. Matter Phys. 4, 51-81 (2013).[7] T. van Leent et al., Phys. Rev. Lett. 124, 010510 (2020).[8] S.-K. Liao et al, Nature 549, 43-47 (2017).[9] W. Jiang et al, Nat. Phys. 19, 1423-1428 (2023).

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[0074] Features described above as well as those claimed below may be combined in various ways without departing from the scope hereof. The following examples illustrate possible, non-limiting combinations of features and embodiments described above. It should be clear that other changes and modifications may be made to the present embodiments without departing from the spirit and scope of this invention:

[0075] (Al) A quantum transducer includes a back gate having a doped semiconductor layer, a tunnel barrier located above the doped semiconductor layer, a quantum dot contacting a top surface of the tunnel barrier, a cap layer located above the tunnel barrier and the quantum dot, a surface acoustic wave (SAW) resonator located above the cap layer, a SAW transducer coupled to the SAW resonator, and a top gate located above the SAW resonator. The SAW resonator is mechanically coupled to the quantum dot.

[0076] (A2) In the quantum transducer denoted (Al), the doped semiconductor layer has an electrical conductivity and a depth, relative to a top surface of the SAW resonator, suchthat SAW attenuation contributes less than 100 kHz to a total phonon loss rate of the SAW resonator.

[0077] (A3) In either of the quantum transducers denoted (Al) and (A2), the doped semiconductor layer has an electrical conductivity and a depth, relative to a top surface of the SAW resonator, such that the SAW transducer has a piezoelectric coupling constant of 0.055% or higher.

[0078] (A4) In any of the quantum transducers denoted (Al) to (A3), the SAW resonator includes first and second SAW mirrors that face each other to form a standing-wave resonance along the top surface of the SAW resonator.

[0079] (A5) In the quantum transducer denoted (A4), the quantum dot is positioned near an antinode of the standing-wave resonance.

[0080] (A6) In any of the quantum transducers denoted (Al) to (A5), the quantum dot is a self-assembled quantum dot.

[0081] (A7) In any of the quantum transducers denoted (Al) to (A6), the SAW resonator is composed of gallium arsenide, indium gallium phosphide, aluminum arsenide, an alloy thereof, or a combination thereof.

[0082] (A8) In any of the quantum transducers denoted (Al) to (A7), each of the tunnel barrier and the cap layer is composed of gallium arsenide, indium gallium phosphide, aluminum arsenide, an alloy thereof, or a combination thereof.

[0083] (A9) In any of the quantum transducers denoted (Al) to (A8), the quantum dot is composed of indium arsenide or indium gallium arsenide.

[0084] (A 10) In any of the quantum transducers denoted (Al) to (A9), the doped semiconductor layer is composed of an n-type semiconductor material.

[0085] (Al l) In the quantum transducer denoted (A10), the n-type semiconductor material includes silicon-doped gallium arsenide or aluminum gallium arsenide.

[0086] (A 12) In either of the quantum transducers denoted (A10) and (Al l), the n-type semiconductor material has an electrical conductivity of 103S / m or more.

[0087] (Al 3) In any of the quantum transducers denoted (Al) to (Al 2), a depth of the doped semiconductor layer, relative to a top surface of the SAW resonator, is 100 nm or more.

[0088] (A14) In any of the quantum transducers denoted (Al) to (A13), the quantum transducer further includes a current blocker located between the cap layer and the SAW resonator.

[0089] (Al 5) In any of the quantum transducers denoted (Al) to (A14), the SAW transducer includes an interdigital transducer located on a top surface of the SAW resonator.

[0090] (A16) In any of the quantum transducers denoted (Al) to (A15), the quantum transducer further includes a microwave electrical circuit electrically connected to the SAW transducer.

[0091] (Al 7) In the quantum transducer denoted (Al 6), the microwave electrical circuit includes a planar transmission line having an end that is electrically connected to the SAW transducer.

[0092] (Al 8) In either of the quantum transducers denoted (Al 6) and (Al 7), the doped semiconductor layer does not extend underneath the microwave electrical circuit.

[0093] (Bl) A method includes electrically driving the SAW resonator of any of the quantum transducers denoted (Al) to (Al 8) of claim 1 to excite a resonance of the SAW resonator. The method also includes applying a bias voltage across the back gate of the quantum transducer and the top gate of the quantum transducer to place the quantum dot of the quantum transducer into a charge state. The method also includes optically pumping the quantum dot while the quantum dot is in the charge state.

[0094] (B2) In the method denoted (Bl), the method further includes detecting photoluminescence or resonance fluorescence emitted by the quantum dot in response to said optically pumping.

[0095] Changes may be made in the above methods and systems without departing from the scope hereof. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween.

Claims

CLAIMSWhat is claimed is:

1. A quantum transducer, comprising: a back gate comprising a doped semiconductor layer; a tunnel barrier located above the doped semiconductor layer; a quantum dot contacting a top surface of the tunnel barrier; a cap layer located above the tunnel barrier and the quantum dot; a surface acoustic wave (SAW) resonator located above the cap layer, the SAW resonator being mechanically coupled to the quantum dot; a SAW transducer coupled to the SAW resonator; and a top gate located above the SAW resonator.

2. The quantum transducer of claim 1, the doped semiconductor layer having an electrical conductivity and a depth, relative to a top surface of the SAW resonator, such that SAW attenuation contributes less than 100 kHz to a total phonon loss rate of the SAW resonator.

3. The quantum transducer of claim 1, the doped semiconductor layer having an electrical conductivity and a depth, relative to a top surface of the SAW resonator, such that the SAW transducer has a piezoelectric coupling constant of 0.055% or higher.

4. The quantum transducer of claim 1, the SAW resonator comprising first and second SAW mirrors that face each other to form a standing-wave resonance along the top surface of the SAW resonator.

5. The quantum transducer of claim 4, the quantum dot being positioned near an antinode of the standing-wave resonance.

6. The quantum transducer of claim 1, the quantum dot comprising a self-assembled quantum dot.

7. The quantum transducer of claim 1, the SAW resonator being composed of galliumarsenide, indium gallium phosphide, aluminum arsenide, an alloy thereof, or a combination thereof.

8. The quantum transducer of claim 1, each of the tunnel barrier and the cap layer being composed of gallium arsenide, indium gallium phosphide, aluminum arsenide, an alloy thereof, or a combination thereof.

9. The quantum transducer of claim 1, the quantum dot being composed of indium arsenide or indium gallium arsenide.

10. The quantum transducer of claim 1, the doped semiconductor layer being composed of an n-type semiconductor material.

11. The quantum transducer of claim 10, the n-type semiconductor material comprising silicon-doped gallium arsenide or aluminum gallium arsenide.

12. The quantum transducer of claim 10, the n-type semiconductor material having an electrical conductivity of 103S / m or more.

13. The quantum transducer of claim 1, a depth of the doped semiconductor layer, relative to a top surface of the SAW resonator, being 100 nm or more.

14. The quantum transducer of claim 1, further comprising a current blocker located between the cap layer and the SAW resonator.

15. The quantum transducer of claim 1, the SAW transducer comprising an interdigital transducer located on a top surface of the SAW resonator.

16. The quantum transducer of claim 1, further comprising a microwave electrical circuit electrically connected to the SAW transducer.

17. The quantum transducer of claim 16, the microwave electrical circuit comprising a planar transmission line having an end that is electrically connected to the SAW transducer.

18. The quantum transducer of claim 16, wherein the doped semiconductor layer does not extend underneath the microwave electrical circuit.

19. A method, comprising:electrically driving the SAW resonator of the quantum transducer of claim 1 to excite a resonance of the SAW resonator; applying a bias voltage across the back gate of the quantum transducer and the top gate of the quantum transducer to place the quantum dot of the quantum transducer into a charge state; and optically pumping the quantum dot while the quantum dot is in the charge state.

20. The method of claim 19, further comprising detecting photoluminescence or resonance fluorescence emitted by the quantum dot in response to said optically pumping.

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