Modulator apparatus

Abstract

A time-varying array of controllable elements configured to receive an input signal in the form of electromagnetic radiation impinging on the array, wherein: each controllable element is configured to have a non-linear response to the input signal; and at least a subset of the controllable elements is configured to: adjust a permeability response of the array; and modulate an input signal receivable at the array based on the adjusted permeability response in order selectively to generate one or more output signals in a range of one or more corresponding target directions, each output signal comprising electromagnetic radiation.

Description

[0001]MODULATOR APPARATUS The present disclosure relates to apparatus and methods for controlling electromagnetic radiation. In particular, but not exclusively, the present disclosure relates 5 to the use of arrays with adjustable permeability responses for modulating input signals comprising electromagnetic radiation. In recent years, the controlled transformation of electromagnetic fields has made significant strides, thanks to the emergence and evolution of dynamic metasurfaces. A new frontier has emerged with a growing interest in space-time periodic metasurfaces. 10 These structures introduce a temporal dimension to static metasurfaces, expanding their capabilities far beyond those that can be achieved with conventional static metasurfaces. Typically, known applications of non-reciprocal, polychromatic beam-steerable metasurfaces achieve space-time modulation by altering material permittivity, using varactors, to tune the capacitance. Whilst effective in wireless communication and 15 detection, these methods typically result in bulky and loss-prone designs. Further, the noise levels and frequency conversion purities associated with such methods mean that there is limited applicability in highly intricate and sensitive systems. Accordingly, in order to harness the full potential of systems, such as quantum information systems, there is a need for innovative solutions for space-time modulation of electromagnetic radiation. 20 It is an object of the disclosure to at least partly address one or more of the shortcomings in the prior art mentioned above. According to an aspect of the disclosure, there is provided a time-varying array of controllable elements configured to receive an input signal in the form of electromagnetic radiation impinging on the array, wherein: each controllable element is configured to have 25 a non-linear response to the input signal; and at least a subset of the controllable elements is configured to: adjust a permeability response of the array; and modulate an input signal receivable at the array based on the adjusted permeability response in order selectively to generate one or more output signals in a range of one or more corresponding target directions, each output signal comprising electromagnetic radiation. Advantageously, the permeability response of an array can be controlled in order to modulate electromagnetic radiation. Beneficially, modulation is provided without the need for additional bulky and loss-prone apparatus, thereby enabling improved signal control in highly sensitive systems, such as quantum information systems, in a way that can be scaled 5 to provide a high degree of control within relatively small spatial areas. Optionally, the frequency of output signal corresponding to each target direction is different, optionally wherein the frequency of output signal for at least one target direction is different from the frequency of the input signal. Optionally, each target direction is configured to correspond to a respective target device of a spatially distributed array of 10 target devices. Beneficially, input signals comprising electromagnetic radiation may be modulated in frequency, space and time domains. Optionally, at least one of the controllable elements comprises a Josephson Junction. Beneficially, Josephson Junctions provide a non-linear response enabling the permeability of the array to be adjusted whilst providing effective operation at low 15 temperatures, such as below 100 mK, used in for quantum information applications. Optionally, the array comprises a distribution network configured to direct one or more electrical control signals to the subset of controllable elements. Advantageously, the controllable elements are selectively controlled to perform a wide range of operations. For example, optionally, the subset of the controllable elements is configured to modulate the 20 input signal thereby to perform at least one of: a mixing operation, a beam splitting operation, an amplification operation and a switching operation. There is also provided a system comprising: the array and one or more target devices, wherein the one or more target devices each correspond to a respective target direction of the range of one or more corresponding target directions. 25 There is also provided a method of modulating an input signal comprising: receiving an input signal in the form of electromagnetic radiation at an array of controllable elements, each controllable element being configured to have a non-linear response to the input signal; controlling at least a subset of the elements in order to adjust the permeability response of the array; modulating the input signal based on the adjusted 30 permeability response; and selectively generating one or more output signals in a range of one or more corresponding target directions, each output signal comprising electromagnetic radiation. Further aspects will be apparent from the description and the appended claims. 5 A detailed description of embodiments is described, by way of example only, with reference to the figures in which: Figure 1 shows a cross-sectional illustration of modulation of electromagnetic radiation by an array of controllable elements; Figure 2 shows a perspective view of an array of controllable elements; 10 Figure 3 shows the array of controllable elements of Figure 2 in combination with a power divider; Figure 4 shows a plan schematic view of circuit elements of the array and power divider of Figure 3; Figure 5 shows a schematic plan view of a controllable element; and 15 Figure 6 shows a cross-sectional view of a diagram illustrating a multiplexing operation. The present disclosure facilitates functionalities such as mixing operations, beam splitting and amplification at the quantum noise level operating below 100 mK through the use of non-linear circuits, such as Josephson Junctions, to engineer space-time modulation 20 in lattice structures. Advantageously, nonlinearity in periodic or aperiodic metasurfaces is exploited by modulating a material’s permeability, thereby enabling new applications in quantum research, such as superconducting frequency conversion devices, beam splitters, amplifiers, frequency multiplexing structures, high-speed switches and other devices characterised by their quantum noise level performance. 25 Figure 1 shows a cross-sectional view of an array 100 of controllable elements 106. The array 100 is a time-varying array of controllable elements 106 configured to receive an input signal 101 in the form of electromagnetic radiation impinging on the array 100. Each controllable element 106 is configured to have a non-linear response to the input signal 101 and at least a subset of the controllable elements 106 is configured to adjust a 30 permeability response of the array 100 and modulate an input signal 101 receivable at the array 100 based on the adjusted permeability response in order selectively to generate one or more output signals 103A, 103B in a range of one or more corresponding target directions, each output signal comprising electromagnetic radiation. In the example shown at Figure 1 the controllable elements 106 each comprise 5 Josephson Junctions. In further examples, at least a subset of the elements 106 comprise additional and / or alternative elements configured to have a non-linear response to the input signal 101. In an example, at least one of the controllable elements 106 comprises a high kinetic inductance material, such as one or more nanowires with non-linear response properties to an input signal 101 comprising electromagnetic radiation. In an example, at 10 least one of the controllable elements 106 comprises a non-linear resonator. In an example, at least one of the controllable elements 106 comprises a superconducting material. In further examples, the controllable elements 106 are configured in any appropriate manner to provide the functionality described herein. As shown in the example of Figure 1, there is a first superconducting electrode 104 15 formed on a substrate 102. In an example, the substrate 102 is a silicon substrate. In a further example, the substrate 102 is a sapphire substrate. In further examples, additionally or alternatively, the substrate 102 may comprise any suitable material. In an example the subset of controllable elements 106 is periodically spaced along at least one axis. For example, a subset of the controllable elements 106 is formed and 20 spaced periodically along an axis, such as with the periodic spacing 105 between adjacent controllable elements 106 shown parallel to the z-axis indicated in Figure 1. Whilst the controllable elements 106 are shown to be periodically spaced, in further examples, alternatively or additionally the controllable elements 106 comprise aperiodic spacings. Advantageously, aperiodic spacing provides more degrees of freedom of control of the 25 output signal 103A, 103B from the array 106. The controllable elements 106 each include a tunnel barrier 108 and a second superconducting electrode 110. The combination of the first superconducting electrode 104, tunnel barrier 108 and second superconducting electrode 110 serves to provide a series of controllable elements 106 comprising Josephson Junctions that are periodically spaced along the longitudinal axis of the first 30 superconducting electrode 104. Whilst the controllable elements 106 are shown to include a common superconducting electrode 104, in further examples at least some of the controllable elements 106 each have their own individual superconducting electrode 104 rather than a portion of a shared superconducting electrode 104. In order to adjust the permeability response of the array 100, alternating current 5 (AC) and / or direct current (DC) signals are applied to the controllable elements 106. In an example, the array 100 comprises a distribution network 300, configured to direct one or more electrical control signals to the subset of controllable elements, as described in more detail below with reference to Figure 4. Optionally, the one or more electrical control signals comprise alternating current, AC, and / or direct current, DC, signals. In further 10 examples, any appropriate mechanism is used for controlling the controllable elements 106 to provide adjustments to the permeability response of the array 100 in accordance with the disclosure. Beneficially, the controlled use of signals, such as AC and / or DC signals, to a Josephson Junction enables the permeability response of the array 100 to be adjusted. For example, the critical current density in a superconductor that is modulated in both 15 space and time can be expressed as in Equation 1: ^^(^^, ^^) = ^^^ sin[^^(^^, ^^)] (Equation 1)Where ^^^ is the critical current of the Josephson Junction and ^^(^^, ^^) is related to20 the magnetic flux Φ as per Equation 2, where Φ^is the flux quantum: (Equation 2) (Equation 3) It can be determined that:25 (Equation 4) 5) and (Equation 6) then ^^(^^, ^^) can be expressed as: (Equation 7) 5 and the time-varying inductance for a superconductor can be expressed as: (Equation 8a)Where F is a general function of ^^^^^^^^ including periodic and aperiodic functions, such as a) Periodic time function:10 (Equation 8b)b) Periodic space − time function: (Equation 8c)c) Aperiodic space − time function:(Equation 8d)15 Accordingly, the permeability of the superconductor in space and time is described as:20 ^^^ ^ ௌ(^^, ^^) =ఓబ^^^ௌ(^^, ^^) = ^^ఓ (Equation 9) = Φ^^^ / (2^^^^^^^^^^), and l and A are the length and area of therespectively. The time-varying inductance expressed at Equation 9 may be subject to a space-time Bloch-Floquet expansion in order to understand the electric and magnetic fields 25 in the array 100, and the dispersion relation. This in turn enables the calculation of reflected and transmitted beams of electromagnetic radiation on the array 100. Advantageously, the use of controllable elements 106 with non-linear responses to an input signal 101 can be used to adjust the permeability of the array 100 in order to modulate the input signal 101 in space, time and / or frequency domains. 5 As shown at Figure 1, an input signal 101 in the form of electromagnetic radiation impinges on the array 100. The input signal 101 is modulated in order to generate output signals based on adjusting the permeability response of the array 100 in accordance with the theory described herein. In order to adjust the permeability response of the array, control signals are applied to at least a subset of the controllable elements 106. For 10 example, the application of a control signal to the first superconducting electrode 104 and / or of a control signal to the second superconducting electrodes 110 associated with each controllable element 106 comprising a Josephson Junction enables the permeability response of the array 100 to be adjusted. In some examples, the control signals applied to the Josephson Junctions are electrical control signals comprising alternating current, AC, 15 and / or direct current, DC, signals. Accordingly, there is disclosed a method of modulating an input signal comprising: receiving an input signal 101 in the form of electromagnetic radiation at an array 100 of controllable elements 106, each controllable element 106 being configured to have a non- linear response to the input signal 101; controlling at least a subset of the elements 106 in 20 order to adjust the permeability response of the array 100; modulating the input signal based on the adjusted permeability response; and selectively generating one or more output signals 103 in a range of one or more corresponding target directions, each output signal 103 comprising electromagnetic radiation. In an example, the frequency of output signal corresponding to each target 25 direction is different. Optionally, the frequency of output signal for at least one target direction is different from the frequency of the input signal. Figure 1 illustrates two output signals 103A, 103B corresponding to two different target directions. The direction and amplitude of the output signals 103A, 103B is determined by adjusting the permeability response of the array 100. In an example, each target direction of output signal, such as the output signal 103B described with reference to Figure 1, is configured to correspond to a respective target device of a spatially distributed array of target devices. In the example of Figure 1, there is shown an input signal 101 directed at an angle to the planar surface of the array 100. Figure 1 shows a first output signal 103A that has 5 the same frequency as the input signal 101 and is transmitted in the same direction based on the angle at which the input signal 101 impinged on the array 100. There is also shown a second output signal 103B that is generated by the array 100 in a different target direction compared to the first output signal 103A. The frequency of radiation of the second output signal 103B is different to the frequency of radiation of the input signal 101 10 and the first output signal 103A. Accordingly, the array 100 enables frequency-conversion beam splitting of an input signal 101 comprising electromagnetic radiation. Beneficially, in an example, input signals 101 with different frequencies of electromagnetic radiation and / or different angles of incidence impinging on the array 100 are used to control the direction and / or frequency of output signals 103 from the array based on adjustment of the 15 permeability response of the array 100. Figure 2 shows a perspective view of an exemplary implementation of the array 100 of Figure 1. There is shown the substrate 102 upon which a first superconducting electrode 104 is provided. The first superconducting electrode 104 extends along an axis (for example parallel to the z axis shown in Figure 2) and a number of controllable 20 elements 106 are formed on the first superconducting electrode 104 such that they are periodically spaced along the axis. Each of the controllable elements 106 comprises a second superconducting electrode 110, which is shown to extend in a direction that is substantially parallel to the y-axis shown at Figure 2. The configuration described with reference to Figure 2 shows an array 100 controllable elements 106 extending along an 25 axis associated with a first superconducting electrode 104. However, in further examples, the array 100 comprises a two-dimensional array of controllable elements 106. In an example, the addition of one or more superconducting electrodes parallel to the first superconducting electrode 104 enables an array of controllable elements 106 to be formed at locations where the second superconducting electrodes 110 intersect with the one or 30 more additional superconducting electrodes formed parallel to the first superconducting electrode 104. In such a manner, the array 100 of controllable elements 106 is scalable to provide increased control over input signals 101 impinging on the array 100. In further examples, the array 100 is provided with a distribution of controllable elements 106 in any appropriate configuration to implement modulation of an input signal 101 comprising 5 electromagnetic radiation through the adjustment of a permeability response of the array 100. Whilst a beam-splitting operation is described above with respect to Figure 1, where an input signal comprising electromagnetic radiation 101 is modulated through adjusting the permeability response of the array 100, in further examples additional and / or 10 alternative functionality is implemented. In an example, the subset of the controllable elements 106 is configured to modulate the input signal 101 thereby to perform at least one of: a mixing operation, a beam splitting operation, an amplification operation and a switching operation. In an example, there is provided a quantum amplifier comprising the array 100. In a further example, there is provided a quantum circulator comprising the 15 array 100. In a further example, there is provided an isolator comprising the array 100. Advantageously, in an example, the array 100 of controllable elements 106 is adapted to provide a mixing operation as described further with reference to Figure 3. Figure 3 shows a perspective view of the array 100 shown at Figure 1 in combination with a power divider 200. The power divider 200 is configured to receive an input signal at a 20 common port 202. The input signal is controlled by the power divider 200 in order to direct output signals via output connections 204 of the power divider 200 to each of the controllable elements 106 of the array 100. Accordingly, the signals output via the connections 204 between the power divider 200 and the array 100 serve as mixing signal inputs at the controllable elements 106. The mixing signal inputs at the controllable 25 elements enable a high degree of control of an input signal 101, comprising electromagnetic radiation, impinging on the array 100. As described above, by adjusting the permeability response of the array 100, the direction and frequency of an input signal 101 may be modulated. The introduction of additional mixing signals provides further control of the output signals 103 of the array. Figure 4 shows a schematic view of the array 100 in combination with the power divider 200. There is shown a distribution network 300 configured to direct one or more electrical control signals to the subset of controllable elements 106 of the array 100. For example, the distribution network 300 is configured to direct one or more electrical control 5 signals comprising alternating current, AC, and / or direct current, DC, signals to at least a subset of the controllable elements 106. There is shown a series of controllable elements 106 arranged along an axis and associated with a common transmission line 312. In an example, the common transmission line 312 enables signals comprising AC and / or DC signals to be directed to the controllable elements 106 of the array 100. Additionally, the 10 distribution network 300 comprises further transmission lines 310 configured to direct signals to each of the controllable elements 106 of the array 100. Each of the transmission lines 310 enables connection to a power divider, such as the power divider 200 described with reference to Figure 3. In an example, AC and / or DC signals are directed to at least a subset of the controllable elements 106 by one or more of the transmission lines 310 that 15 are coupled to the power divider 200. Accordingly, Figure 4 shows a series of output ports 302 of the power divider 200. Each output port 302 is connected to a variable phase shifter 306 by a communication path 304. Each variable phase shifter 306 connects to variable attenuator 308, which in turn has a feed to the transmission line 310 to the controllable element 106 of the array 100. Whilst exemplary connectivity for the 20 controllable elements 106 of the array is shown, in further examples additional and / or alternative connectivity is used to control some or all of the controllable elements 106. The connectivity of the controllable elements 106 described with reference to Figure 4 is shown in greater detail at Figure 5. Figure 5 shows a controllable element 106 comprising a first superconducting electrode 104, a second superconducting electrode 110 25 and a tunnel barrier 108 between the first and second superconducting electrodes 104, 110. Each of the first superconducting electrode 104 and the second superconducting electrode 110 is shown to be connected to a pad 316. In an example, the pads 316 are Aluminium pads that each form part of respective shunt capacitors arranged along the transmission line 312. There is also shown a transmission line 310 that provides an input signal via a 30 connection 314 to the controllable element 106. In an example the transmission line 310 is a coplanar waveguide transmission line. In further examples, the transmission line 310 is implemented using additional and / or alternative elements to provide the functionality described herein. Advantageously, as shown in a cross-sectional view of Figure 6, in an example the 5 array 100 is implemented in a system 600 comprising the array 100 and one or more target devices 604, wherein the one or more target devices 604 each correspond to a respective target direction of a range of one or more corresponding target directions. At Figure 6, there is shown an array 602 of a number of spatially distributed target devices 604. In further examples, there may be any number of target devices 604 arranged in any 10 appropriate spatial configuration. In an example, the array 100 of controllable elements 106 comprises a distribution network, such as the distribution network 300 described with reference to Figure 4, in order to control the controllable elements 106, thereby to adjust the permeability response of the array 100. Figure 6 shows an input signal 101 in the form of electromagnetic radiation 15 impinging on the array 100. The controllable elements 106 of the array 100 are controlled thereby to adjust a permeability response of the array 100 and modulate the output signal 103 in accordance with the disclosure. The array 100 modulates the input signal 101 to selectively direct an output signal 103 to the plurality of target devices 604. The output signal 103 is directed at any number of the plurality of target devices 604 and is modulated 20 in space, time and / or frequency domains as appropriate. The target devices 604 are any appropriate target devices to which output signals 103 of the array 100 can usefully be directed. In an example, the one or more target devices 604 comprise: a circuit quantum electrodynamics, QED, device; a qubit; and / or a quantum dot. In an example, the system 600 is configured to generate one or more 25 entangled photon states. Accordingly, the use of the array 100 enables a method of selectively generating one or more output signals 103 in a range of one or more corresponding target directions, wherein each target direction corresponds to a respective target device 604 of a spatially distributed array 602 of target devices 604, optionally where the target device comprises: a 30 circuit quantum electrodynamics, QED, device; a qubit; and / or a quantum dot. In an example, the array 100 is used for control multiplexing of a target device 604, such as a superconducting circuit. Advantageously, using the apparatus and methods described herein, control of target devices 604 addresses difficulties with known systems. In an example, the target devices 604 comprise qubits that are to be driven at the same 5 time and the same frequency. Therefore, where time multiplexing operations and frequency multiplexing operations are not suitable for multiplexing the qubits, advantageously, the use of controllable elements 106 with non-linear responses enables the permeability response of the array to be adjusted such that input signals 101 of different beams impinging on the array 100 generate output signals 103 of different beams from the 10 array 100 with the same or different frequencies. For example, the use of a baseband input signal 101 enables multiple output signals 103 to be generated for the same or different frequencies. Beneficially, in contrast to the use of multiple baseband signals to control output signals, overlaps between multiple baseband input signals are avoidable. Beneficially, the array 100 is used to perform 15 mixing operations and output signals 103 of a sufficiently high frequency can be achieved without overlap between separate output signals 103 and without loss of information. Advantageously, the ability to modulate input signals 101 as described herein means that input signals 101 can be directed in corresponding target directions without the need for additional, bulky, modulation apparatus. This is particularly important when it is 20 desirable to modulate electromagnetic radiation signals over a small area. For example, the scalability of quantum computing systems is limited by the size of the apparatus required to spatially modulate signals. The array 100 described herein provides modulation in a way that enables target devices such as qubits, to be closely packed. Advantageously, in further examples, breaking reciprocity through the use of 25 controllable elements 106 with non-linear response properties enables the array 100 to be integrated into a quantum amplifier, a non-magnetic quantum circulator and / or an isolator, in order to harness the functionality provided by the array 100. Cross reference to related applications This application claims priority from GB 2403016.5 filed on 01 March 2024, the contents 30 of which are hereby incorporated by reference.

Claims

CLAIMS 1. A time-varying array of controllable elements configured to receive an input signal in the form of electromagnetic radiation impinging on the array, wherein: each controllable element is configured to have a non-linear response to the 5 input signal; and at least a subset of the controllable elements is configured to: adjust a permeability response of the array; and modulate an input signal receivable at the array based on the adjusted permeability response in order selectively to generate one or more0 output signals in a range of one or more corresponding target directions, each output signal comprising electromagnetic radiation.

2. The array according to claim 1, wherein the frequency of output signal corresponding to each target direction is different, optionally wherein the frequency of output signal for at least one target direction is different from the frequency of the input5 signal.

3. The array according to any preceding claim, wherein each target direction is configured to correspond to a respective target device of a spatially distributed array of target devices.

4. The array according to any preceding claim, wherein the subset of controllable0 elements is periodically spaced along at least one axis.

5. The array according to any preceding claim, wherein at least one of the controllable elements comprises a superconducting material.

6. The array according to any preceding claim, wherein at least one of the controllable elements comprises a Josephson Junction. 5 7. The array according to any preceding claim, wherein at least one of the controllable elements comprises a high kinetic inductance material.

8. The array according to any preceding claim, wherein at least one of the controllable elements comprises a non-linear resonator.

9. The array according to any preceding claim, wherein the array comprises a distribution network configured to direct one or more electrical control signals to the 5 subset of controllable elements.

10. The array according to claim 9, the one or more electrical control signals comprise alternating current, AC, and / or direct current, DC, signals.

11. The array according to any preceding claim, wherein the subset of the controllable elements is configured to modulate the input signal thereby to perform at least one of: a0 mixing operation, a beam splitting operation, an amplification operation and a switching operation.

12. A quantum amplifier comprising the array according to any of claims 1 to 11.

13. A quantum circulator comprising the array according to any of claims 1 to 11.

14. An isolator comprising the array according to any of claims 1 to 11. 5 15. A system comprising: the array according to any of claims 1 to 11; and one or more target devices, wherein the one or more target devices each correspond to a respective target direction of the range of one or more corresponding target directions. 0 16. The system according to claim 15, wherein the one or more target devices comprise: a circuit quantum electrodynamics, QED, device; a qubit; and / or a quantum dot.

17. The system according to claim 15 or claim 16, wherein the system is configured to generate one or more entangled photon states.

18. A method of modulating an input signal comprising:receiving an input signal in the form of electromagnetic radiation at an array of controllable elements, each controllable element being configured to have a non- linear response to the input signal; controlling at least a subset of the elements in order to adjust the 5 permeability response of the array; modulating the input signal based on the adjusted permeability response; and selectively generating one or more output signals in a range of one or more corresponding target directions, each output signal comprising electromagnetic0 radiation.

19. The method according to claim 18, wherein selectively generating one or more output signals comprises: selectively generating one or more output signals in a range of one or more corresponding target directions, wherein the frequency of output signal corresponding to5 each target direction is different, optionally wherein the frequency of output signal for at least one target direction is different from the frequency of the input signal.

20. The method according to claim 18 or 19, wherein selectively generating one or more output signals comprises: selectively generating one or more output signals in a range of one or more0 corresponding target directions, wherein each target direction corresponds to a respective target device of a spatially distributed array of target devices, optionally where the target device comprises: a circuit quantum electrodynamics, QED, device; a qubit; and / or a quantum dot.

21. The method according to any of claims 18 to 20, wherein controlling at least a5 subset of the elements comprises:directing one or more electrical control signals to the subset of controllable elements, optionally wherein the one or more electrical control signals comprise alternating current, AC, and / or direct current, DC signals.

22. The method according to any of claims 18 to 21, wherein modulating the input 5 signal comprises at least one of performing: a mixing operation, a beam splitting operation, an amplification operation and a switching operation.

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