WO2017158134A1

WO2017158134A1 - An apparatus and method for microwave generation and amplification by stimulated emission of radiation

Info

Publication number: WO2017158134A1
Application number: PCT/EP2017/056327
Authority: WO
Inventors: Maja Clare Cassidy; Leonardus Petrus KOUWENHOVEN
Original assignee: Technische Universiteit Delft
Priority date: 2016-03-16
Filing date: 2017-03-16
Publication date: 2017-09-21
Also published as: NL2016442B1

Abstract

A Josephson device for microwave generation and amplification by stimulated emission of radiation, the Josephson device comprising: a resonant cavity having a resonance frequency; a Josephson junction configured for exhibiting an AC Josephson effect and is capable of having a zero voltage state and a non-zero voltage state, the Josephson junction being electromagnetically coupled to the resonant cavity; wherein the Josephson device is configured for the microwave generation and amplification by stimulated emission of radiation with an emission frequency based on the resonance frequency of the resonant cavity at the non-zero voltage state, wherein the resonant cavity is configured to be in a strong coupling regime with the Josephson junction, and wherein the resonant cavity is configured to have a higher harmonic mode of the resonance frequency.

Description

An apparatus and method for microwave generation and amplification by stimulated emission of radiation

Field of the invention

[0001] The invention relates to an apparatus and a method for microwave generation and amplification by stimulated emission of radiation.

Background of the invention

[0002] Coherent microwave radiation has applications in technologies ranging from quantum sensing to quantum information processing and astronomical observation. For example, microwave signals are employed for measuring and controlling superconducting and semiconducting qubits, as well as to detect the motion of nanomechanical resonators and to read out the spin information in nitrogen- vacancy centres in diamonds.

[0003] Scaling up from single devices to commercially viable technologies requires a massive increase in the number of individual circuit elements. However for measurements performed in a dilution refrigerator, each additional coaxial line from room temperature adds a significant heat load to the system, placing additional requirements on the cooling power of the system, as well as limitations due to physical space. Efficient, on-chip generation of coherent microwave radiation at cryogenic temperatures is therefore crucial for this scale-up to occur.

[0004] Several techniques have been proposed to make more efficient use of room temperature microwave sources, including frequency multiplexing and frequency reuse, a drawback of these techniques is that the additional requirements for signal routing and power division add a significant technical overhead to the system. Placing conventional microwave oscillators at cryogenic temperatures is challenging, due to their large thermal load.

[0005] The object of the invention therefore is to provide an apparatus and a method for on-chip generation of coherent microwave radiation at cryogenic temperatures unaffected by environmental charge noise. Summary of the invention

[0006] According to a first aspect, the invention provides a Josephson device for microwave generation and amplification by stimulated emission of radiation comprising a resonant cavity having a resonance frequency, a Josephson junction configured for exhibiting an AC Josephson effect and is capable of having a zero voltage state and a non-zero voltage state, the Josephson junction being electromagnetically coupled to the resonant cavity. The Josephson device is configured for the microwave generation and amplification by stimulated emission of radiation with an emission frequency based on the resonance frequency of the resonant cavity at the non-zero voltage state. The resonant cavity is configured to be in a strong coupling regime with the Josephson junction, and wherein the resonant cavity is configured to have a higher harmonic mode of the resonance frequency. Advantageously, by applying the invention, generation of coherent microwave radiation with narrow linewidths at cryogenic temperatures unaffected by environmental charge noise can be achieved.

[0007] In an embodiment, the resonant cavity comprises at least one of the following devices: a coplanar waveguide resonator comprising a central conductor and a ground plane; a halfwave coplanar waveguide resonator; a quarter wave coplanar waveguide resonator; a slot resonator; a ring resonator; a microstrip resonator; a lumped element resonator. Advantageously, the coplanar waveguide resonator can have a quality factor high enough to achieve a strong coupling regime with the Josephson junction.

[0008] In another embodiment, the resonant cavity is capable of supporting a higher order resonance mode in the resonant cavity.

[0009] In yet another embodiment, the Josephson device is configured to mix the higher order resonance mode in the resonant cavity and down-convert the higher order resonance mode in the resonant cavity to the resonance frequency. The resonance frequency can be a fundamental resonance frequency of the resonant cavity.

[0010] In yet another embodiment, the Josephson junction is located at or near an anti- node of an electric or magnetic field of the resonant cavity. This layout advantageously enhances the coupling between the Josephson junction and the resonant cavity.

[0011] In yet another embodiment, the central conductor is electrically connected to the ground plane via the Josephson junction for applying a non-zero DC voltage between the central conductor and the ground plane. This layout advantageously enhances the coupling between the Josephson junction and the resonant cavity.

[0012] In yet another embodiment, the Josephson junction is a part of at least one of the following devices: a superconducting quantum interference device, SQUID, a tunnel junction device comprising an insulator with a superconductor on each side, a superconductor-normal-superconductor junction device wherein the normal section is a Josephson junction weak link, and a superconductor-semiconductor-superconductor device comprising a superconductor proximitized nanowire or 2DEG or graphene or carbon nanotube. Advantageously these devices can exhibit an AC Josephson effect.

[0013] In yet another embodiment, the SQUID or the tunnel junction device comprises an aluminium superconducting layer and an aluminium-oxide layer.

[0014] In yet another embodiment, the microwave generation and amplification by stimulated emission of radiation do not require external seed radiation.

[0015] In yet another embodiment, the emission frequency is a multiple of the resonance frequency.

[0016] In yet another embodiment, a coupling constant described by a coherent interaction of the Josephson junction with the resonant cavity is larger than at least one of a decay rate of photons out of the resonant cavity and a decay rate due to intrinsic effects in the resonant cavity.

[0017] In yet another embodiment, the microwave generation and amplification by stimulated emission of radiation depend on a Josephson energy of the Josephson junction.

[0018] According to another aspect, the invention provides a method for obtaining microwave generation and amplification by stimulated emission of radiation comprising: coupling a Josephson junction configured for exhibiting an AC Josephson effect and is capable of having a zero voltage state and a non-zero voltage state electromagnetically to a resonant cavity having a resonance frequency; configuring the Josephson junction at the non-zero voltage state wherein the Josephson device generates the microwave and creates the microwave amplification by stimulated emission of radiation with an emission frequency based on the resonance frequency of the resonant cavity, wherein the resonant cavity is configured to be in a strong coupling regime with the Josephson junction, and wherein the resonant cavity is has a higher harmonic mode of the resonance frequency. [0019] In an embodiment, the stimulated emission frequency can be altered via at least one of the following techniques injection locking by providing a seed radiation, changing a flux through the SQUID, changing a kinetic inductance of the resonant cavity, changing a capacitance of the resonant cavity, changing a bias voltage applied to the Josephson junction, and matching higher harmonics of the resonance frequency. Advantageously, by applying this embodiment, an in-situ tuning of the emission frequency can be achieved.

[0020] In another embodiment, the stimulated emission can be pulsed via at least one of the following techniques changing a bias voltage applied to the Josephson junction, maintaining the bias voltage and changing a Josephson energy of the Josephson junction, changing a gate voltage if the Josephson junction is part of a superconductor- semiconductor-superconductor device. Advantageously, by applying this embodiment, a pulsed control of the emission can be achieved.

[0021] In yet another embodiment, the microwave generation and amplification by stimulated emission of radiation do not require external seed radiation.

[0022] Further embodiments are disclosed in the attached claims.

Brief description of the Figures

[0023] Embodiments of the present invention will be described hereinafter, by way of example only, with reference to the accompanying drawings which are schematic in nature and therefore not necessarily drawn to scale. Furthermore, like reference signs in the drawings relate to like elements.

[0024] Figure 1A schematically shows a Josephson junction at zero bias voltage.

[0025] Figure IB schematically shows spontaneous emission in a Josephson junction.

[0026] Figure 1C schematically shows stimulated emission in a Josephson junction

[0027] Figure 2 schematically shows a resonant cavity.

[0028] Figure 3 schematically shows a Josephson junction.

[0029] Figure 4A shows experimental results of a Josephson device

[0030] Figure 4B shows experimental results of a Josephson device.

[0031] Figure 5 shows coherence and emission statistics of a Josephson device.

[0032] Figure 6 shows injection locking of a Josephson device.

[0033] Figure 7 shows a frequency comb generation using a Josephson device. Detailed description

[0034] Figures 1A, IB, 1C schematically show various tuning regimes of a Josephson junction 100 in a resonant cavity 102 that is represented by brackets. The Josephson junction 100 consists of two superconductors 1 10, 120 coupled by a weak link 130. The weak link 130 can comprise a thin insulating barrier (known as a superconductor- insulator-superconductor junction, or S-I-S), or a short section of non- superconducting metal (S-N-S), or a gateable semiconductor (e.g. graphene, semiconducting nanowire, 2DEG, carbon nanotube, 1 D or 2D nanomaterial), or a physical constriction that weakens the superconductivity at the point of contact (S-s- S). The horizontal axis in Figure 1 is the geometric position along the Josephson junction 100. The vertical axis is the electrochemical potential reflecting the energy.

[0035] Josephson junctions are natural voltage to frequency converters, via the AC Josephson effect. The Josephson junction 100 has a zero voltage state (Figure 1A) and a non-zero voltage state (Figures IB, 1C). For the Josephson junction 100 at zero applied DC bias (Figure 1A), Cooper pairs 140 can tunnel coherently from one superconducting condensate to the other resulting in a net current flow. This process creates no emission. However, for a non-zero DC bias Vb (depicted in Figures IB and 1C) that is less than the superconducting energy gap Δ 150 of the Josephson junction leads 1 10, 120, transport of Cooper pairs 140 is prohibited unless the resulting energy can be dissipated in the environment. That is nhf_r = 2eVbias , wherein h is the Planck's constant, f_r is the emission frequency, e is the electron charge, n is the number of the microwave photons, and Vbias is the applied bias voltage. The environment can comprise a resonant cavity 102.

[0036] If the voltage bias applied to the Josephson junction is such that the energy released in the Cooper pair tunneling process happens to match a resonance frequency of the resonant cavity, this inelastic process is enhanced and there is a peak in the DC current at that particular voltage bias at the point of the microwave emission. Depending on the Josephson energy Ej, a spontaneous emission (Figure IB) or a stimulated emission (Figure 1C) can be achieved.

[0037] Spontaneous emission is a general term that means that a photon is emitted randomly, if that photon happens to be in the microwave frequency domain, then it can be classed as microwave generation, as microwave photons are generated. The microwave generation in the present invention can be considered as generation of coherent microwave emission.

[0038] Figure 2 shows a resonant cavity 200. In this case, the resonant cavity 200 has a waveguide type structure. In an embodiment, the resonant cavity 200 is a coplanar waveguide resonator. In another embodiment, the resonant cavity 200 is a halfwave coplanar waveguide resonator as depicted in Figure 2. The halfwave coplanar waveguide resonator can be made from thin (approximately 20 nm thick) NbTiN. Besides NbTiN, other superconducting materials can be used as well, such as aluminium, molybdenum rhenium, niobium, niobium-titanium, indium, titanium, vanadium, a high-Tc superconductor, or a combination of superconducting materials. The superconducting materials may comprise the abovementioned materials, but not limited to those materials. The halfwave coplanar waveguide resonator can be designed to have a resonant frequency in the GHz regime. In particular, the depicted halfwave coplanar waveguide resonator has a resonant frequency of 5.4 GHz, an intrinsic quality factor of 20000, and a length of 5650 μιη. Advantageously, a resonant cavity 200 having a high quality factor can achieve a strong coupling regime with the Josephson junction 302.

[0039] The resonant cavity 200 can be other types of resonators or a combination of resonators as well, such as a quarter wave coplanar waveguide resonator, a slot resonator, a ring resonator, a microstrip resonator, a lumped element resonator. The resonant cavity 200 can be an engineered cavity.

[0040] Figure 3 is a zoomed-in scanning electron micrograph of an area comprising an anti-node 210 of an electric or magnetic field of the resonant cavity 200 of Figure 2. Figure 3 shows a device 300 comprising a Josephson junction 302. The depicted device is a superconducting quantum interference device (SQUID) 300. The SQUID 300 effectively acts as a single Josephson junction 302 with a tunable Josephson energy (Ej = EJO I cos (e φ )|, wherein Ejo is a prefactor) adjustable via the magnetic flux φ threading the loop of the SQUID 300. The SQUID 300 is located at or near the anti-node 210 of the electric or magnetic field of the resonant cavity 200. In particular, the SQUID 300 may be located at one end of the halfwave coplanar waveguide resonator in the electric or magnetic field anti-node 210. As well as using a SQUID 300 to make a tunable Josephson junction, one could use a gateable superconductor proximitized semiconductor to change the Josephson coupling. The Josephson device may rely on mixing one or many higher order resonance modes (harmonics) and down-converting the one or many higher order resonance modes (harmonics) that occur in the Josephson device. In particularly, in the resonance cavity or at the cavity antinode.

[0041] The tunability of the Josephson coupling is not a requirement for lasing. The device could operate just as well with a single Josephson junction provided the Josephson coupling can be made to the required amount. This is easily achieved, for example, by changing the materials properties of the insulating layer.

[0042] The SQUID 300 may be positioned in such a way that one side of the SQUID 300 is electrically contacted to the central conductor 310 of the halfwave coplanar waveguide resonator 200, with the other end electrically contacted directly to the ground plane 320 of the halfwave coplanar waveguide resonator 200 to enhance the coupling to the cavity photons. That is, the central conductor 310 is electrically connected to the ground plane 320 via the SQUID 300 for applying a non-zero DC voltage between the central conductor and the ground plane. At zero applied DC voltage, Josephson currents are conducted between the central conductor 310 and the ground plane 320 via the SQUID 300. In another embodiment, The SQUID 300 may be positioned in such a way that one side of the SQUID 300 is electrically contacted to the central conductor 310 of a quarterwave coplanar waveguide resonator, with the other end electrically contacted directly to the ground plane 320 of the quarterwave coplanar waveguide resonator.

[0043] The Josephson junction 302 does not have to be attached to the central conductor 310 or the ground plane 320, however the attaching configuration enhances the coupling between the Josephson junction 302 and the resonant cavity 200. It is desired for the lasing that the Josephson junction 302 resonant cavity 200 system is in a strong coupling regime.

[0044] Emissions from Josephson junctions into low quality factor cavities, either artificial or intrinsic to the junction, in the so called 'weak' coupling regime is not preferred for the present invention, because the output emission is low, making these systems impractical for actual use. A strong coupling regime is preferred for the present invention, which means a coupling constant described by a coherent interaction of the Josephson junction 302 with the resonant cavity 200 is larger than at least one of a decay rate of photons out of the resonant cavity and a decay rate due to intrinsic effects in the resonant cavity 200.

[0045] The dynamics of an emitter in a cavity can be described in two limiting regimes, 1) the strong coupling regime, i.e., the coherent interaction of the emitter with the cavity field described by a coupling constant g is the dominant interaction: g » K, γ', 2) the weak coupling regime, i.e., interaction of the emitter is basically incoherent and dominated by the damping rates κ , γ' : g « κ, γ', wherein κ is the decay of photons out of the cavity (related to the quality factor of the cavity), γ' is the decay due to intrinsic effects in the cavity. The coupling g is largely set by geometric factors.

[0046] In an embodiment, the type of the resonant cavity 200 is optional. The Josephson device mixes the higher order resonance mode(s) in the resonant cavity, and down-converts (i.e. emission of the junction at a multiple of the fundamental resonance frequency of the cavity) the higher order resonance mode(s) to the cavity fundamental resonance frequency. The resonance modes can be resonator modes in the resonant cavity 200 or/and in the Josephson device. The resonant cavity 200 or/and the Josephson device is capable of supporting one or multiple higher order modes. The Josephson device has a coupling between the Josephson junction and the resonant cavity λ =

> 1 , wherein E_j is a Josephson energy of the Josephson junction, 0o is a superconducting flux quantum, C is a capacitance of the resonant cavity to a ground plane, ω₀ is the resonance frequency. In particular, the coupling is strong, that is λ » 1. There can be a large non-linearity (between a current detected from the Josephson device and a voltage applied to the Josephson device) present in the coupling. This nonlinearity can be largely due to the non-linearity of the Josephson junction, but also may be due to the nonlinearity of the superconducting film of the resonator. The impedance of the resonant cavity can be (much) lower than that of the Josephson junction otherwise the junction will short the resonator or get damped. This means that the E_j should be large, but the junction area should be small.

[0047] A large inductor 220 acting as a radio frequency block together with an external biasing circuit (not shown) allows for a stable DC voltage bias to be applied across the SQUID 300. Coupling capacitors (not shown) at each end of the halfwave coplanar waveguide resonator 200 allows for the application of a microwave drive and the leakage of microwave photons out of the cavity 200 to be monitored using standard circuit- quantum electrodynamics techniques. The inductor 220 does not need to be attached to the central conductor 310 of the halfwave coplanar waveguide resonator 200 if the Josephson junction 302 is not attached to the central conductor 310. As well as using the inductor 220, a thin wire with high kinetic inductance that connects to each side of the Josephson junction may also be used.

[0048] Alternative to the SQUID 300, the Josephson junction may be a part of at least one of the following devices, a tunnel junction device comprising an insulator with a superconductor on each side, a superconductor-normal-superconductor junction device wherein the normal (i.e. non-superconducting) section is a Josephson junction weak link, and a superconductor-semiconductor-superconductor device comprising a superconductor proximitized semiconductor, such as nanowire, 2DEG, graphene, carbon nanotube, or a combination of proximitized semiconductors. The superconductor-semiconductor-superconductor device acts then as a Josephson junction. Using semiconductor has the advantage that the junction can be gated at a high frequency.

[0049] The Josephson junction may comprise an aluminium superconducting layer and an aluminium-oxide layer, or a nitride layer.

[0050] Figure 4A and 4B show experimental results demonstrating microwave generation and amplification by stimulated emission (maser) by a Josephson device comprising the resonant cavity 200 having a resonance frequency and a Josephson junction 302 exhibiting an AC Josephson effect and is capable of having a zero voltage state and a non-zero voltage state, the Josephson junction 302 being electromagnetically coupled to the resonant cavity 300. The Josephson device is placed at cryogenic temperatures and the following experiments are carried out at the cryogenic temperatures. The Josephson device functions based on the Josephson effect.

[0051 ] In Figure 4 A, the SQUID 300 is configured in a low Ej regime via the magnetic flux φ threading its loop. This may be achieved through an external magnetic field, generated by a global magnet, or locally by a flux bias line, or in the case of a gated proximitized semiconductor, by changing the gate voltage. A series of discrete microwave emission peaks are visible at bias voltages corresponding to multiples of the cavity resonances (Vbias = nhco). We observe up to n = 10 discrete events, corresponding to up to ten microwave photons of frequency ω simultaneously being emitted into the cavity 200. Each of these emission events is coupled with an increase in current flowing through the SQUID 300, a signature of the inelastic transport process of Cooper pairs across the Josephson junction.

[0052] In Figure 4B, the SQUID 300 is configured in a higher Ej regime compared to the Ej in Figure 4A. Additional emission features appear at higher bias voltages values. These emission features peak in intensity at voltages corresponding to multiples of the cavity resonance, however persist over a large range of bias voltages. Each of these points of intensity corresponds to the release of multiple coherent photons simultaneously into the resonant cavity 200.

[0053] According to Figures 4A and 4B, the stimulated emission can be pulsed via at least one of the following techniques: changing a bias voltage applied to the SQUID 300; and maintaining the bias voltage while changing the Josephson energy Ej of the SQUID 300 via the magnetic flux φ threading the loop of the SQUID 300, or in the case of a gated proximitized semiconductor, by changing a gate voltage. That is, changing the gate voltage coupled to the proximitized semiconductor if the Josephson junction (302) is part of a superconductor-semiconductor-superconductor device.

[0054] According to Figures 4A and 4B, the emission frequency may be a multiple of the resonance frequency of the resonant cavity 200. The multiple is defined to fulfil the resonance condition.

[0055] According to Figures 4C, the linewidth narrowing and additional gain at certain points in bias voltage in the high (Figure 4B) Josephson coupling regime (high Ej) is when stimulated emission occurs.

[0056] Real time analysis of the emission statistics in the high Ej regime is shown in Figure 5. We bias the device at the point of highest emission, corresponding to Vb = 202.5mV in Figure 4B. We demodulate the GHz signal down to a 12.5 MHz intermediate frequency that can be detected using a fast acquisition card. The device clearly shows above threshold lasing, given by the donut type behaviour in the IQ histogram shown in Figure 5A. A time series of the free running maser emission is shown in Fig 5B. The maser emission shows a clear sinusoidal behaviour, never entering a sub-threshold state. This is in contrast to recently demonstrated masers made from quantum dots or superconducting charge qubits, which are strongly affected by charge noise in the system. Instead we note that the coherence of the system is disrupted by discrete phase jumps, most probably due to vortices. To quantify the effect of these phase jumps, we plot the autocorrelation (g(l)) of the signal over a time period of 100 ms in Fig 5C. Instead of a single decay in the autocorrelation function, we see a series of revivals when the signal again becomes phase coherent with its initial phase point. Thus Figure 5 demonstrates that the microwave generation and amplification by stimulated emission of radiation of the present invention do not require external seed radiation. That is, the Josephson device lases by itself without any help from a drive signal, or the need for multiple emitters. The effect is strongest at large Ej and high voltage bias, when there are the more photons feeding into the cavity.

[0057] The linewidth of emission is a key figure of merit for lasers and masers. A narrow linewidth implies high frequency stability and resolution, which is important for a range of technologies including spectroscopy, imaging and sensing application. One technique commonly used for stabilizing lasers is injection locking, whereby the injection of a seed tone of frequency f into the resonant cavity 200 generates stimulated emission in the Josephson device at this injected frequency.

[0058] We demonstrate injection locking of the Josephson maser in Figure 6. Figure 6A shows the emitted power spectral density as a function of input power Pi for an injected signal with frequency f = 5.651 GHz, well within the emission bandwidth of the free running source. Linecuts at Pi=-127 dBm and Pi = -90 dBm are shown in Figure 6B. For very low input power, Pi < -140 dBm, very few photons enter the cavity and the Josephson device remains unaffected by the presence of the input tone. For powers above this critical value, the additional microwave photons result in stimulated emission in the Josephson device, causing the emission linewidth to narrow with increasing power, reaching an ultimate linewidth of 1 1 Hz (Figure 6B inset). This is probably limited by the measurement equipment. And this is more than 1000 times narrower than the free running emission peak, and only slightly broader than the 8 Hz linewidth of the injected tone.

[0059] In contrast to other charge-based devices recently studied, the emission in the Josephson maser is advantageously stabilized by the coherence of the superconducting condensate and is unaffected by environmental charge noise. The linewidth is instead limited by phase jumps, most probably due to superconducting vortices located close to the junction. [0060] Figure 6C shows the effect when the input tone is applied at a frequency f = 5.655 GHz, far off-resonance from the bare emission frequency. At low input powers the emission remains unaffected, similar to the on-resonant case shown earlier. When Pi > - 130dBm, distortion side-bands appear at both positive and negative frequencies, and the free running emission peak is pulled towards the input tone, eventually being locked at Pi > -85dBm. Linecuts at Pi=- 127 dBm and Pi = -90 dBm are shown in Figure 6D. The positions and intensities of these emission sidebands are well described by the Adler theory for the synchronization of coupled oscillators, similar to what has been observed for both traditional and exotic laser and maser systems.

[0061] The frequency range over which the device can be injection locked is strongly dependent on the injected power. Figure 6E shows the emitted power spectral density as a function of f at an input power Pi=-80 dBm, showing an injection locking range Af of almost 5 MHz. Measurements of Af as a function of Pi are shown in Fig. 6F. Adler's theory predicts that it should fit a power law relation Af = A Pi⁰'⁵, with a measured prefactor A = MHz/W^{0 5} agreeing well with the theoretically predicted value of MHz/W^{0 5}

[0062] The stimulated emission frequency can be altered via at least one of the following techniques: injection locking by providing a seed radiation, changing a flux through the SQUID 300, changing a kinetic inductance of the resonant cavity 200, changing a capacitance of the resonant cavity 200, changing a bias voltage applied to the Josephson junction 302, and matching higher harmonics of the resonance frequency.

[0063] By injection locking, the emission frequency follows the injected frequency. By changing a flux through the SQUID 300, Figures 4A and 4B show that the emission frequency is also changed. By changing a kinetic inductance of the resonant cavity 200, or changing a capacitance of the resonant cavity 200, the resonance frequency of the resonant cavity 200 will change, thus affecting the emission frequency. Finally, there are also higher harmonic modes existing in the resonant cavity 200, for example instead of emitting n photons at the cavity resonance frequency, the Josephson device may also emit n/2 photons at two times the cavity resonance frequency, n/3 photons at three times the cavity resonance frequency etc.

[0064] Furthermore, we demonstrate a method of generating a frequency comb using the Josephson device. Optical frequency combs have generated significant interest in recent years, and have made it possible to extend the accuracy of the atomic clocks from the radio to the optical frequency region, leading to breakthroughs in optical metrology, high precision spectroscopy and telecommunication technologies. The time-frequency duality implies that a voltage pulse applied to the junction will create a comb in the frequency domain. Application of a small AC excitation of frequency fmod = 1 1 1 Hz on the DC bias generates a comb with frequency separation f_mod, as seen in Figures 7 A, 7B. Alternatively, we can generate a much wider comb spanning almost 0.5 GHz by pulsing the injection lock signal with f_mod = l GHz (Figures 5C, 5D). These comb frequencies may be individually routed on-chip, providing multiple phase- synchronous signals for example, for qubit drives.

[0065] In an embodiment, we demonstrate lasing in the microwave frequency domain from a DC voltage biased Josephson junction strongly coupled to a superconducting coplanar waveguide resonator. Our device obeys several properties present in conventional optical lasers, including injection locking and frequency comb generation, with an injection locked linewidth of < 1 Hz, which exceeds performance of other state of the art laser systems.

[0066] The laser consists of a halfwave coplanar waveguide (CPW) resonator with resonant frequency f₀ « 5.6 GHz made from thin (20 nm) NbTiN (Figs. 2, 3). A DC superconducting quantum interference device (SQUID), located at the electric field anti-node of the cavity, effectively acts as a single junction with Josephson energy tunable via the magnetic flux φ threading its loop: E_j = E_j0 \cos( n(j)/ φ₀) \ , with E_j0~ 78 GHz, and φ₀ = i/2e the superconducting flux quantum. One side of the SQUID is tied to the central conductor of the CPW, with the other end attached directly to the ground plane to enhance the coupling to the cavity. An on-chip inductor positioned at the electric field node of the cavity allows for a DC voltage bias to be applied across the SQUID. Coupling capacitors at each end of the cavity provide an input and output for microwave photons at rate Ki_n and K_out, as in standard circuit-QED experiments. The device is mounted in a dilution refrigerator with base temperature T = 15 mK, with the magnetic flux through the SQUID tuned via a superconducting vector magnet.

[0067] We first examine the response of the device without applying any microwave power to the cavity input. At the output we measure the power spectral density, S(f), of the emitted microwave radiation as a function of voltage bias Vb. Simultaneously, we record the corresponding current flowing through the device, I_D = 2eT_CP . The coupling between a DC voltage biased Josephson junction and a cavity, λ = EJ/CPQ COJ , is set by the junction's Josephson energy, Ej, together with the cavity inductance L =

. When the device is configured in the weak Josephson coupling regime (A « 1, Fig. 4A), by tuning the external flux close to φ = φ₀, a series of discrete microwave emission peaks are visible at bias voltages corresponding to multiples of the bare cavity resonance (V_b = nV_r = nhf₀/2e « n x 1 1.62 μν). At each of these emission bursts, we observe an increase in DC current, a measure of inelastic Cooper pair transport across the Josephson junction. In this weak coupling regime, both the current and microwave emission are dominated by linear effects, with the rate of photon emission determined by the environmental impedance.

[0068] We increase the microwave emission by increasing Ej via the applied flux, to the extent that the junction and cavity become strongly coupled and the system transitions to nonlinear behavior (Λ » 1). In contrast to the discrete emission peaks seen at low Josephson energy, the emission now shifts to higher bias voltages, persisting continuously even when the voltage bias is detuned from resonance (Fig. 4B), and is accompanied by a constant flow of Cooper pairs tunneling across the junction. The emission peaks at voltages corresponding to multiples of the cavity resonance, exhibiting bifurcations common to non-linear systems under strong driving. Between these points of instability, the emission linewidth narrows to ~ 22 kHz, well below the bare cavity linewidth of ~ 5 MHz, corresponding to a phase coherence time of 15 μβ. The enhancement in emission originates from stimulated emission, as a larger photon number in the cavity increases the probability of reabsorption and coherent reemission by the junction. Notably, the emission power increases here by more than three orders of magnitude, while the average DC power input, P_in = V_bI_D, varies by only a factor of three. By comparing Pi_n with the integrated output power, we estimate a power conversion efficiency Pout/Pin > 0.3, several orders of magnitude greater than achieved for single junctions without coupling to a cavity, and comparable only to arrays containing several hundred synchronized junctions. Similar power conversion efficiencies have been seen in other strongly coupled single emitter-cavity systems. Application of a larger perpendicular magnetic field adjusts the cavity frequency, directly tuning the laser emission frequency by more than 50 MHz.

[0069] To understand the emission characteristics, we numerically simulate the time evolution of the coupled resonator- Jo sephson junction circuit for increasing Ej. If the cavity only supports a single mode, the emission power at n = 1 grows with increasing Ej, however there is only weak emission for bias voltages corresponding to n > 1. Higher-order cavity modes allow for direct emission of higher frequency photons that can be down-converted to the fundamental cavity frequency via the non-linearity of the Jo sephson junction. Simulations for n = 20 modes show that for weak coupling (λ « 1), disconnected resonant peaks are visible in the response, in agreement with the experimental data (Fig. 4A). Only combining strong coupling (λ » 1) with the presence of many higher order modes do we find a continuous narrow emission line as observed in experiment. Simulations show that this behavior persists even if the mode spacing is inhomogeneous, as under strong driving the presence of harmonics and sub harmonics for each mode means that there always can always be down conversion to the frequency of the fundamental mode of the cavity.

[0070] To directly confirm lasing, we measure the emission statistics in the high Josephson coupling regime at Vb = 192.5 μν. The emitted signal is mixed with an external local oscillator and the resulting quadrature components digitized with a fast acquisition card. A time series of the demodulated free running laser emission over a period of 100 (Fig. 5 A) shows a clear sinusoidal behavior, never entering a subthreshold state. This is in contrast to recently demonstrated lasers made from quantum dots or superconducting charge qubits, which are strongly affected by charge noise. Instead the coherence of our system is disrupted by occasional phase slips. To quantify the effect of these phase slips, we plot the autocorrelation g(i) (Fig. 5B) and extract a phase coherence time of 14 μβ, in good agreement with the value extracted from the free running line width.

[0071] To confirm coherence over longer time scales, we plot the in-phase and quadrature components of the down-converted signal from 5 x 10⁵ samples on a two- dimensional histogram (Fig. 5C, D). The donut shape of the histogram confirms lasing, with the radius A = VN = 172 representing the average coherent amplitude of the system, while the finite width σ = j (25A² + N_noise)/2 a result of amplitude fluctuations in the cavity emission δΑ = 2.66 broadened by the thermal noise from the amplifier chain, noise. When the device is not lasing (Vb =18 μν in Fig. 4 (A)), we record a Gaussian peak of width o_th = ^N_noise/2 = 6.36, corresponding to thermal emission (Fig. 5C, D). To extract the photon number distribution at the output of the cavity, the contribution of thermal fluctuations due to the amplifier chain in Fig. 3E is subtracted from the emission data in Fig. 3D. The extracted distribution takes the form p_n oc exp [-(n - JV)²/2N(1 + 4δΑ²)] centered at N « 29 600. In contrast, a perfectly coherent source would show a shot noise limited Poissonian distribution, which tends to a Gaussian distribution of the form p_n oc exp [— (n— N)²/2N] in the limit of large N. The residual fluctuations in the cavity amplitude are most probably due to Ej fluctuations which change the instantaneous photon emission rate into the cavity.

[0072] Emission linewidth is a key figure of merit for lasers. A narrow linewidth implies high frequency stability and resolution, which is important for a range of technologies including spectroscopy, imaging and sensing application. One technique commonly used for stabilizing lasers is injection locking. The injection of a seed tone of frequency finj into the cavity generates stimulated emission in the Josephson junction at this injected frequency, narrowing the emission spectrum. Figure 6A shows S(f) as a function of input power Pmj for an injected signal with frequency/™; = 5.651 GHz, well within the emission bandwidth of the free running source. Linecuts at Pmj = -127 dBm and P j = -90 dBm (Fig. 6B). For very low input power, Pmj < -140 dBm, the average photon occupation of the cavity is N < 1, and the device remains unaffected by the input tone. Once the photon occupancy exceeds N « 1, the injected microwave photons drive stimulated emission in the device, causing the emission linewidth to narrow with increasing power, reaching an ultimate (measurement limited) linewidth of 1 Hz, more than 3 orders narrower than the free running emission peak, and approaching the Schawlow-Townes limit of ~ 15 mHz. In this regime, our device acts as a quantum limited amplifier, similar to other Josephson junction based amplifiers, however no additional microwave pump tone is required to provide amplification. Fig. 6C shows the effect when the input tone is applied at a frequency fnj = 5.655 GHz, outside the cavity bandwidth. When Pmj > -130 dBm, distortion sidebands appear at both positive and negative frequencies, and the free running emission peak is pulled towards the input tone, eventually being locked when Pi_nj > -85 dBm. Linecuts at Pi_nj = -127 dBm and Pi_nj = -90 dBm (Fig. 6D). The positions and intensities of these emission sidebands are well described by the Adler theory for the synchronization of coupled oscillators, similar to what has been observed for both traditional and exotic laser systems. The frequency range over which the device can be injection locked strongly depends on the injected power. Fig. 6E shows S(f) as a function of f_nj at an input power Pi_nj = -90 dBm, showing an injection locking range Αΐ of almost 5 MHz. Here, the distortion sidebands span more than 100 MHz. Measurements of Αΐ as a function of Pinj are shown in the inset of Fig. 6E. Adler's theory predicts that the injection locking range should fit Af =

(20), with a measured prefactor a = (3.66 ± 1.93) MHz/ .

[0073] We can also use the device to generate a microwave frequency comb, an alternative to recently demonstrated four-wave mixing methods. The time- frequency duality implies that a voltage modulation applied to the junction will create a comb in the frequency domain (22). By configuring the device in the on-resonance injection locked regime (Pinj = -1 10 dBm in Fig. 6 A) and applying a small AC excitation of frequency f_mod = 1 1 1 Hz to the DC bias, we generate a comb around the central pump tone with frequency separation 1 1 1 Hz. The total width of the comb is set by the amplitude of the modulation, as well as the input power of the injection lock.

[0074] Our results conclusively demonstrate lasing from a DC biased Josephson junction in the strong coupling regime. Analysis of the output emission statistics shows 15 of phase coherence, with no sub-threshold behavior. The Josephson junction laser does not suffer from charge-noise induced linewidth broadening inherent to semiconductor gain media, and so reaches an injection locked linewidth of < 1 Hz. The device shows frequency tunability of greater than 50 MHz by directly tuning the cavity frequency, and frequency tunability over more than 100 MHz through the generation of injection-locking sidebands. Additional frequency control may be achieved by using a broadband tunable resonator, and pulse control may be provided with a tunable coupler. The phase coherence is likely limited by fluctuations in Ej, either due to 1/f dependent flux noise from magnetic impurities, or due to defects within the Josephson junction, as well as thermal fluctuations in the biasing circuit that vary Vb. We anticipate that improvements to the magnetic shielding and passivating magnetic fluctuators, together with using a cryogenically generated voltage bias will further stabilize the emission. In this case the device would perform at the quantum limit, with a linewidth which is then only limited by residual fluctuations in the photon number in the cavity. The high efficiency together with possibility to engineer the electromagnetic environment and to guide the emitted microwaves on demand lends this system to a versatile source for propagating microwave radiation.

[0075] In the foregoing description of the figures, the invention has been described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the scope of the invention as summarized in the attached claims.

[0076] In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiments disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

[0077] In particular, combinations of specific features of various aspects of the invention may be made. An aspect of the invention may be further advantageously enhanced by adding a feature that was described in relation to another aspect of the invention.

[0078] It is to be understood that the invention is limited by the annexed claims and its technical equivalents only. In this document and in its claims, the verb "to comprise" and its conjugations are used in their non-limiting sense to mean that items following the word are included, without excluding items not specifically mentioned. In addition, reference to an element by the indefinite article "a" or "an" does not exclude the possibility that more than one of the element is present, unless the context clearly requires that there be one and only one of the elements. The indefinite article "a" or "an" thus usually means "at least one".

Claims

1. A Josephson device for microwave generation and amplification by stimulated emission of radiation, the Josephson device comprising:

a resonant cavity (200) having a resonance frequency;

a Josephson junction (302) configured for exhibiting an AC Josephson effect and is capable of having a zero voltage state and a non-zero voltage state, the Josephson junction being electromagnetically coupled to the resonant cavity;

wherein the Josephson device is configured for the microwave generation and amplification by stimulated emission of radiation with an emission frequency based on the resonance frequency of the resonant cavity at the non-zero voltage state

wherein the resonant cavity is configured to be in a strong coupling regime with the Josephson junction, and wherein the resonant cavity is configured to have a higher harmonic mode of the resonance frequency.

2. The Josephson device according to claim 1 , wherein the resonant cavity (200) comprises at least one of the following devices:

a coplanar waveguide resonator comprising a central conductor (310) and a ground plane (320);

a halfwave coplanar waveguide resonator;

a quarter wave coplanar waveguide resonator;

a slot resonator;

a ring resonator;

a microstrip resonator;

a lumped element resonator.

3. The Josephson device according to any one of the claims 1 - 2, wherein the resonant cavity is capable of supporting a higher order resonance mode in the resonant cavity.

4. The Josephson device according to claim 3, wherein the Josephson device is further configured to mix the higher order resonance mode in the resonant cavity and down- convert the higher order resonance mode to the resonance frequency.

5. The Josephson device according to claim 1 , wherein the resonance frequency is a fundamental resonance frequency of the resonant cavity.

6. The Josephson device according to any one of the claims 1 - 5, wherein a coupling between the Josephson junction and the resonant cavity λ =

> 1 , wherein E_j is a Josephson energy of the Josephson junction, φ₀ is a superconducting flux quantum, C is a capacitance of the resonant cavity to a ground plane, ω₀ is the resonance frequency.

7. The Josephson device according to claim 6, wherein the coupling is strong, λ » 1.

8. The Josephson device according to any one of the claims 1 - 7, wherein the Josephson device is configured to have a nonlinearity between a current detected from the Josephson device and a voltage applied to the Josephson device.

9. The Josephson device according to any one of the claims 1 - 8, wherein an impedance of the resonant cavity is lower than an impedance of the Josephson junction.

10. The Josephson device according to any one of the claims 1 - 9, wherein the resonant cavity (200) comprises a superconductor, for example at least one of the following materials:

niobium-titanium-nitride, aluminum, molybdenum rhenium, niobium, niobium-titanium, indium, titanium, vanadium.

1 1. The Josephson device according to any one of the claims 1 - 10, wherein the Josephson junction (302) is located at or near an anti-node (210) of an electric or magnetic field of the resonant cavity (200).

12. The Josephson device according to any one of the claims 1 - 1 1 , wherein the central conductor (310) is electrically connected to the ground plane (320) via the

Josephson junction (302) for applying a non-zero DC voltage between the central conductor and the ground plane.

13. The Josephson device according to any one of the claims 1 - 12, wherein the Josephson junction (302) is a part of at least one of the following devices:

a superconducting quantum interference device, SQUID,

a tunnel junction device comprising an insulator with a superconductor on each side,

a superconductor-normal-superconductor junction device wherein the normal section is a Josephson junction weak link (130), and

a superconductor-semiconductor-superconductor device comprising a superconductor proximitized nanowire or 2DEG or graphene or carbon nanotube or ID or 2D nanomaterial.

14. The Josephson device according to claim 13, wherein the SQUID or the tunnel junction device comprises an aluminum superconducting layer and an aluminum- oxide layer.

15. The Josephson device according to any one of the claims 1 - 14, wherein the microwave generation and amplification by stimulated emission of radiation do not require external seed radiation.

16. The Josephson device according to any one of the claims 1 - 15, wherein the emission frequency is a multiple of the resonance frequency.

17. The Josephson device according to any one of the claims 1 - 15, configured with a coupling constant described by a coherent interaction of the Josephson junction (302) with the resonant cavity (200), said coupling constant is larger than at least one of a decay rate of photons out of the resonant cavity and a decay rate due to intrinsic effects in the resonant cavity.

18. The Josephson device according to any one of the claims 1 - 17, wherein the microwave generation and amplification by stimulated emission of radiation depend on a Josephson energy of the Josephson junction (302).

19. A method for obtaining microwave generation and amplification by stimulated emission of radiation comprising:

coupling a Josephson junction (302) configured for exhibiting an AC Josephson effect and is capable of having a zero voltage state and a non-zero voltage state electromagnetically to a resonant cavity (200) having a resonance frequency; configuring the Josephson junction (302) at the non-zero voltage state wherein the Josephson device generates the microwave and creates the microwave amplification by stimulated emission of radiation with an emission frequency based on the resonance frequency of the resonant cavity, wherein the resonant cavity is in a strong coupling regime with the Josephson junction, and wherein the resonant cavity is has a higher harmonic mode of the resonance frequency.

20. The method according to claim 19, wherein the resonant cavity (200) comprises at least one of the following devices:

a halfwave coplanar waveguide resonator;

a quarter wave coplanar waveguide resonator; a slot resonator;

a ring resonator;

a microstrip resonator;

a lumped element resonator.

21. The method according to any one of the claims 19 - 20, wherein the resonant cavity is capable of supporting a higher order resonance mode in the resonant cavity.

22. The method according to claim 21 , wherein the Josephson device mixes the higher order resonance mode in the resonant cavity and down-convert the higher order resonance mode to the resonance frequency; or/and

wherein a coupling between the Josephson junction and the resonant cavity λ =

EJ/CPQ COJ > 1 , wherein E_j is a Josephson energy of the Josephson junction, φ₀ is a superconducting flux quantum, C is a capacitance of the resonant cavity to a ground plane, ω₀ is the resonance frequency; or/and

wherein the Josephson device has a nonlinearity between a current detected from the Josephson device and a voltage applied to the Josephson device; or/and an impedance of the resonant cavity is lower than an impedance of the Josephson junction; or/and

wherein the coupling is strong, λ » 1.

23. The method according to any one of the claims 19 - 22, further comprising positioning the Josephson junction (302) at or near an anti-node (210) of an electric or magnetic field of the resonant cavity (200).

24. The method according to any one of the claims 19 - 23, further comprising connecting the central conductor (310) electrically to the ground plane (320) via the Josephson junction (302) for applying a non-zero DC voltage between the central conductor and the ground plane.

25. The method according to any one of the claims 19 - 23, wherein the Josephson junction (302) is a part of at least one of the following devices:

a superconducting quantum interference device, SQUID,

a superconductor-normal-superconductor junction device wherein the normal section is a Josephson junction weak link (130), and a superconductor-semiconductor-superconductor device comprising a superconductor proximitized nanowire or 2DEG or graphene or carbon nanotube or ID or 2D nanomaterial.

26. The method according to claim 25, further comprising altering the stimulated emission frequency via at least one of the following techniques:

injection locking by providing a seed radiation,

changing a flux through the SQUID,

changing a kinetic inductance of the resonant cavity (200),

changing a capacitance of the resonant cavity (200),

changing a bias voltage applied to the Josephson junction (302), and matching higher harmonics of the resonance frequency.

27. The method according to any one of the claims 19 - 25, further comprising pulsing the stimulated emission via at least one of the following techniques:

changing a bias voltage applied to the Josephson junction (302),

maintaining the bias voltage and changing a Josephson energy of the Josephson junction,

changing a gate voltage if the Josephson junction (302) is part of a superconductor-semiconductor-superconductor device.

28. The method according to any one of the claims 19 - 27, wherein the microwave generation and amplification by stimulated emission of radiation do not require external seed radiation.

29. The method according to any one of the claims 19 - 28, wherein the emission frequency is a multiple of the resonance frequency.

30 The method according to any one of the claims 19 - 29, wherein the coupling has a coupling constant described by a coherent interaction of the Josephson junction (302) with the resonant cavity (200), said coupling constant is larger than at least one of a decay rate of photons out of the resonant cavity and a decay rate due to intrinsic effects in the resonant cavity.

31. The method according to any one of the claims 19 - 30, wherein the microwave generation and amplification by stimulated emission of radiation depend on a

Josephson energy of the Josephson junction (302).

32. The Josephson device according to any one of the claims 1 - 18 configured to perform the methods of claims 19 - 31.