We present a system which allows to tune the coupling between a superconducting resonator and a transmission line. This storage resonator is addressed through a second, coupling resonator, which is frequency-tunable and controlled by a magnetic flux applied to a superconducting quantum interference device (SQUID). We experimentally demonstrate that the lifetime of the storage resonator can be tuned by more than three orders of magnitude. A field can be stored for 18 μs when the coupling resonator is tuned off resonance and it can be released in 14 ns when the coupling resonator is tuned on resonance. The device allows capture, storage, and on-demand release of microwaves at a tunable rate.
We have designed, fabricated and measured high-Q $λ/2$ coplanar waveguide microwave resonators whose resonance frequency is made tunable with magnetic field by inserting a DC-SQUID array (including 1 or 7 SQUIDs) inside. Their tunability range is 30% of the zero field frequency. Their quality factor reaches up to 3$\times10^4$. We present a model based on thermal fluctuations that accounts for the dependance of the quality factor with magnetic field.
We present an experimental demonstration as well as a theoretical model of an integrated circuit designed for the manipulation of a microwave field down to the single-photon level. The device is made of a superconducting resonator coupled to a transmission line via a second frequency-tunable resonator. The tunable resonator can be used as a tunable coupler between the fixed resonator and the transmission line. Moreover, the manipulation of the microwave field between the two resonators is possible. In particular, we demonstrate the swapping of the field from one resonator to the other by pulsi…
We realize a device allowing for tunable and switchable coupling between two superconducting resonators mediated by an artificial atom. For the latter, we utilize a persistent current flux qubit. We characterize the tunable and switchable coupling in frequency and time domain and find that the coupling between the relevant modes can be varied in a controlled way. Specifically, the coupling can be tuned by adjusting the flux through the qubit loop or by saturating the qubit. Our time domain measurements allow us to find parameter regimes for optimal switch performance with respect to qubit driv…
We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positiv…
We propose a method for fast, deterministic resonator reset based on tunable dissipative modes. The dissipator is based on a Josephson junction with relatively low quality factor. When the dissipator is tuned into resonance with a high quality microwave resonator, resonator photons are absorbed by the dissipator at a rate orders of magnitude faster than the resonator relaxation rate. We determine the optimal parameters for realization of the tunable dissipator, and examine application of the dissipator to removing spurious photon population in the qubit readout resonator in circuit quantum ele…
We design and fabricate two types of superconducting niobium coplanar waveguide microwave resonators with different coupling capacitors on high purity Si substrates. Their microwave transmissions are measured at the temperatures of 20 mK. It is found that these two types of resonators possess significantly-different loaded quality factors; one is $5.6\times{10}^{3}$, and the other is $4.0\times{10}^{4}$. The measured data are fitted well by classical ABCD matrix approach. We found that the transmission peak deviates from the standard Lorentizian with a frequency broadening.
We propose a scheme able to entangle at the steady state a nanomechanical resonator with a microwave cavity mode of a driven superconducting coplanar waveguide. The nanomechanical resonator is capacitively coupled with the central conductor of the waveguide and stationary entanglement is achievable up to temperatures of tens of milliKelvin.
Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spin-like systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N-photon NOON states as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two …
We have measured the backaction of a dc superconducting quantum interference device (SQUID) position detector on an integrated 1 MHz flexural resonator. The frequency and quality factor of the micromechanical resonator can be tuned with bias current and applied magnetic flux. The backaction is caused by the Lorentz force due to the change in circulating current when the resonator displaces. The experimental features are reproduced by numerical calculations using the resistively and capacitively shunted junction (RCSJ) model.
We give a quantum master equation description of the measurement scheme based on a coplanar microwave cavity capacitively coupled to nano mechanical resonator. The system exhibits a rich bifurcation structure that is analogous to sub/second harmonic generation in nonlinear optics. We show how it may be configured as a bifurcation amplifier transducer for weak force detection.
We designed a loop-gap microwave resonator for applications of spin-based hybrid quantum systems, and tested it with impurity spins in diamond. Strong coupling with ensembles of nitrogen-vacancy (NV) centers and substitutional nitrogen (P1) centers was observed. These results show that loop-gap resonators are viable in the prospect of spin-based hybrid quantum systems, especially for an ensemble quantum memory or a quantum transducer.
We report on the design and performance of a cryogenic (300 mK) near-field scanning microwave microscope. It uses a microwave resonator as the near-field sensor, operating at a frequency of 6 GHz and microwave probing amplitudes down to 100 uV, approaching low enough photon population (N~1000) of the resonator such that coherent quantum manipulation becomes feasible. The resonator is made out of a miniaturized distributed fractal superconducting circuit that is integrated with the probing tip, micromachined to be compact enough such that it can be mounted directly on a quartz tuning-fork, and …
We demonstrate coherent tunable coupling between a superconducting phase qubit and a lumped element resonator. The coupling strength is mediated by a flux-biased RF SQUID operated in the non-hysteretic regime. By tuning the applied flux bias to the RF SQUID we change the effective mutual inductance, and thus the coupling energy, between the phase qubit and resonator . We verify the modulation of coupling strength from 0 to $100 MHz$ by observing modulation in the size of the splitting in the phase qubit's spectroscopy, as well as coherently by observing modulation in the vacuum Rabi oscillatio…
We have measured the number of quasiparticles and their lifetime in aluminium superconducting microwave resonators. The number of excess quasiparticles below 160 mK decreases from 72 to 17 $μ$m$^{-3}$ with a 6 dB decrease of the microwave power. The quasiparticle lifetime increases accordingly from 1.4 to 3.5 ms. These properties of the superconductor were measured through the spectrum of correlated fluctuations in the quasiparticle system and condensate of the superconductor, which show up in the resonator amplitude and phase respectively. Because uncorrelated noise sources vanish, fluctuatio…
We consider the coupling of a single mode microwave resonator to a tunnel junction whose contacts are at thermal equilibrium. We derive the quantum master equation describing the evolution of the resonator field in the strong coupling regime, where the characteristic impedance of the resonator is larger than the quantum of resistance. We first study the case of a normal-insulator-normal junction and show that a dc driven single photon source can be obtained. We then consider the case of a superconductor-insulator-normal and superconductor-insulator-superconductor junction. There, we show that …
The Dicke effect is examined in an all-optical system of an optical waveguide side coupled to two interacting ring resonators in a liquid crytal environment. The system is shown to exhibit all the signatures of the Dicke effect under an active and reversible control by an applied voltage.
We describe and characterize a microwave setup to probe the Andreev levels of a superconducting atomic contact. The contact is part of a superconducting loop inductively coupled to a superconducting coplanar resonator. By monitoring the resonator reflection coefficient close to its resonance frequency as a function of both flux through the loop and frequency of a second tone we perform spectroscopy of the transition between two Andreev levels of highly transmitting channels of the contact. The results indicate how to perform coherent manipulation of these states.
The germanium (Ge) hut wire system has strong spin-orbit coupling, a long coherence time due to a very large heavy-light hole splitting, and the advantage of site-controlled large-scale hut wire positioning. These properties make the Ge hut wire a promising candidate for the realization of strong coupling of spin to superconducting resonators and scalability for multiple qubit coupling. We have coupled a reflection line resonator to a hole double quantum dot (DQD) formed in Ge hut wire. The amplitude and phase responses of the microwave resonator revealed that the charge stability diagrams of …
We create a Josephson parametric amplifier from a transmission line resonator whose inner conductor is made from a series SQUID array. By changing the magnetic flux through the SQUID loops, we are able to adjust the circuit's resonance frequency and, consenquently, the center of the amplified band, between 4 and 7.8 GHz. We observe that the amplifier has gains as large as 28 dB and infer that it adds less than twice the input vacuum noise.
We study a one-step approach to the fast generation of Greenberger-Horne-Zeilinger (GHZ) states in a circuit QED system with superconducting flux qubits. The GHZ state can be generated in about 10 ns, which is much shorter than the coherence time of flux qubits and comparable with the time of single-qubit operation. In our proposal, a time-dependent microwave field is applied to a superconducting transmission line resonator (TLR) and displaces the resonator in a controlled manner, thus inducing indirect qubit-qubit coupling without residual entanglement between the qubits and the resonator. Th…
We propose a method for detecting the presence of a single spin in a crystal by coupling it to a high-quality factor superconducting planar resonator. By confining the microwave field in a constriction of nanometric dimensions, the coupling constant can be as high as $5-10$\,kHz. This coupling affects the amplitude of the field emitted by the resonator, and the integrated homodyne signal allows detection of a single spin with unit signal-to-noise ratio within few milliseconds. We further show that a stochastic master equation approach and a Bayesian analysis of the full time dependent homodyne…
We report the observation of strong coupling between the exchange-coupled spins in gallium-doped yttrium iron garnet and a superconducting coplanar microwave resonator made from Nb. The measured coupling rate of 450 MHz is proportional to the square-root of the number of exchange-coupled spins and well exceeds the loss rate of 50 MHz of the spin system. This demonstrates that exchange coupled systems are suitable for cavity quantum electrodynamics experiments, while allowing high integration densities due to their extraordinary high spin densities. Our results furthermore show, that experiment…
We measure photon-occupancy in a thin-film superconducting lumped element resonator coupled to a transmon qubit at 20$\,$mK and find a nonlinear dependence on the applied microwave power. The transmon-resonator system was operated in the strong dispersive regime, where the ac Stark shift ($2χ$) due to a single microwave photon present in the resonator was larger than the linewidth ($Γ$) of the qubit transition. When the resonator was coherently driven at $5.474325\,$GHz, the transition spectrum of the transmon at $4.982\,$GHz revealed well-resolved peaks, each corresponding to an individual ph…
Microwave-frequency superconducting resonators are ideally suited to perform dispersive qubit readout, to mediate two-qubit gates, and to shuttle states between distant quantum systems. A prerequisite for these applications is a strong qubit-resonator coupling. Strong coupling between an electron-spin qubit and a microwave resonator can be achieved by correlating spin- and orbital degrees of freedom. This correlation can be achieved through the Zeeman coupling of a single electron in a double quantum dot to a spatially inhomogeneous magnetic field generated by a nearby nanomagnet. In this pape…
Microring resonators are critical photonic components used in filtering, sensing and nonlinear applications. To date, the development of high performance microring resonators in LNOI has been limited by the sidewall angle, roughness and etch depth of fabricated rib waveguides. We present large free spectral range microring resonators patterned via electron beam lithography in high-index contrast $Z$-cut LNOI. Our microring resonators achieve an FSR greater than 5 nm for ring radius of 30 $μ$m and a large 3 dB resonance bandwidth. We demonstrate 3 pm/V electro-optic tuning of a 70 $μ$m-radius r…
Detection of single, itinerant microwave photons is an important functionality for emerging quantum technology applications as well as of fundamental interest in quantum thermodynamics experiments on heat transport. In a recent experiment [W. Khan et al., Nat. Commun. 12, 5130 (2021)], it was demonstrated that a double quantum dot (DQD) coupled to a microwave resonator can act as an efficient and continuous photodetector by converting an incoming stream of photons to an electrical photocurrent. In the experiment, average photon and electron flows were analyzed. Here we theoretically investigat…
Using optical diffraction, we study the mechanical vibrations of an array of micromechanical resonators. Implementing tunable electrostatic coupling between the suspended, doubly-clamped Au beams leads to the formation of a band of collective vibrational modes within these devices. The evolution of these modes with coupling strength is clearly manifested in the optical diffraction pattern of light transmitted through the array. The experimental results are analyzed using a simple model for one-dimensional phonons. These structures offer unique prospects for spectral analysis of complex mechani…
We present a systematic analysis of the internal losses of superconducting coplanar waveguide microwave resonators based on niobium thin films on silicon substrates. In particular, we investigate losses introduced by Nb/Al interfaces in the center conductor, which is important for experiments where Al based Josephson junctions are integrated into Nb based circuits. We find that these interfaces can be a strong source for two-level state (TLS) losses, when the interfaces are not positioned at current nodes of the resonator. In addition to TLS losses, for resonators including Al, quasiparticle l…
High quality factor mechanical resonators have shown great promise in developing classical or quantum technologies. Simultaneously, progress has been made in developing controlled mechanical nonlinearity. Here we combine these two directions of progress in a single platform consisting of coupled Silicon Nitride (SiNx) and graphene mechanical resonators. We show that nonlinear response can be induced on a large area SiNx resonator mode and can be efficiently controlled by coupling it to a gate-tunable, freely suspended graphene mode. The induced nonlinear response of the hybrid modes, as measur…
In many hybrid quantum systems, a superconducting circuit is required that combines DC-control with a coplanar waveguide (CPW) microwave resonator. The strategy thus far for applying a DC voltage or current bias to microwave resonators has been to apply the bias through a symmetry point in such a way that it appears as an open circuit for certain frequencies. Here, we introduce a microwave coupler for superconducting CPW cavities in the form of a large shunt capacitance to ground. Such a coupler acts as a broadband mirror for microwaves while providing galvanic connection to the center conduct…
Dielectric measurements on insulating materials at cryogenic temperatures can be challenging, depending on the frequency and temperature ranges of interest. We present a technique to study the dielectric properties of bulk dielectrics at GHz frequencies. A superconducting coplanar Nb resonator is deposited directly on the material of interest, and this resonator is then probed in distant-flip-chip geometry with a microwave feedline on a separate chip. Evaluating several harmonics of the resonator gives access to various probing frequencies, in the present studies up to 20 GHz. We demonstrate t…
We present measurements of a hybrid system consisting of a microwave transmission-line resonator and a lateral quantum dot defined on a GaAs heterostructure. The two subsystems are separately characterized and their interaction is studied by monitoring the electrical conductance through the quantum dot. The presence of a strong microwave field in the resonator is found to reduce the resonant conductance through the quantum dot, and is attributed to electron heating and modulation of the dot potential. We use this interaction to demonstrate a measurement of the resonator transmission spectrum u…
Realizing quantum mechanical behavior in micro- and nanomechanical resonators has attracted continuous research effort. One of the ways for observing quantum nature of mechanical objects is via the mechanism of phonon blockade. Here, we show that phonon blockade could be achieved in a system of two weakly nonlinear mechanical resonators coupled by a Coulomb interaction. The optimal blockade arises as a result of the destructive quantum interference between paths leading to two-phonon excitation. It is observed that, in comparison to a single drive applied on one mechanical resonator, driving b…
We have studied microwave response of a high-mobility two-dimensional electron system (2DES) contacted by two side electrodes. Using kinetic inductance of the 2DES and inter-electrode capacitance, we have constructed a subwavelength 2D plasmonic resonator. We have shown that the resonant frequency of this circuit can be controlled by 2D electron density, external magnetic field, or size of the electrodes. This opens up possibilities for using arrays of plasmonic circuits as tunable components in different frequency ranges.
We have fabricated suspended metal paddle resonators with carbon nanotubes functioning as self-detecting torsional springs. We observe gate-tunable resonances, that either tune to higher or to lower frequencies when increasing the dc voltage on the back-gate. We attribute the former modes to flexural vibrations of the paddle resonator, while the latter ones are identified as torsional vibrations. Compared to top-down silicon fabricated paddle resonators, nanotube springs have smaller torsional spring constants and provide a larger frequency tunability.
We have fabricated rhenium microwave resonators from epitaxial films. We have used thin films of different structural quality depending on their growth conditions. The resonators were coupled to a microwave transmission line which allows the measurement of their resonance frequencies and internal quality factors. From the resonance frequency at low temperature , the effective penetration depth and the London penetration depth of the rhenium film are extracted.
The ability to control microwave emission from a spin ensemble is a requirement of several quantum memory protocols. Here, we demonstrate such ability by using a resonator whose frequency can be rapidly tuned with a bias current. We store excitations in an ensemble of rare-earth-ions and suppress on-demand the echo emission (`echo silencing') by two methods: 1) detuning the resonator during the spin rephasing, and 2) subjecting spins to magnetic field gradients generated by the bias current itself. We also show that spin coherence is preserved during silencing.
Circuit quantum electrodynamics (QED) employs superconducting microwave resonators as quantum buses. In circuit QED with semiconductor quantum-dot-based qubits, increasing the resonator impedance is desirable as it enhances the coupling to the typically small charge dipole moment of these qubits. However, the gate electrodes necessary to form quantum dots in the vicinity of a resonator inadvertently lead to a parasitic port through which microwave photons can leak, thereby reducing the quality factor of the resonator. This is particularly the case for high-impedance resonators, as the ratio of…
Controlling the dynamics of mechanical resonators is central to many quantum science and metrology applications. Optomechanical control of diamond resonators is attractive owing to diamond's excellent physical properties and its ability to host electronic spins that can be coherently coupled to mechanical motion. Using a confocal microscope, we demonstrate tunable amplification and damping of a diamond nanomechanical resonator's motion. Observation of both normal mode cooling from room temperature to 80K, and amplification into self--oscillations with $60\,μ\text{W}$ of optical power is observ…
We propose a low noise, triply-resonant, electro-optic (EO) scheme for quantum microwave-to-optical conversion based on coupled nanophotonics resonators integrated with a superconducting qubit. Our optical system features a split resonance - a doublet - with a tunable frequency splitting that matches the microwave resonance frequency of the superconducting qubit. This is in contrast to conventional approaches where large optical resonators with free-spectral range comparable to the qubit microwave frequency are used. In our system, EO mixing between the optical pump coupled into the low freque…
We present a sensitive, tunable radio-frequency resonator designed to detect reactive changes in nanoelectronic devices down to dilution refrigerator temperatures. The resonator incorporates GaAs varicap diodes to allow electrical tuning of the resonant frequency and the coupling to the input line. We find a resonant frequency tuning range of 8.4 MHz at 55 mK that increases to 29 MHz at 1.5 K. To assess the impact on performance of different tuning conditions, we connect a quantum dot in a silicon nanowire field-effect transistor to the resonator, and measure changes in the device capacitance …
We present a design for a tunneling-current-assisted scanning near-field microwave microscope. For stable operation at cryogenic temperatures, making a small and rigid microwave probe is important. Our coaxial resonator probe has a length of approxomately 30 mm and can fit inside the 2-inch bore of a superconducting magnet. The probe design includes an insulating joint, which separates DC and microwave signals without degrading the quality factor. By applying the SMM to the imaging of an electrically inhomogeneous superconductor, we obtain the spatial distribution of the microwave response wit…
Low-cost spintronic devices functioning in zero applied magnetic field are required for bringing the idea of spin-based electronics into the real-world industrial applications. Here we present first microwave measurements performed on nanomagnet devices fabricated by electrodeposition inside porous membranes. In the paper, we discuss in details a microwave resonator consisting of three nanomagnets, which functions in zero external magnetic field. By applying a microwave signal at a particular frequency, the magnetization of the middle nanomagnet experiences the ferromagnetic resonance (FMR), a…
Coupled nanomechanical resonators are interesting for both fundamental studies and practical applications as they offer rich and tunable oscillation dynamics. At present, the mechanical coupling in such systems is often mediated by a fixed geometry, such as a joint clamping point of the resonators or a displacement-dependent force. Here we show a graphene-integrated electromechanical system consisting of two physically separated mechanical resonators -- a comb-drive actuator and a suspended silicon beam -- that are tunably coupled by a graphene membrane. The graphene membrane, moreover, provid…
We have designed, fabricated, and characterized magnetostatic wave (MSW) resonators on a chip. The resonators are fabricated by patterning single-crystal yttrium iron garnet (YIG) film on a gadolinium gallium garnet (GGG) substrate and excited by loop-inductor transducers. We achieved this technology breakthrough by developing a YIG film etching process and fabricating thick aluminum coplanar waveguide (CPW) inductor loop around each resonator to individually address and excite MSWs. At 4.77 GHz, the 0.68 square mm resonator achieves a quality factor Q > 5000 with a bias field of 987 Oe. We al…
With recent advances in the circuit quantum electrodynamics (cQED) architecture, hybrid systems that couple nano-devices to microwave resonators have been developing rapidly. Here we report an experimental demonstration of two graphene double quantum dots (DQDs) coupled over a distance of up to 60 μm, through a microwave resonator. We jointly measure the two DQDs' coupling to the resonator, which causes a nonlinear response in the resonator reflection amplitude in the vicinity of the degeneracy points of the two DQDs. This phenomenon is explained by the Tavis-Cummings (T-C) mode. We further ch…
Experiments have been performed using a spherical superconducting microwave resonator that simulates the geometric structure of the C60 fullerene molecule. The objective was to study with very high resolution the exceptional spectral properties emerging from the symmetries of the icosahedral structure of the carbon lattice. In particular, the number of zero modes has been determined to test the predictions of the Atiyah-Singer index theorem, which relates it to the topology of the curved carbon lattice. This is, to the best of our knowledge, the first experimental verification of the index the…
We experimentally investigate a strongly driven GaAs double quantum dot charge qubit weakly coupled to a superconducting microwave resonator. The Floquet states emerging from strong driving are probed by tracing the qubit - resonator resonance condition. This way we probe the resonance of a qubit that is driven in an adiabatic, a non-adiabatic, or an intermediate rate showing distinct quantum features of multi-photon processes and Landau-Zener-Stückelberg interference pattern. Our resonant detection scheme enables the investigation of novel features when the drive frequency is comparable to th…
The non-linear interaction between two mechanical resonances of the same freely suspended carbon nanotube resonator is studied. We find that in the Coulomb blockade regime, the non-linear modal interaction is dominated by single-electron-tunneling processes, and that the mode-coupling parameter can be tuned with the gate voltage, allowing both mode softening and mode stiffening behavior. This is in striking contrast to tension-induced mode coupling in strings, where the coupling parameter is positive and gives rise to a stiffening of the mode. The strength of the mode coupling in carbon nanotu…
We present microwave frequency measurements of the dynamic admittance of a quantum dot tunnel coupled to a two-dimensional electron gas. The measurements are made via a high-quality 6.75 GHz on-chip resonator capacitively coupled to the dot. The resonator frequency is found to shift both down and up close to conductance resonance of the dot corresponding to a change of sign of the reactance of the system from capacitive to inductive. The observations are consistent with a scattering matrix model. The sign of the reactance depends on the detuning of the dot from conductance resonance and on the…
We present three designs for planar superconducting microwave resonators for electron spin resonance (ESR) experiments. We implement finite element simulations to calculate the resonance frequency and quality factors as well as the three-dimensional microwave magnetic field distribution of the resonators. One particular resonator design offers an increased homogeneity of the microwave magnetic field while the other two show a better confinement of the mode volume. We extend our model simulations to calculate the collective coupling rate between a spin ensemble and a microwave resonator in the …
Coulomb interaction has important consequences on the physics of quantum spin Hall edge states, weakening the topological protection via two-particle scattering and renormalizing both the velocity and charge of collective plasmon modes compared to that of free electrons. Despite these effects, interactions remain difficult to quantify. We propose here simple and robust edge resonator geometries to characterize Coulomb interaction by means of high-frequency measurements. They rely on a transmission line approach, and take advantage of the impedance mismatch between the edge states and their mic…
