Superconducting Quantum Devices Research Articles

Fabrication and Characterization of Molybdenum Thin-Film Resistor for Superconducting Quantum Devices

As part of the efforts to establish a reliable fabrication process of superconducting integrated circuits at Center for Excellence in Superconducting Electronics (CENSE) in China, we investigated the influences of various deposition conditions on the properties of molybdenum (Mo) thin films. Thin-film resistors were fabricated based on these films by using a lift-off process. It was found that Mo structures made from films peeled off easily from the substrate after lift-off. We have optimized the deposition conditions to grow Mo films with compressive or weakly tensile stress. Mo thin-film resistors with a sheet resistance of several ohm/square and surface roughness of less than 1 nm were successfully fabricated and were used in the fabrication of superconducting quantum interference devices and small-scale superconducting integrated circuits.

Superfluid flow in disordered superconductors with Dynes pair-breaking scattering: Depairing current, kinetic inductance, and superheating field

We investigate the effects of Dynes pair-breaking scattering rate $\Gamma$ on the superfluid flow in a narrow thin-film superconductor and a semi-infinite superconductor by self-consistently solving the coupled Maxwell and Usadel equations for the BCS theory in the diffusive limit for all temperature $T$, all $\Gamma$, and all superfluid momentum. We obtain the depairing current density $j_d(\Gamma, T)$ and the current-dependent nonlinear kinetic inductance $L_k(j_s, \Gamma, T)$ in a narrow thin-film and the superheating field $H_{sh}(\Gamma, T)$ and the current distribution in a semi-infinite superconductor, taking the nonlinear Meissner effect into account. The analytical expressions for $j_d(\Gamma,T)|_{T=0}$, $L_k(j_s, \Gamma, T)|_{T=0}$, and $H_{sh}(\Gamma, T)|_{T=0}$ are also derived. The theory suggests $j_d$ and $H_{sh}$ can be ameliorated by reducing $\Gamma$, and $L_k$ can be tuned by a combination of the bias current and $\Gamma$. Tunneling spectroscopy can test the theory and also give insight into how to engineer $\Gamma$ via materials processing. Implications of the theory would be useful to improve performances of various superconducting quantum devices.

Quantum breakdown of superconductivity in low-dimensional materials

In order to understand the emergence of superconductivity it is useful to study and identify the various pathways leading to the destruction of superconductivity. One way is to use the increase in Coulomb-repulsion due to the increase in disorder, which overpowers the attractive interaction responsible for Cooper-pair formation. A second pathway, applicable to uniformly disordered materials, is the competition between superconductivity and Anderson localization, which leads to electronic granularity in which phase and amplitude fluctuations of the superconducting order parameter play a role. Finally, a third pathway is an array of superconducting islands coupled by some form of proximity-effect, due to Andreev-reflections, and which leads from a superconducting state to a state with finite resistivity, which appears like a metallic groundstate. This review summarizes recent progress in understanding of these different pathways, including experiments in low dimensional materials and application in superconducting quantum devices.

Hybrid superconductor-semiconductor systems for quantum technology

Superconducting quantum devices provide excellent connectivity and controllability, while semiconductor spin qubits stand out with their long-lasting quantum coherence, fast control, and potential for miniaturization and scaling. In the last few years, remarkable progress has been made in combining superconducting circuits and semiconducting devices into hybrid quantum systems that benefit from the physical properties of both constituents. Superconducting cavities can mediate quantum-coherent coupling over long distances between electronic degrees of freedom such as the spin of individual electrons on a semiconductor chip and, thus, provide essential connectivity for a quantum device. Electron spins in semiconductor quantum dots have reached very long coherence times and allow for fast quantum gate operations with increasing fidelities. We summarize recent progress and theoretical models that describe superconducting–semiconducting hybrid quantum systems, explain the limitations of these systems, and describe different directions where future experiments and theory are headed.

Tunable superconductivity of epitaxial TiN films through oxygen doping

Titanium nitride (TiN) film is a remarkable material for a variety of applications ranging from superhard coating to superconducting quantum devices, which can be easily oxidized when it works in the atmosphere. However, the study of its oxidation effect on the crystal and electronic structures of epitaxial TiN films is rare as yet. Here, we coherently synthesize TiN epitaxial films on MgO single crystal substrates via reactive magnetron sputtering and, then, dope oxygen into these films via a controllable oxidation process. The crystal and electronic structures are characterized by high-resolution x-ray diffraction, x-ray photoelectron spectra, and Raman spectra. It is revealed that the crystal structure remains to be of the rocksalt type in these films even with heavy oxygen doping. The data of temperature-dependent electrical transport measurements indicate that the superconducting critical temperature (kinetic inductance) decreases (increases) from 4.6 K (0.672 pH/□) in the pristine TiN film to 3.4 K (1.13 pH/□) in the film with a maximum oxygen doping level. Our work provides a controllable way to tune the superconductivity of TiN films, which enables the flexibility to engineer the resultant performance of TiN-based superconducting quantum devices.

Weak-field dissipative conductivity of a dirty superconductor with Dynes subgap states under a dc bias current up to the depairing current density

We study the dissipative conductivity $\sigma_1$ of a dirty superconductor with a finite Dynes parameter $\Gamma$ under a dc-biased weak time-dependent field. The Usadel equation for the current-carrying state is solved to calculate the pair potential, penetration depth, supercurrent density, and quasiparticle spectrum. It is shown that, while the depairing current density $j_d$ for $\Gamma=0$ is coincident with the Kupriyanov-Lukichev theory, a finite $\Gamma$ decreases the superfluid density, resulting in a reduction of $j_d$. The broadening of the peaks of the quasiparticle density of states induced by a combination of a finite $\Gamma$ and a dc bias can reduce $\sigma_1$ below that for the ideal dirty BCS superconductor with $\Gamma=0$, while subgap states at Fermi level proportional to $\Gamma$ results in a residual conductivity at $T\to 0$. We find the optimum combination of $\Gamma$ and the dc bias to minimize $\sigma_1$ by scanning all $\Gamma$ and all currents up to $j_d$. By using the results, it is possible to improve $j_d$ and reduce electromagnetic dissipation in various superconducting quantum devices.

Anomalous Anisotropy in Superconducting Nanodiamond Films Induced by Crystallite Geometry

Superconducting thin films underpin the function of a large variety of devices. As a promising and intriguing system with tunable electronic properties, lab-grown diamond films exhibit superconductivity upon heavy boron doping. This work reveals an anomalous superconducting anisotropy in such films: In contrast to other superconducting thin films featuring a larger in-plane upper critical field, these show a larger $o\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}t\ensuremath{-}o\phantom{\rule{0}{0ex}}f\ensuremath{-}p\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}e$ upper critical field, due to quantum confinement correlated with crystallite geometry. This study provides physical insight for developing nanodiamond-based superconducting quantum devices, by exploiting grain or twin boundaries.

Suppression of Qubit Crosstalk in a Tunable Coupling Superconducting Circuit

Parasitic crosstalk in superconducting quantum devices is a leading limitation for quantum gates. We demonstrate the suppression of static ZZ crosstalk in a two-qubit, two-coupler superconducting circuit, where the frequency of a tunable coupler can be adjusted such that the ZZ interaction from each coupler destructively interfere. We verify the crosstalk elimination with simultaneous randomized benchmarking, and use a parametrically activated iSWAP interaction to achieve a Bell state preparation fidelity of 98.5% and a $\sqrt{\textrm{iSWAP}}$ gate fidelity of 94.8% obtained via quantum process tomography.

Fine-Tuning and Optimization of Superconducting Quantum Magnetic Sensors by Thermal Annealing.

In the present article, we present the experimental results concerning the fine-tuning and optimization of superconducting quantum interference device (SQUID) parameters by thermal annealing. This treatment allows for the modification of the parameters in order to meet a specific application or to adjust the device parameters to prevent the increase of magnetic field noise and work instability conditions due to a different critical current with respect to the design value. In particular, we report the sensor critical current, the voltage–flux (V–Φ) characteristics and the spectral density of the magnetic field of SQUID magnetometers for different annealing temperatures. The measurements demonstrate that it is possible to achieve a fine control of the most important device parameters. In particular, we show that thermal annealing allows for the reduction of SQUID noise by more than a factor of 5 and makes the device working operations very stable. These results are very useful in view of quantum technology applications related to superconducting quantum computing where the correct functioning of the quantum bit depends on the fine control of the superconducting quantum device parameters and selectable annealing is possible by using a suitable laser as a thermal source.

Microwave Spectroscopy of a Weakly Pinned Charge Density Wave in a Superinductor.

A chain of small Josephson junctions (a.k.a. superinductor) emerged recently as a high-inductance, low-loss element of superconducting quantum devices. We notice that the intrinsic parameters of a typical superinductor in fact place it into the Bose glass universality class for which the propagation of waves in a sufficiently long chain is hindered by pinning. Its weakness provides for a broad crossover from the spectrum of well-resolved plasmon standing waves at high frequencies to the low-frequency excitation spectrum of a pinned charge density wave. We relate the scattering amplitude of microwave photons reflected off a superinductor to the dynamics of a Bose glass. The dynamics at long and short scales compared to the Larkin pinning length determines the low- and high-frequency asymptotes of the reflection amplitude.

Leaps of quantum phase

Energy levels in superconducting quantum devices are highly sensitive to charge fluctuations. Generally, this is considered a bug, but new work transforms this sensitivity into the defining feature of a novel device.

Superconducting nanoribbon with a constriction: A quantum-confined Josephson junction

Extended defects are known to strongly affect nanoscale superconductors. Here, we report the properties of superconducting nanoribbons with a constriction formed between two adjacent step edges by solving the Bogoliubov-de Gennes equations self-consistently in the regime where quantum confinement is important. Since the quantum resonances of the superconducting gap in the constricted area are different from the rest of the nanoribbon, such constriction forms a quantum-confined S-S'-S Josephson junction, with a broadly tunable performance depending on the length and width of the constriction with respect to the nanoribbon, and possible gating. These findings provide an intriguing approach to further tailor superconducting quantum devices where Josephson effect is of use.

Periodically modulated dark states

Phenomena of electromagnetically induced transparency (PEIT) may be interpreted by the Autler–Townes Splitting (ATS), where the coupled states are split by the coupling laser field, or by the quantum destructive interference (QDI), where the atomic phases caused by the coupling laser and the probe laser field cancel. We propose modulated experiments to explore the PEIT in an alternative way by periodically modulating the coupling and the probe fields in a Λ-type three-level system initially in a dark state. Our analytical and numerical results rule out the ATS interpretation and show that the QDI interpretation is more appropriate for the modulated experiments. Interestingly, dark state persists in the double-modulation situation where control and probe fields never occur simultaneously, which is significant difference from the traditional dark state condition. The proposed experiments are readily implemented in atomic gases, artificial atoms in superconducting quantum devices, or three-level meta-atoms in meta-materials.

Storing quantum information in spins and high-sensitivity ESR

Quantum information, encoded within the states of quantum systems, represents a novel and rich form of information which has inspired new types of computers and communications systems. Many diverse electron spin systems have been studied with a view to storing quantum information, including molecular radicals, point defects and impurities in inorganic systems, and quantum dots in semiconductor devices. In these systems, spin coherence times can exceed seconds, single spins can be addressed through electrical and optical methods, and new spin systems with advantageous properties continue to be identified. Spin ensembles strongly coupled to microwave resonators can, in principle, be used to store the coherent states of single microwave photons, enabling so-called microwave quantum memories. We discuss key requirements in realising such memories, including considerations for superconducting resonators whose frequency can be tuned onto resonance with the spins. Finally, progress towards microwave quantum memories and other developments in the field of superconducting quantum devices are being used to push the limits of sensitivity of inductively-detected electron spin resonance. The state-of-the-art currently stands at around 65 spins per Hz, with prospects to scale down to even fewer spins.

Strong coupling of magnons in a YIG sphere to photons in a planar superconducting resonator in the quantum limit

We report measurements made at millikelvin temperatures of a superconducting coplanar waveguide resonator (CPWR) coupled to a sphere of yttrium-iron garnet. Systems hybridising collective spin excitations with microwave photons have recently attracted interest for their potential quantum information applications. In this experiment the non-uniform microwave field of the CPWR allows coupling to be achieved to many different magnon modes in the sphere. Calculations of the relative coupling strength of different mode families in the sphere to the CPWR are used to successfully identify the magnon modes and their frequencies. The measurements are extended to the quantum limit by reducing the drive power until, on average, less than one photon is present in the CPWR. Investigating the time-dependent response of the system to square pulses, oscillations in the output signal at the mode splitting frequency are observed. These results demonstrate the feasibility of future experiments combining magnonic elements with planar superconducting quantum devices.

Microwave attenuators for use with quantum devices below 100 mK

To reduce the level of thermally generated electrical noise transmitted to superconducting quantum devices operating at 20 mK, we have developed thin-film microwave power attenuators operating from 1 to 10 GHz. The 20 and 30 dB attenuators are built on a quartz substrate and use 75 nm thick films of nichrome for dissipative components and 1 μm thick silver films as hot electron heat sinks. The noise temperature of the attenuators was quantified by connecting the output to a 3D cavity containing a transmon qubit and extracting the dephasing rate of the qubit as a function of temperature and dissipated power Pd in the attenuator. The minimum noise temperature Tn of the output from the 20 dB attenuator was Tn≤53 mK for no additional applied power and Tn≈120 mK when dissipating 30 nW. In the limit of large dissipated power (Pd>1 nW), we find Tn∝Pd1/5.4, consistent with detailed thermal modeling of heat flow in the attenuators.

Towards noise engineering: Recent insights in low-frequency excess flux noise of superconducting quantum devices

The comprehensive analysis of low-frequency excess flux noise both in terms of magnetic flux noise SΦ,1/f and energy sensitivity ϵ1∕f of 84 superconducting quantum devices studied at temperatures below 1 K reveals a universal behavior. When analyzing data in terms of ϵ1∕f, we find that noise spectra of independent devices cross each other all at certain crossing frequencies fc. Besides this main result of our paper, we further show that superconducting quantum interference device (SQUID) arrays systematically feature higher noise exponents than single SQUIDs and give evidence for a material and device type dependence of low-frequency excess flux noise. The latter results facilitate to engineer the shape of magnetic flux noise spectra and thus to experimentally modify key properties such as coherence or measurement times of superconducting quantum devices.

Roadmap on quantum optical systems

This roadmap bundles fast developing topics in experimental optical quantum sciences, addressing current challenges as well as potential advances in future research. We have focused on three main areas: quantum assisted high precision measurements, quantum information/simulation, and quantum gases. Quantum assisted high precision measurements are discussed in the first three sections, which review optical clocks, atom interferometry, and optical magnetometry. These fields are already successfully utilized in various applied areas. We will discuss approaches to extend this impact even further. In the quantum information/simulation section, we start with the traditionally successful employed systems based on neutral atoms and ions. In addition the marvelous demonstrations of systems suitable for quantum information is not progressing, unsolved challenges remain and will be discussed. We will also review, as an alternative approach, the utilization of hybrid quantum systems based on superconducting quantum devices and ultracold atoms. Novel developments in atomtronics promise unique access in exploring solid-state systems with ultracold gases and are investigated in depth. The sections discussing the continuously fast-developing quantum gases include a review on dipolar heteronuclear diatomic gases, Rydberg gases, and ultracold plasma. Overall, we have accomplished a roadmap of selected areas undergoing rapid progress in quantum optics, highlighting current advances and future challenges. These exciting developments and vast advances will shape the field of quantum optics in the future.

Atomic structure and oxygen deficiency of the ultrathin aluminium oxide barrier in Al/AlOx/Al Josephson junctions.

Al/AlOx/Al Josephson junctions are the building blocks of a wide range of superconducting quantum devices that are key elements for quantum computers, extremely sensitive magnetometers and radiation detectors. The properties of the junctions and the superconducting quantum devices are determined by the atomic structure of the tunnel barrier. The nanoscale dimension and disordered nature of the barrier oxide have been challenges for the direct experimental investigation of the atomic structure of the tunnel barrier. Here we show that the miniaturized dimension of the barrier and the interfacial interaction between crystalline Al and amorphous AlOx give rise to oxygen deficiency at the metal/oxide interfaces. In the interior of the barrier, the oxide resembles the atomic structure of bulk aluminium oxide. Atomic defects such as oxygen vacancies at the interfaces can be the origin of the two-level systems and contribute to decoherence and noise in superconducting quantum circuits.

Analysis of high quality superconducting resonators: consequences for TLS properties in amorphous oxides

noise caused by microscopic two-level systems (TLS) is known to be very detrimental to the performance of superconducting quantum devices but the nature of these TLS is still poorly understood. Recent experiments with superconducting resonators indicates that interaction between TLS in the oxide at the film-substrate interface is not negligible. Here we present data on the loss and frequency noise from two different Nb resonators with and without Pt capping and discuss what conclusions can be drawn regarding the properties of TLS in amorphous oxides. We also estimate the concentration and dipole moment of the TLS.