We observed a strong non-linearity in the system of quasiparticles of a superconducting aluminum resonator, due to the Cooper-pair breaking from the absorbed readout power. We observed both negative and positive feedback effects, controlled by the detuning of the readout frequency, which are able to alter the relaxation time of quasiparticles by a factor greater than 10. We estimate that the (70+/-5) % of the total non-linearity of the device is due to quasiparticles.
It is shown that there are a significant number of quasiparticles present in the superconductor even at the temperature far below the transition temperature and that those quasiparticles seriously contribute to the characteristics of superconducting thin-film resonators.
In a superconductor absorption of photons with an energy below the superconducting gap leads to redistribution of quasiparticles over energy and thus induces a strong non-equilibrium quasiparticle energy distribution. We have measured the electrodynamic response, quality factor and resonant frequency, of a superconducting aluminium microwave resonator as a function of microwave power and temperature. Below 200 mK, both the quality factor and resonant frequency decrease with increasing microwave power, consistent with the creation of excess quasiparticles due to microwave absorption. Counterint…
Nonequilibrium quasiparticles represent a significant source of decoherence in superconducting quantum circuits. Here we investigate the mechanism of quasiparticle poisoning in devices subjected to local quasiparticle injection. We find that quasiparticle poisoning is dominated by the propagation of pair-breaking phonons across the chip. We characterize the energy dependence of the timescale for quasiparticle poisoning. Finally, we observe that incorporation of extensive normal metal quasiparticle traps leads to a more than order of magnitude reduction in quasiparticle loss for a given injecte…
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…
Microwave kinetic inductance detectors (MKIDs) are thin film, cryogenic, superconducting resonators. Incident Cooper pair-breaking radiation increases their kinetic inductance, thereby measurably lowering their resonant frequency. For a given resonant frequency, the highest MKID responsivity is obtained by maximizing the kinetic inductance fraction $α$. However, in circuits with $α$ close to unity, the low supercurrent density reduces the maximum number of readout photons before bifurcation due to self-Kerr non-linearity, therefore setting a bound for the maximum $α$ before the noise equivalen…
Vortices trapped in thin-film superconducting microwave resonators can have a significant influence on the resonator performance. Using a variable-linewidth geometry for a weakly coupled resonator we are able to observe the effects of a single vortex trapped in the resonator through field cooling. For resonant modes where the vortex is near a current antinode, the presence of even a single vortex leads to a measurable decrease in the quality factor and a dispersive shift of the resonant frequency. For modes with the vortex located at a current node, the presence of the vortex results in no det…
We report an experimentally observed anomalous doubly split spectrum and its split-width fluctuation in an ultrastrongly coupled superconducting qubit and resonator. From an analysis of Rabimodel and circuit model Hamiltonians, we found that the doubly split spectrum and split-width fluctuation are caused by discrete charge hops due to quasiparticle tunnelings and a continuous background charge fluctuation in islands of a flux qubit. During 70 hours in the spectrum measurement, split width fluctuates but the middle frequency of the split is constant. This result indicates that quasiparticles i…
Quasiparticle Quality Factors in Superconducting Resonators: Effects of Bath Temperature and Readout Power
School of Integrated Circuits, Tsinghua University（清华大学集成电路学院）；Cavendish Laboratory（卡文迪许实验室）；Clarendon Laboratory（克拉伦登实验室）；James Watt School of Engineering, University of Glasgow（格拉斯哥大学詹姆斯·瓦特工程学院）
The quasiparticle relaxation time in superconducting films has been measured as a function of temperature using the response of the complex conductivity to photon flux. For tantalum and aluminium, chosen for their difference in electron-phonon coupling strength, we find that at high temperatures the relaxation time increases with decreasing temperature, as expected for electron-phonon interaction. At low temperatures we find in both superconducting materials a saturation of the relaxation time, suggesting the presence of a second relaxation channel not due to electron-phonon interaction.
We report on the on-chip detection of microwaves in the frequency range around 100GHz. For the purpose of detection, we employ a discrete transport channel triggered in a superconducting single-electron transistor by photon-assisted tunneling of quasiparticles. The technique is successfully applied to observe the spectrum of the dressed states of a model cQED system consisting of a superconducting coplanar resonator coupled to a quantum Josephson oscillator. The dressed states appear as typical resonance anticrossing exhibiting, in our case, an expectedly wide frequency splitting corresponding…
Out of equilibrium quasiparticles (QPs) are one of the main sources of decoherence in superconducting quantum circuits, and are particularly detrimental in devices with high kinetic inductance, such as high impedance resonators, qubits, and detectors. Despite significant progress in the understanding of QP dynamics, pinpointing their origin and decreasing their density remain outstanding tasks. The cyclic process of recombination and generation of QPs implies the exchange of phonons between the superconducting thin film and the underlying substrate. Reducing the number of substrate phonons wit…
Oval-shaped resonance distortion as a signature of quasiparticle heating effect in a niobium superconducting resonator
School of Integrated Circuits, Tsinghua University（清华大学集成电路学院）；Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室）；Department of Astronomy, Tsinghua University（清华大学天文系）
We measure temperature dependent quasiparticle fluctuations in a small Al volume, embedded in a NbTiN superconducting microwave resonator. The resonator design allows for read-out close to equilibrium. By placing the Al film on a membrane, we enhance the fluctuation level and separate quasiparticle from phonon effects. When lowering the temperature, the recombination time saturates and the fluctuation level reduces a factor $\sim$100. From this we deduce that the number of free quasiparticles is still thermal. Therefore, the theoretical, inverse relation between quasiparticle number and recomb…
We calculate the energy decay rate of Josephson qubits and superconducting resonators from non-equilibrium quasiparticles. The decay rates from experiments are shown to be consistent with predictions based on a prior measurement of the quasiparticle density n_qp = 10/um^3, which suggests that non-equilibrium quasiparticles are an important decoherence source for Josephson qubits. Calculations of the energy-decay and diffusion of quasiparticles also indicate that prior engineered gap and trap structures, which reduce the density of quasiparticles, should be redesigned to improve their efficacy.…
Superconducting boron doped silicon is a promising material for integrated silicon quantum devices. In particular, its low electronic density and moderate disorder make it a suitable candidate for the fabrication of large inductances with low losses at microwave frequencies. Here, we study experimentally the electrodynamics of superconducting silicon thin layers patterned in coplanar waveguide resonators, targeting three key properties: kinetic inductance, internal losses, and the variation of these quantities with the read-out power. We report the first observation in a doped semiconductor of…
We have calculated the non-equilibrium quasiparticle and phonon distributions $f(E)$, $n(Ω)$, where $E$ and $Ω$ are the quasiparticle and phonon energies respectively, generated by the photons of the probe signal of a low temperature superconducting resonator SR operating well-below its transition temperature $T_c$ as the absorbed probe power per unit volume $P_{abs}$ was changed. The calculations give insight into a rate equation estimate which suggests that the quasiparticle distributions can be driven far from the thermal equilibrium value for typical readout powers. From $f(E)$ the driven …
We describe an experimental protocol to characterize magnetic field dependent microwave losses in superconducting niobium microstrip resonators. Our approach provides a unified view that covers two well-known magnetic field dependent loss mechanisms: quasiparticle generation and vortex motion. We find that quasiparticle generation is the dominant loss mechanism for parallel magnetic fields. For perpendicular fields, the dominant loss mechanism is vortex motion or switches from quasiparticle generation to vortex motion, depending on cooling procedures. In particular, we introduce a plot of the …
We present an analysis of the dynamics of a nanomechanical resonator coupled to a superconducting single electron transistor (SSET) in the vicinity of the Josephson quasiparticle (JQP) and double Josephson quasiparticle (DJQP) resonances. For weak coupling and wide separation of dynamical timescales, we find that for either superconducting resonance the dynamics of the resonator is given by a Fokker-Planck equation, i.e., the SSET behaves effectively as an equilibrium heat bath, characterised by an effective temperature, which also damps the resonator and renormalizes its frequency. Depending …
We study the effect of non-equilibrium quasiparticles on the operation of a superconducting device (a qubit or a resonator), including heating of the quasiparticles by the device operation. Focusing on the competition between heating via low-frequency photon absorption and cooling via photon and phonon emission, we obtain a remarkably simple non-thermal stationary solution of the kinetic equation for the quasiparticle distribution function. We estimate the influence of quasiparticles on relaxation and excitation rates for transmon qubits, and relate our findings to recent experiments.
Superconducting high kinetic inductance elements constitute a valuable resource for quantum circuit design and millimeter-wave detection. Granular aluminum (GrAl) in the superconducting regime is a particularly interesting material since it has already shown a kinetic inductance in the range of nH$/\Box$ and its deposition is compatible with conventional Al/AlOx/Al Josephson junction fabrication. We characterize microwave resonators fabricated from GrAl with a room temperature resistivity of $4 \times 10^3\,μΩ\cdot$cm, which is a factor of 3 below the superconductor to insulator transition, sh…
Superconducting resonators have to date been used for photon detection in a non-equilibrium manner. In this paper, we demonstrate that such devices can also be used in a thermal quasi-equilibrium manner to detect X-ray photons. We have used a resonator to measure the temperature rise induced by an X-ray photon absorbed in normal metal and superconducting absorbers on continuous and perforated silicon nitride membranes. We observed two distinct pulses with vastly different decay times. We attribute the shorter pulses to non-equilibrium quasiparticle relaxation and the longer pulses to a thermal…
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 investigate the complex conductivity of a highly disordered MoC superconducting film with $k_Fl\approx 1$, where $k_F$ is the Fermi wavenumber and $l$ is the mean free path, derived from experimental transmission characteristics of coplanar waveguide resonators in a wide temperature range below the superconducting transition temperature $T_c$. We find that the original Mattis-Bardeen model with a finite quasiparticle lifetime, $τ$, offers a perfect description of the experimentally observed complex conductivity. We show that $τ$ is appreciably reduced by scattering effects. Characteristics …
We present a formalism for modelling parametric amplification by resonators subject to rate-limited nonlinearity of mixed reactive/dissipative character, with particular relevance to superconducting devices. The non-linearity is assumed to be characterised by a single state parameter, which responds to changes in the energy stored in the resonator with finite response time. We show how the operating point and small signal amplification behaviour of the pumped resonator can be calculated, characterised and optimised in terms of a set of three dimensionless parameters. The formalism is then illu…
We numerically and experimentally investigate the phononic loss for superconducting resonators fabricated on a piezoelectric substrate. With the help of finite element method simulations, we calculate the energy loss due to electromechanical conversion into bulk and surface acoustic waves. This sets an upper limit for the resonator internal quality factor $Q_i$. To validate the simulation, we fabricate quarter wavelength coplanar waveguide resonators on GaAs and measure $Q_i$ as function of frequency, power and temperature. We observe a linear increase of $Q_i$ with frequency, as predicted by …
We have fabricated a single Cooper-pair box (SCB) together with an on-chip lumped element resonator. By utilizing the quantum capacitance of the SCB, its state can be read out by detecting the phase of a radio-frequency (rf) signal reflected off the resonator. The resonator was optimized for fast readout. By studying quasiparticle tunneling events in the SCB, we have characterized the performance of the readout and found that we can perform a single shot parity measurement in approximately 50 ns. This is an order of magnitude faster than previously reported measurements.
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…
We have fabricated planar amorphous Indium Oxide superconducting resonators ($T_c\sim2.8$ K) that are sensitive to frequency-selective radiation in the range of 7 to 10 GHz. Those values lay far below twice the superconducting gap that worths about 200 GHz. The photons detection consists in a shift of the fundamental resonance frequency. We show that the detected frequency can be adjusted by modulating the total length of the superconducting resonator. We attribute those observations to the excitation of higher-order resonance modes. The coupling between the fundamental lumped and the higher o…
High kinetic inductance materials constitute a valuable resource for superconducting quantum circuits and hybrid architectures. Superconducting granular aluminum (grAl) reaches kinetic sheet inductances in the nH/$\square$ range, with proven applicability in superconducting quantum bits and microwave detectors. Here we show that the single photon internal quality factor $Q_{\mathrm{i}}$ of grAl microwave resonators exceeds $10^5$ in magnetic fields up to 1T, aligned in-plane to the grAl films. Small perpendicular magnetic fields, in the range of 0.5mT, enhance $Q_{\mathrm{i}}$ by approximately…
Quasiparticle spectroscopy in tantalum films with different Ta/sapphire interfaces
Ames National Laboratory（艾姆斯国家实验室）；Iowa State University（爱荷华州立大学）；National Institute of Standards and Technology（国家标准与技术研究院）；University of Virginia（弗吉尼亚大学）
We use determinant quantum Monte Carlo to study the single particle properties of quasiparticles and phonons in a variant of the two-dimensional Holstein model that includes an additional non-linear electron-phonon (e-ph) interaction. We find that a small positive non-linear interaction reduces the effective coupling between the electrons and the lattice, suppresses charge-density wave (CDW) correlations, and hardens the effective phonon frequency. Conversely, a small negative non-linear interaction can enhance the e-ph coupling resulting in heavier quasiparticles, an increased tendency toward…
We analyze the current and zero-frequency current noise properties of a superconducting single electron resonator (SSET) coupled to a resonator, focusing on the regime where the SSET is operated in the vicinity of the Josephson quasiparticle resonance. We consider a range of coupling strengths and resonator frequencies to reflect the fact that in practice the system can be tuned to quite a high degree with the resonator formed either by a nanomechanical oscillator or a superconducting stripline fabricated in close proximity to the SSET. For very weak couplings the SSET acts on the resonator li…
In-plane microwave penetration depth $λ_{ab}$ and quaiparticle conductivity at 28 GHz are measured in underdoped single crystals of the Fe-based superconductor PrFeAsO$_{1-y}$ ($T_c\approx 35$ K) by using a sensitive superconducting cavity resonator. $λ_{ab}(T)$ shows flat dependence at low temperatures, which is incompatible with the presence of nodes in the superconducting gap $Δ({\bf k})$. The temperature dependence of the superfluid density demonstrates that the gap is non-zero ($Δ/k_BT_c\gtrsim 1.6$) all over the Fermi surface. The microwave conductivity below $T_c$ exhibits an enhancemen…
We present a method to systematically locate and extract capacitive and inductive losses in superconducting resonators at microwave frequencies by use of mixed-material, lumped element devices. In these devices, ultra-low loss titanium nitride was progressively replaced with aluminum in the inter-digitated capacitor and meandered inductor elements. By measuring the power dependent loss at 50 mK as the Al-TiN fraction in each element is increased, we find that at low electric field, i.e. in the single photon limit, the loss is two level system in nature and is correlated with the amount of Al c…
Thin-film superconductors with thickness 30 to 500 nm are used as non-equilibrium quantum detectors for photons, phonons or more exotic particles. One of the most basic questions in determining their limiting sensitivity is the efficiency with which the quanta of interest couple to the detected quasiparticles. As low temperature superconducting resonators, thin-films are attractive candidates for producing quantum-sensitive arrayable sensors and the readout uses an additional microwave probe. We have calculated the quasiparticle generation efficiency eta_s for low energy photons in a represent…
We have measured the absorption of terahertz radiation in a BCS superconductor over a broad range of frequencies from 200 GHz to 1.1 THz, using a broadband antenna-lens system and a tantalum microwave resonator. From low frequencies, the response of the resonator rises rapidly to a maximum at the gap edge of the superconductor. From there on the response drops to half the maximum response at twice the pair-breaking energy. At higher frequencies, the response rises again due to trapping of pair-breaking phonons in the superconductor. In practice this is the first measurement of the frequency de…
Readout and control of fermionic spins in solid-state systems are key primitives of quantum information processing and microscopic magnetic sensing. The highly localized nature of most fermionic spins decouples them from parasitic degrees of freedom, but makes long-range interoperability difficult to achieve. In light of this challenge, an active effort is underway to integrate fermionic spins with circuit quantum electrodynamics (cQED), which was originally developed in the field of superconducting qubits to achieve single-shot, quantum-non-demolition (QND) measurements and long-range couplin…
A major issue for the implementation of large scale superconducting quantum circuits is the interaction with interfacial two-level system defects (TLS) that leads to qubit relaxation and impedes qubit operation in certain frequency ranges that also drift in time. Another major challenge comes from non-equilibrium quasiparticles (QPs) that result in qubit dephasing and relaxation. In this work we show that such QPs can also serve as a source of TLS. Using spectral and temporal mapping of TLS-induced fluctuations in frequency tunable resonators, we identify a subset of the general TLS population…
Nonequilibrium pulse dynamics and metastable latching in nonlinear kinetic inductance detectors
t0.technology（t0科技公司）；California Institute of Technology（加州理工学院）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；McGill University（麦吉尔大学）
Localized quasiparticles in a fluxonium with quasi-two-dimensional amorphous kinetic inductors
University of Colorado Boulder（科罗拉多大学博尔德分校）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Northwestern University（西北大学）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
Quantum bits (qubits) with long coherence times are an important element for the implementation of medium- and large-scale quantum computers. In the case of superconducting planar qubits, understanding and improving qubits' quality can be achieved by studying superconducting planar resonators. In this Paper, we fabricate and characterize coplanar waveguide resonators made from aluminum thin films deposited on silicon substrates. We perform three different substrate treatments prior to aluminum deposition: One chemical treatment based on a hydrofluoric acid clean, one physical treatment consist…
We discuss how reactive and dissipative non-linearities affect the intrinsic response of superconducting thin-film resonators. We explain how most, if not all, of the complex phenomena commonly seen can be described by a model in which the underlying resonance is a single-pole Lorentzian, but whose centre frequency and quality factor change as external parameters, such as readout power and frequency, are varied. What is seen during a vector-network-analyser measurement is series of samples taken from an ideal Lorentzian that is shifting and spreading as the readout frequency is changed. Accord…
We find that stray infrared light from the 4 K stage in a cryostat can cause significant loss in superconducting resonators and qubits. For devices shielded in only a metal box, we measured resonators with quality factors Q = 10^5 and qubits with energy relaxation times T_1=120 ns, consistent with a stray light-induced quasiparticle density of 170-230 μm^{-3}. By adding a second black shield at the sample temperature, we found about an order of magnitude improvement in performance and no sensitivity to the 4 K radiation. We also tested various shielding methods, implying a lower limit of Q = 1…
