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 that are highly coherent TLS with a low reconfiguration temperature $\sim$ 300 mK, and a non-uniform density of states. These properties can be understood if these TLS are formed by QPs trapped in shallow subgap states formed by spatial fluctutations of the superconducting order parameter $Δ$. Magnetic field measurements of one such TLS reveals a link to superconductivity. Our results imply that trapped QPs can induce qubit relaxation.
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…
Identifying, quantifying, and suppressing decoherence mechanisms in qubits are important steps towards the goal of engineering a quantum computer or simulator. Superconducting circuits offer flexibility in qubit design; however, their performance is adversely affected by quasiparticles (broken Cooper pairs). Developing a quasiparticle mitigation strategy compatible with scalable, high-coherence devices is therefore highly desirable. Here we experimentally demonstrate how to control quasiparticle generation by downsizing the qubit, capping it with a metallic cover, and equipping it with suitabl…
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…
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.
We have observed that the supercurrent across phase-biased, highly transmitting atomic size contacts is strongly reduced within a broad phase interval around π. We attribute this effect to quasiparticle trapping in one of the discrete sub-gap Andreev bound states formed at the contact. Trapping occurs essentially when the Andreev energy is smaller than half the superconducting gap Δ, a situation in which the lifetime of trapped quasiparticles is found to exceed 100 \mus. The origin of this sharp energy threshold is presently not understood.
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.
Non-equilibrium quasiparticles are possible sources for decoherence in superconducting qubits because they can lead to energy decay or dephasing upon tunneling across Josephson junctions (JJs). Here, we investigate the impact of the intrinsic properties of two-dimensional transmon qubits on quasiparticle tunneling (QPT) and discuss how we can use quasiparticle dynamics to gain critical information about the quality of JJ barrier. We find the tunneling rate of the nonequilibrium quasiparticles to be sensitive to the choice of the shunting capacitor material and their geometry in qubits. In some…
Superconducting qubits probe environmental defects such as non-equilibrium quasiparticles, an important source of decoherence. We show that "hot" non-equilibrium quasiparticles, with energies above the superconducting gap, affect qubits differently from quasiparticles at the gap, implying qubits can probe the dynamic quasiparticle energy distribution. For hot quasiparticles, we predict a non-neligable increase in the qubit excited state probability P_e. By injecting hot quasiparticles into a qubit, we experimentally measure an increase of P_e in semi-quantitative agreement with the model and r…
Within the kinetic energy driven superconducting mechanism, we study the interplay between superconductivity and the nodal and antinodal superconducting quasiparticle coherences in cuprate superconductors, and find the s-wave superconducting transition temperature is heavily suppressed by the antinodal superconducting quasiparticle coherence, while the d-wave superconducting transition temperature is enhanced, therefore the antinodal superconducting quasiparticle coherence plays a more crucial role in superconductivity of cuprate superconductors.
Designing the spatial profile of the superconducting gap -- gap engineering -- has long been recognized as an effective way of controlling quasiparticles in superconducting devices. In aluminum films, their thickness modulates the gap; therefore, standard fabrication of Al/AlOx/Al Josephson junctions, which relies on overlapping a thicker film on top of a thinner one, always results in gap-engineered devices. Here we reconsider quasiparticle effects in superconducting qubits to explicitly account for the unavoidable asymmetry in the gap on the two sides of a Josephson junction. We find that di…
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…
Quasiparticle tunneling across a Josephson junction sets a limit for the lifetime of a superconducting qubit state. We develop a general theory of the corresponding decay rate in a qubit controlled by a magnetic flux. The flux affects quasiparticles tunneling amplitudes, thus making the decay rate flux-dependent. The theory is applicable for an arbitrary quasiparticle distribution. It provides estimates for the rates in practically important quantum circuits and also offers a new way of measuring the phase-dependent admittance of a Josephson junction.
It is usually argued that the presence of gapless quasiparticle excitations at the nodes of the d-wave superconducting gap should strongly decohere the quantum states of a d-wave qubit, making quantum effects practically unobservable. Using a self-consistent linear response non-equilibrium quasiclassical formalism, we show that this is not necessarily true. We find quasiparticle conductance of a d-wave grain boundary junction to be strongly phase dependent. Midgap states as well as nodal quasiparticles contribute to the conductance and therefore decoherence. Quantum behavior is estimated to be…
As low-loss non-linear elements, Josephson junctions are the building blocks of superconducting qubits. The interaction of the qubit degree of freedom with the quasiparticles tunneling through the junction represent an intrinsic relaxation mechanism. We develop a general theory for the qubit decay rate induced by quasiparticles, and we study its dependence on the magnetic flux used to tune the qubit properties in devices such as the phase and flux qubits, the split transmon, and the fluxonium. Our estimates for the decay rate apply to both thermal equilibrium and non-equilibrium quasiparticles…
Superconducting circuits have attracted growing interest in recent years as a promising candidate for fault-tolerant quantum information processing. Extensive efforts have always been taken to completely shield these circuits from external magnetic field to protect the integrity of superconductivity. Surprisingly, here we show vortices can improve the performance of superconducting qubits by reducing the lifetimes of detrimental single-electron-like excitations known as quasiparticles. Using a contactless injection technique with unprecedented dynamic range, we quantitatively distinguish betwe…
Extending the qubit coherence times is a crucial task in building quantum information processing devices. In the three-dimensional cavity implementations of circuit QED, the coherence of superconducting qubits was improved dramatically due to cutting the losses associated with the photon emission. Next frontier in improving the coherence includes the mitigation of the adverse effects of superconducting quasiparticles. In these lectures, we review the basics of the quasiparticles dynamics, their interaction with the qubit degree of freedom, their contribution to the qubit relaxation rates, and …
The presence of quasiparticles in superconducting qubits emerges as an intrinsic constraint on their coherence. While it is difficult to prevent the generation of quasiparticles, keeping them away from active elements of the qubit provides a viable way of improving the device performance. Here we develop theoretically and validate experimentally a model for the effect of a single small trap on the dynamics of the excess quasiparticles injected in a transmon-type qubit. The model allows one to evaluate the time it takes to evacuate the injected quasiparticles from the transmon as a function of …
Scanning tunneling spectroscopy measurements of superconducting thin lanthanum films grown on a normal metal tungsten substrate reveal an extraordinarily large broadening of the coherence peaks. The observed broadening corresponds to very short electron-like quasiparticle lifetimes in the tunneling process. A thorough analysis considering the different relaxation processes reveals that the dominant mechanism is an efficient quasiparticle relaxation at the interface between the superconducting film and the underlying substrate. This process is of general relevance to scanning tunneling spectros…
Quasiparticle properties in the superconducting state are masked by the superfluid and are not directly accessible to infrared spectroscopy. We show how one can use a Kramers--Kronig transformation to separate the quasiparticle from superfluid response and extract intrinsic quasiparticle properties in the superconducting state. We also address the issue of a narrow quasiparticle peak observed in microwave measurements, and demonstrate how it can be combined with infrared measurements to obtain unified picture of electrodynamic properties of cuprate superconductors.
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…
We present experiments on the dynamics of a two-state parametric fluctuator in a superconducting flux qubit. In spectroscopic measurements, the fluctuator manifests itself as a doublet line. When the qubit is excited in resonance with one of the two doublet lines, the correlation of readout results exhibits an exponential time decay which provides a measure of the fluctuator transition rate. The rate increases with temperature in the interval 40 to 158 mK. Based on the magnitude of the transition rate and the doublet line splitting we conclude that the fluctuation is induced by quasiparticle t…
We use femtosecond spectroscopy to investigate the quasiparticle relaxation and low-energy electronic structure in a near-optimally doped pnictide superconductor with T_c=49.5 K. Multiple relaxation processes are evident, with distinct superconducting state quasiparticle (QP) recombination dynamics exhibiting a T-dependent superconducting (SC) gap, and a clear "pseudogap" (PG) -like feature with an onset around 200K indicating the existence of a temperature-independent gap of magnitude Δ_PG= 61 +- 9 meV above T_c. Both the SC and PG components show saturation as a function of fluence with dist…
We investigate the role of gap characteristics such as anisotropy and inequality of the gaps in the quasiparticle interferences of iron pnictides using a five-orbital tight-binding model. We examine how the difference in the sensitivities exhibited by the sign-changing and -preserving $s$-wave superconductivity in an annular region around ($π, 0$), which can be used to determine the sign change of the superconducting gap, gets affected when the gaps are unequal on the electron and hole pocket. In addition, we also discuss how robust these differentiating features are on changing the quasiparti…
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.
Numerical study of momentum-dependent gap function is presented to make clear the origin of superconductivity in copper oxides. We claim that antinodal region with pronounced nesting feature of the Fermi contour gives rise to superconducting pairing with large momentum under screened Coulomb repulsion. Such a pairing results in both spatial checkerboard pattern of the superconducting state below Tc and a gapped state of incoherent pairs in a broad temperature range above Tc. We explain the momentum dependence of the coherent spectral weight detected in angle-resolved photoemission spectroscopy…
We have developed a semiclassical approach to solving the Bogoliubov - de Gennes equations for superconductors. It is based on the study of classical orbits governed by an effective Hamiltonian corresponding to the quasiparticles in the superconducting state and includes an account of the Bohr-Sommerfeld quantisation rule, the Maslov index, torus quantisation, topological phases arising from lines of phase singularities (vortices), and semiclassical wave functions for multi-dimensional systems. The method is illustrated by studying the problem of an SNS junction and a single vortex.
We present microwave measurements of a high quality factor superconducting resonator incorporating two aluminum nanobridge Josephson junctions in a loop shunted by an on-chip capacitor. Trapped quasiparticles (QPs) shift the resonant frequency, allowing us to probe the trapped QP number and energy distribution and to quantify their lifetimes. We find that the trapped QP population obeys a Gibbs distribution above 75 mK, with non-Poissonian trapping statistics. Our results are in quantitative agreement with the Andreev bound state model of transport, and demonstrate a practical means to quantif…
Quasiparticle excitations adversely affect the performance of superconducting devices in a wide range of applications. They limit the sensitivity of photon detectors in astronomy, the accuracy of current sources in metrology, the cooling power of micro-refrigerators, and could break the topological protection of Majorana qubits. In superconducting circuits for quantum information processing, tunneling of quasiparticles across Josephson junctions constitutes a decoherence mechanism. As relaxation and pure dephasing times of transmon-type charge qubits now reach 100 microseconds, understanding w…
The Josephson quasiparticle (JQP) cycle in a voltage-biased superconducting single-electron transistor (SSET) combines coherent Cooper pair tunneling with incoherent quasiparticle decay. We have measured the influence of current flow through an independently-biased SSET on the JQP cycle when the two SSET's have a strong mutual capacitive coupling. We find, among other effects, that the JQP current in one SSET is enhanced by the presence of a quasiparticle current in the other SSET. A simplified model of the coupled-SSET system is presented which reproduces the enhancement effect.
The electronic structure of the giant vortex states in a mesoscopic superconducting disk is studied in a dirty limit using the Usadel approach. The local density of states profiles are shown to be strongly affected by the effect of quasiparticle (QP) tunneling between the states localized in the vortex core and the ones bound to the sample edge. Decreasing temperature leads to a crossover between the edge-dominated and core-dominated regimes in the magnetic field dependence of the tunneling conductance. This crossover is discussed in the context of the efficiency of quasiparticle cooling by th…
We consider the behavior of quasiparticles in the superconducting state of high-T_c metals within the framework of the theory of superconducting state based on the fermion condensation quantum phase transition. We show that the behavior coincides with the behavior of Bogoliubov quasiparticles, whereas the maximum value of the superconducting gap and other exotic properties are determined by the presence of the fermion condensate. If at low temperatures the normal state is recovered by the application of a magnetic field suppressing the superconductivity, the induced state can be viewed as Land…
Dynamical error suppression techniques are commonly used to improve coherence in quantum systems. They reduce dephasing errors by applying control pulses designed to reverse erroneous coherent evolution driven by environmental noise. However, such methods cannot correct for irreversible processes such as energy relaxation. In this work, we investigate a complementary, stochastic approach to reducing errors: instead of deterministically reversing the unwanted qubit evolution, we use control pulses to shape the noise environment dynamically. In the context of superconducting qubits, we implement…
Recent improvements in momentum resolution by a factor of 32 lead to qualitatively new ARPES results on the spectra of Bi2Sr2CaCu2O8 (Bi2212) along the (pi,pi) direction, where there is a node in the superconducting gap. With improved resolution, we now see the intrinsic lineshape, which indicates the presence of true quasiparticles at the Fermi momentum in the superconducting state, and lack thereof in the normal state. The region of momentum space probed here is relevant for charge transport, motivating a comparison of our results to conductivity measurements by infrared reflectivity.
The distribution of the current density and the profile of the trapped magnetic field of a superconducting disk magnetized by uniform field are calculated from first principles. The effect of the superconducting parameters is taken into account by assuming the voltage-current law and the material law. The sample volume, the critical current density and the flux creep exponent dominate the strength of the trapped magnetic field. The flux creep exponent determines the decay rate of the trapped magnetic field. The aspect ratio of the sample influences the shape of the trapped magnetic flux lines.…
We study a superconducting artificial atom which is represented by a single Josephson junction or a Josephson junction chain, capacitively coupled to a coherently driven transmission line, and which contains exactly one residual quasiparticle (or up to one quasiparticle per island in a chain). We study the dissipation in the atom induced by the quasiparticle tunneling, taking into account the quasiparticle heating by the drive. We calculate the transmission coefficient in the transmission line for drive frequencies near resonance and show that, when the artificial atom spectrum is nearly harmo…
We study the quasiparticle energy relaxation processes in superconducting Nb films of different thicknesses corresponding to different electron mean free paths in a state far from equilibrium, that is the highly dissipative flux-flow state driven up to the instability point. From the measured current-voltage curves we derive the vortex critical velocity $v^{*}$ for several temperatures. From the $v^{*}(T)$ values, the quasiparticle energy relaxation time $τ_ε$ is evaluated within the Larkin-Ovchinnikov model and numerical calculations of the quasiparticle energy relaxation rates are carried ou…
We investigate subgap quasiparticles of a single level quantum dot coupled to the superconducting and normal leads, whose energy level is periodically driven by external potential. Using the Floquet formalism we determine the quasienergies and analyze redistribution of their spectral weights between individual harmonics upon varying the frequency and amplitude of the driving potential. We also propose feasible spectroscopic methods for probing the in-gap quasiparticles observable in the differential conductance of the charge current averaged over a period of oscillations.
The magnitude and the temperature dependence of the superconducting order parameter Δ(T) of single-crystals of Cd2Re2O7 (Tc = 1.02 K) was measured using point contact spectroscopy. In order to fit the conductance spectra and to extract the order parameter at different temperatures we generalized the Blonder-Tinkham-Klapwijk theory by including the self-energy of the quasiparticles into the Bogoliubov equations. This modification enabled excellent fits of the conductance spectra. Δ(T) increases steeply below the superconducting transition temperature of 1.02 K and levels off below about 0.8 K d…
We have measured the complex conductivity of a BSCCO(2212) thin film between 0.2 and 1.0 THz. We find the conductivity in the superconducting state to be well described as the sum of contributions from quasiparticles, the condensate, and order parameter fluctuations which draw 30% of the spectral weight from the condensate. An analysis based on this decomposition yields a quasiparticle scattering rate on the order of k_(B)*T/(hbar) for temperatures below Tc.
We have examined the relaxation of photoinduced quasiparticles in the heavy-fermion superconductor PuCoGa5. The deduced electron-phonon coupling constant is incompatible with the measured superconducting transition temperature Tc=18.5 K, which speaks against phonon-mediated superconducting pairing. Upon lowering the temperature, we observe an order-of-magnitude increase of the quasiparticle relaxation time in agreement with the phonon bottleneck scenario - evidence for the presence of a hybridization gap in the electronic density of states. The modification of photoinduced reflectance in the s…
We calculate the quasiparticle scattering rate in the superconducting state of the overdoped cuprates, in the context of the Eliashberg formalism for a Fermi liquid with strong van Hove singularities close to the chemical potential. For a $d_{x^2-y^2}$ superconducting gap, we demonstrate analytically that the scattering rate is linear in the maximum of temperature or energy, but with different intercepts and momentum dependence. We discuss our results in view of angle-resolved photoemission experiments. We also discuss the case of a s-wave gap.
Spin ordering and its effect on low energy quasiparticles in a p-wave superconducting liquid are investigated. We show that there is a new 2D p-wave superconducting liquid where the ground state is rotation invariant. In quantum spin disordered liquids, the low energy quasiparticles are bound states of the bare Bogolubov- De Gennes (${\em BdeG}$) quasiparticles and zero energy skyrmions, which are charge neutral bosons at the low energy limit. Further more, spin collective excitations are fractionalized ones carrying a half spin and obeying fermionic statistics. In thermally spin disordered li…
