Phonon traps reduce the quasiparticle density in superconducting circuits
Fabio Henriques, Francesco Valenti, Thibault Charpentier, Marc Lagoin, Clement Gouriou, Maria Martínez, Laura Cardani, Marco Vignati, Lukas Grünhaupt, Daria Gus… 展开作者
Fabio Henriques, Francesco Valenti, Thibault Charpentier, Marc Lagoin, Clement Gouriou, Maria Martínez, Laura Cardani, Marco Vignati, Lukas Grünhaupt, Daria Gusenkova, Julian Ferrero, Sebastian T. Skacel, Wolfgang Wernsdorfer, Alexey V. Ustinov, Gianluigi Catelani, Oliver Sander, Ioan M. Pop
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 with frequencies exceeding the spectral gap of the superconductor should result in a reduction of QPs. Indeed, we demonstrate that surrounding high impedance resonators made of granular aluminum (grAl) with lower gapped thin film aluminum islands increases the internal quality factors of the resonators in the single photon regime, suppresses the noise, and reduces the rate of observed QP bursts. The aluminum islands are positioned far enough from the resonators to be electromagnetically decoupled, thus not changing the resonator frequency, nor the loading. We therefore attribute the improvements observed in grAl resonators to phonon trapping at frequencies close to the spectral gap of aluminum, well below the grAl gap.
When quasiparticles in a BCS superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at 2$Δ$. We show that a phonon bandgap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon bandgap can be realized and matched to the recombination energy with a phononic crystal, a periodically-patterned dielectric membrane. We discuss in detail the non-equilibrium quasiparticle and phonon distributions that arise in a supercondu…
Measurements of the transverse (k_{xy}) and longitudinal (k_{xx}) thermal conductivity in high magnetic fields are used to separate the quasiparticle thermal conductivity (k_{xx}^{el}) of the CuO_2-planes from the phononic thermal conductivity in YBa_2Cu_3O_{7-δ}. k_{xx}^{el} is found to display a pronounced maximum below T_c. Our data analysis reveals distinct transport (τ) and Hall (τ_H) relaxation times below T_c: Whereas τis strongly enhanced, τ_H follows the same temperature dependence as above T_c.
We measure the anisotropic mid-infrared response of electrons and phonons in bulk YBa2Cu3O7 after femtosecond photoexcitation. A line shape analysis of specific lattice modes reveals their transient occupation and coupling to the superconducting condensate. The apex oxygen vibration is strongly excited within 150 fs demonstrating that the lattice absorbs a major portion of the pump energy before the quasiparticles are thermalized. Our results attest to substantial electron-phonon scattering and introduce a powerful concept probing electron-lattice interactions in a variety of complex materials…
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…
There is an ongoing debate about the nature of the bosonic excitations responsible for the quasiparticle self energy in high temperature superconductors -- are they phonons or spin fluctuations? We present a careful analysis of the bosonic excitations as revealed by the `kink' feature at 70 meV in angle resolved photoemission data using Eliashberg theory for a d-wave superconductor. Starting from the assumption that nodal quasiparticles are not coupled to the $(π,π)$ magnetic resonance, the sharp structure at $70 $meV can be assigned to phonons. We find that not only can we account for the shi…
We use radio-frequency reflectometry to measure quasiparticle tunneling rates in the single-Cooper-pair-transistor. Devices with and without quasiparticle traps in proximity to the island are studied. A $10^2$ to $10^3$-fold reduction in the quasiparticle tunneling rate onto the island is observed in the case of quasiparticle traps. In the quasiparticle trap samples we also measure a commensurate decrease in quasiparticle tunneling rate off the island.
We investigate effects of a nonadiabatic electron-phonon(boson) interaction on the quasiparticle self-energy in the lowest order in the coupling constant. Existing approaches either overestimate, or underestimate these effects because of different approximations for momentum and frequency dependences of the vertex corrections. The connection between the nonadiabaticity and a possible instability of the interacting Fermi system is discussed as well.
We use a first-principles based self-consistent momentum-resolved density fluctuation (MRDF) model to compute the combined effects of electron-electron and electron-phonon interactions to describe the superconducting dome in the correlated MoS2 thin flake and TiSe2. We find that without including the electron-electron interaction, the electron-phonon coupling and the superconducting transition temperature (Tc) are overestimated in both these materials. However, once the full angular and dynamical fluctuations of the spin and charge density induced quasiparticle self-energy effects are included…
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.
The phonon contribution to the thermal conductivity at low temperature in superconductors with line nodes is calculated assuming that scattering by both nodal quasiparticles and the sample boundaries is significant. It is determined that, within the regime in which the quasiparticles are in the universal limit and the phonon attenuation is in the hydrodynamic limit, there exists a wide temperature range over which the phonon thermal conductivity varies as $T^2$. This behaviour comes from the fact that transverse phonons propagating along certain directions do not interact with nodal quasiparti…
We investigate the quasiparticle relaxation and low-energy electronic structure in undoped SrFe_2As_2 exhibiting spin-density wave (SDW) ordering using optical pump-probe femtosecond spectroscopy. A remarkable critical slowing down of the quasiparticle relaxation dynamics at the SDW transition temperature T_SDW = 200K is observed. From temperature dependence of the transient reflectivity amplitude we determine the SDW-state charge gap magnitude, 2Delta_SDW/k_BT_SDW=7.2+-1. The second moment of the Eliashberg function, lambda<(hbar omega)^2>=110+-10meV^2, determined from the relaxation time abo…
Quasiparticles represent an intrinsic source of perturbation for superconducting qubits, leading to both dissipation of the qubit energy and dephasing. Recently, it has been shown that normal-metal traps may efficiently reduce the quasiparticle population and improve the qubit lifetime, provided the trap surpasses a certain characteristic size. Moreover, while the trap itself introduces new relaxation mechanisms, they are not expected to harm state-of-the-art transmon qubits under the condition that the traps are not placed too close to extremal positions where electric fields are high. Here, …
We investigate the behavior of quasiparticles in a hybrid electron turnstile with the aim of improving its performance as a metrological current source. The device is used to directly probe the density of quasiparticles and monitor their relaxation into normal metal traps. We compare different trap geometries and reach quasiparticle densities below 3um^-3 for pumping frequencies of 20 MHz. Our data show that quasiparticles are excited both by the device operation itself and by the electromagnetic environment of the sample. Our observations can be modelled on a quantitative level with a sequent…
A 6x6 array of symmetrical V/Al/AlOx/Al/V Superconducting Tunnel Junctions (STJs) was fabricated. The base electrode is a high quality epitaxial film with a residual resistance ratio (RRR) of ~30. The top film is polycrystalline with an RRR of ~10. The leakage currents of the 25x25 mm^2 junctions are of the order of 0.5 pA/mm^2 at a bias voltage of 100 mV, which corresponds to a dynamical resistance of ~ 3 10^5 ohms. When the array was illuminated by 6 keV X-ray photons from a 55Fe radioactive source the single photon charge output was found to be low and strongly dependent on the temperature …
Microwave penetration depth $λ$ and surface resistance at 27 GHz are measured in high quality crystals of KOs$_2$O$_6$. Firm evidence for fully-gapped superconductivity is provided from $λ(T)$. Below the second transition at $T_{\rm p}\sim 8$ K, the superfluid density shows a step-like change with a suppression of effective critical temperature $T_{\rm c}$. Concurrently, the extracted quasiparticle scattering time shows a steep enhancement, indicating a strong coupling between the anomalous rattling motion of K ions and quasiparticles. The results imply that the rattling phonons help to enhanc…
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.
The performance of many superconducting devices is degraded in presence of non-equilibrium quasiparticles in the superconducting part. One promising approach towards their evacuation is the use of normal-metal quasiparticle traps, where normal metal is brought into good metallic contact with the superconductor. A voltage biased normal-metal--insulator--superconductor junction equipped with such a trap is used to investigate on the trapping performance and the part played by the superconducting proximity effect therein. This involves an appropriate one-dimensional model of the junction and the …
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 dynamics of FeSe single crystals revealed by dual-color transient reflectivity measurements (ΔR/R) provides unprecedented information on Fe-based superconductors. The amplitude of fast component in ΔR/R clearly tells a competing scenario between spin fluctuations and superconductivity. Together with the transport measurements, the relaxation time analysis further exhibits anomalous changes at 90 K and 230 K. The former manifests a structure phase transition as well as the associated phonon softening. The latter suggests a previously overlooked phase transition or crossover in FeS…
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 …
In a superconductor with magnetic impurities, Kondo scattering results in the formation of localized states inside the superconducting gap. We show that inelastic electronic transitions involving quasiparticle scattering into and out of the localized states may result in significant changes in the non equilibrium properties of the superconductor. Using the model of Muller-Hartmann and Zittartz for the extreme dilute limit, and including both deformation potential and spin-lattice coupling we have calculated the rates of such inelastic transitions between continuum and discrete states, and show…
Hybrid Superconductor/Ferromagnet structures have been investigated recently to address the interplay between ferromagnetism and superconductivity. They also open up new routes for the investigation of out of equilibrium superconductivity. Here, we show how it is possible for out of equilibrium excitations produced in a superconducting thin film (S) to be localized in a ferromagnetic trap (F). Specifically, a ferromagnetic nano-volume in good contact with S represents a potential well for the quasiparticles (QPs) at the gap edge. As the superconducting proximity effect is highly suppressed in …
The point-contact spectra of tantalum in the superconducting state, with $Ta$, $Cu$, and $Au$ counterelectrodes, have been studied. We discovered some new distinctive features, whose position on the $eV$ axis is determined by the critical power required for the injection of nonequilibriumquasiparticles. At this level of power the band gap $Δ$ decreases abruptly in the vicinity of the contact. A correction to the point-contact spectrum, with the sign opposite to that of the usual correction, arises in the region of phonon energies. The maxima in the $Ta$ spectrum become sharper and their positi…
The effect of Holstein electron-phonon interaction on a Hubbard model close to a Mott-Hubbard transition at half-filling is investigated by means of Dynamical Mean-Field Theory. We observe a reduction of the effective mass that we interpret in terms of a reduced effective repulsion. When the repulsion is rescaled to take into account this effect, the quasiparticle low-energy features are unaffected by the electron-phonon interaction. Phonon features are only observed within the high-energy Hubbard bands. The lack of electron-phonon fingerprints in the quasiparticle physics can be explained int…
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 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 report ultrafast quasiparticle (QP) dynamics and coherent acoustic phonons in undoped CaFe_2As_2 iron pnictide single crystals exhibiting spin-density wave (SDW) and concurrent structural phase transition at temperature TSDW ~ 165 K using femtosecond time-resolved pump-probe spectroscopy. The contributions in transient differential reflectivity arising from exponentially decaying QP relaxation and oscillatory coherent acoustic phonon mode show large variations in the vicinity of T_SDW. From the temperature-dependence of the QP recombination dynamics in the SDW phase, we evaluate a BCS-like …
We present a comprehensive theoretical framework for the Andreev bound state population dynamics in superconducting weak links. Contrary to previous works, our approach takes into account the generated nonequilibrium distribution of the continuum quasiparticle states in a self-consistent way. As application of our theory, we show that the coupling of the superconducting contact to environmental phase fluctuations induces a charge imbalance of the continuum quasiparticle population. This imbalance is due to the breaking of the left-right symmetry in the rates connecting continuum quasiparticles…
In many superconducting devices, including qubits, quasiparticle excitations are detrimental. A normal metal ($N$) in contact with a superconductor ($S$) can trap these excitations; therefore such a trap can potentially improve the devices performances. The two materials influence each other, a phenomenon known as proximity effect which has drawn attention since the '60s. Here we study whether this mutual influence places a limitation on the possible performance improvement in superconducting qubits. We first revisit the proximity effect in uniform $NS$ bilayers; despite the long history of th…
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…
Dirac semimetal PdTe2 single-crystal temperature-dependent ultrafast carrier and phonon dynamics were studied using ultrafast optical pump-probe spectroscopy. Two distinct carrier and coherent phonons relaxation processes were identified in the 5 K - 300 K range. Quantitative analysis revealed a fast relaxation process (τ_f) occurring on a subpicosecond time scale which originated from electron-phonon thermalization. This was followed by a slower relaxation process (τ_s) with a time scale of ~ 7-9.5 ps which originated from phonon-assisted electron-hole recombination. Two significant vibration…
Controlling quasiparticle dynamics can improve the performance of superconducting devices. For example, it has been demonstrated effective in increasing lifetime and stability of superconducting qubits. Here we study how to optimize the placement of normal-metal traps in transmon-type qubits. When the trap size increases beyond a certain characteristic length, the details of the geometry and trap position, and even the number of traps, become important. We discuss for some experimentally relevant examples how to shorten the decay time of the excess quasiparticle density. Moreover, we show that…
We generalize the numerical renormalization group scheme to study the phonon-mediated retarded interactions in the high Tc cuprates. We find that three sets of phonon-mediated retarded quasiparticle scatterings grow under RG flow. These scatterings share the following common features: 1) the initial and final quasiparticle momenta are in the antinodal regions, and 2) the scattering amplitudes have a $x^2-y^2$ symmetry. All three sets of retarded interaction are driven to strong coupling by the magnetic fluctuations around $(π,π)$. After growing strong, these retarded interaction will trigger d…
The energy of the electron wave packet interacting with lattice distortion, is considered in anisotropic crystal. Anisotropy of the electron and phonon spectra as well as of the electron-phonon interaction are taken into account. The height of the barrier between free and self-trapped states is calculated in dependence on the anisotropy parameters. The calculation is done numerically, using continual aproximation. The analytical solution is obtained for some cases of quasi-two and quasi-one-dimensional spectra. Key words: anisotropy; polarons; barrier.
Distinctive superconducting behaviors between bulk and monolayer FeSe make it challenging to obtain a unified picture of all FeSe-based superconductors. We investigate the ultrafast quasiparticle (QP) dynamics of an intercalated superconductor (Li1-xFex)OHFe1-ySe, which is a bulk crystal but shares a similar electronic structure with single-layer FeSe on SrTiO3. We obtain the electron-phonon coupling (EPC) constant λA1g (0.22 +/- 0.04), which well bridges that of bulk FeSe crystal and single-layer FeSe on SrTiO3. Moreover, we find that such a positive correlation between λA1g and superconducti…
Quantum error correction can preserve quantum information in the presence of local errors, but correlated errors are fatal. For superconducting qubits, high-energy particle impacts from background radioactivity produce energetic phonons that travel throughout the substrate and create excitations above the superconducting ground state, known as quasiparticles, which can poison all qubits on the chip. We use normal metal reservoirs on the chip back side to downconvert phonons to low energies where they can no longer poison qubits. We introduce a pump-probe scheme involving controlled injection o…
We study an interacting spinless Bose-Einstein condensate to clarify theoretically whether the spectra of its quasiparticles (one-particle excitations) and collective modes (two-particle excitations) are identical, as concluded by Gavoret and Nozières [Ann. Phys. 28, 349 (1964)]. We derive analytic expressions for their first and second moments so as to extend the Bijl-Feynman formula for the peak of the collective-mode spectrum to its width (inverse lifetime) and also to the one-particle channel. The obtained formulas indicate that the width of the collective-mode spectrum manifestly vanishes…
We investigate tunneling properties of Bogoliubov phonons in a Bose-Einstein condensate. We find the anomalous enhancement of the quasiparticle current $J_{\rm q}$ carried by Bogoliubov phonons near a potential barrier, due to the supply of the excess current from the condensate. This effect leads to the increase of quasiparticle transmission probability in the low energy region found by Kovrizhin {\it et al.}. We also show that the quasiparticle current twists the phase of the condensate wavefunction across the barrier, leading to a finite Josephson supercurrent $J_{\rm s}$ through the barrie…
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…
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…
The temperature and magnetic-field (H) dependences of thermal conductivity (κ) of Bi_2Sr_2CaCu_2O_{8+δ} (Bi2212) are systematically measured for a broad doping range by using both pure Bi2212 single crystals with tuned oxygen contents and Bi_2Sr_2Ca_{1-x}Dy_xCu_2O_{8+δ} (Dy-Bi2212) single crystals with different Dy contents x. In the underdoped samples, the quasiparticle (QP) peak below T_c is strongly suppressed, indicating strong QP scattering by impurities or oxygen defects, whereas the phonon conductivity is enhanced in moderately Dy-doped samples and a phonon peak at 10 K is observed for …
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…
We examine multiple techniques for extracting information from angle-resolved photoemission spectroscopy (ARPES) data, and test them against simulated spectral functions for electron-phonon coupling. We find that, in the low-coupling regime, it is possible to extract self-energy and bare-band parameters through a self-consistent Kramers-Kronig bare-band fitting routine. We also show that the effective coupling parameters deduced from the renormalization of quasiparticle mass, velocity, and spectral weight are momentum dependent and, in general, distinct from the true microscopic coupling; the …
