We demonstrate the operation of a differential single Cooper-pair box, a charge qubit consisting of two aluminum islands, isolated from ground, coupled by a pair of small-area Josephson junctions, and read out with a superconducting differential radio-frequency single electron transistor. We have tested four devices, all of which show evidence of quasiparticle poisoning. The devices are characterized with microwave spectroscopy and temperature dependence studies, and Coulomb staircases are shown to be e-periodic in all samples. However, coherent control is still possible with non-adiabatic voltage pulses. Coherent oscillation experiments and a relaxation time measurement were performed using a charge derivative readout technique.
Qubits based on Majorana zero modes are a promising path towards topological quantum computing. Such qubits, though, are susceptible to quasiparticle poisoning which does not have to be small by topological argument. We study the main sources of the quasiparticle poisoning relevant for realistic devices -- non-equilibrium above-gap quasiparticles and equilibrium localized subgap states. Depending on the parameters of the system and the architecture of the qubit either of these sources can dominate the qubit decoherence. However, we find in contrast to naive estimates that in moderately disorde…
We present radio-frequency measurements on a single-Cooper-pair-transistor in which individual quasiparticle poisoning events were observed with microsecond temporal resolution. Thermal activation of the quasiparticle dynamics is investigated, and consequently, we are able to determine energetics of the poisoning and un-poisoning processes. In particular, we are able to assign an effective quasiparticle temperature to parameterize the poisoning rate.
We consider the problem of quasiparticle poisoning in a nanowire-based realization of a Majorana qubit, where a spin-orbit-coupled semiconducting wire is placed on top of a (bulk) superconductor. By making use of recent experimental data exhibiting evidence of a low-temperature residual non-equilibrium quasiparticle population in superconductors, we show by means of analytical and numerical calculations that the dephasing time due to the tunneling of quasiparticles into the nanowire may be problematically short to allow for qubit manipulation.
We propose a method of measuring the fermion parity lifetime of Majorana fermion modes due to quasiparticle poisoning. We model quasiparticle poisoning by coupling the Majorana modes to electron reservoirs, explicitly breaking parity conservation in the system. This poisoning broadens and shortens the resonance peak associated with Majorana modes. In a two lead geometry, the poisoning decreases the correlation in current noise between the two leads from the maximal value characteristic of crossed Andreev reflection. The latter measurement allows for calculation of the poisoning rate even if te…
We increase the isolation of a superconducting double dot from its environment by galvanically isolating it from any electrodes. We probe it using high frequency reflectometry techniques, find 2e-periodic behaviour, and characterise the energy structure of its charge states. By modelling the response of the device, we determine the quasiparticle poisoning rate to be significantly worse than that of a unisolated double dot, and conclude that quasiparticle exchange between the dot and the leads is an important relaxation mechanism.
We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (~ 1 μs) and sets a bound for a weakly coupled island (> 10 μs). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the r…
Majorana zero modes have been attracting considerable attention because of their prospective applications in fault-tolerant topological quantum computing. In recent years, some schemes have been proposed to detect and manipulate Majorana zero modes using superconducting qubits. However, manipulating and reading the Majorana zero modes must be kept in the time window of quasiparticle poisoning. In this work, we study the problem of quasiparticle poisoning in a split transmon qubit containing hybrid Josephson junctions involving Majorana zero modes. We show that Majorana coupling will cause pari…
The fractional Josephson effect remains one of the decisive hallmarks of topologically protected Majorana zero modes. We analyze the effects of parity violating quasiparticle poisoning onto the current voltage characteristics of topological Josephson junctions. We include poisoning events directly within the resistively shunted junction (RSJ) model in the overdamped limit both in the short- and long-junction regime. We calculate the current voltage characteristics numerically where poisoning is modeled either via additional rates in the Fokker-Planck equations or by a time dependent parity and…
We present a theoretical analysis of quasiparticle poisoning in Coulomb-blockaded Majorana fermion systems tunnel-coupled to normal-conducting leads. Taking into account finite-energy quasiparticles, we derive the effective low-energy theory and present a renormalization group analysis. We find qualitatively new effects when a quasiparticle state with very low energy is localized near a tunnel contact. For $M=2$ attached leads, such "dangerous" quasiparticle poisoning processes cause a spin $S=1/2$ single-channel Kondo effect, which can be detected through a characteristic zero-bias anomaly co…
We introduce a toy model that allows us to study the physical properties of a spin impurity coupled to the electrons in the superconducting island. We show that when the coupling of the spin is of the order of the superconducting gap two almost degenerate subgap states are formed. By computing the Berry phase that is associated with the superconducting phase rotations in this model, we prove that these subgap states are characterized by a different charge and demonstrate that the switching between these states has the same effect as quasiparticle poisoning (unpoisoning) of the island. We also …
We study single-electron charging events in an Al/InAs nanowire hybrid system with deliberately introduced gapless regions. The occupancy of a Coulomb island is detected using a nearby radio-frequency quantum dot as a charge sensor. We demonstrate that a 1 micron gapped segment of the wire can be used to efficiently suppress single electron poisoning of the gapless region and therefore protect the parity of the island while maintaining good electrical contact with a normal lead. In the absence of protection by charging energy, the 1e switching rate can be reduced below 200 per second. In the s…
We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all …
We propose a novel method for suppression of quasiparticle poisoning in Al Coulomb blockade devices. The method is based on creation of a proper energy gap profile along the device. In contrast to the previously used techniques, the energy gap is controlled by the film thickness. Our transport measurements confirm that the quasiparticle poisoning is suppressed and clear 2$e$ periodicity is observed only when the island is made much thinner than the leads. This result is consistent with the existing model and provides a simple method to suppress quasiparticle poisoning.
We study a superconducting charge qubit coupled to an intensive electromagnetic field and probe changes in the resonance frequency of the formed dressed states. At large driving strengths, exceeding the qubit energy-level splitting, this reveals the well known Landau-Zener-Stuckelberg (LZS) interference structure of a longitudinally driven two-level system. For even stronger drives we observe a significant change in the LZS pattern and contrast. We attribute this to photon-assisted quasiparticle tunneling in the qubit. This results in the recovery of the qubit parity, eliminating effects of qu…
Spin/magnetisation relaxation and coherence times, respectively T_1 and T_2, initially defined in the context of nuclear magnetic resonance (NMR), are general concepts applicable to a wide range of systems, including quantum bits [1-4]. At first glance, these ideas might seem to be irrelevant to conventional Bardeen-Cooper-Schrieffer (BCS) superconductors, as the BCS superconducting ground state is a condensate of Cooper pairs of electrons with opposite spins (in a singlet state) [5]. It has recently been demonstrated, however, that a non-equilibrium magnetisation can appear in the quasipartic…
Quasiparticle poisoning and diabatic transitions may significantly narrow the window for the experimental observation of the $4π$-periodic $dc$ Josephson effect predicted for topological Josephson junctions. Here, we show that switching current measurements provide accessible and robust signatures for topological superconductivity which persist in the presence of quasiparticle poisoning processes. Such measurements provide access to the phase-dependent subgap spectrum and Josephson currents of the topological junction when incorporating it into an asymmetric SQUID together with a conventional …
Quasiparticle (qp) poisoning is a major issue that impairs the operation of various superconducting devices. Even though these devices are often operated at temperatures well below the critical point where the number density of excitations is expected to be exponentially suppressed, their bare operation and stray microwave radiation excite the non-equilibrium qps. Here we use voltage-biased superconducting junctions to demonstrate and quantify qp extraction in the turnstile operation of a superconductor-insulator-normal metal-insulator-superconductor single-electron transistor. In this operati…
We study the kinetics of the quasiparticle capture and emission process in a small superconducting island (Cooper-pair box) connected by a tunnel junction to a massive superconducting lead. At low temperatures, the charge on the box fluctuates between two states, even and odd in the number of electrons. Assuming that the odd-electron state has the lowest energy, we evaluate the distribution of lifetimes of the even- and odd-electron states of the Cooper-pair box. The lifetime in the even-electron state is an exponentially distributed random variable corresponding to a homogenous Poisson proces…
We introduce error-correcting codes that can correct for fermion parity-violating (quasiparticle poisoning) and parity-conserving errors in systems of complex fermions and of Majorana fermions. After establishing properties of fermion codes, we introduce a generic construction of fermion codes from weakly self-dual classical, binary error-correcting codes. We use this method to construct (i) the shortest fermion code to correct for quasiparticle poisoning errors, (ii) translationally-invariant fermion codes and (iii) other codes that correct higher-weight errors. We conclude by discussing a po…
We study fundamental limitations on the energy relaxation rate of a superconducting charge qubit with a large-gap Cooper-pair box, $Δ_b > Δ_r$. At a sufficiently large mismatch between the gap energies in the box $Δ_b$ and in the reservoir $Δ_r$,"quasiparticle poisoning" becomes ineffective even in the presence of nonequilibrium quasiparticles in the reservoir. The qubit relaxation still may occur due to higher-order (Andreev) processes. In this paper we evaluate the qubit energy relaxation rate due to Andreev processes.
We study the effect of quantum charge fluctuations on the even-odd energy difference for a small superconducting island (Cooper-pair box) connected to a large finite-size superconductor by a tunnel junction. Even-odd energy difference is important for understanding the quasiparticle "poisoning" effect, and determines the activation energy of a trapped quasiparticle in the Cooper-pair box. We find that renormalization of the activation energy due to quantum charge fluctuations depends on the dimensionless normal-state conductance of the junction g_T, and becomes strong at g_T >> 1.
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 …
We propose a universal gate set acting on a qubit formed by the degenerate ground states of a Coulomb-blockaded time-reversal invariant topological superconductor island with spatially separated Majorana Kramers pairs: the "Majorana Kramers Qubit". All gate operations are implemented by coupling the Majorana Kramers pairs to conventional superconducting leads. Interestingly, in such an all-superconducting device, the energy gap of the leads provides another layer of protection from quasiparticle poisoning independent of the island charging energy. Moreover, the absence of strong magnetic field…
We investigate the energy and phase relaxation of a superconducting qubit caused by a single quasiparticle. In our model, the qubit is an isolated system consisting of a small island (Cooper-pair box) and a larger superconductor (reservoir) connected with each other by a tunable Josephson junction. If such system contains an odd number of electrons, then even at lowest temperatures a single quasiparticle is present in the qubit. Tunneling of a quasiparticle between the reservoir and the Cooper-pair box results in the relaxation of the qubit. We derive master equations governing the evolution o…
We examine energy relaxation of non-equilibrium quasiparticles in "dirty" superconductors with the electron mean free path much shorter than the superconducting coherence length. Relaxation of low-energy non-equilibrium quasiparticles is dominated by phonon emission. We derive the corresponding collision integral and find the quasiparticle relaxation rate. The latter is sensitive to the breaking of time reversal symmetry (TRS) by a magnetic field (or magnetic impurities). As a concrete application of the developed theory, we address quasiparticle trapping by a vortex and a current-biased const…
Design of a Fabry-Perot (double point contact) interferometer to measure fractional quantum Hall effect quasiparticle charge properties, and in particular the 5/2 excitations, poses an important trade-off: the device size should be minimized to allow two path interference, since the coherence length of the quasiparticles in the correlated states are expected be limited, yet a small device promotes the dominance of Coulomb charging effects which would overwhelm the Aharonov-Bohm interference effect. In this study a series of small but different size interferometers from the same high density he…
By now it is known that in a singlet superconductor/ferromagnet (S/F) structure the superconducting correlations carried by opposite-spin pairs penetrate into the ferromagnet over a short distance of the order of magnetic coherence length. The long-range proximity effect (LRPE), taking place on the length scale of the normal metal coherence length, can only be maintained by equal-spin pairs, which can be generated by magnetic inhomogeneities in the system. In this work we have predicted a new type of LRPE, which can take place in S/F heterostructures under non-equilibrium conditions. The super…
We clarify the path integral calculation, recently suggested by Golubev and Zaikin, and show, contrary to their claim, that quasiparticles become fully coherent quantum particles in the $T \to 0$ limit. The important physical point is the inclusion of the recoil of the quasiparticle when interacting with fluctuations in the rest of the Fermi gas.
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…
We investigate the quasiparticle density of states in disordered d-wave superconductors. By constructing a quantum map describing the quasiparticle dynamics in such a medium, we explore deviations of the density of states from its universal form ($\propto E$), and show that additional low-energy quasiparticle states exist provided (i) the range of the impurity potential is much larger than the Fermi wavelength [allowing to use recently developed semiclassical methods]; (ii) classical trajectories exist along which the pair-potential changes sign; and (iii) the diffractive scattering length is …
Nowadays superconductors serve in numerous applications, from high-field magnets to ultra-sensitive detectors of radiation. Mesoscopic superconducting devices, i.e. those with nanoscale dimensions, are in a special position as they are easily driven out of equilibrium under typical operating conditions. The out-of-equilibrium superconductors are characterized by non-equilibrium quasiparticles. These extra excitations can compromise the performance of mesoscopic devices by introducing, e.g., leakage currents or decreased coherence times in quantum devices. By applying an external magnetic field…
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…
We study quasiparticle tunneling in Josephson tunnel junctions embedded in an electromagnetic environment. We identify tunneling processes that transfer electrical charge and couple to the environment in a way similar to that of normal electrons, and processes that mix electrons and holes and are thus creating charge superpositions. The latter are sensitive to the phase difference between the superconductor and are thus limited by phase diffusion even at zero temperature. We show that the environmental coupling is suppressed in many environments, thus leading to lower quasiparticle decay rates…
By performing experiments with thin-film resonators of NbSi, we elucidate a decoherence mechanism at work in disordered superconductors. This decoherence is caused by charged Two Level Systems (TLS) which couple to the conduction electrons in the BCS ground state; it does not involve any out-of-equilibrium quasiparticles, vortices, etc. Standard theories of mesoscopic disordered conductors enable making predictions regarding this mechanism, notably that decoherence should increase as the superconductor cross section decreases. Given the omnipresence of charged TLS in solid-state systems, this …
The transmon superconducting qubit is being intensely investigated as a promising approach for the physical implementation of quantum information processing, and high quality factors of order $10^6$ have been achieved both in two- and three-dimensional architectures. These high quality factors enable detailed investigations of decoherence mechanisms. An intrinsic decoherence process originates from the coupling between the qubit degree of freedom and the quasiparticles that tunnel across Josephson junctions. In a transmon, tunneling of a single quasiparticle is associated with a change in pari…
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 …
Exploiting inversion symmetry breaking (ISB) in systems with strong spin-orbit coupling promises control of spin through electric fields - crucial to achieve miniaturization in spintronic devices. Delivering on this promise requires a two-dimensional electron gas with a spin precession length shorter than the spin coherence length and a large spin splitting so that spin manipulation can be achieved over length scales of nanometers. Recently, the transition metal oxide terminations of delafossite oxides were found to exhibit a large Rashba spin splitting dominated by ISB. In this limit, the Fer…
Increasing the degree of control over physical qubits is a crucial component of quantum computing research. We report a superconducting qubit of fluxonium type with the Ramsey coherence time reaching $T_2^*= 1.48 \pm 0.13 \mathrm{~ms}$, which exceeds the state of the art value by an order of magnitude. As a result, the average single-qubit gate fidelity grew above $0.9999$, surpassing, to our knowledge, any other solid-state quantum system. Furthermore, by measuring energy relaxation of the parity-forbidden transition to second excited state, we exclude the effect of out-of-equilibrium quasipa…
We have experimentally demonstrated pumping of Cooper pairs in a single-island mesoscopic structure. The island was connected to leads through SQUID (Superconducting Quantum Interference Device) loops. Synchronized flux and voltage signals were applied whereby the Josephson energies of the SQUIDs and the gate charge were tuned adiabatically. From the current-voltage characteristics one can see that the pumped current increases in 1e steps which is due to quasiparticle poisoning on the measurement time scale, but we argue that the transport of charge is due to Cooper pairs.
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…
The quantum Hall (QH) effect represents a unique playground where quantum coherence of electrons can be exploited for various applications, from metrology to quantum computation. In the fractional regime it also hosts anyons, emergent quasiparticles that are neither bosons nor fermions and possess fractional statistics. Their detection and manipulation represent key milestones in view of topologically protected quantum computation schemes. Exploiting the high degree of phase coherence, edge states in the QH regime have been investigated by designing and constructing electronic interferometers,…
In superconducting qubits, the interaction of the qubit degree of freedom with quasiparticles defines a fundamental limitation for the qubit coherence. We develop a theory of the pure dephasing rate Γ_ϕ caused by quasiparticles tunneling through a Josephson junction and of the inhomogeneous broadening due to changes in the occupations of Andreev states in the junction. To estimate Γ_ϕ, we derive a master equation for the qubit dynamics. The tunneling rate of free quasiparticles is enhanced by their large density of states at energies close to the superconducting gap. Nevertheless, we find that…
We analyze bilayer quantum Hall ferromagnets, whose underlying symmetry group is SU(4). Spin-pseudospin coherence develops spontaneously when the total electron density is low enough. Quasiparticles are CP^3 skyrmions. One skyrmion induces charge modulations on both of the two layers. At the filling factor$ν=2/m$ one elementary excitation consists of a pair of skyrmions and its charge is $2e/m$. Recent experimental data due to Sawada et al. [Phys. Rev. Lett. {\bf 80}, 4534 (1998)] support this conclusion.
The work is motivated by the puzzling results of the recent experiment [S. Tewari et al., Phys. Rev. B 93, 035420 (2016)], where a robust coherence recovery from a certain energy was detected for an electron injected into the quantum Hall edge at the filling factor 2. After passing through a quantum dot the electron then tunnels into the edge with a subsequent propagation towards a symmetric Mach-Zender interferometer, after which the visibility of Aharonov-Bohm (AB) oscillations is measured. According to conventional understanding its decay with the increasing energy of the injected electron …
We present comprehensive results on the edge-mode velocities in a quantum Hall droplet with realistic interaction and confinement at various filling fractions. We demonstrate that the charge-mode velocity scales roughly with the valence Landau level filling fraction and the Coulomb energy in the corresponding Landau level. At Landau level filling fraction nu = 5/2, the stark difference between the bosonic charge-mode velocity and the fermionic neutral-mode velocity can manifest itself in the thermal smearing of the non-Abelian quasiparticle interference. We estimate the dependence of the coher…
Solid state quantum condensates often differ from previous examples of condensates (such as Helium, ultra-cold atomic gases, and superconductors) in that the quasiparticles condensing have relatively short lifetimes, and so as for lasers, external pumping is required to maintain a steady state. On the other hand, compared to lasers, the quasiparticles are generally more strongly interacting, and therefore better able to thermalise. This leads to questions of how to describe such non-equilibrium condensates, and their relation to equilibrium condensates and lasers. This chapter discusses in det…
Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy studies of these surface states have provided a wealth of spectroscopic characterization, with the successful cooperation of ab initio calculations. The method of quasiparticle interference imaging proves to be particularly useful for probing the dispersion relation of the surface bands. Herein, how a variety of additional fundamental electronic properties c…
