Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Electron Heating and Quasiparticle Tunnelling in Superconducting Charge Qubits

Matthew D. Shaw, Juan Bueno, Per Delsing, P. M. Echternach

Published Aug 6, 2008• 0 citations
OpenAlex

Abstract

We have directly measured non-equilibrium quasiparticle tunnelling in the time domain as a function of temperature and RF carrier power for a pair of charge qubits based on the single Cooper-pair box, where the readout is performed with a multiplexed quantum capacitance technique. We have extracted an effective electron temperature for each applied RF power, using the data taken at the lowest power as a reference curve. This data has been fit to a standard T? electron heating model, with a reasonable correspondence with established material parameters.

Related papers

Electron heating and quasiparticle tunneling in superconducting charge qubits

Matthew D. Shaw, Juan Bueno, Per Delsing +1 more

We have directly measured non-equilibrium quasiparticle tunneling in the time domain as a function of temperature and RF carrier power for a pair of charge qubits based on the single Cooper-pair box, where the readout is performed with a multiplexed quantum capacitance technique. We have extracted an effective electron temperature for each applied RF power, using the data taken at the lowest power as a reference curve. This data has been fit to a standard T 5 electron heating model, with a qualitative correspondence with established material parameters.

Journal of Physics Conference Series•Feb 1, 2009•0 citations

Towards Single Shot Measurements of a Cooper Pair Box Qubit Using an RF Single Electron Transistor

Carlos Alberto Sánchez

I report an investigation into using an rf Single Electron Transistor (rf-SET) to implement single shot readout of the quantum state of a Cooper pair box. I fabricated Al/AlOx/Al SETs and Cooper pair boxes using e-beam lithography and double-angle evaporation. The devices had typical charging energies of about 1 K and were measured at 30 mK in a dilution refrigerator. I built rf-SETs with an LC resonant circuit integrated on the chip and operating frequencies of 650 MHz and 1.5 GHz. The rf-SETs had a typical bandwidth of 30 MHz and the best achieved charge sensitivity was 8X10-6 erms/(Hz)1/2 at 1.5 GHz. The rf-SETs were used to measure the Coulomb staircase on the Cooper pair box. Measurements of the staircase show features due to quasiparticle poisoning that are dependent on temperature and SET bias. The data was compared to a theory I developed to extend existing theories of quasiparticle poisoning. My model is based on the calculation of tunneling rates to explain observations of parity effects in the Cooper pair box over a wide temperature range. Quantum state control of the Cooper pair box was demonstrated by using fast voltage pulses applied to the gate. Temporal oscillations of charge states and spectroscopy measurements reveal a dephasing time T2=200 ps at 30 mK, for a drive frequency of 30 GHz. The energy relaxation time T1=140 ns was determined from time domain measurements of the decay of the Cooper pair box charge. The fidelity of single shot measurements and the feasibility of this quantum readout scheme based on the results are discussed.

•Dec 5, 2005•0 citations

Kinetics of the superconducting charge qubit in the presence of a quasiparticle

Roman M. Lutchyn, L. I. Glazman, A. I. Larkin

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 a 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 of the qubit coherences and populations. We find that the kinetics of the qubit can be characterized by two time scales---quasiparticle escape time from the reservoir to the box ${\ensuremath{\Gamma}}_{\text{in}}^{\ensuremath{-}1}$ and quasiparticle relaxation time $\ensuremath{\tau}$. The former is determined by the dimensionless normal-state conductance ${g}_{T}$ of the Josephson junction and one-electron level spacing ${\ensuremath{\delta}}_{r}$ in the reservoir $({\ensuremath{\Gamma}}_{\text{in}}\ensuremath{\sim}{g}_{T}{\ensuremath{\delta}}_{r})$, and the latter is due to the electron-phonon interaction. We find that phase coherence is damped on the time scale of ${\ensuremath{\Gamma}}_{\text{in}}^{\ensuremath{-}1}$. The qubit energy relaxation depends on the ratio of the two characteristic times $\ensuremath{\tau}$ and ${\ensuremath{\Gamma}}_{\text{in}}^{\ensuremath{-}1}$ and also on the ratio of temperature $T$ to the Josephson energy ${E}_{J}$.

arXiv:cond-mat/0603640•Physical Review B•Aug 30, 2006•58 citations

Kinetics of nonequilibrium quasiparticle tunneling in superconducting charge qubits

Matthew D. Shaw, Roman M. Lutchyn, Per Delsing +1 more

We directly observe low-temperature nonequilibrium quasiparticle tunneling in charge qubits based on the single-Cooper-pair box. We measure even- and odd-state dwell-time distributions as a function of temperature, and interpret these results using a kinetic theory. While the even-state lifetime is exponentially distributed, the odd-state distribution is more heavily weighted to short times, implying that odd-to-even tunnel events are not described by a homogenous Poisson process. The mean odd-state dwell time increases sharply at low temperature, which is consistent with quasiparticles tunneling out of the island before reaching thermal equilibrium.

arXiv:0803.3102•Physical Review B•Jul 1, 2008•104 citations

Rate of tunneling nonequilibrium quasiparticles in superconducting qubits

Mohammad H. Ansari

In superconducting qubits the lifetime of quantum states cannot be prolonged arbitrarily by decreasing temperature. At low temperature quasiparticles tunneling between electromagnetic environment and superconducting islands takes the condensate state out of equilibrium due to charge imbalance. We obtain the tunneling rate from a phenomenological model of non-equilibrium, where nonequilibrium quasiparticle tunnelling stimulates a temperature-dependent chemical potential shift in superconductor. As a result we obtain a non-monotonic behavior for relaxation rate as function of temperature. Depending on the fabrication parameters for some qubits the lowest tunneling rate of nonequilibrium quasiparticles can take place only near the onset temperature below which nonequilibrium quasiparticles dominate over equilibrium one. Our theory also indicates that such tunnelings can influence the probability of transitions in qubits through a coupling to the zero-point energy of phase fluctuations.

arXiv:1303.1453•Superconductor Science and Technology•Feb 6, 2015•11 citations

Charge dynamics in superconducting double dots

Adam Ashiq Esmail

The work presented in this thesis investigates transitions between quantum states in superconducting double dots (SDDs), a nanoscale device consisting of two aluminium superconducting islands coupled together by a Josephson junction, with each dot connected to a normal state lead. The energy landscape consists of a two level manifold of even charge parity Cooper pair states, and continuous bands corresponding to charge states with single quasiparticles in one or both islands. These devices are fabricated using shadow mask evaporation, and are measured at sub Kelvin temperatures using a dilution refrigerator. We use radio frequency reflectometry to measure quantum capacitance, which is dependent on the quantum state of the device. We measure the quantum capacitance as a function of gate voltage, and observe capacitance maxima corresponding to the Josephson coupling between even parity states. We also perform charge sensing and detect odd parity states. These measurements support the theoretical model of the energy landscape of the SDD. By measuring the quantum capacitance in the time domain, we observe random switching of capacitance between two levels. We determine this to be the stochastic breaking and recombination of single Cooper pairs. By carrying out spectroscopy of the bath responsible for the pair breaking we attribute it to black-body radiation in the cryogenic environment. We also drive the breaking process with a continuous microwave signal, and find that the rate is linearly proportional to incident power. This suggests that a single photon process is responsible, and demonstrates the potential of the SDD as a single photon microwave detector. We investigate this mechanism further, and design an experiment in which the breaking rate is enhanced when the SDD is in the antisymmetric state rather than the symmetric state. We also measure the quantum capacitance of a charge isolated double dot. We observe 2e periodicity, indicating the tunnelling of Cooper pairs and the lack of occupation of quasiparticle states. This work is relevant to the range of experiments investigating the effect of non-equilibrium quasiparticles on the operation of superconducting qubits and other superconducting devices.

•Oct 31, 2017•0 citations
We have directly measured non-equilibrium quasiparticle tunnelling in the time domain as a function of temperature and RF carrier power for a pair of charge qubits based on the single Cooper-pair box, where the readout is performed with a multiplexed quantum capacitance technique. We have extracted an effective electron temperature for each applied RF power, using the data taken at the lowest power as a reference curve. This data has been fit to a standard T? electron heating model, with a reasonable correspondence with established material parameters.
We have directly measured non-equilibrium quasiparticle tunneling in the time domain as a function of temperature and RF carrier power for a pair of charge qubits based on the single Cooper-pair box, where the readout is performed with a multiplexed quantum capacitance technique. We have extracted an effective electron temperature for each applied RF power, using the data taken at the lowest power as a reference curve. This data has been fit to a standard T 5 electron heating model, with a qualitative correspondence with established material parameters.
I report an investigation into using an rf Single Electron Transistor (rf-SET) to implement single shot readout of the quantum state of a Cooper pair box. I fabricated Al/AlOx/Al SETs and Cooper pair boxes using e-beam lithography and double-angle evaporation. The devices had typical charging energies of about 1 K and were measured at 30 mK in a dilution refrigerator. I built rf-SETs with an LC resonant circuit integrated on the chip and operating frequencies of 650 MHz and 1.5 GHz. The rf-SETs had a typical bandwidth of 30 MHz and the best achieved charge sensitivity was 8X10-6 erms/(Hz)1/2 at 1.5 GHz. The rf-SETs were used to measure the Coulomb staircase on the Cooper pair box. Measurements of the staircase show features due to quasiparticle poisoning that are dependent on temperature and SET bias. The data was compared to a theory I developed to extend existing theories of quasiparticle poisoning. My model is based on the calculation of tunneling rates to explain observations of parity effects in the Cooper pair box over a wide temperature range. Quantum state control of the Cooper pair box was demonstrated by using fast voltage pulses applied to the gate. Temporal oscillations of charge states and spectroscopy measurements reveal a dephasing time T2=200 ps at 30 mK, for a drive frequency of 30 GHz. The energy relaxation time T1=140 ns was determined from time domain measurements of the decay of the Cooper pair box charge. The fidelity of single shot measurements and the feasibility of this quantum readout scheme based on the results are discussed.
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 a 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 of the qubit coherences and populations. We find that the kinetics of the qubit can be characterized by two time scales---quasiparticle escape time from the reservoir to the box ${\ensuremath{\Gamma}}_{\text{in}}^{\ensuremath{-}1}$ and quasiparticle relaxation time $\ensuremath{\tau}$. The former is determined by the dimensionless normal-state conductance gT{g}_{T}gT​ of the Josephson junction and one-electron level spacing ${\ensuremath{\delta}}_{r}$ in the reservoir $({\ensuremath{\Gamma}}_{\text{in}}\ensuremath{\sim}{g}_{T}{\ensuremath{\delta}}_{r})$, and the latter is due to the electron-phonon interaction. We find that phase coherence is damped on the time scale of ${\ensuremath{\Gamma}}_{\text{in}}^{\ensuremath{-}1}$. The qubit energy relaxation depends on the ratio of the two characteristic times $\ensuremath{\tau}$ and ${\ensuremath{\Gamma}}_{\text{in}}^{\ensuremath{-}1}$ and also on the ratio of temperature TTT to the Josephson energy EJ{E}_{J}EJ​.
We directly observe low-temperature nonequilibrium quasiparticle tunneling in charge qubits based on the single-Cooper-pair box. We measure even- and odd-state dwell-time distributions as a function of temperature, and interpret these results using a kinetic theory. While the even-state lifetime is exponentially distributed, the odd-state distribution is more heavily weighted to short times, implying that odd-to-even tunnel events are not described by a homogenous Poisson process. The mean odd-state dwell time increases sharply at low temperature, which is consistent with quasiparticles tunneling out of the island before reaching thermal equilibrium.
In superconducting qubits the lifetime of quantum states cannot be prolonged arbitrarily by decreasing temperature. At low temperature quasiparticles tunneling between electromagnetic environment and superconducting islands takes the condensate state out of equilibrium due to charge imbalance. We obtain the tunneling rate from a phenomenological model of non-equilibrium, where nonequilibrium quasiparticle tunnelling stimulates a temperature-dependent chemical potential shift in superconductor. As a result we obtain a non-monotonic behavior for relaxation rate as function of temperature. Depending on the fabrication parameters for some qubits the lowest tunneling rate of nonequilibrium quasiparticles can take place only near the onset temperature below which nonequilibrium quasiparticles dominate over equilibrium one. Our theory also indicates that such tunnelings can influence the probability of transitions in qubits through a coupling to the zero-point energy of phase fluctuations.
The work presented in this thesis investigates transitions between quantum states in superconducting double dots (SDDs), a nanoscale device consisting of two aluminium superconducting islands coupled together by a Josephson junction, with each dot connected to a normal state lead. The energy landscape consists of a two level manifold of even charge parity Cooper pair states, and continuous bands corresponding to charge states with single quasiparticles in one or both islands. These devices are fabricated using shadow mask evaporation, and are measured at sub Kelvin temperatures using a dilution refrigerator. We use radio frequency reflectometry to measure quantum capacitance, which is dependent on the quantum state of the device. We measure the quantum capacitance as a function of gate voltage, and observe capacitance maxima corresponding to the Josephson coupling between even parity states. We also perform charge sensing and detect odd parity states. These measurements support the theoretical model of the energy landscape of the SDD. By measuring the quantum capacitance in the time domain, we observe random switching of capacitance between two levels. We determine this to be the stochastic breaking and recombination of single Cooper pairs. By carrying out spectroscopy of the bath responsible for the pair breaking we attribute it to black-body radiation in the cryogenic environment. We also drive the breaking process with a continuous microwave signal, and find that the rate is linearly proportional to incident power. This suggests that a single photon process is responsible, and demonstrates the potential of the SDD as a single photon microwave detector. We investigate this mechanism further, and design an experiment in which the breaking rate is enhanced when the SDD is in the antisymmetric state rather than the symmetric state. We also measure the quantum capacitance of a charge isolated double dot. We observe 2e periodicity, indicating the tunnelling of Cooper pairs and the lack of occupation of quasiparticle states. This work is relevant to the range of experiments investigating the effect of non-equilibrium quasiparticles on the operation of superconducting qubits and other superconducting devices.