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IEEE Transactions on Applied Superconductivity

Backaction Effects of a SSET Measuring a Qubit Spectroscopy and Ground State Measurement

Benjamin Turek, Johannes Majer, Aashish A. Clerk, S. M. Girvin, Andreas J. Wallraff, Kevin Bladh, David Gunnarsson, T. Duty, Per Delsing, Robert J. Schoelkopf

Published Jun 1, 2005• 1 citation
Publisher

Abstract

We investigate the backaction of superconducting single-electron transistor (SSET) continuously measuring a Cooper-pair box. Due to the minimized backaction of the SSET, we observe a 2e periodic Coulomb staircase according to the two-level system Hamiltonian of the Cooper-pair box. We demonstrate that we can control the quantum broadening of the ground state in-situ. We perform spectroscopy measurements and demonstrate that we have full control over the Cooper-pair box Hamiltonian. The ability to reduce the backaction is a necessary condition to use the SSET as a quantum state readout for the CPB as a qubit.

DOI
10.1109/tasc.2005.850096

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We investigate the backaction of superconducting single-electron transistor (SSET) continuously measuring a Cooper-pair box. Due to the minimized backaction of the SSET, we observe a 2e periodic Coulomb staircase according to the two-level system Hamiltonian of the Cooper-pair box. We demonstrate that we can control the quantum broadening of the ground state in-situ. We perform spectroscopy measurements and demonstrate that we have full control over the Cooper-pair box Hamiltonian. The ability to reduce the backaction is a necessary condition to use the SSET as a quantum state readout for the CPB as a qubit.
We have measured the fully 2e2e2e periodic Coulomb staircase of a single Cooper pair box (SCB) in superconducting quantum interference design geometry, using a radio-frequency single-electron transistor. We have determined the energies of the SCB with microwave spectroscopy and compared the calculated shape of the Coulomb staircases to the measured staircases. We find excellent agreement as the Josephson coupling energy is tuned by an external magnetic field.
We report an experimental observation of the backaction of a single-electron transistor (SET) measuring the Coulomb staircase of a single-electron box. As current flows through the SET, the charge state of the SET island fluctuates. These fluctuations capacitively couple to the box and cause changes in the position, width, and asymmetry of the Coulomb staircase. A sequential tunneling model accurately recreates these effects, confirming this mechanism of the backaction of a SET. This is a first step toward understanding the effects of quantum measurement on solid-state qubits.
We report on the effect of the backaction of a single Cooper pair transistor electrometer (E\mathbf{E}E) on the charge state of a superconducting box (B\mathbf{B}B). The charge is eee periodic in the gate bias of B\mathbf{B}B when E\mathbf{E}E is operated near voltages $2\ensuremath{\Delta}/e$ or $4\ensuremath{\Delta}/e$. We show that this is due to quasiparticle poisoning of B\mathbf{B}B at a rate proportional to the number of quasiparticle tunneling events in E\mathbf{E}E per second. We are able to eliminate this backaction and recover 2e2e2e-charge periodicity using a new measurement method based on switching-current modulation of E\mathbf{E}E.
We present a series of measurements on nine single Cooper-pair boxes (SCBs), where the charging energy, E C , and the Josephson coupling energy, E J , have been varied. We have investigated both the ground state properties of the SCBs and their quantum coherent properties. The state of the SCBs could be manipulated by an external gate voltage and the charge was measured by coupling it capacitatively to a radio-frequency single-electron-transistor (RF-SET). By ramping the gate voltage and simultaneously measuring the charge of the SCBs using the RF-SET, we could measure the Coulomb staircases of the SCBs. For sufficiently low E C the SCBs showed a fully 2 e periodic Coulomb staircase. For samples with higher E C the staircase showed a short step for odd number of charges indicating quasi-particle 'poisoning'. However, if E C was not too large, the short step could be removed by applying a parallel magnetic field. We attribute this effect to a stronger suppression of the superconducting energy gap in the reservoir than in the box. Using microwave spectroscopy we have determined E C and E J for the SCBs. These values agree well with the shape of the Coulomb staircases which we measure. For a limited range of gate voltage, the SCBs were found to behave as model two-level quantum-mechanical systems. A non-adiabatic change in the induced island charge was used to bring two charge states into resonance. The resulting time evolution showed clear charge oscillations between the ground and excited state, with an amplitude above 70% and a frequency given by the energy level separation divided by Planck's constant. These oscillations had a longest coherence time of T 2 = 9 ns, at a point where the pure charge states are degenerate. The coherence time at this point was found to be limited by the relaxation rate. Away from the charge degeneracy point, the coherence time was limited by the pure dephasing rate. The dependence of T 2 on gate charge suggested that low frequency fluctuators were the main source of dephasing away from the degeneracy point.
For quantum computers to become reality, not only do the qubits have to be carefully engineered to be well isolated during operation time, but this also puts great strain on the measurement setup. We have looked at the backaction from a single-electron transistor (SET), operated both in the normal and in the superconducting state, on a single Cooper-pair box qubit. We have also designed a new read-out setup for a flux qubit using a Cooper-pair transistor that would allow read-out at the flux degeneracy point. In the first case we calculate the mixing time and the influence on the qubit steady-state distribution. We find that the mixing time is larger than typical experimental measurement times, indicating the possibility of single shot read-out. For the steady-state distribution of the qubit, we calculate the Coulomb staircase, finding additional structure due to the noise in the SET. For the flux qubit we design a read-out scheme involving a quantum flip-flop process, where the measurement outcome results in the presence or absence of an incoherent tunneling process. We estimate read-out and mixing times and find that single shot read-out should be achievable.
We study the quantum charge noise and measurement properties of the double Cooper-pair resonance point in a superconducting single-electron transistor (SSET) coupled to a Josephson charge qubit. Using a density-matrix approach for the coupled system, we obtain a full description of the measurement backaction; for weak coupling, this is used to extract the quantum charge noise. Unlike the case of a nonsuperconducting SET, the backaction here can induce population inversion in the qubit. We find that the Cooper-pair resonance process allows for a much better measurement than a similar nonsuperconducting SET, and can approach the quantum limit of efficiency.