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arXiv:cond-mat/0601522 · Physical Review B

Decoherence processes in a current biased dc SQUID

Julien Claudon, Aurélien Fay, Laurent-Patrick Lévy, O. Buisson

Published May 5, 2006• 19 citations
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Abstract

A current biased dc superconducting quantum interference device behaves as an anharmonic quantum oscillator controlled by a bias current and an applied magnetic flux. We consider here its two level limit consisting of the two lower energy states \ensuremath{\mid}0⟩ and \ensuremath{\mid}1⟩. We have measured energy relaxation times and microwave absorption for different bias currents and fluxes in the low microwave power limit. Decoherence times are extracted. The low frequency flux and current noise have been measured independently by analyzing the probability of current switching from the superconducting to the finite voltage state, as a function of applied flux. The high frequency part of the current noise is derived from the electromagnetic environment of the circuit. The decoherence of this quantum circuit can be fully accounted for by these current and flux noise sources.

DOI
10.1103/physrevb.73.180502

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A current biased dc superconducting quantum interference device behaves as an anharmonic quantum oscillator controlled by a bias current and an applied magnetic flux. We consider here its two level limit consisting of the two lower energy states \ensuremath{\mid}0⟩ and \ensuremath{\mid}1⟩. We have measured energy relaxation times and microwave absorption for different bias currents and fluxes in the low microwave power limit. Decoherence times are extracted. The low frequency flux and current noise have been measured independently by analyzing the probability of current switching from the superconducting to the finite voltage state, as a function of applied flux. The high frequency part of the current noise is derived from the electromagnetic environment of the circuit. The decoherence of this quantum circuit can be fully accounted for by these current and flux noise sources.
We report detailed measurements of the relaxation and dephasing time in a flux-qubit measured by a switching DC SQUID. We studied their dependence on the two important circuit bias parameters: the externally applied magnetic flux and the bias current through the SQUID in two samples. We demonstrate two complementary strategies to protect the qubit from these decoherence sources. One consists in biasing the qubit so that its resonance frequency is stationary with respect to the control parameters ({\it optimal point}) ; the second consists in {\it decoupling} the qubit from current noise by chosing a proper bias current through the SQUID. At the decoupled optimal point, we measured long spin-echo decay times of up to 4μs4 μs4μs.
We have observed coherent oscillations in a multilevel quantum system, formed by a current-biased dc SQUID. These oscillations have been induced by applying resonant microwave pulses of flux. Quantum measurement is performed by a nanosecond flux pulse that projects the final state onto one of two different voltage states of the dc SQUID, which can be read out. The number of quantum states involved in the coherent oscillations increases with increasing microwave power. The dependence of the oscillation frequency on microwave power deviates strongly from the linear regime expected for a two-level system and can be very well explained by a theoretical model taking into account the anharmonicity of the multilevel system.
This paper presents our procedure to measure the quantum state of a dc superconducting quantum interference device (SQUID) within a few nanoseconds, using an adiabatic dc flux pulse. Detection of the ground state is governed by standard macroscopic quantum tunneling (MQT) theory, with a small correction due to residual noise in the bias current. In the two-level limit, where the SQUID constitutes a phase qubit, an observed contrast of 0.54 indicates a significant loss in contrast compared to the MQT prediction. It is attributed to spurious depolarization (loss of excited state occupancy) during the leading edge of the adiabatic flux measurement pulse. We give a simple phenomenological relaxation model which is able to predict the observed contrast of multilevel Rabi oscillations for various microwave amplitudes.
Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance Cs{C}_{s}Cs​ and resistance Rs{R}_{s}Rs​ in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.
We present a systematic study of the phase coherent dynamics of a superconducting three-Josephson-junction flux qubit. The qubit state is detected with the integrated-pulse method, which is a variant of the pulsed switching-dc-superconducting quantum interference device (SQUID) method. In this scheme, the dc SQUID bias current pulse is applied via a capacitor instead of a resistor, giving rise to a narrow bandpass instead of a pure low-pass filter configuration of the electromagnetic environment. Measuring one and the same qubit with both setups allows a direct comparison. With the capacitive method about four times faster switching pulses and an increased visibility are achieved. Furthermore, the deliberate engineering of the electromagnetic environment, which minimizes the noise due to the bias circuit, is facilitated. Right at the degeneracy point, the qubit coherence is limited by energy relaxation. We find two main noise contributions. White noise limits the energy relaxation and contributes to the dephasing far from the degeneracy point. 1∕f1∕f1∕f noise is the dominant source of dephasing in the direct vicinity of the optimal point. The influence of 1∕f1∕f1∕f noise is also supported by nonrandom beatings in the Ramsey and spin echo decay traces. Numeric simulations of a coupled qubit-oscillator system indicate that these beatings are due to the resonant interaction of the qubit with at least one pointlike fluctuator, coupled especially strongly to the qubit.
We have measured the low-frequency noise in the critical current Ic of six dc superconducting quantum interference devices (SQUIDs) with resistively shunted Nb–NbOx–PbIn Josephson junctions in the temperature range T=0.09–4.2K. Each device is voltage biased, the applied flux is an integer number of flux quanta, and the current fluctuations are measured with a second dc SQUID. At low frequencies f, there is a component of the power spectrum of the critical current fluctuations given approximately by SIc(f)=CIc2T2∕Af, where A is the area of both junctions, and C≈(3.9±0.4)×10−23m2∕K2. For quantum bits based on Josephson junctions, the scaling of SIc(f) with T2 implies that the dephasing time limited by critical current l∕f noise should scale as 1∕T for temperatures down to at least 0.09K.