We have measured flux-noise correlations in a tunable superconducting flux qubit. The device consists of two loops that independently control the qubit's energy splitting and tunnel coupling. Low-frequency flux noise in the loops causes fluctuations of the qubit frequency and leads to dephasing. Since the noises in the two loops couple to different terms of the qubit Hamiltonian, a measurement of the dephasing rate at different bias points provides a way to extract both the amplitude and the sign of the noise correlations. We find that the flux fluctuations in the two loops are anticorrelated, consistent with a model where the flux noise is generated by randomly oriented unpaired spins on the metal surface.
We have investigated decoherence in Josephson-junction flux qubits. Based on the measurements of decoherence at various bias conditions, we discriminate contributions of different noise sources. We present a Gaussian decay function extracted from the echo signal as evidence of dephasing due to 1/f flux noise whose spectral density is evaluated to be about (10(-6)Phi0)2/Hz at 1 Hz. We also demonstrate that, at an optimal bias condition where the noise sources are well decoupled, the coherence observed in the echo measurement is limited mainly by energy relaxation of the qubit.
A complete analysis of the decoherence properties of a Josephson junction qubit is presented. The qubit is of the flux type and consists of two large loops forming a gradiometer, one small loop, and three Josephson junctions. We develop a complete, quantitative description of the inductances and capacitances of the circuit. Including two stray capacitances makes the quantum mechanical modeling of the system five dimensional. To make the required calculation tractable, we devise a general Born-Oppenheimer approximation which reduces the effective dimensionality in the calculation to one. Contributions to relaxation
(T1) and dephasing $({T}_{\ensuremath{\phi}})$ arising from two different control circuits, one coupled to the small loop and one coupled to a large loop, is computed. We explore
T1 and ${T}_{\ensuremath{\phi}}$ along an optimal line in the space of applied fluxes; along this ``S line'' we see significant and rapidly varying contributions to the decoherence parameters, primarily from the circuit coupling to the large loop.
We compute the decoherence caused by
1∕f fluctuations at low frequency
f in the critical current
I0 of Josephson junctions incorporated into flux, phase, charge, and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ scales as ${I}_{0}∕\ensuremath{\Omega}\ensuremath{\Lambda}{S}_{{I}_{0}}^{1∕2}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$, where $\ensuremath{\Omega}∕2\ensuremath{\pi}$ is the energy-level splitting frequency,
SI0(1Hz) is the spectral density of the critical-current noise at
1Hz, and $\ensuremath{\Lambda}\ensuremath{\equiv}\ensuremath{\mid}{I}_{0}d\ensuremath{\Omega}∕\ensuremath{\Omega}d{I}_{0}\ensuremath{\mid}$ is a parameter computed for given parameters for each type of qubit that specifies the sensitivity of the level splitting to critical-current fluctuations. Computer simulations show that the envelope of the coherent oscillations of any qubit after time
t scales as $\mathrm{exp}(\ensuremath{-}{t}^{2}∕2{\ensuremath{\tau}}_{\ensuremath{\phi}}^{2})$ when the dephasing due to critical-current noise dominates the dephasing from all sources of dissipation. We compile published results for fluctuations in the critical current of Josephson tunnel junctions fabricated with different technologies and a wide range in
I0 and area
A, and show that their values of
SI0(1Hz) scale to within a factor of 3 of $[144{({I}_{0}∕\ensuremath{\mu}\mathrm{A})}^{2}∕(\mathcal{A}∕\ensuremath{\mu}{\mathrm{m}}^{2})]{(\mathrm{pA})}^{2}∕\mathrm{Hz}$ at
4.2K. We empirically extrapolate
SI01∕2(1Hz) to lower temperatures using a scaling
T(K)∕4.2. Using this result, we find that the predicted values of ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ at
100mK range from $0.8\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}12\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, and are usually substantially longer than values measured experimentally at lower temperatures.
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∕f noise is the dominant source of dephasing in the direct vicinity of the optimal point. The influence of
1∕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.
Abstract : Qubit dephasing is governed by low-frequency noise in the bias parameters that control the energy separation between the qubit states. It has been shown that dephasing in phase and flux qubits is dominated by an excess low frequency magnetic flux noise with a 1/f power spectrum and magnitude at 1 Hz of order 1 microPhi0/sqrt(Hz). Recent experiments by McDermott et al. provide clear evidence for the existence of unpaired magnetic states on the surfaces of superconducting thin film devices; it is now believed that fluctuations of these surface spin states are the source of the ubiquitous 1/f flux noise. However, the microscopic mechanism that drives fluctuations of these spins is not understood; moreover, there is no clear path to reducing the flux noise magnitude. This program is devoted to a systematic investigation of magnetic surface defects in SQUIDs and phase qubits. Measurements of surface spin susceptibility and susceptibility noise will yield valuable clues about the microscopic nature of the magnetic fluctuators, and shed light on interactions between defects. The role of qubit loop geometry on flux noise magnitude and dephasing will be explored in detail. The experiments will guide theoretical efforts to develop improved models for flux noise.