We present a measurement of the relaxation and the dephasing times in a flux qubit. In order to improve coherence of the qubit, two external parameters were optimized: the applied flux through the qubit loop and the bias current of the SQUID which serves as a readout device of the qubit state. At the optimal point the dephasing time measured with spin‐echo technique was twice longer than the energy relaxation time. By changing one of the two bias parameters while keeping the other at the optimal value, one can separate the contribution of the noise in each parameter to the decoherence of the qubit.
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
4μs.
For many types of superconducting qubits, magnetic flux noise is a source of pure dephasing. Measurements on a representative dc superconducting quantum interference device (SQUID) over a range of temperatures show that ${S}_{\ensuremath{\Phi}}(f)={A}^{2}/{(f/1\phantom{\rule{0.28em}{0ex}}\text{Hz})}^{\ensuremath{\alpha}}$, where ${S}_{\ensuremath{\Phi}}$ is the flux noise spectral density,
A is of the order of 1 $\ensuremath{\mu}{\ensuremath{\Phi}}_{0}\phantom{\rule{0.28em}{0ex}}{\text{Hz}}^{\ensuremath{-}1/2}$, $0.61\ensuremath{\leqslant}\ensuremath{\alpha}\ensuremath{\leqslant}0.95$, and ${\ensuremath{\Phi}}_{0}$ is the flux quantum. For a qubit with an energy level splitting linearly coupled to the applied flux, calculations of the dependence of the pure dephasing time ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ of Ramsey and echo pulse sequences on $\ensuremath{\alpha}$ for fixed
A show that ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ decreases rapidly as $\ensuremath{\alpha}$ is reduced. We find that ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ is relatively insensitive to the noise bandwidth, ${f}_{1}\ensuremath{\leqslant}f\ensuremath{\leqslant}{f}_{2}$, for all $\ensuremath{\alpha}$ provided the ultraviolet cutoff frequency ${f}_{2}>1/{\ensuremath{\tau}}_{\ensuremath{\varphi}}$. We calculate the ratio ${\ensuremath{\tau}}_{\ensuremath{\varphi},E}/{\ensuremath{\tau}}_{\ensuremath{\varphi},R}$ of the echo (
E) and Ramsey (
R) sequences and the dependence of the decay function on $\ensuremath{\alpha}$ and
f2. We investigate the case in which ${S}_{\ensuremath{\Phi}}({f}_{0})$ is fixed at the ``pivot frequency'' ${f}_{0}\ensuremath{\ne}1$ Hz while $\ensuremath{\alpha}$ is varied and find that the choice of
f0 can greatly influence the sensitivity of ${\ensuremath{\tau}}_{\ensuremath{\varphi},E}$ and ${\ensuremath{\tau}}_{\ensuremath{\varphi},R}$ to the value of $\ensuremath{\alpha}$. Finally, we present calculated values of ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ in a qubit corresponding to the values of
A and $\ensuremath{\alpha}$ measured in our SQUID.
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.
We have studied the dephasing of a superconducting flux qubit coupled to a dc-SQUID based oscillator. By varying the bias conditions of both circuits we were able to tune their effective coupling strength. This allowed us to measure the effect of such a controllable and well-characterized environment on the qubit coherence. We can quantitatively account for our data with a simple model in which thermal fluctuations of the photon number in the oscillator are the limiting factor. In particular, we observe a strong reduction of the dephasing rate whenever the coupling is tuned to zero. At the optimal point we find a large spin-echo decay time of .
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.