Low-frequency noise caused by critical-current fluctuations in Josephson junctions can lead to substantial, measurement-induced dephasing in superconducting qubits. The purpose of this work is to measure this noise as a function of temperature and to simulate its effect on the measurement dynamics associated with superconducting qubits. In Nb trilayer junctions we measure the noise power at 1 Hz down to 10 mK and verify a T2 dependence for T > 1 K, below which we observe a flattening of the noise magnitude versus temperature. In Al trilayer junctions we measure the critical-current noise power at 1 Hz from 10 mK to 1.4 K and find no dependence on temperature over this range. Possible reasons for the deviation from a T2 dependence are explored, including heating and sample quality. Simulations of the effect of 1/f noise are performed to examine the consequence of using different qubit sampling methods on expected dephasing times. Using the two sampling methods, we can probe the spectral nature and possible source of the dominant noise in a qubit.
We show that charge noise
SQ in Josephson qubits can be produced by fluctuating two level systems (TLS) with electric dipole moments in the substrate using a flat density of states. At high frequencies the frequency and temperature dependence of the charge noise depends on the ratio
J/Jc of the electromagnetic flux
J to the critical flux
Jc. It is not widely appreciated that TLS in small qubits can easily be strongly saturated with
J/Jc≫1. Our results are consistent with experimental conclusions that
SQ∼1/f at low frequencies and
SQ∼f at high frequencies.
We present measurements of 1/f frequency noise in both linear and Josephson-junction-embedded superconducting aluminum resonators in the low power, low temperature regime—typical operating conditions for superconducting qubits. The addition of the Josephson junction does not result in additional frequency noise, thereby placing an upper limit for fractional critical current fluctuations of 1×10−8 (1/Hz) at 1 Hz for sub-micron, shadow evaporated junctions. These values imply a minimum dephasing time for a superconducting qubit due to critical current noise of 40–1400 μs depending on qubit architecture. Occasionally, at temperatures above 50 mK, we observe the activation of individual fluctuators which increase the level of noise significantly and exhibit Lorentzian spectra.
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 demonstrate a spurious contribution to low-frequency critical current noise in Josephson junctions—normally attributed to charge trapping in the barrier—arising from temperature instabilities inherent in cryogenic systems. These temperature fluctuations modify the critical current via its temperature dependence. Cross-correlations between measured temperature and critical current noise in Al-AlOx-Al junctions show that, despite excellent temperature stability, temperature fluctuations induce observable critical current fluctuations. Particularly, because 1/f critical current noise has decreased with improved fabrication techniques in recent years, it is important to understand and eliminate this additional noise source.
Author(s): Yu, Clare C; Constantin, Magdalena; Martinis, John M | Abstract: We show that charge noise
SQ in Josephson qubits can be produced by fluctuating two level systems (TLS) with electric dipole moments in the substrate using a flat density of states. At high frequencies the frequency and temperature dependence of the charge noise depends on the ratio
J/Jc of the electromagnetic flux
J to the critical flux
Jc. It is not widely appreciated that TLS in small qubits can easily be strongly saturated with
J/Jc≫1. Our results are consistent with experimental conclusions that
SQ∼1/f at low frequencies and
SQ∼f at high frequencies.