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.
Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where
I0 is the critical current,
C is the junction capacitance, and
Ls is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the
LsC resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.
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.
Abstract Decoherence in quantum bits (qubits) is a major challenge for realizing scalable quantum computing. One of the primary causes of decoherence in qubits and quantum circuits based on superconducting Josephson junctions is the critical current fluctuation. Many efforts have been devoted to suppressing the critical current fluctuation in Josephson junctions. Nonetheless, the efforts have been hindered by the defect-induced trapping states in oxide-based tunnel barriers and the interfaces with superconductors in the traditional Josephson junctions. Motivated by this, along with the recent demonstration of 2D insulator h -BN with exceptional crystallinity and low defect density, we fabricated a vertical NbSe 2 / h -BN/Nb Josephson junction consisting of a bottom NbSe 2 superconductor thin layer and a top Nb superconductor spaced by an atomically thin h -BN layer. We further characterized the superconducting current and voltage ( I – V ) relationships and Fraunhofer pattern of the NbSe 2 / h -BN/Nb junction. Notably, we demonstrated the critical current noise (1/ f noise power) in the h -BN-based Josephson device is at least a factor of four lower than that of the previously studied aluminum oxide-based Josephson junctions. Our work offers a strong promise of h -BN as a novel tunnel barrier for high-quality Josephson junctions and qubit applications.
The zero-voltage state of a Josephson junction biased with constant current consists of a set of metastable quantum energy levels. We probe the spacings of these levels by using microwaves to induce transitions and thereby enhance the escape rate to the voltage state. The widths of the resonances give a measurement of the spectroscopic coherence time of the two metastable states involved in the transitions. We observe a decoherence time shorter than that expected from dissipation alone in resonantly isolated $20\ifmmode\times\else\texttimes\fi{}5\ensuremath{\mu}{\mathrm{m}}^{2}$ area
Al/AlOx/Al junctions at 60 mK. The data are well fit by a model that includes the dephasing effects of both low-frequency current noise and the escape rate to the voltage state. We discuss implications for quantum computation using current-biased Josephson-junction qubits, including limits on the minimum number of levels needed in the well.