We show that charge noise
SQ in Josephson qubits can be produced by\nfluctuating two level systems (TLS) with electric dipole moments in the\nsubstrate using a flat density of states. At high frequencies the frequency and\ntemperature dependence of the charge noise depends on the ratio
J/Jc of the\nelectromagnetic flux
J to the critical flux
Jc. It is not widely\nappreciated that TLS in small qubits can easily be strongly saturated with\n
J/Jcgg1. Our results are consistent with experimental conclusions that\n
SQsim1/f at low frequencies and
SQsimf at high frequencies.
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.
We study the charge noise
SQ in Josephson qubits produced by fluctuating two-level systems (TLSs) with electric-dipole moments in the substrate. The TLSs are driven by an alternating electric field of angular frequency $\ensuremath{\Omega}$ and electric field intensity
I. It is not widely appreciated that TLS in small qubits can easily be strongly saturated if
I⪢Ic, where
Ic is the critical electric field intensity. To investigate the effect of saturation on the charge noise, we express the noise spectral density in terms of density-matrix elements. To determine the dependence of the density-matrix elements on the ratio
I/Ic, we find the steady-state solution for the density matrix using the Bloch-Redfield differential equations. We then obtain an expression for the spectral density of charge fluctuations as a function of frequency
f and the ratio
I/Ic. We find
1/f charge noise at low frequencies, and that the charge noise is white (constant) at high frequencies. Using a flat density of states, we find that TLS saturation has no effect on the charge noise at either high or low frequencies.
The electrical noise of mesoscopic devices can be strongly influenced by the quantum motion of electrons. To probe this effect, we have measured the current fluctuations at high frequency (5 to 90 gigahertz) using a superconductor-insulator-superconductor tunnel junction as an on-chip spectrum analyzer. By coupling this frequency-resolved noise detector to a quantum device, we can measure the high-frequency, nonsymmetrized noise as demonstrated for a Josephson junction. The same scheme is used to detect the current fluctuations arising from coherent charge oscillations in a two-level system, a superconducting charge qubit. A narrow band peak is observed in the spectral noise density at the frequency of the coherent charge oscillations.
Noise and decoherence are major obstacles to the implementation of Josephson junction qubits in quantum computing. Recent experiments suggest that two-level systems (TLS) in the oxide tunnel barrier are a source of decoherence. We explore two decoherence mechanisms in which these two-level systems lead to the decay of Rabi oscillations that result when Josephson junction qubits are subjected to strong microwave driving. (A) We consider a Josephson qubit coupled resonantly to a two-level system, i.e., the qubit and TLS have equal energy splittings. As a result of this resonant interaction, the occupation probability of the excited state of the qubit exhibits beating. Decoherence of the qubit results when the two-level system decays from its excited state by emitting a phonon. (B) Fluctuations of the two-level systems in the oxide barrier produce fluctuations and
1∕f noise in the Josephson junction critical current
I0. This in turn leads to fluctuations in the qubit energy splitting that degrade the qubit coherence. We compare our results with experiments on Josephson junction phase qubits.
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.