Dynamicaldecoupling noise spectroscopy at an optimal working point of a qubit
Abstract
I present a theory of environmental noise spectroscopy via dynamical decoupling of a qubit at an optimal working point. Considering a sequence of n pulses and pure dephasing due to quadratic coupling to Gaussian distributed noise ξ (t), I use the linkedcluster (cumulant) expansion to calculate the coherence decay. Solutions allowing for reconstruction of spectral density of noise are given. For noise with correlation time shorter than the time scale on which coherence decays, the noise filtered by the dynamical decoupling procedure can be treated as effectively Gaussian at large n, and wellestablished methods of noise spectroscopy can be used to reconstruct the spectrum of ξ^{2}(t) noise. On the other hand, for noise of dominant lowfrequency character (1/^{fβ} noise with β >1), an infiniteorder resummation of the cumulant expansion is necessary, and it leads to an analytical formula for coherence decay having a powerlaw tail at long times. In this case, the coherence at time t depends both on spectral density of ξ (t) noise at ω =nπ/t, and on the effective lowfrequency cutoff of the noise spectrum, which is typically given by the inverse of the data acquisition time. Simulations of decoherence due to purely transverse noise show that the analytical formulas derived in this paper apply in this often encountered case of an optimal working point, provided that the number of pulses is not very large, and that the longitudinal qubit splitting is much larger than the transverse noise amplitude.
 Publication:

Physical Review A
 Pub Date:
 October 2014
 DOI:
 10.1103/PhysRevA.90.042307
 arXiv:
 arXiv:1308.3102
 Bibcode:
 2014PhRvA..90d2307C
 Keywords:

 03.67.Pp;
 03.65.Yz;
 05.40.Ca;
 Quantum error correction and other methods for protection against decoherence;
 Decoherence;
 open systems;
 quantum statistical methods;
 Noise;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Quantum Physics
 EPrint:
 Substantially expanded final version, includes discussion of dynamical decoupling from transverse noise