2,570 research outputs found
Numerical and experimental study of the effects of noise on the permutation entropy
We analyze the effects of noise on the permutation entropy of dynamical
systems. We take as numerical examples the logistic map and the R\"ossler
system. Upon varying the noise strengthfaster, we find a transition from an
almost-deterministic regime, where the permutation entropy grows slower than
linearly with the pattern dimension, to a noise-dominated regime, where the
permutation entropy grows faster than linearly with the pattern dimension. We
perform the same analysis on experimental time-series by considering the
stochastic spiking output of a semiconductor laser with optical feedback.
Because of the experimental conditions, the dynamics is found to be always in
the noise-dominated regime. Nevertheless, the analysis allows to detect
regularities of the underlying dynamics. By comparing the results of these
three different examples, we discuss the possibility of determining from a time
series whether the underlying dynamics is dominated by noise or not
Soft-pulse dynamical decoupling in a cavity
Dynamical decoupling is a coherent control technique where the intrinsic and
extrinsic couplings of a quantum system are effectively averaged out by
application of specially designed driving fields (refocusing pulse sequences).
This entails pumping energy into the system, which can be especially dangerous
when it has sharp spectral features like a cavity mode close to resonance. In
this work we show that such an effect can be avoided with properly constructed
refocusing sequences. To this end we construct the average Hamiltonian
expansion for the system evolution operator associated with a single ``soft''
pi-pulse. To second order in the pulse duration, we characterize a symmetric
pulse shape by three parameters, two of which can be turned to zero by shaping.
We express the effective Hamiltonians for several pulse sequences in terms of
these parameters, and use the results to analyze the structure of error
operators for controlled Jaynes-Cummings Hamiltonian. When errors are cancelled
to second order, numerical simulations show excellent qubit fidelity with
strongly-suppressed oscillator heating.Comment: 9pages, 5eps figure
Soft-Pulse Dynamical Decoupling with Markovian Decoherence
We consider the effect of broadband decoherence on the performance of
refocusing sequences, having in mind applications of dynamical decoupling in
concatenation with quantum error correcting codes as the first stage of
coherence protection. Specifically, we construct cumulant expansions of
effective decoherence operators for a qubit driven by a pulse of a generic
symmetric shape, and for several sequences of - and -pulses. While,
in general, the performance of soft pulses in decoupling sequences in the
presence of Markovian decoherence is worse than that of the ideal
-pulses, it can be substantially improved by shaping.Comment: New version contains minor content clarification
- …