Decoherence reduction via continuous dynamical decoupling: Analytical study of the role of the noise spectrum

We analyze the robust character against the nonstatic noise of clock transitions implemented via a method of continuous dynamical decoupling (CDD) in a hyperfine Zeeman multiplet in 87Rb. The emergence of features specific to the quadratic corrections to the linear Zeeman effect is evaluated. Our analytical approach, which combines methods of stochastic analysis with time-dependent perturbation theory, allows tracing the decoherence process for generic noise sources. Working first with a basic CDD scheme, it is shown that the amplitude and frequency of the (sinusoidal driving) field of control can be appropriately chosen to force the nonstatic random input to have a (time-dependent) perturbative character. Moreover, in the dressed-state picture, the effect of noise is described in terms of an operative random variable whose properties, dependent on the driving field, can be analytically characterized. In this framework, the relevance of the spectral density of the fluctuations to the performance of the CDD technique is precisely assessed. In particular, the range of noise correlation times where the method of decoherence reduction is still efficient is identified. The results obtained in the basic CDD framework are extrapolated to concatenated schemes. The generality of our approach allows its applicability beyond the specific atomic system considered.

Automated summary

In this study, we analyze the robustness of continuous dynamical decoupling (CDD) against nonstatic noise in a hyperfine Zeeman multiplet in 87Rb. By combining stochastic analysis methods with time-dependent perturbation theory, we are able to track the decoherence process caused by generic noise sources. The results show that the amplitude and frequency of the control field can be chosen appropriately to minimize the impact of nonstatic random input, and the effect of noise can be described using a random variable in the dressed-state picture. The importance of spectral density of fluctuations to the performance of CDD technique is evaluated.