Abstract
A system under constant observation is practically freezed to the measurement subspace. If the system driving is a random classical field, the survival probability of the system in the subspace becomes a random variable described by the Stochastic Quantum Zeno Dynamics (SQZD) formalism. Here, we study the time and ensemble average of this random survival probability and demonstrate how time correlations in the noisy environment determine whether the two averages do coincide or not. These environment time correlations can potentially generate non-Markovian dynamics of the quantum system depending on the structure and energy scale of the system Hamiltonian. We thus propose a way to detect time correlations of the environment by coupling a quantum probe system to it and observing the survival probability of the quantum probe in a measurement subspace. This will further contribute to the development of new schemes for quantum sensing technologies, where nanodevices may be exploited to image external structures or biological molecules via the surface field they generate.
Highlights
Multidimensional[28,29] subspace of the measurement operator
We propose a method based on the Stochastic Quantum Zeno Dynamics (SQZD)[20,26] to detect time correlations in random classical fields
By studying SQZD in time-correlated environments we have shown how an ergodicity property quantitatively depends on the time scale of the noise correlations
Summary
Multidimensional[28,29] subspace of the measurement operator. QZD has been experimentally realized first with a rubidium Bose–Einstein condensate in a five-level Hilbert space[30], and later in a multi-level Rydberg state structure[31]. A recent theoretical study and experimental demonstration with atom-chips has shown how different statistical samplings of a randomly-distributed sequence of projective measurements coincides in the quantum Zeno regime, proving an ergodicity hypothesis for randomly perturbed quantum systems[21]. In this regard, the sensitivity of the survival probability to the stochasticity in the time interval between measurements has been properly analyzed by means of the Fisher information[22]. In this work we want to analyze just the time correlations of the environment, that are independent from the system coupled to it
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