Ergodicity in randomly perturbed quantum systems

Abstract

The theoretical cornerstone of statistical mechanics is the ergodic assumption, i.e. the assumption that the time average of an observable equals its ensemble average. Here, we show how such a property is present when an open quantum system is continuously perturbed by an external environment effectively observing the system at random times while the system dynamics approaches the quantum Zeno regime. In this context, by large deviation theory we analytically show how the most probable value of the probability for the system to be in a given state eventually deviates from the non-stochastic case when the Zeno condition is not satisfied. We experimentally test our results with ultra-cold atoms prepared on an atom chip.

Noise sensing via stochastic quantum Zeno

“…Here, we have already named three main contributions in the beginning of this section. If we ignore for a moment errors (ii) and (iii) and focus on (i), we can make the following considerations concerning the possible breaking of the ergodic hypothesis of the system-environment interaction modes [33]. In this regard, if the duration t N of the single experiment is long enough to effectively reduce the stochasticity due to error (i), then one could just find, also experimentally, that ln 2 P cn ≈ ln 2 P cn .…”

Exact nonequilibrium quantum observable statistics: A large-deviation approach

“…, is set to unity and τ α ≡ t α − t α−1 . We also assume that, in accordance with the recently introduced stochastic quantum Zeno phenomena [5,6,33], there exists for each propagator U α at least one dynamical parameter λ, that is a fluctuating variable. For example, one could consider as in [38,39] that each λ α is equal to the time interval τ α , with τ α random.…”

“…On the other hand, repeated quantum measurements could correspond to a process exchanging photons with the environment [11] or could be adopted to ensure the protection of coherent evolutions of a quantum system by decoherence (quantum Zeno dynamics) [12]. Experimentally, together with strong coupling methods, such dynamics have been realized in several physical setups such as solid-state spins, superconducting qubits or ultracold atomic gases [5,[13][14][15][16][17]. They are also relevant in quantum metrology [18] to probe the phase evolution of an atomic ensemble by means of interleaved interrogations and feedback corrections [19,20].…”

Experimental proof of quantum Zeno-assisted noise sensing

“…Recently, sequences of Zeno measurements have been studied in the presence of additional stochastic contributions to analyze how the confinement probability of the system to remain in the measured subspace changes with the amount and type of stochasticity [36][37][38]. Such a regime is called weak quantum Zeno (WQZ) and it has been observed that, although projective measurements could constantly monitor a quantum system, its decay is boosted by the presence of disorder.…”