On the relevance of weak measurements in dissipative quantum systems

Abstract

We investigate the impact of dissipation on weak measurements. While weak measurements have been successful in signal amplification, dissipation can compromise their usefulness. More precisely, we show that in systems with non-degenerate eigenstates, weak values always converge to the expectation value of the measured observable as dissipation time tends to infinity, in contrast to systems with degenerate eigenstates, where the weak values can remain anomalous, i.e., outside the range of eigenvalues of the observable, even in the limit of an infinite dissipation time. In addition, we propose a method for extracting information about the dissipative dynamics of a system using weak values at short dissipation times. Specifically, we explore the amplification of the dissipation rate in a two-level system and the use of weak values to differentiate between Markovian and non-Markovian dissipative dynamics. We also find that weak measurements operating around a weak atom-cavity coupling can probe the atom dissipation through the weak value of non-Hermitian operators within the rotating-wave approximation of the weak interaction.

References in corpus (9)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification
• Anomalous Weak Values Are Proofs of Contextuality
• Weak Value Amplification Can Outperform Conventional Measurement in the Presence of Detector Saturation
• Approaching quantum-limited metrology with imperfect detectors by using weak-value amplification
• Quantum sensors based on weak-value amplification cannot overcome decoherence
• Taming the Rotating Wave Approximation
• Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems
• Renormalization in the Theory of Open Quantum Systems via the Self-Consistency Condition

Cited by in corpus (4)

• Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation
• Probing parameters estimation with Gaussian non-commutative measurements
• A paradox in the quantum-mechanical treatment of destructive measurements on photons
• Wick rotation derivation for weak values of the density and time-dependent density functional theory