Driving quantum systems with repeated conditional measurements

Abstract

We investigate the effect of conditional null measurements on a quantum system and find a rich variety of behaviors. Specifically, quantum dynamics with a time independent $H$ in a finite dimensional Hilbert space are considered with repeated strong null measurements of a specified state. We discuss four generic behaviors that emerge in these monitored systems. The first arises in systems without symmetry, along with their associated degeneracies in the energy spectrum, and hence in the absence of dark states as well. In this case, a unique final state can be found which is determined by the largest eigenvalue of the survival operator, the non-unitary operator encoding both the unitary evolution between measurements and the measurement itself. For a three-level system, this is similar to the well known shelving effect. Secondly, for systems with built-in symmetry and correspondingly a degenerate energy spectrum, the null measurements dynamically select the degenerate energy levels, while the non-degenerate levels are effectively wiped out. Thirdly, in the absence of dark states, and for specific choices of parameters, two or more eigenvalues of the survival operator match in magnitude, and this leads to an oscillatory behavior controlled by the measurement rate and not solely by the energy levels. Finally, when the control parameters are tuned, such that the eigenvalues of the survival operator all coalesce to zero, one has exceptional points that corresponds to situations that violate the null measurement condition, making the conditional measurement process impossible.

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Cited by in corpus (13)

• Restart uncertainty relation for monitored quantum dynamics
• Engineering unsteerable quantum states with active feedback
• Stable many-body localization under random continuous measurements in the no-click limit
• Tight-binding model subject to conditional resets at random times
• Uncertainty relation between detection probability and energy fluctuations
• Resonances of recurrence time of monitored quantum walks
• Interaction-induced transition in quantum many-body detection probability
• Error threshold in active steering protocols for few-qubit systems
• Repeated measurements and random scattering in quantum walks
• Experimental measurement of quantum first-passage-time distributions
• Towards scalable active steering protocols for genuinely entangled state manifolds
• An almost deterministic cooling by measurements
• Localized states in monitored quantum walks