Measurements on an Anderson Chain

Abstract

We study the dynamics of a monitored single particle in a one-dimensional, Anderson-localized system. The time evolution is governed by Hamiltonian dynamics for fixed time intervals, interrupted by local, projective measurements. The competition between disorder-induced localization and measurement-induced jumps leads to interesting behaviour of readout-averaged quantities. We find that measurements at random positions delocalize the average position, similar to a classical random walk. Along each quantum trajectory, the particle remains localized, however with a modified localization length. In contrast to measurement-induced delocalization, controlled measurements can be used to introduce transport in the system and localize the particle at a chosen site. In this sense, the measurements provide a controlled environment for the particle.

14 pages, 10 figures. Comments welcome

References in corpus (4)

• Anderson Transitions
• Detection of a quantum particle on a lattice under repeated projective measurements
• Entanglement transitions with free fermions
• Entanglement negativity in a fermionic chain with dissipative defects: Exact results

Cited by in corpus (15)

• Theory of free fermions under random projective measurements
• Disordered monitored free fermions
• Localization properties in disordered quantum many-body dynamics under continuous measurement
• Entanglement phases, localization and multifractality of monitored free fermions in two dimensions
• Quantum criticality under imperfect teleportation
• Localization, fractality, and ergodicity in a monitored qubit
• Quantifying measurement-induced quantum-to-classical crossover using an open-system entanglement measure
• Unscrambling of single-particle wave functions in systems localized through disorder and monitoring
• Measurement Induced Chirality II: Diffusion and Disorder
• Multifractality in monitored single-particle dynamics
• Measurement-induced phase transitions for free fermions in a quasiperiodic potential
• Effect of the readout efficiency of quantum measurement on the system entanglement
• Enhanced localization in the prethermal regime of continuously measured many-body localized systems
• Motion from Measurement: The Role of Symmetry of Quantum Measurements
• Fractionally Quantized Recurrence Detection Times in Monitored Quantum Many-Body Systems