Quantum Measurements on Localized Particles

Christian Beck

Ian Colin Percival, B. M. Garraway

Pushkar Mohile, Paul M. Goldbart

Proximity measurements probe whether pairs of particles are close to one another. We consider the impact of post-selected random proximity measurements on a quantum fluid of many distinguishable particles. We show that such measurements induce random spatial localization of a fraction of the particles, and yet preserve homogeneity macroscopically. Eventually, all particles localize, with a distribution of localization lengths that saturates at a scale controlled by the typical measurement rate. The steady-state distribution of these lengths is governed by a familiar scaling form.

Paul Pöpperl, I. V. Gornyi, Yuval Gefen

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 behavior 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.

Meinard Kuhlmann

Sandu Popescu, Nicolas Gisin