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Weak measurement enables the extraction of targeted information from a quantum system while minimizing decoherence due to measurement backaction. However, in many-body quantum systems, backaction can have unexpected effects on wave-function collapse. We theoretically study a minimal many-particle model consisting of weakly measured noninteracting fermions in a one-dimensional lattice. Repeated measurement of the on-site occupation number with single-site resolution stochastically drives the system toward a Fock state, regardless of the initial state. This need not be the case for measurements that do not, even in principle, have single-site spatial resolution. We numerically show for systems with up to 16 sites that decreasing the spatial resolution strongly affects both the rate of stochastic evolution for each quantum trajectory and the allowed final states. The full Hilbert space can be partitioned into backaction-free subspaces (BFSs), the elements of which are indistinguishable for these measurements. Repeated measurements will drive any initial state into a single BFS, leading to a steady state that is a fixed point of the measurement process. We exactly calculate the properties of these BFSs for systems up to 32 sites, and we find that even for moderate reductions in measurement resolution, they yield nontrivial steady-state entanglement and coherence.
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Geometric approach to nonequilibrium hasty shortcuts
Complex and even non-monotonic responses to external control can be found in many thermodynamic systems. In such systems, nonequilibrium shortcuts can rapidly drive the system from an initial state to a desired final state. One example is the Mpemba effect, where preheating a system allows it to cool faster. We present nonequilibrium hasty shortcuts—externally controlled temporal protocols that rapidly steer a system from an initial steady state to a desired final steady state. The term “hasty” indicates that the shortcut only involves fast dynamics without relying on slow relaxations. We provide a geometric analysis of such shortcuts in the space of probability distributions by using timescale separation and eigenmode decomposition. We further identify the necessary and sufficient condition for the existence of nonequilibrium hasty shortcuts in an arbitrary system. The geometric analysis within the probability space sheds light on the possible features of a system that can lead to hasty shortcuts, which can be classified into different categories based on their temporal pattern. We also find that the Mpemba-effect-like shortcuts only constitute a small fraction of the diverse categories of hasty shortcuts. This theory is validated and illustrated numerically in the self-assembly model inspired by viral capsid assembly processes.
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- Award ID(s):
- 2145256
- PAR ID:
- 10593570
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 159
- Issue:
- 8
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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