Hybrid evolution protocols, composed of unitary dynamics and repeated, weak or projective measurements, give rise to new, intriguing quantum phenomena, including entanglement phase transitions and unconventional conformal invariance. Defying the complications imposed by the non-linear and stochastic nature of the measurement process, we introduce a scenario of measurement-induced many body evolution, which possesses an exact analytical solution: bosonic Gaussian measurements. The evolution features a competition between the continuous observation of linear boson operators and a free Hamiltonian, and it is characterized by a unique and exactly solvable covariance matrix. Within this framework, we then consider an elementary model for quantum criticality, the free boson conformal field theory, and investigate in which way criticality is modified under measurements. Depending on the measurement protocol, we distinguish three fundamental scenarios (a) enriched quantum criticality, characterized by a logarithmic entanglement growth with a floating prefactor, or the loss of criticality, indicated by an entanglement growth with either (b) an area-law or (c) a volume-law. For each scenario, we discuss the impact of imperfect measurements, which reduce the purity of the wavefunction and are equivalent to Markovian decoherence, and present a set of observables, e.g., real-space correlations, the relaxation time, and the entanglement structure, to classify the measurement-induced dynamics for both pure and mixed states. Finally, we present an experimental tomography scheme, which grants access to the density operator of the system by using the continuous measurement record only.
Cited by 3
Sharma et al., Measurement-induced criticality in extended and long-range unitary circuits
SciPost Phys. Core 5, 023 (2022) [Crossref]
Ladewig et al., Monitored open fermion dynamics: Exploring the interplay of measurement, decoherence, and free Hamiltonian evolution
Phys. Rev. Research 4, 033001 (2022) [Crossref]
Altland et al., Dynamics of measured many-body quantum chaotic systems
Phys. Rev. Research 4, L022066 (2022) [Crossref]
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Vienna Center for Quantum Science and Technology [VCQ]
- 2 Universität zu Köln / University of Cologne [UoC]
- Austrian Science Fund (FWF) (through Organization: Fonds zur Förderung der wissenschaftlichen Forschung / FWF Austrian Science Fund [FWF])
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]