UnRAVElling the dynamics of many-body open systems: Collective dynamics of quantum trajectories

Project Information

RAVE

Grant agreement ID: 101053159

DOI

10.3030/101053159

EC signature date 30 May 2022

Start date 1 November 2022

End date 31 October 2027

Funded under

• European Research Council (ERC)

Total cost

€ 1 075 000,00

EU contribution

€ 1 075 000,00

Coordinated by

UNITED NATIONS EDUCATIONAL SCIENTIFIC AND CULTURAL ORGANIZATION
France

Periodic Reporting for period 1 - RAVE (UnRAVElling the dynamics of many-body open systems: Collective dynamics of quantum trajectories)

Reporting period: 2022-11-01 to 2025-04-30

Summary of the context and overall objectives of the project

The influence of an external environment on the dynamics of quantum systems has been a central question since the early days of quantum theory. With the flourishing of quantum information processing, the study of open quantum system dynamics has become of paramount importance for the ultimate success of quantum technologies. The phenomenology becomes increasingly rich in quantum systems with many degrees of freedom. RAVE is devoted to the study of collective phenomena in synthetic, many-body open quantum systems through investigation of the dynamics of quantum trajectories. Following the dynamics at the level of its trajectories will capture features that are washed out by looking at averaged observables, i.e. encoded in the density matrix, therefore leading to a much richer characterization of the many-body phases of a quantum system coupled to its external environment. The goal of RAVE is to study collective phenomena visible only in the dynamics of single trajectories, and propose experimental schemes to observe them.
The development of stochastic thermodynamics in the last decades has enabled the description of work, heat and entropy production at the level of single trajectories in non-equilibrium processes; this has led to the discovery of universal relations constraining the statistics of fluctuating quantities. These questions have never been considered in a many-body context. RAVE will address these aspects to further explore the relation between entanglement, correlations and non-equilibrium thermodynamics.
The statistics associated with the behavior of quantum jumps in many-body systems is also important for characterizing the quality and performance of quantum information processing protocols. RAVE's objective here is, among others, to explore the properties of time-crystals and its connection to quantum synchronization.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The discovery of measurement-induced phase transitions in quantum circuits with measurements has opened the way to investigate phenomena that are invisible to the dynamics of the density matrix. The objective of RAVE is to show that this phenomenology is generic to any many-body open system, leading to a much richer classification of phases and phase transitions. This possibility is however hampered by the enormous difficulty in finding efficient methods to monitor open many-body systems.
In G. Passarelli et al [Phys. Rev. Lett. 132, 163401 (2024)] we found an experimentally accessible system where the post-selection barrier can be avoided. Motivated by these encouraging results we further explored the idea that long-range systems could be an interesting option for post-selection mitigated dynamics. In A. Delmonte et al [arXiv:2010.05394] we performed a thorough investigation of monitored dynamics and phase transitions in a variety of infinite-range systems. The analysis of generic long-range systems required to develop new computational techniques [Z. Li, et al arXiv:2405.12124 submitted to Nat. Comm. and A. Lerose et al, arXiv:2309.12504 to be published in Phys. Rev. X]. A detailed analysis of the full counting statistics as a probe of the entanglement transition has been performed in [E. Tirrito et al, SciPost Phys. 15, 096 (2023)].
In parallel, we wanted to further characterize the properties of entanglement transition. In particular, we concentrated on the role of interacting systems, a case that is very hard to address analytically. For this reason, we resorted to a detailed numerical analysis [L. Lumia et al, Phys. Rev. Research 6, 023176 (2024) and B. Xing et al, Phys. Rev. B 109, L060302 (2024)]. The deep connection between the measurement-induced transition and the associated complexity of the two different phases has been explored in [G. Fux et al, Phys. Rev. Research 6, L042030 (2024) and G. Passarelli et al, Phys. Rev. A 110, 022436 (2024)] where we found a new phase transition between a power law and constant scaling of non-stabilizerness. The same circuit also exhibits a phase transition in entanglement that appears, however, at a different critical measurement rate. A further analysis of these types of circuits [G. Fux et al, arXiv:2410.09001 submitted to Phys. Rev. Lett.] might lead to considerable improvement in our ability to perform classical simulations of many-body systems.
The planned work on adiabatic computation and the statistics of trajectories was performed in [L. Viotti et al, Quantum 7, 1029 (2023)], we studied the statistics of geometric phases along quantum trajectories. During these two years, we also completed a review article on the properties of many-body open systems [R. Fazio et al, arXiv:2409.10300 submitted to SciPost]
Concerning time crystals, we first extended [A. Delmonte et al, Physical Review A 108 (3), 032219 (2023)] the Kuramoto model to the quantum domain. We then started to study how time crystals can serve for sensing and clocks[F. Iemini, R. Fazio, and A. Sanpera, Phys. Rev. A 109, L050203 (2024); Gribben et al, arXiv:2406.06273 submitted to SciPost] .

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Most significant publications
1) G. Passarelli, X. Turkeshi, A. Russomanno, P. Lucignano, M. Schirò, and R. Fazio, Phys. Rev. Lett. 132, 163401 (2024).
2) D. Rattacaso, G. Passarelli, A. Russomanno, P. Lucignano, G.E. Santoro, and R. Fazio, Phys. Rev. Lett. 132, 160401 (2024).
3) A. Lerose, T. Parolini, R. Fazio, D. Abanin, and S. Pappalardi, arXiv:2309.12504 to be published in Phys. Rev. X
4) Z. Li, A. Delmonte, X. Turkeshi, and R. Fazio, arXiv:2405.12124 submitted to Nat. Comm.
5) G. Fux, B. Beri, R. Fazio, and E. Tirrito, arXiv:2410.09001 submitted to Phys. Rev. Lett.


- The series of works on post-selection free/mitigated systems is a relevant result in view of the experimental investigation of monitored many-body systems. In these three works, [G. Passarelli et al, Phys. Rev. Lett. 132, 163401 (2024); A. Delmonte et al, arXiv:2010.05394 submitted to Phys. Rev. Research; Z. Li, et al arXiv:2405.12124 submitted to Nat. Comm.], we succeeded in finding an experimentally accessible system where the post-selection barrier could be avoided.
Infinite-range models can easily realized in laboratories, we made a detailed analysis of possible experimental challenges and we are confident that the statistics of observables evolving along trajectories can be observed in the near future. Besides entanglement, we also investigated higher moments in the fluctuations of the emitted photons and saw that these can be used as witnesses of measurement-induced transition.

- The method developed in [Z. Li, et al arXiv:2405.12124 submitted to Nat. Comm.] to study monitored long-range systems. The method, based on a stochastic version of spin-wave expansion has several merits and can be of great importance in several different experimentally relevant regimes. From a theoretical point of view the method i) is very accurate for long- and medium-range interacting systems, ii) it allows to address both linear and non-linear (in the quantum state) quantities, thus offering the possibility of a full state characterization of the steady-state and the dynamics to reach it, iii) it is computational advantageous allowing to study d-dimensional systems also in the volume-law phase, iv) through a combination with a classical analysis of the output data, it allows to avoid post-selection.