Quantum many-body theory

Low-temperature atomic systems manifest phenomena that are strikingly different from classical mechanics. Quantum mechanics implies that energy levels are discrete and this is the foundation of the current definition of the second.

Accuracy and precision of optical clocks are entering a regime where not only single-atom quantum mechanics is crucial, but also quantum many-body phenomena play a relevant role. When going beyond mean-field or perturbative theoretical approaches, their study generically requires massively parallel computation on HPC resources.

We are presently investigating:

• the role of ultracold atomic collisions in confined geometries, such as those of optical atomic clocks, to improve their accuracy, by means of quantum Monte Carlo methods;

• the dynamics of ultracold atoms in an optical cavity, as a means to generate entanglement for better precision in quantum metrology, by means of computational libraries such as QuTiP, mean-field approaches such as cumulant expansion, and novel time-dependent quantum Monte Carlo methods;

• the equation of state of trapped ultracold Fermi and Bose gas mixtures;

• the vibrational dynamics of complex molecules

Contact: Gianluca Bertaina

Full list of publications: see here or here

Collaborators:

Stefano Gregorio Giaccari (publications)

Available Master theses:

• Full list of available Master theses / long internships, with references

• Theoretical and computational study of quantum entangled states in a cavity-enhanced optical clock

In this thesis, the candidate will learn and employ theoretical and computational approaches (alternatively the QuTiP Python libraries, the cumulant expansion or time-dependent variational Monte Carlo) to simulate the quantum dynamics of alkaline-earth atoms in an optical lattice embedded in an optical cavity, with the aim to investigate the best parameters to optimize the generation of non classical states (e.g. spin squeezing) and the reduction of the variance of population measurements.

• Quantum Monte Carlo study of interacting cold gases

Cold dilute gases are used for quantum simulation and in optical lattice clocks. Direct interaction between ultracold atoms can be characterized by a few scattering parameters in a partial wave expansion. In spite of the relative simplicity of the theoretical description, the solution of the full many-body Schroedinger equation is a daunting task, that can be efficiently tackled by quantum Monte Carlo simulations. In this thesis, the candidate will develop a quantum Monte Carlo code for the massively parallel computation of the equation of state and structural properties of interacting Fermi or Bose gases in optical traps, possibly investigating their interplay with Rabi coupling to the internal degrees of freedom

Fellowships:

• Andrea Caprotti, INRiM (2022). Funding source: Q-Clocks QuantERA 2017

Generazione di entanglement in atomi freddi accoppiati ad una cavità

Supervisor: Dr. Gianluca Bertaina

Publication: Analysis of spin-squeezing generation in cavity-coupled atomic ensembles with continuous measurements 

PhD students:

• Jacopo D'Alberto, Università degli Studi di Milano (2021-2024)

Supervisor: Prof. Davide E. Galli. Co-supervisor: Dr. Gianluca Bertaina

Publication: Quantum Monte Carlo and perturbative study of two-dimensional Bose-Fermi mixtures 

• Christian Apostoli, Università degli Studi di Milano (2020-2023)

Ab-initio dynamics in strongly interacting many-body systems

Supervisor: Prof. Davide E. Galli. Co-supervisor: Dr. Gianluca Bertaina

Publication: Spectrum of density, spin, and pairing fluctuations of an attractive two-dimensional Fermi gas 

Master theses:

• Giulia Dellea, Università degli Studi di Milano (2024)

Adiabatic elimination in a cavity-coupled open atomic system beyond the leading order

Supervisors: Prof.  Marco G. Genoni, Dr. Gianluca Bertaina

• Davide Barbiero, Università degli Studi di Milano (2023)

Anharmonicity and quantum effects in the vibrational spectroscopy and kinetics of challenging molecular systems

Supervisor: Dr. Riccardo Conte. Co-supervisor: Dr. Gianluca Bertaina

Publication: Anharmonic Assignment of the Water Octamer Spectrum in the OH Stretch Region 

• Nitya Cuzzuol, Università degli Studi di Bologna (2022)

Quantum Monte Carlo Study of Effective Masses in a Polarized Unitary Fermi Gas

Supervisor: Prof. Pierbiagio Pieri. Co-supervisor: Dr. Gianluca Bertaina

• Andrea Caprotti, Università degli Studi di Milano (2022)

Theoretical modeling and simulation of the generation of spin-squeezed states for quantum enhanced atomic clocks

Supervisors: Prof.  Marco G. Genoni, Dr. Gianluca Bertaina. Co-supervisor: Dr. Marco G. Tarallo

Publication: Analysis of spin-squeezing generation in cavity-coupled atomic ensembles with continuous measurements 

• Jacopo D'Alberto, Università degli Studi di Bologna (2021)

Study of a 2D Bose-Fermi mixture with Quantum Monte Carlo methods

Supervisor: Prof. Pierbiagio Pieri, Co-supervisor: Dr. Gianluca Bertaina

Publication: Quantum Monte Carlo and perturbative study of two-dimensional Bose-Fermi mixtures 

• Christian Apostoli, Università degli Studi di Milano (2020)

Study of ultracold Rydberg gases via the multiconfiguration time-dependent approach

Supervisor: Prof. Davide E. Galli. Co-supervisor: Dr. Gianluca Bertaina

Publication: Evolution of static and dynamical density correlations of one-dimensional soft-core bosons from the Tonks-Girardeau limit to a clustering fluid 

Internships during Master:

• Mirko Quarto, Laurea in Ingegneria Matematica, Politecnico di Torino (2025)

• Alessandro Di Grazia, Laurea in Ingegneria Matematica, Politecnico di Torino (2025)

Bachelor theses:

• Tommaso Peritore, Università degli Studi di Milano (2024)

Simulation of spin squeezing dynamics in long-range Ising models

Supervisors: Prof. Davide E. Galli, Dr. Gianluca Bertaina. Co-supervisor: Dr. Christian Apostoli

• Stefano Lonardoni, Università degli Studi di Milano (2024)

Efficient parallelization of quantum trajectories with the open time-dependent variational Monte Carlo algorithm

Supervisors: Prof. Davide E. Galli, Dr. Gianluca Bertaina. Co-supervisor: Dr. Christian Apostoli

Internships during Bachelor:

• Vincenzo Fogliani, Laurea in Ingegneria Fisica, Politecnico di Torino (2023)

Quantum Monte Carlo Methods for trapped Fermionic and Bosonic Particles

Former collaborators:

Andrea Caprotti (now PhD University of Vienna, ORCID)

Funding

2024-2027 Metrology Partnership 23FUN02 "Controlled confinement to reduce the inaccuracy of clocks based on optical lattices" (CoCoRICO) (Tarallo)

2023-2025 Ministero dell'Università e della Ricerca PRIN "Efficient simulation and design of quantum CONtrol sTRategies for mAny-Body quAntum SystemS" (CONTRABASS) (UNIMI: Prof. M. Genoni, INRIM: G. Bertaina)

EU QuantERA Q-Clocks (Levi, Tarallo)

EMPIR USOQS (Levi, Tarallo)

Computational Resources

2025 Principal Investigator of the CINECA-Iscra C grant “SDOQS”, consisting of 32500 cpu-hours on the GALILEO100 supercomputing facility 

2023 Principal Investigator of the CINECA-Iscra C grant “PSIOQUAS”, consisting of 33000 cpu-hours on the GALILEO100 supercomputing facility

2021 Contributor to the CINECA-Iscra C grant “BF2D”, consisting of 32000 cpu-hours on the M100 supercomputing facility