Syllabi

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Metrology and sensing

Academic year: 2024/25

Semester: 1

CFU: 6

Hours: 45

 Teachers

 Syllabus

  1. Random Variables and Stochastic Processes (2+1 CFU)
    • Basic concepts of probability. Introduction to random variables.
    • Discrete random variables (binomial, ipergeometric, geometric and Poisson distributions).
    • Continuous random variables (normal, gamma, exponential, chi-square distributions).
    • Convergence in probability and Law of large numbers; convergence in law and central limit theorem.
    • Introduction to stochastic processes. Discrete-time Markov chain on a finite state space.
    • Metropolis algorithm and simulated annealing. Brownian motions and stationary processes.
  2. Metrology and Quantum Sensing (2+1 CFU)
    • Introduction to quantum measurements.
    • Projective measurements and positive operator valued measures.
    • Measurement backaction and sequential measurements.
    • Weak post-selected measurements and continuous measurements.
    • Quantum state reconstruction via two sequential or joint measurements
    • Classical and quantum estimation theory.
    • The second quantum revolution.
    • Quantum sensing and quantum sensors: definitions.
    • Approaches for quantum sensing (Neutral atoms, Trapped ions, Rydberg Atoms, solid-state spins, superconducting circuits, photons, plasmons), principles and protocols.
    • Quantum sensing based on spectroscopy.
    • Quantum sensitivity and noise.
    • Exploitation of nanostructured systems, molecular systems and photon towards environmental and biomedical quantum sensing.
    • Experimental realizations and some results.
    • The NV centers in diamond.

 Bibliography

  1. Random Variables and Stochastic Processes
    1. V. Romano, Metodi Matematici per i Corsi di Ingegneria, CittàStudi
    2. A. Rotondi, P. Pedroni, A. Pievatolo, Probabilità Statistica e Simulazione, Springer
    3. Appunti del docente.
  2. Metrology and Quantum Sensing
    1. J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, ch.1 and 2
    2. J. von Neumann, Mathematical Foundations of Quantum Mechanics, ch. 5 and 6
    3. V. B. Braginsky and F. Ya Khalili, Quantum Measurement, ch. 2, 3, 5, and 6
    4. H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control, ch. 1 and 2
    5. C. W. Helstrom, Quantum Detection and Estimation Theory, ch. 2, 4 and 8
  3. Additional Text
    1. Y. Aharonov, D.Z. Albert, and L. Vaidman, How the Result of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to be 100, PRL 60, 1351.
    2. I. M. Duck, P. M. Stevenson, and E.C.G. Sudarshan, The sense in which a \"weak measurement\" of a spin-1/2 particle\'s spin component yields a value 100, PRD 40, 2112.
    3. R. Jozsa, Complex weak values in quantum measurement, PRA 76, 044103.
    4. A. Di Lorenzo, Quantum state tomography from sequential measurement of two variables in a single setup, PRA 88, 042114.

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