Synthetic quantum systems

Advanced course given by , Marcello Dalmonte

Term: 0

Start: 28-04-2020 End: 22-05-2020 Room: Online

Credits: 3

Schedule: TBA

Program

Idea of the course: make people familiar with techniques in the field of synthetic quantum systems, in particular cold atom and trapped ion architectures.

Goals: gain the basic tools to understand in some detail experiments in synthetic quantum systems.

Enabling skills: being able to propose a novel technique to realize or probe quantum matter.

Pre-requisites: master equation, a tiny bit of band theory (Bloch theorem), atomic physics (solution of the Hydrogen atom and angular momentum theory), advanced quantum mechanics (including some basics of scattering). I will not cover laser theory.

Add ons: Some of the topics will be illustrated with open source software (qutip).

Modules:

  1. ) Atom–light interactions — review: [2 Lects]
    • atoms in a standing wave: light–matter interactions (single photon quantization, cavity QED basics)
    • laser and sysyphus cooling: how cold is cold?
    • what atoms can and cannot do:
      • spontaneous emission in red/blue detuned lattices
      • scattering properties
      • the magic of SU(N) — where does it come from?
      • [extra] how noisy can a laser be? the real limitation of atoms in optical lattices
    • [if time allows] how to treat dissipation? quantum trajectories
  2. ) Cold atoms in optical lattices: [1 Lect]
    • Basic Hubbard, quantum registers
    • review of experiments; limitations; how to cool
    • observables: correlations, in situ imaging
    • from weak to strong lattices: sine-Gordon–Hubbard crossover
  3. ) Beyond Hubbard: the cold atom Hubbard model toolbox [2 Lects]
    • classical gauge potentials: Jaksch–Zoller and Gerbier–Dalibard approaches
      • finite temperature effects in band structures
      • Floquet approaches (quick review)
    • alkaline-earth–like atoms and SU(N) Hubbard models
    • magnetic atoms and polar molecules: spin and Hubbard physics with dipolar interactions
    • lattice gauge theories and quantum magnets (quick review)
    • advanced probes: can we measure or witness entanglement?
  4. ) Rydberg atoms in optical lattices and tweezers [2 Lects]:
    • basic atomic physics of Rydberg states
    • how to excite atoms to Rydberg states
    • interaction engineering with Rydberg states: frozen regime
    • interaction engineering with Rydberg states: dressing regime
    • interaction engineering with Rydberg states: interactions within the Rydberg manifold (may be skipped)
  5. ) Trapped ions: basics [1.5 Lects]
    • Paul traps, Penning traps, and microtraps
    • cooling ions in a standing wave
    • light–matter interactions: how spins talk to collective modes via light
  6. ) Trapped ions: many-body systems [1.5 Lects]:
    • quantum gates: the Cirac–Zoller controlled-NOT proposal; Molmer–Sorensen entangling gate
    • universal digital quantum simulators: theory and experiments
    • spin models with trapped ions in Paul traps
    • Rydberg ions: available transitions and use for mode shaping

At the end of modules 3, 4 and 6, we will work out a specific example taken from recent literature in some detail.