Ordinary call: orientations and renunciation

En caso de que las condiciones sanitarias impidan la realización de

una evaluación presencial, se activará una evaluación no presencial de

la que será informado el alumnado puntualmente.

Temary

I. Ultra-cold atoms in optical lattices, Superconducting quantum technologies



- Quick Review on Optical lattices potentials. 1D optical lattice: a standing wave. Square and cubic lattices. Reminder on band theory. Bloch’s theorem and Bloch’s waves. Band structure. Wannier functions. Very deep lattices: disconnected harmonic wells. Tight-binding limit. Square and cubic lattices. Dynamics of a Bose-Einstein condensate in an optical lattice. Adiabatic loading. Time of flight. Band mapping. Superfluid-Mott insulator transition.



- Single-electron effects. Plasma oscillation. Quantum LC oscillator: harmonic oscillator. Driven LC oscillator. Coherent states. Coupled LC resonators. Bogoliubov transformation. Modes of transmission lines resonators. Semi-infinite transmission lines, dissipation and input/output theory. Superconducting qubits. Quick review of the Josephson effect. The Cooper pair box. Inductively shunted qubits. The 0-pi qubit. Noise and decoherence. Rate equation analysis: two-level systems. Noise induced decoherence in qubit circuits. Density matrix description of decoherence. Circuit QED.





II. NV centers, Trapped ions



- Quantum control. Two-level systems quantum control. The rotating wave approximation. Electron spin resonances. Coherent electron-nucleus couplings. The nitrogen vacancy center in diamond. Quantum sensing and polarization. Dynamical decoupling techniques.



- Quantum information processing.

Trapped ion systems. Laser-driven and microwave-driven setups. Controlled entanglement generation in trapped ions for quantum computing.

Bibliography

Basic bibliography

Part I.



R. Grimm et al., Optical dipole traps for neutral atoms, Adv. At. Mol. Opt. Phys. 42, 95 (2000).

G. Grynberg and C. Robilliard, Cold atoms in dissipative optical lattices, Phys. Rep. 355, 335 (2001). I. Bloch et al., Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).

I. Bloch et al., Quantum simulations with ultracold quantum gases, Nat. Phys. 8, 267 (2012).

Makhlin et al., Quantum-state engineering with Josephson-junction devices, Rev. Mod. Phys. 73, 357 (2001).

Blais et al., Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69, 062320 (2004).

Clerk et al., Introduction to quantum noise, measurement and amplification, Rev. Mod. Phys (2008).

M. Devoret, Quantum Fluctuations in Electrical Circuits, Les Houches, Session LXIII 1995, Elsevier 1997.

S. Girvin, Circuit QED: Superconducting Qubits Coupled to Microwave Photons.



Part II.



Malcom H. Levitt, Spin dynamics: Basics of Nuclear Magnetic Resonance (Wiley, 2008).

Nitrogen-Vacancy Centers in Diamond: Nanoscale Sensors for Physics and Biology (2014).

Programmable quantum simulations of spin systems with trapped ions (2021).