Laboratoire de Physique Théorique
Toulouse - UMR 5152

This talk is a "tapas selection", reviewing recent advances in the design of shortcuts to adiabaticity in many-body systems.
 Adiabatic invariants, and the inversion of dynamical scaling laws, will be applied to trapped ultracold gases [1-3]. In particular, a proposal will be discussed to drive controlled expansions in which quantum correlations are preserved, essentially realizing a quantum dynamical microscope [2,3].
 Controlling the dynamics through a quantum phase transition implies an additional challenge : to prevent the formation of excitations in spite of the critical slowing down in the neighborhood of the critical point. According to the Kibble-Zurek mechanism, in inhomogeneous systems with a spatially varying critical point, whenever the speed of the spatial front crossing the transition is lower than the sound velocity excitations can be completely suppressed [4,5]. Experimentally, this scenario has recently been explored in ion Coulomb crystals [6].
 An alternative approach in quantum critical systems exploits recent advances in the simulation of coherent $k$-body-interactions and transitionless quantum driving [7,8,9]. This method is ideally suited to access the ground state manifold in quantum simulators.
 We shall close introducing a generalized time-energy uncertainty relation which is applicable to both isolated and open quantum systems. This relation constitutes a fundamental quantum speed limit for any dynamical process [10].

REFERENCES :

1. X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guery-Odelin, J. G. Muga, Fast optimal frictionless atom coolingin harmonic traps, Phys. Rev. Lett. 104, 063002 (2010) .

2. A. del Campo, Frictionless quantum quenches in ultracold gases : a quantum dynamical microscope, Phys. Rev. A 84, 031606(R) (2011) .

3. A. del Campo, M. G. Boshier, Shortcuts to adiabaticity in a time-dependent box, Sci. Rep. 2, 648 (2012).

4. A. del Campo, G. De Chiara, G. Morigi, M. B. Plenio, A. Retzker, Structural defects in ion crystals by quenching the external potential : the inhomogeneous Kibble-Zurek mechanism, Phys. Rev. Lett. 105, 075701 (2010) .

5. K. Pyka, J. Keller, H. L. Partner, R. Nigmatullin, T. Burgermeister, D. M. Meier, K. Kuhlmann, A. Retzker, M. B. Plenio, W.H. Zurek, A. del Campo, T. E. Mehlstäubler, Symmetry Breaking and Topological Defect Formation in Ion Coulomb Crystals, Nature Communications 4, 2291 (2013)

6. A. del Campo, T. W. B. Kibble, W. H. Zurek, Causality and non-equilibrium second-order phase transitions ininhomogeneous systems, J. Phys. : Condens. Matter 25, 404210 (2013). 7. A. del Campo, M. Rams, W. H. Zurek, Assisted finite-rate adiabatic passage across a quantum critical point : Exact solution for the quantum Ising model, Phys. Rev. Lett. 109, 115703 (2012) 8. A. del Campo, Shortcuts to adiabaticity by counter-diabatic driving, Phys. Rev. Lett. 111, 100502 (2013).

9. S. Deffner, C. Jarzynski, A. del Campo, Classical and quantum shortcuts to adiabaticity for scale-invariant driving, Phys. Rev. X (2014) ; arXiv:1401.1184

10. A. del Campo, I. L. Egusquiza, M. B. Plenio, S. F. Huelga, Quantum speed limits in open system dynamics, Phys. Rev. Lett. 110, 050403 (2013).