# Shortcuts to adiabaticity in many-body systems

Adolfo del Campo (Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, USA)

11.07.2012 at 11:00

In this talk, I will review recent theoretical advances in the design of shortcuts to adiabaticity in many-body systems systems by a variety of complementary approaches. Adiabatic invariants, and the inversion of dynamical scaling laws, will be applied to trapped ultracold gases [1-4]. In particular, a proposal will be discussed to realize controlled expansions in harmonic and box-like traps, in which quantum correlations are preserved, essentially realizing a quantum dynamical microscope. The design of shortcuts to adiabaticity is particularly challenging for the dynamics through a quantum phase transition, inextricably woven with the formation of excitations, as a result of the critical slowing down in the neighborhood of the critical point. The paradigmatic theory to capture this dynamics, the Kibble-Zurek mechanism, predicts the formation of excitations no matter how slowly the transition is crossed. We shall show that 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. Trapped ion crystals and thermal atomic clouds will be proposed as a test-bed to study shortcuts to adiabaticity in this scenario [5-7]. Finally, we shall exploit recent advances in the simulation of coherent $k$-body interactions and transitionless quantum driving to explore an alternative to quantum adiabatic protocols, and assist a fully adiabatic finite-rate passage across a quantum critical point in a broad family of many-body systems [8]. This method is ideally suited to access the ground state manifold in quantum simulators.

REFERENCES:

1. X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guery-Odelin, J. G. Muga, Fast optimal frictionless atom cooling in 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, Fast frictionless dynamics as a toolbox for low-dimensional Bose-Einstein condensates, EPL 96, 60005 (2011).

4. A. del Campo, M. G. Boshier, Shortcuts to adiabaticity in a time-dependent box, submitted, arXiv:1201.6627.

5. 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) .

6. G. De Chiara, A. del Campo, G. Morigi, M. B. Plenio, A. Retzker, Spontaneous nucleation of structural defects in inhomogeneous ion chains, New J. Phys. 12, 115003 (2010) .

7. A. del Campo, A. Retzker, M. B. Plenio, Inhomogeneous Kibble-Zurek mechanism: vortex nucleation during Bose-Einstein condensation, New J. Phys. 13, 083022 (2010) .

8. A. del Campo, M. Rams, W. H. Wojciech, Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model, arXiv:1206.2670.

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