We study the approach to the adiabatic limit in periodically driven systems. Specifically focusing on a spin-1/2 in a magnetic field we find that, when the parameters of the Hamiltonian lead to a quasi-degeneracy in the Floquet spectrum, the evolution is not adiabatic even if the frequency of the field is much smaller than the spectral gap of the Hamiltonian. We argue that this is a general phenomenon of periodically driven systems. Although an explanation based on a perturbation theory in cannot be given, because of the singularity of the zero frequency limit, we are able to describe this phenomenon by means of a mapping to an extended Hilbert space, in terms of resonances of an effective two-band Wannier-Stark ladder. Remarkably, the phenomenon survives in presence of dissipation towards an environment and can be therefore easily experimentally observed.

Floquet resonances close to the adiabatic limit and the effect of dissipation / Russomanno, Angelo; Santoro, Giuseppe E.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2017:10(2017), pp. 1-16. [10.1088/1742-5468/aa8702]

Floquet resonances close to the adiabatic limit and the effect of dissipation

Russomanno, Angelo;Santoro, Giuseppe E.
2017

Abstract

We study the approach to the adiabatic limit in periodically driven systems. Specifically focusing on a spin-1/2 in a magnetic field we find that, when the parameters of the Hamiltonian lead to a quasi-degeneracy in the Floquet spectrum, the evolution is not adiabatic even if the frequency of the field is much smaller than the spectral gap of the Hamiltonian. We argue that this is a general phenomenon of periodically driven systems. Although an explanation based on a perturbation theory in cannot be given, because of the singularity of the zero frequency limit, we are able to describe this phenomenon by means of a mapping to an extended Hilbert space, in terms of resonances of an effective two-band Wannier-Stark ladder. Remarkably, the phenomenon survives in presence of dissipation towards an environment and can be therefore easily experimentally observed.
2017
10
1
16
103104
https://iopscience.iop.org/article/10.1088/1742-5468/aa8702/meta
https://arxiv.org/abs/1707.04508
Russomanno, Angelo; Santoro, Giuseppe E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/87937
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