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Abstract
A recent experiment by Bordia et al. [P. Bordia et al., Nat. Phys. 13, 5 (2017)] has demonstrated that periodically modulating the potential of a localised many-body quantum system described by the Aubry-André Hamiltonian with on-site interactions can lead to a many-body localisation-delocalisation transition, provided the modulation amplitude is big enough. Here, we consider the noninteracting counterpart of that model in order to explore its phase diagram as a function of the strength of the disordered potential, the driving frequency and its amplitude. We will first of all mimic the experimental procedure of Bordia et al. and use the even-odd sites imbalance as a parameter in order to discern between different phases. Then we compute the Floquet eigenstates and relate the localisation-delocalisation transition to their IPR. Both these approaches show that the delocalisation transition occurs for frequencies that are low compared to the bandwidth of the time independent model. Moreover, in agreement with [P. Bordia et al., Nat. Phys. 13, 5 (2017)] there is an amplitude threshold below which no delocalisation transition occurs. We estimate both the critical values for the frequency and the amplitude.Graphical abstract
Highlights
The study of periodically driven quantum systems has gained interest in the last years
Before moving to the results for the driven lattice we show how the Imbalance behaves around the phase transition for the time independent model
|b(in)|4, i,n calculating the asymptotic Imbalance for different values of the disorder strength λ. It shows how the transition is marked by a nonzero value of the imbalance as a function of λ, at the critical value λc = 2J
Summary
The study of periodically driven quantum systems has gained interest in the last years. One of its most interesting consequences is that it allows to write the evolution over multiples of the driving period in terms of a time independent effective Hamiltonian [1,2] The existence of such an effective Hamiltonian can open the way to the so called Floquet engineering, that is, the possibility to realise non trivial time independent models by periodically modulating a quantum system with a suitable protocol. This concept has been employed very successfully in various experiments with ultracold atoms in driven optical lattices [3]. This includes dynamic localisation [4,5,6,7], “photon”-assisted tunneling [8,9], control of the bosonic superfluid-to-Mott-insulator transition [10,11] and the realisation of artificial magnetic fields [12,13,14,15]
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