Abstract
The behavior of the square lattices of coupled two-level quantum oscillators is investigated. As quantum oscillators, we use the model of Rydberg atoms obtained using the approximation of a fully factorized density matrix. To investigate the behavior of the system the Lyapunov exponents spectra are calculated. Chaos and hyperchaos in the systems are revealed. It was shown that the number of positive Lyapunov exponents almost linearly depends on the number of atoms in the system, at a rate suggesting that adding three atoms leads to the appearance of an additional positive Lyapunov exponent. Using an external parametric effect and continuous feedback is suggested to control the complicated dynamics in the system. Using continuous feedback allows reducing the number of positive Lyapunov exponents from 3 to only 2 while introducing external parametric influence into the system allows reducing their number down to 0 and completely suppresses hyperchaos.
Highlights
Nowadays, the problems of controlling quantum systems with Rydberg atoms are of considerable interest due to the fact that such problems are closely related to the problem of creating quantum computers [Jaksch et al, 2000; Zagoskin, 2011]
We suggest using an external parametric effect and continuous feedback to control the complicated dynamics in the system
We have investigated the behavior of the square lattices of N coupled quantum oscillators (Rydberg atoms) using the calculation of Lyapunov exponents spectra
Summary
The problems of controlling quantum systems with Rydberg atoms are of considerable interest due to the fact that such problems are closely related to the problem of creating quantum computers [Jaksch et al, 2000; Zagoskin, 2011]. The problem of chaotic behavior in a quantum system is of special interest [Ivanchenko et al, 2014; Ostrovskaya and Nori, 2016; Eastman et al, 2017] It is interesting from a practical point of view when solving problems with quantum calculations for clusters of atoms introduced into a solid while in the Rydberg state [Saffman et al, 2010]. Such systems with Rydberg atoms are promising for storing and transmitting information. Feedback allows reducing the number of positive Lyapunov exponents from 3 to only 2 while introducing external parametric influence into the system allows reducing their number down to 0 and completely suppresses hyperchaos
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