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Scientific School Dynamics of Complex Networks and their Applications (DCNA)

Chaos and hyperchaos in a chain of coupled Rydberg atoms

Alexander G. Balanov, Andrey V. Andreev

Published Sep 1, 2019• 0 citations
Publisher

Abstract

Partially quantum coherent arrays of artificial atoms (e.g., superconducting qubits) may be used as analogue simulators of other quantum systems, when the behaviour of the latter cannot be directly observed or modeled by classical means. Here we show that a chain of superconducting qubits can simulate the chaotic behaviour predicted in chains of Rydberg atoms. We investigate the transition from periodic to chaotic dynamics and show the increase of the number of positive Lyapunov exponents as the number of atoms grows. The possibility of an external control and suppression of hyperchaos in the chain is demonstrated.

DOI
10.1109/dcnair.2019.8875616

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Partially quantum coherent arrays of artificial atoms (e.g., superconducting qubits) may be used as analogue simulators of other quantum systems, when the behaviour of the latter cannot be directly observed or modeled by classical means. Here we show that a chain of superconducting qubits can simulate the chaotic behaviour predicted in chains of Rydberg atoms. We investigate the transition from periodic to chaotic dynamics and show the increase of the number of positive Lyapunov exponents as the number of atoms grows. The possibility of an external control and suppression of hyperchaos in the chain is demonstrated.
Progress in the creation of large scale, artificial quantum coherent structures demands the investigation of their nonequilibrium dynamics when strong interactions, even between remote parts, are non-perturbative. Analysis of multiparticle quantum correlations in a large system in the presence of decoherence and external driving is especially topical. Still, scaling behaviour of dynamics and related emergent phenomena are not yet well understood. We investigate how the dynamics of a driven system of several quantum elements (e.g., qubits or Rydberg atoms) changes with increasing number of elements. Surprisingly, a two-element system exhibits chaotic behaviours. For larger system sizes a highly stochastic, far from equilibrium, {\em hyperchaotic} regime emerges. Its complexity systematically scales with the size of the system, proportionally to the number of elements. Finally, we demonstrate that these chaotic dynamics can be efficiently controlled by a periodic driving field. The insights provided by our results indicate the possibility of a reduced description for the behaviour of a large quantum system in terms of the transitions between its qualitatively different dynamical regimes, which are controlled by a relatively small number of parameters, and may prove useful in the design, characterization and control of large artificial quantum structures.
We study the chaos and hyperchaos of Rydberg-dressed Bose–Einstein condensates (BECs) in a one-dimensional optical lattice. Due to the long-range, soft-core interaction between the dressed atoms, the dynamics of the BECs are described by the extended Bose-Hubbard model. In the mean-field regime, we analyze the dynamical stability of the BEC by focusing on the ground state and localized state configurations. Lyapunov exponents of the two configurations are calculated by varying the soft-core interaction strength, potential bias, and length of the lattice. Both configurations can have multiple positive Lyapunov exponents, exhibiting hyperchaotic dynamics. We show the dependence of the number of the positive Lyapunov exponents and the largest Lyapunov exponent on the length of the optical lattice. The largest Lyapunov exponent is directly proportional to areas of phase space encompassed by the associated Poincaré sections. We demonstrate that linear and hysteresis quenches of the lattice potential and the dressed interaction lead to distinct dynamics due to the chaos and hyperchaos. Our work is relevant to current research on chaos as well as collective and emergent nonlinear dynamics of BECs with long-range interactions.
Abstract Progress in the creation of large-scale, artificial quantum coherent structures demands the investigation of their nonequilibrium dynamics when strong interactions, even between remote parts, are non-perturbative. Analysis of multiparticle quantum correlations in a large system in the presence of decoherence and external driving is especially topical. Still, the scaling behavior of dynamics and related emergent phenomena are not yet well understood. We investigate how the dynamics of a driven system of several quantum elements (e.g., qubits or Rydberg atoms) changes with increasing number of elements. Surprisingly, a two-element system exhibits chaotic behaviors. For larger system sizes, a highly stochastic, far from equilibrium, hyperchaotic regime emerges. Its complexity systematically scales with the size of the system, proportionally to the number of elements. Finally, we demonstrate that these chaotic dynamics can be efficiently controlled by a periodic driving field. The insights provided by our results indicate the possibility of a reduced description for the behavior of a large quantum system in terms of the transitions between its qualitatively different dynamical regimes. These transitions are controlled by a relatively small number of parameters, which may prove useful in the design, characterization, and control of large artificial quantum structures.
The task of sampling the output distribution of random quantum circuits will drive a multiqubit system into chaos, reaching the Porter-Thomas distribution where small multiqubit probabilities appear most often. Such a task is hard to be computed classically and has been proposed as an important measure for quantum supremacy. An equivalent route to reach chaos is the controlled dynamics uniformly exploring the large Hilbert space of coupled qubits, and a proof-of-concept experiment was recently demonstrated by Neill et al. [Science 360, 195 (2018)] in a chain of nine qubits featuring only neighboring couplings. Here, we show numerically that a faster convergence to chaos is possible when full connectivity, instead of partial connectivity, is present among the qubits, i.e., cycles or time required to reach chaotic regime increase only slightly with the number of qubits. We validate the numerical result by carrying out an experiment using up to 12 qubits in a fully connected superconducting quantum processor. Based on a machine learning model, we quantify the evolution error rate to be less than (0.5%/cycle)/qubit, which is mostly determined by qubit dephasing.
The surprisingly long-lasting oscillations observed in the dynamics of highly excited states of chains of Rydberg atoms defy the expectation that interacting systems should thermalize fast. The phenomenon is reminiscent of wavepackets in quantum billiards that trace classical periodic orbits. While analogs of the associated scarred eigenfunctions have been found for Rydberg chains, an underlying classical limit hosting periodic orbits has remained elusive. Here we generalize the Rydberg (pseudospin S=1/2S=1/2S=1/2) system to a chain of arbitrary spin SSS. Its classical limit features unexpectedly stable periodic orbits that are essential to understand the emergence of robust, parametrically suppressed quantum chaoticity, with semi-classical coherence times diverging as S\sqrt{S}S​. The classical limit successfully explains several empirical features of the quantum limit.