Exploring quantum chaos with a single nuclear spin

Abstract

Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to their discrete spectrum. Nonetheless, the dynamics of quantum systems whose classical counterparts are chaotic are expected to show some features that resemble chaotic motion. Among the many controversial aspects of the quantum-classical boundary, the emergence of chaos remains among the least experimentally verified. Time-resolved observations of quantum chaotic dynamics are particularly rare, and as yet unachieved in a single particle, where the subtle interplay between chaos and quantum measurement could be explored at its deepest levels. We present here a realistic proposal to construct a chaotic driven top from the nuclear spin of a single donor atom in silicon, in the presence of a nuclear quadrupole interaction. This system is exquisitely measurable and controllable, and possesses extremely long intrinsic quantum coherence times, allowing for the observation of subtle dynamical behavior over extended periods. We show that signatures of chaos are expected to arise for experimentally realizable parameters of the system, allowing the study of the relation between quantum decoherence and classical chaos, and the observation of dynamical tunneling.

revised and published version

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• Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields
• Exploring quantum chaos with a single nuclear spin
• Photon blockade and the quantum-to-classical transition in the driven-dissipative Josephson pendulum coupled to a resonator
• Measuring out-of-time-ordered correlation functions without reversing time evolution
• Quantum chaos in a Bose-Hubbard dimer with modulated tunnelling
• Coherent control via weak measurements in ${}^{31}$P single-atom electron and nuclear spin qubits
• The effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators
• Hyperfine spectroscopy and fast, all-optical arbitrary state initialization and readout of a single, ten-level ${}^{73}$Ge vacancy nuclear spin qudit in diamond
• Digital Quantum Simulation, Learning of the Floquet Hamiltonian, and Quantum Chaos of the Kicked Top
• Novel characterisation of dopant-based qubits
• Quantum instability and Ehrenfest time for an inverted harmonic oscillator
• Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces
• Quantum Signatures of Chaos in Anisotropic Quantum Rabi Model
• Superradiant-like dynamics by electron shuttling on a nuclear-spin island
• Classical route to quantum chaotic motions
• Long-time signatures of chaos in large atom-light frequency ratios Rabi model
• Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations