Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives

Ergodicity of quantum dynamics is often defined through statistical properties of energy eigenstates, as exemplified by Berry's conjecture in single-particle quantum chaos and the eigenstate thermalization hypothesis in many-body settings. In this work, we investigate whether quantum systems can exhibit a stronger form of ergodicity, wherein any time-evolved state uniformly visits the entire Hilbert space over time. We call such a phenomenon complete Hilbert-space ergodicity (CHSE), which is more akin to the intuitive notion of ergodicity as an inherently dynamical concept. CHSE cannot hold for time-independent or even time-periodic Hamiltonian dynamics, owing to the existence of (quasi)energy eigenstates which precludes exploration of the full Hilbert space. However, we find that there exists a family of aperiodic, yet deterministic drives with minimal symbolic complexity -- generated by the Fibonacci word and its generalizations -- for which CHSE can be proven to occur. Our results provide a basis for understanding thermalization in general time-dependent quantum systems.Comment: 6 pages, 3 figures (main text); 14 pages, 3 figures (supplemental material

Improving Metrology with Quantum Scrambling

Quantum scrambling describes the fast spreading of quantum information into many degrees of freedom of a many-body quantum system. This concept embraces many apparently unconnected phenomena such as the thermalization of closed quantum systems, the growth of entanglement, and the black-hole information paradox. The fastest scramblers disperse the information exponentially quickly into the system's degrees of freedom. Out-of-time-order correlators (OTOCs) have been invented as a mean to characterize quantum scrambling. To experimentally probe OTOCs, it is necessary to reverse the sign of the many-body Hamiltonian, effectively evolving the system backwards in time, a technique that has also been shown as powerful for entanglement-enhanced metrology. However, despite experimental progress, to date no exponentially fast scrambling of quantum information has been experimentally demonstrated. Here we probe the exponential scrambling nature of the Lipkin-Meshkov-Glick (LMG) many-body Hamiltonian. We measure an exponentially growing OTOC; moreover, we elucidate and experimentally validate the close conceptual relation between quantum information scrambling and quantum-enhanced metrology. Our experiment paves the way to the investigation of quantum chaos and scrambling in controlled tabletop experiments. Moreover, we demonstrate that entanglement-enhanced quantum metrology can be performed with general fast-scrambling Hamiltonians capable of generating entanglement exponentially quickly.Comment: 6 pages, 5 figure

Chaos and Thermalization in the Spin-Boson Dicke Model

We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called “efficient basis” over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis