Quantum scrambling describes the spreading of local information into many degrees freedom in quantum systems. This provides conceptual connection among diverse phenomena ranging from thermalizing dynamics to models black holes. Here we experimentally probe exponential a multi-particle system near bistable point phase space and utilize it for entanglement-enhanced metrology. We use time-reversal protocol observe simultaneous growth both metrological gain out-of-time-order correlator, thereby...

In this work, the term “quantum chaos” refers to spectral correlations similar those found in random matrix theory. Quantum chaos can be diagnosed through analysis of level statistics using, e.g., form factor, which detects both short- and long-range correlations. The factor corresponds Fourier transform two-point correlation function exhibits a typical slope-dip-ramp-plateau structure (aka hole) when system is chaotic. We discuss how could detected quench dynamics two physical quantities...

Quantum chaos refers to signatures of classical found in the quantum domain. Recently, it has become common equate exponential behavior out-of-time order correlators (OTOCs) with chaos. The quantum-classical correspondence between OTOC growth and limit indeed been corroborated theoretically for some systems there are several projects do same experimentally. Dicke model, particular, which a regular chaotic regime, is currently under intense investigation by experiments trapped ions. We show,...

Ergodicity of quantum dynamics is often defined through statistical properties energy eigenstates, as exemplified by Berry's conjecture in single-particle chaos and the eigenstate thermalization hypothesis many-body settings. In this work, we investigate whether systems can exhibit a stronger form ergodicity, wherein any time-evolved state uniformly visits entire Hilbert space over time. We call such phenomenon complete Hilbert-space ergodicity (CHSE), which more akin to intuitive notion an...

The maximum entropy principle is foundational for statistical analyses of complex dynamics. This has been challenged by the findings a previous work [Phys. Rev. X 7, 031034 (2017)], where it was argued that quantum system driven in time certain aperiodic sequence without any explicit symmetries, dubbed Thue-Morse drive, gives rise to emergent nonergodic steady states which are underpinned effective conserved quantities. Here, we resolve this apparent tension. We rigorously prove drive...

We compare the entire classical and quantum evolutions of Dicke model in its regular chaotic domains. This is a paradigmatic interacting spin-boson great experimental interest. By studying survival probabilities initial coherent states, we identify features long-time dynamics that are purely discuss their impact on equilibration times. show ratio between asymptotic values probability serves as metric to determine proximity separatrix regime distinguish two manifestations chaos: scarring...

We present a detailed analysis of the connection between chaos and onset thermalization in spin-boson Dicke model. This system has well-defined classical limit with two degrees freedom, it presents both regular chaotic regions. Our studies eigenstate expectation values distributions off-diagonal elements number photons excited atoms validate diagonal hypothesis (ETH) region, thus ensuring thermalization. The validity ETH reflects structure eigenstates, which we corroborate using von Neumann...

Abstract As the name indicates, a periodic orbit is solution for dynamical system that repeats itself in time. In regular regime, orbits are stable, while chaotic they become unstable. The presence of unstable directly associated with phenomenon quantum scarring, which restricts degree delocalization eigenstates and leads to revivals dynamics. Here, we study Dicke model superradiant phase identify two sets fundamental orbits. This experimentally realizable atom–photon at low energies high...

In this work, we use the term ``quantum chaos'' to refer spectral correlations similar those found in random matrix theory. Quantum chaos can be diagnosed through analysis of level statistics using form factor, which detects both short- and long-range correlations. The factor corresponds Fourier transform two-point correlation function exhibits a typical slope-dip-ramp-plateau structure (aka hole) when system is chaotic. We discuss how could detected dynamics two physical quantities...

Measuring the degree of localization quantum states in phase space is essential for description dynamics and equilibration systems, but this topic far from being understood. There no unique way to measure localization, individual measures can reflect different aspects same state. Here we present a general scheme define spaces, which based on what call R\'enyi occupations, any be derived. We apply four-dimensional unbounded interacting spin-boson Dicke model. In particular, make detailed...

There is no unique way to quantify the degree of delocalization quantum states in unbounded continuous spaces. In this work, we explore a recently introduced localization measure that quantifies portion classical phase space occupied by state. The based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&amp;#x03B1;</mml:mi></mml:math>-moments Husimi function and known as Rényi occupation order...

Abstract In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to point of the available phase space after long time, filling it uniformly. Using Born’s rules connect quantum states with probabilities, one might then expect all in regime should uniformly distributed space. This simplified picture was shaken by discovery scarring, where some eigenstates are concentrated along unstable periodic orbits. Despite that, widely accepted most models indeed...

By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces finite effective dimension in infinite-dimensional Hilbert space. We compare our general expressions with numerical results for the spin-boson Dicke model chaotic energy regime, restricting its four-dimensional to classically shell. This can be employed characterize quantum phenomena systems, such as localization and scarring.

Quantum scrambling describes the spreading of local information into many degrees freedom in quantum systems. This provides conceptual connection among diverse phenomena ranging from thermalizing dynamics to models black holes. Here we experimentally probe exponential a multi-particle system near bistable point phase space and utilize it for entanglement-enhanced metrology. We use time-reversal protocol observe simultaneous growth both metrological gain out-of-time-order correlator, thereby...

Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes dynamics, including driven systems, has not been fully established. Here we introduce and study notion for closed systems with time-dependent Hamiltonians, defined as statistical randomness exhibited in their long-time dynamics. Concretely, consider the temporal ensemble states (time-evolution operators) generated by evolution, investigate conditions necessary them be statistically...

This review article describes major advances associated with the Dicke model, starting in 1950s when it was introduced to explain transition from a normal superradiant phase. Since then, this spin-boson interacting model has raised significant theoretical and experimental interest various contexts. The present focuses on isolated version of covers properties phenomena that are better understood seen both classical quantum perspectives, particular, onset chaos, localization, scarring.

Quantum thermalization describes how closed quantum systems can effectively reach thermal equilibrium, resolving the apparent incongruity between reversibility of Schr\"odinger's equation and irreversible entropy growth dictated by second law thermodynamics. Despite its ubiquity conceptual significance, a complete proof has remained elusive for several decades. Here, we prove that must occur in any qubit system with local interactions satisfying three conditions: (i) high effective...

Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes dynamics, including driven systems, has not been fully established. Here we introduce and study notion for closed systems with time-dependent Hamiltonians, defined as statistical randomness exhibited in their longtime dynamics. Concretely, consider the temporal ensemble states (time-evolution operators) generated by evolution, investigate conditions necessary them be statistically...

Ergodicity of quantum dynamics is often defined through statistical properties energy eigenstates, as exemplified by Berry's conjecture in single-particle chaos and the eigenstate thermalization hypothesis many-body settings. In this work, we investigate whether systems can exhibit a stronger form ergodicity, wherein any time-evolved state uniformly visits entire Hilbert space over time. We call such phenomenon complete Hilbert-space ergodicity (CHSE), which more akin to intuitive notion an...

We present a detailed analysis of the connection between chaos and onset thermalization in spin-boson Dicke model. This system has well-defined classical limit with two degrees freedom, it presents both regular chaotic regions. Our studies eigenstate expectation values distributions off-diagonal elements number photons excited atoms validate diagonal hypothesis (ETH) region, thus ensuring thermalization. The validity ETH reflects structure eigenstates, which we corroborate using von Neumann...

Resumen.En este artículo presentamos el teorema de Haar inverso, originalmente demostrado por Weil en 1940.El garantiza que grupos equipados con cierta topología, siempre existe una medida no cambia al trasladarla medio la operación del grupo, es decir, invariante.Esta -llamada Haar-guarda relación estrecha topología grupo.El inverso que, cierto sentido, todas las medidas invariantes son Haar.Dado un grupo -sin

By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces finite effective dimension in infinite dimensional Hilbert space. We compare our general expressions with numerical results for the spin-boson Dicke model chaotic energy regime, restricting its four-dimensional to classically shell. This can be employed characterize quantum phenomena systems, such as localization and scarring.