2 research outputs found
Many-body quantum chaos in stroboscopically-driven cold atoms
Seeking signatures of quantum chaos in experimentally realizable many-body
systems is of vigorous interest. In such systems, the spectral form factor
(SFF), defined as the Fourier transform of two-level spectral correlation
function, is known to exhibit random matrix theory (RMT) behaviors, namely a
'ramp' followed by a 'plateau' in sufficiently late time. Recently, a generic
early-time deviation from the RMT behavior, which we call the 'bump', has been
shown to exist in random quantum circuits and spin chains as toy models for
many-body quantum chaotic systems. Here we demonstrate the existence of the
'bump-ramp-plateau' behavior in the SFF for a number of paradigmatic,
stroboscopically-driven cold atom models of interacting bosons in optical
lattices and spinor condensates. We find that the scaling of the many-body
Thouless time -- the time of the onset of the (RMT) ramp
behavior -- and the increase of the bump amplitude in atom number are
significantly slower in (effectively 0D) chaotic spinor gases than in 1D
optical lattices, demonstrating the role of locality in many-body quantum
chaos. Moreover, scaling and the bump amplitude are more
sensitive to variations in atom number than the system size regardless of the
hyperfine structure, the symmetry classes, or the choice of the driving
protocol. We obtain scaling functions of SFF which suggest power-law behavior
for the bump regime in quantum chaotic cold-atom systems. Finally, we propose
an interference measurement protocol to probe SFF in the laboratory.Comment: 10 pages, 7 figures, supplementary materia
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