Treelike Interactions and Fast Scrambling with Cold Atoms

Abstract

We propose an experimentally realizable quantum spin model that exhibits fast scrambling, based on non-local interactions which couple sites whose separation is a power of 2. By controlling the relative strengths of deterministic, non-random couplings, we can continuously tune from the linear geometry of a nearest-neighbor spin chain to an ultrametric geometry in which the effective distance between spins is governed by their positions on a tree graph. The transition in geometry can be observed in quench dynamics, and is furthermore manifest in calculations of the entanglement entropy. Between the linear and treelike regimes, we find a peak in entanglement and exponentially fast spreading of quantum information across the system. Our proposed implementation, harnessing photon-mediated interactions among cold atoms in an optical cavity, offers a test case for experimentally observing the emergent geometry of a quantum many-body system.

Overlapping two standing waves in a microcavity for a multi-atom photon interface

“…The control of a single atom of the array can be used to generates Schrödinger cat-state [41] or to perform controlled-string operation [42]. Finally, the control over the local coupling at each site between the atoms via the cavity field enable the simulation of specific spin models [19,43].…”

QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: bosons, fermions and higher spins

“…The reason for this often times relies on the fact that the underlying physics of these problems cannot be explained without taking into consideration the contribution from high-energy states excited during the nonequilibrium process. Some prominent examples of such problems include the study of the many-body localisation (MBL) transition [24,25,26,27,28], the Eigenstate Thermalisation hypothesis [29], ergodicity breaking, thermalization and scrambling [30,31,32], quantum quench dynamics [33], periodically-driven systems [34,35,36,37,38,39,40,41,42], non-demolition measurements in many-body systems [43], long-range quantum coherence [44], dynamics-induced instabilities [45,46,47,48,49,50,51,52], adiabatic and counter-diabatic state preparation [53,54,55,56,57], dynamical [58,59] and topological [60] phase transitions applications of Machine Learning to (non-equilibrium) physics [61,49,62,63,64,65,66], optimal control [67,<...>…”

A multipoint conformal block chain in d dimensions

“…In fact, all results presented in this paper also admit a p-adic counterpart -various recent accounts of comparison and translation between objects in the usual (real) and p-adic holographic settings can be found in refs. [48,55,56,71,72,[75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92]. Essentially, to recover the p-adic result, one can truncate all power series expansions featured in this paper to their respective first terms, since the infinite multi-fold series expansions in real CFTs sum up descendant contributions which do not exist in p-adic CFTs.…”