Periodically driving a many-body localized quantum system

Abstract

We experimentally study a periodically driven many-body localized system realized by interacting fermions in a one-dimensional quasi-disordered optical lattice. By preparing the system in a farfrom-equilibrium state and monitoring the remains of an imprinted density pattern, we identify a localized phase at high drive frequencies and an ergodic phase at low ones. These two distinct phases are separated by a dynamical phase transition which depends on both the drive frequency and the drive strength. Our observations are quantitatively supported by numerical simulations and are directly connected to the change in the statistical properties of the effective Floquet Hamiltonian.Introduction.-Quantum many-body systems far from equilibrium arise naturally in a variety of disciplines, ranging from condensed matter to cosmology. In recent years, there has been an intense focus on understanding the dynamical evolution of quantum manybody systems that are well isolated from their environment [1,2]. Particularly, in periodically driven systems exotic phenomena can emerge that are absent in their undriven counterparts. For example, topologically nontrivial band structures can be realized by driving topologically trivial systems [3][4][5][6][7][8][9] and ergodic phases can be created by driving non-ergodic quantum systems [10][11][12][13][14][15][16].In undriven systems, a robust non-ergodic phase can be realized by adding strong disorder to an interacting many-body system, leading to the phenomenon of manybody localization (MBL) [17][18][19][20][21][22][23][24][25]. In an ideal MBL phase, global transport and thermalization are absent, and some memory of the initial conditions persists locally for arbitrarily long times even at finite energy densities [19,20], as underlined in experiments [22][23][24][25]. Recent theoretical works have further proposed that combining MBL and periodic driving can lead to novel symmetry protected topological phases with no direct equilibrium analogues [26][27][28][29][30][31][32]. It is therefore highly pertinent to experimentally study the interplay of disorder and periodic driving in interacting quantum systems. FIG. 1. Schematic of the experiment and the dynamical phase diagram. (a)A density-wave pattern of spinful fermionic atoms occupying only the even sites of a disordered optical lattice evolves under (b) a periodic modulation of the on-site disorder potentials ∆i with frequency ν and amplitude A. (c) The phase diagram for the strongly driven system (A = ∆) as a function of inverse frequency 1/ν and characteristic disorder strength ∆: In the infinite-frequency limit (x-axis), the disorder-induced phase transition from an ergodic phase to a many-body localized phase is recovered at a critical disorder strength ∆c (black point). While at high but finite drive frequencies the system remains localized for strong disorder, it delocalizes at low drive frequencies. These phases are separated by a drive-induced transition (blue line). In this work, we experimentally study a periodically modul...

Rare‐region effects and dynamics near the many‐body localization transition

“…In the MBL phase, the system consists of essentially isolated two-level systems; again, the initial absorption is linear with a rate ∼ A 2 , but the average absorption of near-resonant two-level systems saturates on a timescale ∼ 1/A [48]. A key distinction between these phases is that in the MBL phase, response is dominated by a small number of resonant transitions (so most degrees of freedom do not heat up at all, and the system enters a Floquet MBL phase, provided the drive is not too strong [27,42,43,48]) whereas in the thermal phase the entire system heats up. The response of a large MBL inclusion (with characteristic timescale τ W/A 2 ) in the thermal phase can be understood by a combination of these effects.…”

“…That such questions can be probed experimentally at all is the result of advances in preparing, controlling and measuring such systems in a variety of platforms, including ultracold atomic [14,15], trapped ion systems [16,17], superconducting qubit arrays [18], NV-centers [19] etc. These developments bring the investigation of outof-equilibrium many-body quantum dynamics within experimental reach; and, indeed, both the failure of thermalization in integrable one-dimensional quantum systems [6,20,21] and the presence of MBL regimes have been experimentally demonstrated [22][23][24][25][26][27].…”

Observation of a discrete time crystal

“…We measure persistent oscillations and synchronizations of interacting spins in a chain and show that the discrete time crystal is rigid, or robust to perturbations in the drive. Our Floquet-MBL system with long-range interactions provides an ideal testbed for out-of-equilibrium quantum dynamics and the study of novel phases of matter that exist only in a Floquet setting [7][8][9][10]30,31 . Such phases can also exhibit topological order 31-35 and can be used for various quantum information tasks, such as implementing a robust quantum memory 36 .…”

Signatures of many-body localization in the dynamics of two-site entanglement

“…The intense theoretical efforts of the last decade stimulated an exciting race towards its experimental verification. Last year the first beautiful experiments providing evidence of MBL appeared in cold atomic systems 35,36 and trapped ions 37 . However, it is still debatable whether unique features of MBL, which are not present in AL systems, have been observed or not: experiments have focused on the propagation of particles which are frozen arXiv:1608.08901v3 [quant-ph] 9 Jan 2017 in both phases.…”