Quantum Optics Group (LMU) - Quantum Many Body Systems Division (MPQ)

Ultracold Fermions in Optical Lattices

Dynamics of highly excited fermions in optical lattices

While generic many-body systems will typically reach a thermal “featureless” state via their intrinsic time evolution, in disordered systems, where neighboring sites have different on-site energies, quantum correlations can persist for infinite times. Anderson found (PR 109, 1492 (1958)) that the introduction of disorder results in the localization of single particles. The generalization of this effect to interacting systems is known as many-body localization (MBL).

We investigate the behavior of highly excited many-body systems by monitoring the decay of a charge-density wave (CDW) initial state, where every second lattice site is empty (1). In a thermal system this population imbalance quickly relaxes and atoms spread across all lattice sites (2). Upon the introduction of sufficiently strong disorder, however, the system enters the MBL phase and thus retains a memory of its initial state (3).

Experimental Setup

In our setup, we use (bosonic) 87Rb atoms to sympathetically cool a gas of (fermionic) 40K atoms to quantum degeneracy. In our dipole trap, we reach temperatures of T = 0.15TF, where TF denotes the Fermi-Temperature.

Our optical lattice setup features a superlattice, which is created via the superposition of a lattice laser with its second harmonic and a well-defined phase. The superlattice is used to prepare and read out the CDW state. Additionally, our setup is equipped with an incommensurate lattice on top of the superlattice that creates the (quasi-periodic) disorder required for localization.



Observation of many-body localization of interacting fermions in a quasi-random optical lattice

Disorder can stop the transport of non-interacting particles in its tracks and therefore freeze the dynamics. This phenomenon, known as Anderson localization, occurs in disordered solids, as well as photonic and cold atom settings. Interactions tend to make localization less likely, but disorder, interactions, and localization may coexist in the so-called many-body localized phase. This phase is very special in the sense that it challenges the common understanding of thermalization in quantum mechanical systems. Usually, systems rapidly relax and approach thermal equilibrium, if prepared in a state far from thermal equilibrium. Systems in the many-body localized phase, however, can get “stuck” in non-equilibrium states that persist for very long times. Here, we detect many-body localization in a one-dimensional optical lattice initially filled with atoms occupying alternating sites. Externally induced disorder and interactions prevented the system from relaxing quickly to a state with a single atom on each site. For more detailed information see our publication:

Science 349, 843-845 (2015)


Signatures of Many-Body Localization in a Controlled Open Quantum System

The behavior of an isolated quantum system follows one of two distinct paradigms. It can approach a thermal equilibrium state, where any initial quantum correlations spread throughout the system, rendering the system effectively classical. Alternatively, in the presence of disorder, a system can be what is known as “many-body localized” (MBL). However, experimental investigation of this novel state is complicated by unavoidable interference from the environment, which acts as a source of fluctuations (a “bath”) that eventually thermalizes the system. We develop a method to implement a controllable bath and present a systematic study of its effects on a MBL system. In our experiment, we illuminate a charge-density pattern in an ensemble of ultracold potassium atoms (the MBL system) with nearly resonant light, and we investigate the system’s response. Here, the light intensity controls the coupling of the MBL system to the bath. We find that the susceptibility of the MBL system to the photon bath strongly increases when approaching the MBL transition, which is analogous to the effects of finite temperatures in the vicinity of a quantum phase transition.

Phys. Rev. X 7, 011034 (2017)



Coupling Identical 1D Many-Body Localized Systems

Many-Body Localization (MBL) marks a new paradigm in condensed matter and statistical physics. It describes an insulating phase in which a disordered, interacting many-body quantum system fails to act as its own heat bath. In isolation, these systems will never achieve local thermal equilibrium and conventional statistical physics approaches break down. Here, we study the effects of coupling one-dimensional Many-Body Localized (MBL) systems with identical disorder. Using a gas of ultracold fermions in an optical lattice, we artificially prepare an initial charge density wave in an array of 1D tubes with quasi-random onsite disorder and monitor the subsequent dynamics over several thousand tunneling times. We find a strikingly different behavior between MBL and Anderson Localization. While the non-interacting Anderson case remains localized, in the interacting case any coupling between the tubes leads to a delocalization of the entire system.

Phys. Rev. Lett. 116, 140401 (2016)

Periodically Driving a Many-Body Localized Quantum System

Periodically driven quantum many-body systems can display rich dynamics and host exotic phases that are absent in their un-driven counterparts. However, in the presence of interactions such systems are expected to eventually heat up to a simple infinite-temperature state. One possible exception is a periodically driven many-body localized system, in which heating is precluded by strong disorder. Here, we use a gas of ultracold fermionic potassium atoms in optical lattices to prepare and probe such a driven system and show that it is indeed stable for high enough driving frequency. Moreover, we find a novel regime, in which the system is exceedingly stable even at low drive frequencies. Our experimental findings are well supported by numerical simulations and may provide avenues for engineering novel phases in periodically driven matter.

Nature Physics 13, 460–464 (2017)

Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems

In the presence of strong applied disorder, quantum mechanical systems can reach a so called many-body localized phase. One important hallmark of this phase is that the system, if prepared in a non-equilibrium state, is not able to equilibrate but instead gets stuck in a non-equilibrium state. Much is known about the many-body localized phase in one dimension, but the stability of this phase in higher dimensions is an open question, because of the lack of theoretical and numerical methods. Also, a conclusive picture of the transition between the many-body localized and the thermal phase is still open to debate. In this work we experimentally explore these questions using ultra-cold potassium atoms loaded in quasi-periodic two dimensional optical lattices. We start our system far from equilibrium (with atoms loaded into alternate columns) and observe if the system preserves the memory of this striped pattern. We find hints for the existence of a many-body localized phase in two dimensions.

Phys. Rev. X 7, 041047 (2017)

Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasi-Periodic Systems

In the presence of sufficiently strong disorder or quasi-periodic fields, an interacting many-body system can fail to thermalize and become many-body localized. The associated transition is of particular interest, since it occurs not only in the ground state but over an extended range of energy densities. So far, theoretical studies of the transition have focused mainly on the case of true-random disorder. In this work, we experimentally and numerically investigate the regime close to the many-body localization transition in quasi-periodic systems. We find slow relaxation of the density imbalance close to the transition, strikingly similar to the behavior near the transition in true-random systems. This dynamics is found to continuously slow down upon approaching the transition and allows for an estimate of the transition point.

Phys. Rev. Lett. 119, 260401 (2017)

Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice

A single-particle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In one-dimensional systems with uncorrelated disorder, a SPME cannot exist, since all single-particle states localize for arbitrarily weak disorder strengths. However, if correlations are present in the disorder potential, the localization transition can occur at a finite disorder strength and SPMEs become possible. In this work, we find experimental evidence for the existence of such a SPME in a one-dimensional quasi-periodic optical lattice. Specifically, we find a regime where extended and localized single-particle states coexist, in good agreement with theoretical simulations, which predict a SPME in this regime.

Phys. Rev. Lett. 120, 160404 (2018)



Nonequilibrium Mass Transport in the 1D Fermi-Hubbard Model

We experimentally and numerically investigate mass transport of fermions in a one-dimensional optical lattice by releasing an initially trapped gas suddenly into a homogeneous potential landscape. For initial states with an appreciable amount of doublons, we observe a dynamical phase separation between rapidly expanding singlons and slow doublons remaining in the trap center, realizing the key aspect of fermionic quantum distillation in the strongly-interacting limit. For initial states without doublons, we find a reduced interaction dependence of the asymptotic expansion speed compared to bosons, which is explained in terms of the interaction energy produced by dynamically generated doublons in the interaction quench.

Phys. Rev. Lett. 121, 130402 (2018)

Observation of Many-Body Localization in a
One-Dimensional System with a Single-Particle Mobility Edge

A single-particle mobility edge marks a critical energy separating extended from localized states and characterizes the single-particle intermediate phase of our one-dimensional non-interacting quantum system with a weak quasiperiodic potential. Here, we investigate the corresponding interacting system, where the existence of many-body localization (MBL) and a many-body intermediate phase (MBIP) are still open and heavily debated questions. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL, when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-André model, which does not exhibit a single-particle intermediate phase, in order to identify signatures of a potential MBIP.

Phys. Rev. Lett. 122, 170403 (2019)

Former Members

Dr. Simon Braun   
PhD Student
Dr. Henrik LüschenPhD Student
Felix DraxlerBachelor student
Daniel Garbe
Master student
Pau Gomez-Kabelka
Master student
Frederik GörgMaster student
Dr. Sean HodgmanPostdoc
Dr. Lucia Hackermüller
Dr. Tim Rom
PhD Student/Postdoc
Dr. Pranjal Bordia
PhD Student/Postdoc
Dr. Jens Philipp Ronzheimer
PhD Student
Dr. Ulrich Schneider
Project leader
Dr. Sebastian Will
PhD Student