Ultracold Fermions in Optical Lattices
Dynamics of highly excited fermions in optical lattices
While generic manybody systems will typically reach a thermal “featureless” state via their intrinsic time evolution, in disordered systems, where neighboring sites have different onsite 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 manybody localization (MBL).
We investigate the behavior of highly excited manybody systems by monitoring the decay of a chargedensity 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) ^{87}Rb atoms to sympathetically cool a gas of (fermionic) ^{40}K atoms to quantum degeneracy. In our dipole trap, we reach temperatures of T = 0.15T_{F}, where T_{F} denotes the FermiTemperature.
Our optical lattice setup features a superlattice, which is created via the superposition of a lattice laser with its second harmonic and a welldefined 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 (quasiperiodic) disorder required for localization.
Observation of manybody localization of interacting fermions in a quasirandom optical lattice
Disorder can stop the transport of noninteracting 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 socalled manybody 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 manybody localized phase, however, can get “stuck” in nonequilibrium states that persist for very long times. Here, we detect manybody localization in a onedimensional 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:
Signatures of ManyBody 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 “manybody 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 chargedensity 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.
Coupling Identical 1D ManyBody Localized Systems
ManyBody Localization (MBL) marks a new paradigm in condensed matter and statistical physics. It describes an insulating phase in which a disordered, interacting manybody 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 onedimensional ManyBody 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 quasirandom 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 noninteracting Anderson case remains localized, in the interacting case any coupling between the tubes leads to a delocalization of the entire system.
Periodically Driving a ManyBody Localized Quantum System
Periodically driven quantum manybody systems can display rich dynamics and host exotic phases that are absent in their undriven counterparts. However, in the presence of interactions such systems are expected to eventually heat up to a simple infinitetemperature state. One possible exception is a periodically driven manybody 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.
Probing Slow Relaxation and ManyBody Localization in TwoDimensional QuasiPeriodic Systems
In the presence of strong applied disorder, quantum mechanical systems can reach a so called manybody localized phase. One important hallmark of this phase is that the system, if prepared in a nonequilibrium state, is not able to equilibrate but instead gets stuck in a nonequilibrium state. Much is known about the manybody 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 manybody localized and the thermal phase is still open to debate. In this work we experimentally explore these questions using ultracold potassium atoms loaded in quasiperiodic 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 manybody localized phase in two dimensions.
Observation of Slow Dynamics near the ManyBody Localization Transition in OneDimensional QuasiPeriodic Systems
In the presence of sufficiently strong disorder or quasiperiodic fields, an interacting manybody system can fail to thermalize and become manybody 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 truerandom disorder. In this work, we experimentally and numerically investigate the regime close to the manybody localization transition in quasiperiodic systems. We find slow relaxation of the density imbalance close to the transition, strikingly similar to the behavior near the transition in truerandom systems. This dynamics is found to continuously slow down upon approaching the transition and allows for an estimate of the transition point.
SingleParticle Mobility Edge in a OneDimensional Quasiperiodic Optical Lattice
A singleparticle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In onedimensional systems with uncorrelated disorder, a SPME cannot exist, since all singleparticle 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 onedimensional quasiperiodic optical lattice. Specifically, we find a regime where extended and localized singleparticle 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 FermiHubbard Model
We experimentally and numerically investigate mass transport of fermions in a onedimensional 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 stronglyinteracting 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.
Observation of ManyBody Localization in a
OneDimensional System with a SingleParticle Mobility Edge
A singleparticle mobility edge marks a critical energy separating extended from localized states and characterizes the singleparticle intermediate phase of our onedimensional noninteracting quantum system with a weak quasiperiodic potential. Here, we investigate the corresponding interacting system, where the existence of manybody localization (MBL) and a manybody 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 tightbinding AubryAndré model, which does not exhibit a singleparticle intermediate phase, in order to identify signatures of a potential MBIP.
People
Phone: +49 89 2180 6143 

Phone: +49 89 32905 138 

Hebbe Madhusudhana, Bharath, Dr. Phone: +49 89 2180 6137 

Phone: +49 89 2180 6137 

Phone: +49 89 2180 6137 

Schreiber, Michael, Dipl. Phys. Phone: +49 89 2180 6137 
Former Members
Dr. Simon Braun  PhD Student 
Dr. Henrik Lüschen  PhD Student 
Felix Draxler  Bachelor student 
Daniel Garbe  Master student 
Pau GomezKabelka  Master student 
Frederik Görg  Master student 
Dr. Sean Hodgman  Postdoc 
Dr. Lucia Hackermüller  Postdoc 
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 