Thomas Kohlert received the Best Poster Prize at the 669. International WE-Heraeus-Seminar on Quantum Gases and Quantum Coherence

Aidelsburger, M.

Bloch, I.

Bordia, P.

Kohlert, T.

Li, X.

Lüschen, H.

Sarma, S.

Scherg, S.

Schreiber, M.

MPG.PuRe

Single-Particle Mobility EdgeExperimental RealizationTheoryNon-Interacting ResultsReferencesInteracting resultsCompensate anti-trapping potential of the blue-detuned lattice with dipole trapExtract FWHMConclusionsIn a nutshell, we find the following intriguing results:1. Realization of a lattice model with SPME and mapping out of the corresponding phase diagram2. MBL present in a system with SPME, but only in a regime where all single-particle eigenstates are lo-calized.3. Single-particle extended states do not serve as an efficient bath for localized states on experimentally accessible timescales.For the future:4. Extend experimentally acessible timescales5. Find better diagnostics for  the possible many-body intermediate phaseTime ( ) log-scaleImbalance  log-scaleU=4J (or U=1J better?)MBLSP-ext.0.51 100Pow-lawtherm.change offunctionalform? therm.??????Existence of MBME open debate in theory:- Phys. Rev. B 92, 064203 (2015): “MBME due to symmetry-constrained dynamics and strong interactions”- Phys. Rev. B 93, 014203 (2016): “Absence of MBME”0.2 0.4 0.6 0.8 1.0Vd  (Epr )0.00.10.20.30.40.5Exponent »AAGAA2 3 4 5¢/J00.000.250.50»SPint.101 102 103 104Time (¿)0.0020.0100.1000.500Imbalance IVd =1.0 EprVd =0.55 EprVd =0.2 EprS.P. Extended S.P. Int. S.P. LocalizedBAMBLETHUVd- MBL in a model with SPME?- Does an SPME survive finite interactions and does         a many-body mobility edge (MBME) exist?- What are the timescales involved?- What would the experimental signatures of                                        an MBME be? Which disgnostics are    required?Conjectured Phase DiagramTheoretical investigationRelaxation between 100 and 500τOpen questionsMBL phaseImbalance decay (power-law?)non-ergodic metal phasethermal phaseMBL phasefinite plateauRelaxation between 10 and 100τTime scales limited by inter-tube coupling and residual photon scattering.Use numerics to explore longer lifetimesBy comparing the GAA model (SPME) and the AA model (no SPME), we can look for differ-ences in the relaxation dynamics.No accelerated relaxation from single-particle extended states on experimentally accessible timescales0.5 0.6 0.7 0.8 0.9 1.0Vd  (Epr )0.00.20.40.60.8Exponent »AAGAAExperimental investigationMB-Int.?MBME plausible, but no direct evidencesDifference in relaxation dynamics -> Do ex-tended states contrib-ute on this timescale?1. Schreiber et al., Science 349, 842–845 (2015)    (MBL observation)2. Lüschen et al., arXiv:1709:03478 (2017)    (SPME observation)3. Li et al., PRB 96, 085119 (2017)    (SPME theory)4. Lüschen et al., PRL 119, 260401 (2017)    (Slow dynamics)5. Bordia et al., PRL 116, 140401 (2016)    (Coupling of MBL systems)6. Lüschen at al., PRX 7, 011034 (2017)    (Photon scattering)7. Ronzheimer et al., PRL 110, 205301 (2013)    (Expansion in lattices)IPR =∑m |u(i)m |4(∑m |u(i)m |2)2NPR =(L∑m|u(i)m |4)−1IPRNPRLocalized Extendedfinitefinite00Energy bands split up in the presence of de-tuning lattice. For different energies the IPR depends on the detuning lattice strength. This gives rise to a coexistence of localized and extended states in the intermediate regimeVp = 4Erp Vp = 6Erp Vp = 8ErpMobility edge present in shallow 1D lattice, but disappears intight-binding limit where Hamiltonian maps to Aubry-André Hamiltonian0.0 0.2 0.4 0.6 0.8 1.0Vd (Epr )0.00.10.20.30.40.50.60.7<NPR>, <IPR><NPR><IPR><NPR> exact<IPR> exact- Phase diagram clearly exhibits intermediate regime between   localized and extended states => Single-Particle Mobility Edge- Good agreement between experiment and tube-averaged (solid   lines) exact diagonalization (ED) calculations- Extraction of VI and VE via heuristic fit functions to the data points- Vanishing mobility edge for large primary lattice depth (mapping to  tight-binding Aubry-André Hamiltonian for Vp ≥ 8Erp)Density Imbalance I:- sensitive to first localized   state emerging at disorder  strength VI- measured at 200 tunneling  times due to finite imbalance  lifetimeExpansion E:- sensitive to first delocalized  state emerging at disorder   strength VE- measured at 3000 tunneling  times due to extremely slow  dynamics in the presence of  disorderIf VI ≠ VE shows existence of a SPMEPhysical observables0 0.15 0.3 VI 0.6 0.75 VE 1.00.00.10.20.30.40.50.6E, IIE0 0.15 VI 0.3 VE 0.5 0.6 0 0.1VI VE 0.350 0.15 0.3 VI 0.6 0.75 VD 1.0Vd (Epr )0.00.10.20.30.40.50.6D, IID0 0.15 VI VD 0.5 0.6Vd (Epr )0 0.1VI VD 0.35Vd (Epr )a b cd e fExperimentTheoryVp =4 Epr Vp =6 Epr Vp =8 Epr3 4 5 6 7 8Vp (Epr )0.00.20.40.60.81.01.2Vd(Ep r)extendedlocalizedintermediateVIVE3 4 5 6 7 8Vp (Epr )0.00.40.81.2Vd(Ep r)ObservablesImbalance Detection I● Stop dynamics by freezing     the system by ramping    up long and short lattices,    still with phase shift ● Remove disorder, traverse     2nd-3rd band crossing     by non-adiabatically     compressing long lattice● Remove short lattice    and band map the long    latticeDouble wellsDisordered LatticesLong Lattice of Super lattice (1064 nm):Short Lattice of Superlattice (532 nm)Disorder Lattice (738 nm) - incommensurate to 532 nm1D Tubes:Expansion Measurement EImbalance     =e e eeo o ooU2∆Experimental realizationExpansion E = FWHMThe incommensurate lattice modelĤcon = −h̄22md2dx2︸ ︷︷ ︸Kinetic Energy+Vp2cos(2kpx)︸ ︷︷ ︸Primary Lattice+Vd2cos(2kdx+ φ)︸ ︷︷ ︸Detuning LatticeThis continuum Hamiltonian is valid in all paramter regimes. For a deep primary lattice the tight-binding approximation results in the Aubry-André-Hamiltonian:For shallow primary lattices, corrections have to be added to account for the appearance of a single-particle mobility edge:ĤU = U∑jn̂j,↑n̂j,↓ĤGAA = ĤAA + Ĥ′ĤAA = −J0∑j,σ(ĉ†j+1,σ ĉj,σ + h.c.) + ∆∑j,σcos(2παj + φ)n̂j,σ40K-40K Feshbach resonanceTunable Interactionsatoms in mF = -9/2 and -7/2 states:0200400600-200200180160 220 240Scattering length [a0]B field [G]Single-Particle Mobility Edge (SPME):- Critical energy separating localized and delocalized energy eigenstates- Absent in 1D and 2D Aubry-André model (quasi-random disorder)- First observation of an exact SPME in 1DcInitialStateext.loc.ext.loc.1extended phaseintermediate phaselocalized phaseStrong detuning:Localized statesIntermediate detuning: Coexistence of localized and extended statesMobility EdgeWeak detuning:Extended states Thomas Kohlert1,2, Sebastian Scherg1,2,  Henrik Lüschen1,2, Pranjal Bordia1,2, Monika Aidelsburger1,2, Michael Schreiber1,2,  Xiao Li3, Sankar Das Sarma3, and Immanuel Bloch1,21Ludwig-Maximilians-Universität, Schellingstr. 4, 80799 München, Germany2Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany3Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742-4111, USAExploring the Single-Particle Mobility Edge and Many-Body Localized Phase in a 1D Quasiperiodic Optical Lattice with Ultracold Atoms

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Exploring the Single-Particle Mobility Edge and Many-Body Localized Phase in a 1D Quasiperiodic Optical Lattice with Ultracold Atoms

Exploring the Single-Particle Mobility Edge and Many-Body Localized Phase in a 1D Quasiperiodic Optical Lattice with Ultracold Atoms

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