One-dimensional disordered bosons from weak to strong interactions Luca Tanzi Lens, Università di Firenze July 11, 2014 – “Waves and disorder” school, Cargèse, France

Waves and disorder Energy Quantum nature of particles: Localization due quantum interference (Anderson localization) Quantum tunneling between holes Interactions between particles break Anderson localization coupling localized states, but also avoid quantum tunneling localizing particles in different wells (Mott insulator) Complex interplay between disorder and (repulsive) interactions

1D disordered bosons One dimensional bosons are the prototypal disordered systems, with an established theoretical framework (see Hans Kroha’s talk) No lattice Interactions Disorder SF BG Lattice Giamarchi & Schultz, PRB 37 325 (1988) Fisher et al PRB 40, 546 (1989), Rapsch, et al., EPL 46 559 (1999), … And many others (1988-2013)… Experiments: Fallani et al. PRL 98 (2007), Pasienski et al. Nature Physics 6 (2010), Gadway et al., PRL 107 (2011)

Disorder and cold atoms Atoms cooled down to quantum degeneracy: quantum gas T>>TC T≈TC T<TC Ultracold atoms offer the possibility to tune and control independently disorder, dimensionality, interactions… (see Vincent Josse’s talk) Urbana-Champaign Florence Palaiseau Houston, Hannover, NIST-Maryland, Stony-Brook, Nice, Zurich Review: L. Sanchez-Palencia and M. Lewenstein, Nat. Phys. 6, 87 (2010);

Disordered Bose-Hubbard 39K bosonic atoms with controlled inter-particle repulsive interactions in a quasiperiodic lattice potential Set J by fixing the strength of the primary lattice (λ=1064 nm) Tune disorder by varying the strenght of the secondary lattice Δ J Aubry-Andrè Hamiltonian: metal-insulator transition at Δ=2J J U S. Aubry and G. André, Ann. Israel Phys. Soc. 3, 133 (1980). Theory by Modugno, Minguzzi

Tuning the interaction Bose-Einstein condensate: a dilute quantum gas scattering length 39Potassium BEC: broad magnetic Feshbach resonance allows to control the interactions between atoms G. Roati et al., Phys. Rev. Lett. 99, 010403 (2007)

Disordered Bose-Hubbard 39K bosonic atoms with controlled inter-particle repulsive interactions in a quasiperiodic lattice potential Set J by fixing the strength of the primary lattice Tune disorder by varying the strenght of the secondary lattice Tune interaction by varying the external magnetic field J J Δ U

Tuning the dimensionality Optical lattices allow to trap quantum gases in controllable potentials harmonic trap naxial∼150 Hz nr∼50 kHz Lattices Quasiperiodic lattice BEC Quasi-1D systems: the radial trapping energy is much larger than any other energy scale A weak longitudinal trapping makes each system inhomogeneous

Experimental results Experimental investigation of the D-U diagram “Observation of a disordered bosonic insulator from weak to strong interactions” Experiment: Chiara D’Errico, Eleonora Lucioni, Luca Tanzi, Lorenzo Gori, Massimo Inguscio, Giovanni Modugno (Florence) Theory: Guillaume Roux (Orsay), Ian P. McCulloch (Brisbane), Thierry Giamarchi (Geneva) arXiv:1405.1210 Transport instability at the fluid insulator transition “Transport of a Bose gas in 1D disordered lattices at the fluid-insulator transition” Luca Tanzi, Eleonora Lucioni, Saptarishi Chaudhuri, Lorenzo Gori, Avinash Kumar, Chiara D'Errico, Massimo Inguscio, Giovanni Modugno Phys. Rev. Lett. 111, 115301 (2013)

Coherence measurements FT TOF Spatially averaged correlation function Momentum distribution Agreement with theory

Coherence diagram G (units of p/d) D/J U/J Incoherent regime AI BG? SF MI Finite size system with non-uniform density: phase transitions become crossovers

Incoherent regimes are also insulating Transport experiment prepare in equilibrium kick, wait 0.8ms free expansion ideal fluid D/J U/J Incoherent regimes are also insulating

Excitation spectra Δ U main lattice modulation “energy” measurement (15%, 200ms) “energy” measurement (variation of the BEC fraction) prepare in equilibrium Δ U D/J U/J Ströferle, Phys. Rev. Lett. 92, 130403 (2004); Iucci, Phys. Rev. A 73, 041608 (2006); Fallani, PRL 98, 130404 (2007).

Excitation spectra D=6.3J D=9.5J Comparison with the calculated energy absorption rate (fermionized boson model) D=6.3J D=9.5J Strongly-correlated Bose glass: response of non-interacting fermions The strongly-correlated SF is Anderson-localized by disorder G. Orso et al., Phys. Rev. A 80 033625 (2009) + G. Pupillo et al, New. J. Phys. 8, 161 (2006)

Strongly interacting BG Mott Insulator (commensurate filling) Tonks-Girardeau gas (incommensurate filling) U>>J Bose glass (gapless) Disordered Mott Insulator gapped for D<U

Excitation at weak interactions Bosonic excitations: long-distance/small-ν excitations

Excitation at weak interactions Many local quasi-condensates, global coherence is lost Transition at Eint=Un≈Δ-2J Anderson insulator Bose glass Superfluid ??

Experimental results Experimental investigation of the D-U diagram “Observation of a disordered bosonic insulator from weak to strong interactions” Experiment: Chiara D’Errico, Eleonora Lucioni, Luca Tanzi, Lorenzo Gori, Massimo Inguscio, Giovanni Modugno (Florence) Theory: Guillaume Roux (Orsay), Ian P. McCulloch (Brisbane), Thierry Giamarchi (Geneva) arXiv:1405.1210 Transport instability at the fluid insulator transition “Transport of a Bose gas in 1D disordered lattices at the fluid-insulator transition” Luca Tanzi, Eleonora Lucioni, Saptarishi Chaudhuri, Lorenzo Gori, Avinash Kumar, Chiara D'Errico, Massimo Inguscio, Giovanni Modugno Phys. Rev. Lett. 111, 115301 (2013)

Transport revisited: clean system prepare in equilibrium kick, variable time free expansion Undamped oscillation (no interactions) Low damping Strong damping pc U=1.26J n=3.5 A. Smerzi et al., Phys. Rev. Lett. 89, 170402 (2002); E. Altman et al., Phys. Rev. Lett. 95, 020402 (2005) L. Fallani et al., Phys. Rev. Lett. 93, 140406 (2004); J. Mun et al., Phys. Rev. Lett. 99, 150604 (2007)

Dynamical instability: clean system SF MI Similar result in 3D: J. Mun et al., PRL 99, 150604 (2007)

Transport: disordered system U=1.26J n=3.5 D/J=0 D/J=3.6 SF BG D/J=10 The damping rate is enhanced and the critical momentum is reduced by disorder Can we use this to find the SF-BG crossover?

Fluid-insulator crossover from transport L. Fontanesi, PRL 103, 030403 (2009) R. Vosk and E. Altman, PRB 85, 024531 (2012)

Conclusion First characterization of the U-Δ diagram, from weak to strong interactions (coherence, transport measurements). Evidence of a strongly correlated BG from the excitation spectra. Clear signature of a sharp fluid-insulator crossover from transport. Perspectives: Disentangle Bose-glass from Mott physics in continuous disorder in one dimension. Higher dimensionalities. Many body localization and the T dependence of the fluid-insulator transition. Homogeneous cold atoms systems?

THANK YOU !!! Massimo Inguscio Saptarishi Chauduri Giovanni Modugno (group supervisor) Saptarishi Chauduri Giovanni Modugno Eleonora Lucioni Lorenzo Gori Chiara D’Errico Avinash Kumar Theory: Thierry Giamarchi Guillaume Roux Michele Modugno (now @ Bilbao)