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

2. 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

3. 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 (1988)
Fisher et al PRB 40, 546 (1989), Rapsch, et al., EPL (1999), …
And many others ( )…
Experiments: Fallani et al. PRL 98 (2007), Pasienski et al. Nature Physics 6 (2010), Gadway et al., PRL 107 (2011)

4. 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);

5. 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

6. 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, (2007)

7. 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

8. 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

9. 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:
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, (2013)

10. Coherence measurementsFT
TOF
Spatially averaged
correlation function
Momentum distribution
Agreement with theory

11. 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

12. 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

13. 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, (2004); Iucci, Phys. Rev. A 73, (2006); Fallani, PRL 98, (2007).

14. 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 (2009)
+ G. Pupillo et al, New. J. Phys. 8, 161 (2006)

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

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

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

18. 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:
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, (2013)

19. 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, (2002); E. Altman et al., Phys. Rev. Lett. 95, (2005)
L. Fallani et al., Phys. Rev. Lett. 93, (2004); J. Mun et al., Phys. Rev. Lett. 99, (2007)

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

21. 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?

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

23. 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?

24. 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 Bilbao)