Insulating Phases of a BEC Novel Optical Lattices · Insulating Phases of a BEC in Novel Optical...
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Insulating Phases of a BEC
in
Novel Optical Lattices
LENS European Laboratory for Nonlinear SpectroscopyDipartimento di Fisica – Università di Firenze
Massimo Inguscio
Quantum Noise in Correlated Systems, January 9, 2008 Weizmann Institute
Noise interferometry
“Ideal” BEC
Ultracold atoms in optical lattices
Adding disorder
Ultracold atoms in disordered potentials
Localization effects
- Bose glasses, spin glasses (strongly interacting systems)
- Anderson localization (weakly interacting systems)
Why disorder?
- Disorder is a key ingredient of the microscopic (and macroscopic) world- Fundamental element for the physics of conduction- Superfluid-insulator transition in condensed-matter systems
�
�
- Ultracold atoms are a versatile tool to study disorder-related phenomena- Precise control on the kind and amount of disorder in the system
- Quantum simulation
Why cold atoms?�
hopping energy interaction energy
J U
At zero temperature the state of the system is determined by the competition between twoenergy scales: the hopping energy J and the on-site interaction energy U
Bose-Hubbard model for interacting bosons in a lattice:
Interacting bosons in a lattice
hopping energy interaction energy
J U
At zero temperature the state of the system is determined by the competition between twoenergy scales: the hopping energy J and the on-site interaction energy U
Bose-Hubbard model for interacting bosons in a lattice:
SUPERFLUID
� Long-range phase coherence� High number fluctuation� Gapless excitation spectrum
� Compressible
MOTT INSULATOR
� No phase coherence� Zero number fluctuation (Fock states)� Gap in the excitation spectrum
� Not compressible
Interacting bosons in a lattice
Experimental scheme
3D optical lattice
strongly interacting regime:
Mott insulator phase first realized in
M. Greiner et al., Nature 415, 39 (2002).
Superfluid to Mott Insulator transition at LENS
increasing the lattice height U/J increases
momentum distribution of the atomic sample after expansiontest of phase coherence
Fallani, Fort , Guarrera, Lye, M.I. (2005)
Measuring the excitation spectrum
U 2U
Mott Insulator spectrum
Measuring the excitation spectrum
U 2U
Mott Insulator spectrum
Noise interferometry
“Ideal” BEC
Ultracold atoms in optical lattices
Adding disorder
Speckle potential
The random potential is produced by shining an off-resonant laser beam onto a diffusive plateand imaging the resulting speckle pattern on the BEC.
optical dipole potentialstationary in time
randomly varying in space
J. Lye et al., PRL 95, 070401 (2005)
LENS, 2004. Now: Orsay, Hannover, Rice, Illinois...
BEC expansion in a disordered waveguide
In-situ images of the BEC expanding in the disordered waveguide:
experiments also in Orsay (Aspect)
Fort et al. PRL 95, 170410 (2005)
issue #1: producing “dense” disorder
bichromatic latticespeckle pattern
issue #2: role of interactions!
The bichromatic lattice
bichromatic lattice
The bichromatic lattice
Energy minima of the lattice
potential along y direction
Non-periodic modulation of the energy minima
with length scale
sites
Localization in a quasi-periodic lattice
extended states
localized states
λ1 = 830 nm s1 = 10 / λ2 = 1076 nm
localization transition in 1D(Aubry-André)Ann.Israel Phys.Soc. 3 133(1980)
square modulus of the ground state wavefunction
Localization in a quasi-periodic lattice + harmonic trap (no interactions)
s2=1
quasi-periodic
potential
s1=10 s2=0.1
s2=0.25
randomsite to site energy
J. Lye et al.,
Phys.Rev.A75,
061603 R (2007)
Localization in a quasi-periodic lattice + harmonic trap adding interactions
Increasing interactions the “size” of the ground state progressively increases going from
a localized state to an extended state…characterization through transport properties at
low atom number
s1=10
s2=0.25 N=0
N=10
N=15000
s2=0.5
s2=1
s2=2
s1=10
N=15000
AUBRY-ANDRE
Thanks to Nir Davidson
Colloquium on Group Theoretical Methods in PhysicsKiriat Anavim (Israel) 25-30 Mars 1979
Analyticity Breaking and Anderson Localization in Incommensurate Lattices
Disordered systems: Role of interactions
hopping energy interaction energy
J U
disorder
∆∆∆∆
In the presence of disorder an additional energy scale ∆ enters the description of the system. The interplay between these energy terms may induce new quantum phase transitions
Bose-Hubbard model with bounded disorder in the external potential
Adding disorder
Phase diagrams
Qualitative phase-diagram for a system of interacting bosons in a disordered lattice
for ultracold atoms see B. Damski et al., PRL 91, 080403 (2003); R. Roth et al., PRA 68, 023604 (2003).
from M. P. A. Fisher et al., PRB 40, 546 (1989)
Phase diagrams
Qualitative phase-diagram for a system of interacting bosons in a disordered lattice
for ultracold atoms see B. Damski et al., PRL 91, 080403 (2003); R. Roth et al., PRA 68, 023604 (2003).
from M. P. A. Fisher et al., PRB 40, 546 (1989)
BOSE-GLASS
� No long-range phase coherence� Gapless excitation spectrum� Finite compressibility
(T. Giamarchi and H. J. Schulz, PRB 37, 325 (1988))
Broadening the MI spectrum
Starting from a Mott Insulator and adding disorder, the energy required for the
hopping of a boson from a site to a neighboring one becomes a function of position
When ∆j = U the excitation energy goes to zero and the gap disappears
---
Experimental geometry
λ1 = 830 nm s1 = 40
λ1 = 830 nm s1 < 20
λ2 = 1076 nm s2 < 3
x
z
y
1D atomic systems + 1D disorder
Excitation spectraL. Fallani et al., PRL 98, 130404 (2007)
Excitation spectrum for s1=16 and increasing disorder strength from s2=0 to s2=2.5:
MI spectral brodening
Excitation maximum at U
as a function of disorder strength:
∆=U
No agreement for strong
disorder ∆>U when the gap goes to zero
Good agreement with the
MI broadening for weak
disorder ∆<U
L. Fallani et al., PRL 98, 130404 (2007)
Phase coherence
Visibility of the interference pattern after time-of-flight:
L. Fallani et al., PRL 98, 130404 (2007)
Insulating state (no long-range phase coherence)
with broad excitation spectrum
Bose-Glass
Noise interferometry
“Ideal” BEC
Ultracold atoms in optical lattices
Adding disorder
HB&T noise interferometry in quantum gases
in a single image we have approx. 30000 detectors!
absorption image of a Mott Insulator state
Noise correlations
Nature 434, 481 (2005)
first proposal by E. Altman et al., Phys. Rev. A 70, 013603 (2004).
noise correlations
Experiments: Mainz (Nature 2005)
JILA (PRL 2005) – pairs from molecules
NIST- Maryland (PRL 2007)
LENS (2007) – Breaking of Mott order
Noise correlations (Mott phase) V.Guarrera, N.Fabbri, L.Fallani, C.Fort,
K.M.R.van der Stam, M.I. (2007)
k1
uniform filling of regularly-spaced lattice
Breaking the MI order
1 optical lattice
uniform filling of regularly-spaced lattice
Breaking the MI order
1 optical lattice2 optical lattices
controlled creation of particle / holes
inhomogeneous filling of (almost) regularly-spaced lattice
Breaking the MI order
1st and 2nd order correlations
noise correlations reveal the inhomogeneous filling of the lattice
when first-order coherence does not provide any spatial information
1st: Harmonic potential
site filling
site energy
site filling
site energy
2nd: Harmonic potential + incommensurate lattice
s2=0 s2=0.5 s2=1 s2=3 s2=5
Destroying the MI domains
the disordering lattice destroys the “wedding cake”
Calculating noise correlations
calculation of the ground state for J=0
the ground state is a disordered Mott insulator with
the site filling minimizing the total energy
Controlled breaking of Mott insulator order detected via noise correlation interferometry
theory (disordered MI)experiment
V.Guarrera, N.Fabbri, L.Fallani, C.Fort, K.M.R.van der Stam, M.I. (2007)
k1k2
k1 - k2
Noise correlations in the bichromatic lattice
Observable:
the ratio between the heights of the k2 peak and the k1 peak along the horizontal median line
Quantitative analysis of the k2 peak growth
Disordered systems: Role of interactions
CONTROLLED BREAKING of
MOTT DOMAINS
Noise interferometry
“Ideal” BEC
Ultracold atoms in optical lattices
Adding disorder
87Rb
Science 2001Modugno et al
41K boson
87Rb
40K fermion
PRL 2002Roati et al
2007Roati et al
...the last stable alkali isotope!
39K boson
0
Density d
istr
ibutio
n
Horizontal position (µm)
0 200-200 0 200-200 0 200-200
3 s 3.2 s 3.5 s
0 1 2 30,0
0,5
1,0
39K BEC
Lase
r p
ow
er (
arb
. u
nit
s)
B=395.2 G
aKRb
= 28 a0
Time (s)
aK = -33 a
0
aKRb
= 150 a0
aK = 150 a
0
B = 316 G
T=800 nKT=150 nK
K-K
K-Rb
280 300 320 340 360 380 400 420 440-200
-100
0
100
200
aB
B (a
0)
B (G)
(1) (2)
NK = 7*104
Tc~ 100 nK
B0 = 317.9 G
B0 = 402.4 G
BEC of 39K Roati et al PRL 99, 010403 (2007)
Feshbach assisted sympatetic cooling in a mixture with 87Rb
39K BEC with tunable interactionsRoati et al Phys.Rev.Lett. 99, 010403 (2007)
Collisional physics: see also D’Errico et al N.J.P. 9, 223 (2007)
Interference with degenerate trapped atoms___________________________________________________________________
• Confined-atom interferometers are promising in terms of
compactness and portability
• They offer the possibility of extending interrogation times beyond the
typical 0.5 s achievable in atomic fountains
• They offer high spatial resolution for study of atom surface
interaction, Casimir Polder forces, deviations from Newtonian
gravitational law at small distances
• Main problems: interaction induced shift, decoherence induced by
the trapping potential
CCD
Resonant laser (imaging)
Ultracold atoms
Non resonantlattice
MirrorHigh vacuum cell
Interferometry with a vertical optical lattice
A multiple well interferometer
2
λFE =∆
Wannier-Stark states
-2 -1 0 1 2Momentum
Interference of Wannier-Stark states:
Bloch oscillations
h2/λω FB =
Combination of high brightness and ultralow momentum spread: in principle ideal sources for
matter wave interferometry …
222 2cos ( )
2R
i sE kx gt m
ψψ ψ
∂= − ∇ + +
∂
hh
… however
g
Bloch oscillations of 40K fermions trapped in a
vertical optical lattice in presence of gravity
G.Roati, E. De Mirandes, F.Ferlaino, H.Ott, G.Modugno, M.I. Phys.Rev.Lett. 92, 230402 (2004)
Bloch oscillations with fermions
Atom interferometry with 39K BEC Fattori et al Phys.Rev.Lett. In press___________________________________________________________________
Lattice parameters: λ = 1032 nm, slattice= 6, νradial=40 Hz 100 a0 vs 1 a0
0 ms 0.4 ms 0.8 ms 1.2 ms 1.6 ms 2 ms 2.4 ms 2.8 ms 3.2 ms 3.6 ms 4 ms
100 a0
1 a0
-100 -50 0 50 100
100
200
300
400
500
600
700
800
900
Ato
mic
density (
a.u
.)
z axis (px)
-100 -50 0 50 100
100
200
300
400
500
600
700
800
900
Ato
mic
density (
a.u
.)
z axis (px)
T =0 ms T =4 ms
Widths of central peak!
0 100 1300 1310
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
y
or
sig
ma
y (
pix
)
Time (ms)
Towards a high sensitivity local sensing of forces
Sensitivity:
6×10-5g per shot (10-6g achievable)
∆g/g = [ ∆x/(xbragg) / Nosc ]
also Innsbruck with cesium
Conclusions and outlook
Atom-atom interaction in 39K Bose condensate can be accurately
tuned over a large range and and controlled around zero.
This is a very interesting system to investigate phenomena that can
be destroyed by atom-atom interactions:
BEC-based interferometry – forces at short distance
disorder (Anderson localization, tuning U versus J)
Vortices, with IDEAL BEC (J.Dalibard talk)
2D physics (Z. Hadzibabic talk)
R.Van der Stam M.Jona-Lasinio M.Modugno G.Modugno F.Minardi G.Roati M.Fattori J.Catani
L.Fallani G.Barontini C.Fort M.I. N.Fabbri V.Guarrera C.D’Errico M.Zaccanti L.DeSarlo