Transport of a 1D Bose gas in disorder
Transport of a 1D Bose gas in disorder
Avinash KumarLENS and Dipartimento di Fisica e Astronomia,
Universita di Firenze, and INO-CNR
Leibniz Universität Hannover, Hannover
Disorder
November 14, 2013 Avinash Kumar
The disorder in physical systems
In most of the physical systems the disorder and interaction is difficult to control and hence to study.
Light propagation in random media
GrapheneSuperfluids in porous mediaSuperconducting thin films
Disorder
November 14, 2013 Avinash Kumar
Ultracold quantum gases to study disorder. Ultracold quantum gases to study disorder.
Hannover Florence
Palaiseau
UrbanaRice U.
L. Sanchez-Palencia and M. Lewenstein, Nat. Phys. 6, 87 (2010);G. Modugno, Rep. Prog. Phys. 73, 102401 (2010).
Anderson localization in 1D, 2D and 3D, Strongly correlated systems, Transport in disorder…
1D Bose gas
November 14, 2013 Avinash Kumar
Quasicondensate – phase fluctuations (linear with the size) – effects the system globally
Interactions –Interactions –
No condensation at non-zero temperature
Bosonic properties Fermionic properties (Tonks gas)
1D Bose gas1D Bose gas
0∞
Non interactingfermions
SF SCSF Interaction
Periodic potential
November 14, 2013 Avinash Kumar
Interactions
External potential (periodic)External potential (periodic)
MI (n=1)SF SCSF (n≠1) /
����������������������������� =
���~1
Disorder
November 14, 2013 Avinash Kumar
AISCBG
InteractionsBG
SF
Single particle problem: Anderson localization
Weak interactions: BG (Superfluid Islands)Eint ≥ ∆min
Eint ≥ ∆max Superfluid (disordered)
Eint ≥ KE SCSF (fermionic)
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1D disordered, interacting bosons
November 14, 2013 Avinash Kumar
Giamarchi & Schultz, PRB 37 325 (1988); Fisher et al PRB 40, 546 (1989)
Rapsch, et al.EPL 46 559 (1999)One dimensional bosons are the prototyal disordered systems, with an established theoretical framework.
Theories established.
Quantum phases in disordered bosons
November 14, 2013 Avinash Kumar
Interaction
Diso
rder
Superfluid Mott insulator/Tonks gas
Bose glass: a gapless insulator
Anderson localization
Quantum phases in disordered bosons
November 14, 2013 Avinash Kumar
Interaction
Diso
rder
Superfluid
Anderson localization
Mott insulator/Tonks gas
Bose glass: a gapless insulator
Palaiseau, Firenze 2008
Firenze 2006
Firenze 2010-11
Urbana 2010
Quantum phases in disordered bosons
November 14, 2013 Avinash Kumar
Interaction
Diso
rder
Superfluid
Anderson localization
Mott insulator/Tonks gas
Bose glass: a gapless insulator
Palaiseau, Firenze 2008
Firenze 2006
Firenze 2010-11
Urbana 2010
L. Tanzi et. al, Phys. Rev. Lett. 111, 115301 – Published 9 September 2013
Disordered optical lattice
λ1 = 1064nm, λ2 = 859nm
quasi-periodic lattice
Metal-insulator transition at ∆=2J
In the tight binding limit: Aubry-Andrè or Harper model
J Strength of primary lattice∆ Strength of secondary lattice
U = 2πh2
ma |φ(x) |4 d3x∫
‘a’ 39K Feshbach resonances
November 14, 2013 Avinash Kumar
Experimental setup
1D quasicondensate confinement of the 39K BEC
Strong 2D lattices (s=30)
Weak 1D q.p.lattice (s=10)
November 14, 2013 Avinash Kumar
νz = 150Hzνr = 50kHz
N = 50 atomsn = 2-4 atoms per site
r
z
J = hx150Hz
U = 0.3-10 J
Momentum distribution
November 14, 2013 Avinash Kumar
Momentum distribution
Γ −1 coherence
Time of flight image
Γ
Coherence
November 14, 2013 Avinash Kumar
Incoherent regime
Coherent regime
∆/J
U/J
Γ (units ofπ/d)
Chiara D’Errico et. al, Observation of the Bose glass from weak to strong interactions, under progress.
Superfluid
Insulator
????
Momentum Kick
t=0trap minimum is
shifted
t=t*all fields are switched off
System at equilibrium
November 14, 2013 Avinash Kumar
4 μm
g field
Momentum Kick
t=0trap minimum is
shifted
t=t*all fields are switched off
TOF image (16.6 ms)
System at equilibrium
t*=0
t*≠0
∆k
November 14, 2013 Avinash Kumar
4 μm
g field
Time evolution of momentum
November 14, 2013 Avinash Kumar
No disorderNo disorder
Dynamical instability driven by quantum and thermal fluctuations.
Damped Oscillation
L. Fallani et al., Phys. Rev. Lett. 93, 140406 (2004)J. Mun et al., Phys. Rev. Lett. 99, 150604 (2007)
Time evolution of momentum
November 14, 2013 Avinash Kumar
No disorderNo disorder
A. Smerzi et al., Phys. Rev. Lett. 89, 170402 (2002)E. Altman et al., Phys. Rev. Lett. 95, 020402 (2005)I. Danshita, ArXiv:1303.1616
Dynamical instability driven by quantum and thermal fluctuations.
Band Energy and effective mass of a particle in a periodic potential vs quasimomentum.
Damped Oscillation
L. Fallani et al., Phys. Rev. Lett. 93, 140406 (2004)J. Mun et al., Phys. Rev. Lett. 99, 150604 (2007)
Dynamical Instability
Superfluid decay model
Damping due to Quantum phase slips (T<T0)
November 14, 2013 Avinash Kumar
Damping due to Thermally activated phase slips (T>T0)
−−∝Γ
2/51
227.1exp
h
λπ pUnJ
Q
−
−∝Γ
31
2234exp
h
λπ pTknJB
T
Crossover Temperature T0
nJUTkB ≅0
E. Altman, A. Polkovnikov, E. Demler, B. I. Halperin, and M. D. Lukin, Phys. Rev. Lett. 95, 020402 (2005).
Experimental T=3J
Superfluid decay model
Damping due to Quantum phase slips (T<T0)
November 14, 2013 Avinash Kumar
Damping due to Thermally activated phase slips (T>T0)
−−∝Γ
2/51
227.1exp
h
λπ pUnJ
Q
−
−∝Γ
31
2234exp
h
λπ pTknJB
T
Crossover Temperature T0
nJUTkB ≅0
E. Altman, A. Polkovnikov, E. Demler, B. I. Halperin, and M. D. Lukin, Phys. Rev. Lett. 95, 020402 (2005).
)(nf∝ΓLess density -> more damping
Our 1D system
0 ER
0.25 ER
0.5 ER
2.0 ER
C. D. Fertig et.al., PRL 94, 120403 (2005)
Experimental T=3J
Critical Momentum
November 14, 2013 Avinash Kumar
Without disorder: ∆/J=0
pC
pc U
U=1.26J, n=3.6
pc ∆
Critical Momentum vs Interaction
November 14, 2013 Avinash Kumar
Fluid Insulator
J. Mun et al., Phys. Rev. Lett. 99, 150604 (2007).
U/J
∆
5.9
SF MI
Phase diagram
I. Danshita and A. Polkovnikov, Phys. Rev. A 84, 063637 (2011).
Experimental UC/J = 5.9 Theoretical UC/J = 4.535 for n=2
Quantum vs Thermal phase slips
November 14, 2013 Avinash Kumar
0 2 4 6 8 10 120.0
0.1
0.2
0.3
0.4Experiment quantum phase slip model thermal phase slip model
p c(h/
λ 1)
U/J
Quantum phase slips
Initial damping rate
Disorder
November 14, 2013 Avinash Kumar
∆/J=0pC
∆/J=3.6pC
Fixed interaction energy: U/J=1.26
∆/J=10
Disorder
November 14, 2013 Avinash Kumar
∆/J=0pC
∆/J=3.6pC
Fixed interaction energy: U/J=1.26
∆/J=10
pc
C∆C
Fluid Insulator
Disorder
November 14, 2013 Avinash Kumar
∆/J=0pC
∆/J=3.6pC
Fixed interaction energy: U/J=1.26
∆/J=10
∆C
∆
SFBG
U/J1.26
pc
C∆C
Fluid Insulator
Critical disorder
November 14, 2013 Avinash Kumar
∆/J
U/J
Fluid regime
Insulating regime
Theory
November 14, 2013 Avinash Kumar
Critical Disorder to enter the insulating phase at a given interaction energy.
α
=
∆J
nUAJ
c
L. Fontanesi et.al, Phys. Rev. Lett.103, 030403 (2009).P. Lugan, et.al , Phys. Rev. Lett. 98, 170403 (2007).R. Vosk and E. Altman, Phys. Rev. B 85, 024531 (2012).
Phase Diagram
November 14, 2013 Avinash Kumar
After curve fitting α=0.83, A=1.3
α
=
−∆J
nUAJ
Jc )2(
L. Tanzi et. al, Phys. Rev. Lett. 111, 115301 – Published 9 September 2013
Curve fitted
0 2 4 6 80
2
4
6
8
10
∆/J
nU/J
Insulator
Fluid
Conclusion
November 14, 2013 Avinash Kumar
•We have studied the fluid-insulator crossover in weakly interacting systems in interaction-disorder plane.
•Study of the effect of temperature in the fluid insulator transition.
• Study of strongly interacting 1D gases (Tonks gas): excitations, transport.
Towards long range anisotropic interaction : Study similar physics under dipolar interactions (Ultracold molecules).Towards long range anisotropic interaction : Study similar physics under dipolar interactions (Ultracold molecules).
U
V
X. Deng, R. Citro, E. Orignac, A. Minguzzi, and L. Santos, Phys. Rev. B 87, 195101 (2013)
STIRAP transfer
November 14, 2013 Avinash Kumar
5 10 150
2
4
6
8
10
12
14
16
183(0+)
X1Σ+
Ener
gy (c
m-1
x 10
00)
r (a0)
a3Σ+
855 nm 1320 nm
STImulated Raman Adiabatic Passage
B
a (a0)
100
180
402 G318 G
K-Rb Feshbach resonance
��� � 3 � 10��e��
��� � 1e��
O. Duleau et. al. unpublished
Raman lasers setup
November 14, 2013 Avinash Kumar
Phase lock accuracy ~1kHz over the frequency difference of 125 THz.
DL
PDPIDOptical cavity(finesse ~1000)
<10kHz
ν
νr
0
νoff
1320 laser
855 laser
beat
Lasers line narrowed to < 10kHz. Wavemeter +FC accuracy 2MHz
Quartz + Rb clock + GPSQuartz + Rb clock + GPS
Towards physics with molecules
November 14, 2013 Avinash Kumar
Towards double mott insulatorDouble Mott Insulator
1D physics
Collisionally Unstable
+ +
KRb KRb Rb2 K2
Experimental team
November 14, 2013 Avinash Kumar
Massimo Inguscio Giovanni Modugno
SaptarishiChaudhuri
ChiaraD’errico
EleonoraLucioni
LucaTanzi
LorenzoGori