Transport of a 1D Bose gas in disorder - RTG1729Transport of a 1D Bose gas in disorder Avinash Kumar LENS and Dipartimento di Fisica e Astronomia, Universita di Firenze, and INO-CNR

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


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


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


Interactions

External potential (periodic)External potential (periodic)

MI (n=1)SF SCSF (n≠1) /

�� =

��~1

Disorder


AISCBG

InteractionsBG

SF

Single particle problem: Anderson localization

Weak interactions: BG (Superfluid Islands)Eint ≥ ∆min

Eint ≥ ∆max Superfluid (disordered)

Eint ≥ KE SCSF (fermionic)

� � ��

1D disordered, interacting bosons


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


Interaction

Diso

rder

Superfluid Mott insulator/Tonks gas

Bose glass: a gapless insulator

Anderson localization



Interaction

Diso

rder

Superfluid


Mott insulator/Tonks gas


Palaiseau, Firenze 2008

Firenze 2006

Firenze 2010-11

Urbana 2010



Interaction

Diso

rder

Superfluid


Mott insulator/Tonks gas


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


Experimental setup

1D quasicondensate confinement of the 39K BEC

Strong 2D lattices (s=30)

Weak 1D q.p.lattice (s=10)


νz = 150Hzνr = 50kHz

N = 50 atomsn = 2-4 atoms per site

r

z

J = hx150Hz

U = 0.3-10 J

Momentum distribution


Momentum distribution

Γ −1 coherence

Time of flight image

Γ

Coherence


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


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


4 μm

g field

Time evolution of momentum


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


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)


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)


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


Without disorder: ∆/J=0

pC

pc U

U=1.26J, n=3.6

pc ∆

Critical Momentum vs Interaction


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


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


∆/J=0pC

∆/J=3.6pC

Fixed interaction energy: U/J=1.26

∆/J=10

Disorder


∆/J=0pC

∆/J=3.6pC


∆/J=10

pc

C∆C

Fluid Insulator

Disorder


∆/J=0pC

∆/J=3.6pC


∆/J=10

∆C

∆

SFBG

U/J1.26

pc

C∆C

Fluid Insulator

Critical disorder


∆/J

U/J

Fluid regime

Insulating regime

Theory


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


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


•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


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


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


Towards double mott insulatorDouble Mott Insulator

1D physics

Collisionally Unstable

+ +

KRb KRb Rb2 K2

Experimental team


Massimo Inguscio Giovanni Modugno

SaptarishiChaudhuri

ChiaraD’errico

EleonoraLucioni

LucaTanzi

LorenzoGori

Documents

Transport of a 1D Bose gas in disorder - RTG1729Transport of a 1D Bose gas in disorder Avinash Kumar LENS and Dipartimento di Fisica e Astronomia, Universita di Firenze, and INO-CNR