„Fermi-Bose mixtures of 40K and 87Rb atoms:Does a Bose Einstein condensate float in a Fermi sea?"

Klaus Sengstock

Krynica, June 2005 Quantum Optics VI

Institut für Laserphysik Universität Hamburg

Mixtures of ultracold Bose- and Fermi-gases

Bright Fermi-Bose solitons

Dynamics of the system: e.g.: mean field driven collapse

Cold Quantum Gas GroupCold Quantum Gas GroupHamburgHamburg

Fermi-Bose-Mixture Spinor-BEC

BEC ‘in Space‘

Atom-Guiding in PBF

Cold Quantum Gas GroupCold Quantum Gas GroupHamburgHamburg

Fermi-Bose-Mixture Spinor-BEC

Poster by Silke Ospelkauson Tuesday

Poster by Jochen Kronjägeron Monday

Bose-Einstein Condensation

TTc

1

N0/N

1-(T/Tc)3

T>Tc T<Tc

Bose-Einstein distribution

S. N. Bose A. Einstein

1

1)( /)(

ekTf

critical temperature for BEC

31

94.0 NkTc

Bose-Einstein Condensation

TTc

1

N0/N

1-(T/Tc)3

T>Tc T<Tc

Bose-Einstein distribution

1

1)( /)(

ekTf

31

94.0 NkTc

critical temperature for BEC

High-temperature effect !!!

Fermions in a Harmonic Trap

F

1

f()T>TF T=0

Fermi-Dirac distribution

E. Fermi P.A.M. Dirac

1

1

ekT

f/)(

)(

T=0 T~TF

T>TF

31

81,1 NkTF

Fermi temperature

F

Quantum statistical effects also forT~TF, but more difficult to see...

Fermions in a Harmonic Trap

F

1

f()T>TF T<TF

Fermi-Dirac distribution

1

1

ekT

f/)(

)(

T=0 T~TF

T>TF

Fermi temperature

31

81,1 NkTF

Fermionic Quantum Gasesdifficulty to reach low temperatures for Fermi gases:

no s-wave scattering of identical fermions! no thermalization in evaporative cooling

a) use different spin components (D. Jin et al. 98)

b) use e.g. a BEC to cool a Fermi sea(and look to the details...) thermal

Bosons

Fermionscondensate

fraction

e.g.: Momentum Distributions of Fermions and Bosons

0 p

P(p)

0 p

P(p)

pF-pF

T<<Tc,TF

0

0

p

p

P(p)

P(p)

0

0

p

p

P(p)

P(p)

pF-pF

pF-pF

T>>Tc,TF

T<Tc,TF

e.g.: Momentum Distributions of Fermions and Bosons

0

0

p

p

P(p)

P(p)

0

0

p

p

P(p)

P(p)

pF-pF

pF-pF

T>>Tc,TF

T<Tc,TF

e.g.: Superfluidity in Quantum Gases: a) Bosons

C. Raman et al., PRL. 83, 2502-2505 (1999).

Image from: P. Engels and E. A. Cornell

O.M. Maragò et al., PRL 84, 2056 (2000)

• drag free motion

• scissors modes

• vortices, vortex lattice

MIT

Oxford

JILA, ENS, MIT

Superfluidity in Quantum Gases: b) Fermions

Cooper pairs - BCS superfluidity

k

k

T0 exponentially difficult to reach

akFBCS

FeTT 2280

.

(valid for kF|a|<<1)

e.g.: kFa=-0.2 -> TBCS ~ 10-4 TF (very very small)

(very) low-temperature effect

Superfluidity in Quantum Gases: b) Fermions

ways out of it:

manipulate TBCS using a Feshbach resonance

BEC of molecules

BEC/BCS crossover

• Duke• ENS• Innsbruck• JILA • MIT• Rice

use additional particles to mediate interactions - Bosons

• ? ...

Fermi-Bose Mixtures

• boson mediated superfluidity

• boson mediated superfluidity in a lattice

F. Illuminati and A. Albus, Phys. Rev. Lett. 93, 090406 (2004)...

L. Viverit, Phys. Rev. A 66, 023605 (2002)F. Matera, Phys. Rev. A 68, 043624 (2003)T. Swislocki, T. Karpiuk, M. Brewsczyk, Poster 1, Monday...

interplay between tunneling and various on-site-interactions

Fermi-Bose Mixtures

• special interest: mixtures in optical lattices

new phases, composite particles, ...

• composite fermions

M. Cramer et al., Phys. Rev. Lett. 93, 190405 (2004)

there is even more:

Ubf

Ubb 0

1

2

-1

-2

IIFD

IISF

IIFL

IFL

IDM

IDM

IISF

IIFL

IIDM

IIFL

0 1bUbb

.

.

IIDM

M. Lewenstein et al., Phys. Rev. Lett. 92, 050401 (2004)

effective interactions:

)()()()()()(

)()()()()()()()(

,

Fj

BBBF

Fj

Ftrap

Fj

Fj

N

i

BFiBF

BBBB

BBtrap

BB

NgVmt

i

gNgVmt

iF

222

1

2222

2

2

bosons

fermions

Bose-Bose int. Bose-Fermi int.

see also:G. Modugno et al., Science 297, 2240 (2002)

S. Inouye et al., PRL 93, 183201 (2004)

e.g.: 40K - 87Rb mixture:

gB > 0 (aBB ~ 100 a0)

gBF < 0 (aBF ~ -280 a0)

Fermi-Bose Mixtures

new degrees of freedom due to additional interactions

tunable by Feshbach resonances!

Fermi-Bose Mixtures

detailed understanding of interactions and also of loss processes is necessary

Bose-Fermi interaction physics

- system boundary conditions- coupled excitations (e.g. exp. in Jin group, JILA and Inguscio group, LENS)

- Bose-Fermi interactions

- interspecies correlations- novel phases- heteronuclear molecules

Bose-Fermi interaction physics

- system boundary conditions- coupled excitations (e.g. exp. in Jin group, JILA and Inguscio group, LENS)

- Bose-Fermi interactions

- interspecies correlations- novel phases- heteronuclear molecules

6Li/7Liat Duke U., ENS Paris, Innsbruck U., Rice U.6Li/23Na at MIT40K/87Rb at LENS Florence, Jila Boulder, Hamburg U., ETH Zürich

Hamburg Setup

two-species 2D-MOTflux: 87Rb ~ 5 · 109 s-1

40K ~ 5·106 s-1

two-species 3D-MOT Rb ~ 1010

K ~ 3·107

within 10..20 s

magnetic trapax ~ 11 Hz (Rb)rad ~ 260 Hz (Rb)

in addition: dipole trap

soon: optical lattice

Hamburg Setup

experimental setup

laser systems

Mai 2003

first BEC 7/2004

first degenerateFermi gas 8/2004

Sympathetic Cooling

state of the art(temperature):

5x107 6Li at T~0.05 TF

1x106 40K at T~0.15 TF (for K-Rb cooling)

num

ber

of

K-a

tom

s

number of Rb-atoms

ax=11Hz, r=330Hzax=11Hz, r=267Hz

only BEC: >5*106

only Fermions: >1*106

state of the art(particlenumbers):

Attractive Boson-Fermion Interaction

experimental signatures:

Fermion cloud without BEC

aK-Rb ~ -279 a0

+

BEC

=

effective potential for fermions:

Fermion cloud with BEC

Mean Field Instability of the System

BEC

Fermi-Sea

BEC attractionof fermions

BEC density increase

runaway

collapsecollapse

Collapse Experiments7Li collapse Sackett et al., PRL 82, 876 (1999)J.M. Gerton et al., Nature 8, 692 (2000)

85Rb "Bosenova" Donley et al., Nature 412, 295 (2001)

G. Modugno et al., Science 297, 2240 (2002)

Images from: http://spot.colorado.edu/~cwieman/Bosenova.html

40K / 87Rb Fermi-Bose collapse

Fermi-Bose Mixtures in the Large Particle Limit:Local Collapse Dynamics

Fermi-Bose Mixtures in the Large Particle Limit: Collapse

but...: is it just losses??

locally high density: enhanced two- and three-body losses??

Lifetime Regimes

= 21ms = 197ms

time/frequency scales:

- r(K) = 394 Hz- ax(K) = 17 Hz- thermalization 10..50 ms- collapse: ~ 20 ms- loss processes 100..200 ms

3-body-loss-> collapse-time

due to trap dynamics

loss and collapse dynamics can be distinguished!

3-Body Lossesmeasurement of the 3-body KRb decay rate

N K

N K

1 K K Rb Rb

N K

d3

r nB2

r , t nF r , tmodel for 3-body inelastic decay in thermal mixture:

integration over time: ln NK T ln NK 0T

KK Rb Rb 0

Tdt

d3 r nB2 r ,t nF r , t

NK t

-2.5

-2

-1.5

-1

-0.5

0

0 20 40 60 80 100 120 140 160 180

0

T

dtd

3r nB

2r , t nF r ,t

N K t10

38m

6s

ln N K T ln N K 0T

Measurement does not depend on K atom

Rb |2,2> decay, we reproduce the

Result:

number calibration

For 87

value from Söding et al. [Appl. Phys. B69, 257 (1999)]

K K Rb Rb 3.5 10 28 cm6

s( +/- 0.2)

Fermi-Bose Mixtures in the Large Particle Limit:Stability Diagram

stable mixture

non stable mixture aKRb=-281 a0(S. Inouye et al., PRL 93, 183201 (2004))

NBoson

NFermion

Does a Bose Einstein condensate float in a Fermi sea?

... it depends ...

Solitons in Matter Waves

S. Burger et al., PRL 83, 5198 (1999)

J. Denschlag et al., Science 287, 97 (2000)

g>0

B. P. Anderson et al., PRL 86, 2926 (2001)

filled solitons

B. Eiermann et al. PRL 92, 230401(2004)

gap solitons"negative mass"

dark solitons

quantum pressure

interactions

L. Khaykovich et al., Science 296, 1290 (2002)

g<0

bright solitons

quasi-1D regime

collapse for Eint>Eradial

NSoliton< 104

K.S. Strecker et al., Nature 417, 150 (2002)

1D: Bright Mixed ‘‘Solitons‘‘F

crBFBB ngng Bose-Bose repulsion versus Fermi-Bose attraction

T. Karpiuk, M. Brewczyk, S. Ospelkaus-Schwarzer, K. Bongs, M. Gajda, and K. Rzążewski, PRL 93, 100401 (2004)

behaviour inthe trap:

after switchingoff the trap: cr

BFBF gg

crBFBF gg

dynamics:

constantenvelope

simulation from M. Brewczyk et al.

theoryour data

theory by T. Karpiuk, M. Brewczyk, M. Gaida, K. Rzazewski

Collisionsimulation shows complex dynamics:

- repulsive

- shape oscillations

- particle exchange

fermionic character due to the Pauli-principle ?

Simulation from M. Brewczyk et al.

Bose-Fermi Mixtures with Attractive InteractionsPhysics in the High Density Limit

trap aspect ratio

effective interaction("density")

collapse

brightmixedsoliton

att

ract

ive

repuls

ive boson-induced BCS ?

Influence of loss processes ?Influence of loss processes ?

Hamburg TeamHamburg Team

Kai Bongs - Atom optics V. M. Baev - Fibre lasersSpinor BEC:Spinor BEC:Jochen KronjägerChristoph BeckerThomas GarlMartin Brinkmann Fermi-Bose mixtures K-Rb:Silke Ospelkaus-SchwarzerChristian OspelkausPhilipp ErnstOliver WilleManuel Succo

Stefan SalewskiOrtwin Hellmig Arnold StarkSergej WexlerOliver BackGerald Rapior

Victoria RomanoDieter BarloesiusReinhard Mielck

K. Se

Staff

Q. Gu - Theory

BEC in Space:Anika VogelMalte Schmidt

Atom guiding in PCF:Stefan VorathPeter Moraczewski

Cold Quantum Gas GroupCold Quantum Gas GroupHamburgHamburg

Hamburg is a nice city...Hamburg is a nice city...(for physics ) (and for visits!)(for physics ) (and for visits!)