1. Institut für Laserphysik
Krynica, June Quantum Optics VI
„Fermi-Bose mixtures of 40K and 87Rb atoms: Does a Bose Einstein condensate float in a Fermi sea?"
Klaus Sengstock
Mixtures of ultracold Bose- and Fermi-gases
Bright Fermi-Bose solitons
Dynamics of the system: e.g.: mean field driven collapse
Institut für Laserphysik
Universität Hamburg

2. Hamburg Cold Quantum Gas Group Spinor-BEC Fermi-Bose-Mixture
BEC ‘in Space‘
Atom-Guiding in PBF

3. Hamburg Cold Quantum Gas Group Spinor-BEC Fermi-Bose-Mixture
Poster by Silke Ospelkaus on Tuesday
Poster by Jochen Kronjäger on Monday

4. Bose-Einstein Condensation
Bose-Einstein distribution
critical temperature for BEC
S. N. Bose
A. Einstein
T>Tc
T<Tc
N0/N
1-(T/Tc)3 1 Tc T

5. Bose-Einstein Condensation
Bose-Einstein distribution
High-temperature effect !!!
critical temperature for BEC
T>Tc
T<Tc
N0/N
1-(T/Tc)3 1 Tc T

6. Fermions in a Harmonic Trap
Fermi-Dirac distribution
Fermi temperature
E. Fermi
P.A.M. Dirac
T>TF
T=0
f(e)
T=0
T~TF 1 eF
T>TF eF e

7. Fermions in a Harmonic Trap
Fermi-Dirac distribution
Quantum statistical effects also for T~TF, but more difficult to see...
Fermi temperature
T>TF
T<TF
f(e)
T=0
T~TF 1
T>TF eF e

8. Fermionic Quantum Gases
difficulty 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
condensate
fraction
Fermions

9. e.g.: Momentum Distributions of Fermions and Bosons
P(p)
P(p)
T>>Tc,TF p
-pF pF p
P(p)
P(p)
T<Tc,TF p p
-pF pF
P(p)
P(p)
T<<Tc,TF p p
-pF pF

10. e.g.: Momentum Distributions of Fermions and Bosons
P(p)
P(p)
T>>Tc,TF p
-pF pF p
P(p)
P(p)
T<Tc,TF p p
-pF pF

11. e.g.: Superfluidity in Quantum Gases: a) Bosons
drag free motion
MIT
C. Raman et al., PRL. 83, (1999).
scissors modes
Oxford
O.M. Maragò et al., PRL 84, 2056 (2000)
vortices, vortex lattice
JILA, ENS, MIT
Image from: P. Engels and E. A. Cornell

12. Superfluidity in Quantum Gases: b) Fermions
Cooper pairs - BCS superfluidity
T0
exponentially difficult to reach
(valid for kF|a|<<1)
e.g.: kFa=-0.2 -> TBCS ~ 10-4 TF (very very small)
(very) low-temperature effect

13. 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
? ...

14.   Fermi-Bose Mixtures
boson mediated superfluidity
L. Viverit, Phys. Rev. A 66, (2002)
F. Matera, Phys. Rev. A 68, (2003)
T. Swislocki, T. Karpiuk, M. Brewsczyk, Poster 1, Monday
...
boson mediated superfluidity in a lattice
F. Illuminati and A. Albus, Phys. Rev. Lett. 93, (2004)
...
 interplay between tunneling and various on-site-interactions

15. Fermi-Bose Mixtures there is even more:
special interest: mixtures in optical lattices
 new phases, composite particles, ...
Ubf
Ubb 1 2 -1 -2
IIFD
IISF
IIFL
IFL
IDM
IIDM
mb/Ubb .
composite fermions
M. Lewenstein et al.,
Phys. Rev. Lett. 92, (2004)
M. Cramer et al.,
Phys. Rev. Lett. 93, (2004)

16. Fermi-Bose Mixtures effective interactions:
Bose-Bose int.
Bose-Fermi int.
bosons
fermions
new degrees of freedom due to additional interactions
e.g.: 40K - 87Rb mixture:
gB > 0 (aBB ~ 100 a0)
gBF < 0 (aBF ~ -280 a0)
tunable by Feshbach resonances!
S. Inouye et al., PRL 93, (2004)
see also:
G. Modugno et al., Science 297, 2240 (2002)

17. 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
6Li/7Li at Duke U., ENS Paris, Innsbruck U., Rice U.
6Li/23Na at MIT
40K/87Rb at LENS Florence, Jila Boulder, Hamburg U., ETH Zürich

18. Hamburg Setup two-species 2D-MOT flux: 87Rb ~ 5 · 109 s-1
40K ~ 5·106 s-1
two-species 3D-MOT
Rb ~ 1010
K ~ 3·107
within s
in addition: dipole trap
magnetic trap
nax ~ 11 Hz (Rb)
nrad ~ 260 Hz (Rb)
soon: optical lattice

19. Hamburg Setup laser systems experimental setup Mai 2003
first BEC 7/2004
first degenerate
Fermi gas 8/2004

20. Sympathetic Cooling 5x107 6Li at T~0.05 TF
state of the art (temperature):
5x107 6Li at T~0.05 TF
1x106 40K at T~0.15 TF (for K-Rb cooling)
nax=11Hz, nr=330Hz
state of the art (particle
numbers):
nax=11Hz, nr=267Hz
number of K-atoms
only BEC: >5*106
only Fermions: >1*106
number of Rb-atoms

21. Attractive Boson-Fermion Interaction
aK-Rb ~ -279 a0 +
BEC =
effective potential for fermions:
Fermion cloud with BEC
experimental signatures:
Fermion cloud without BEC

22. Mean Field Instability of the System
BEC
BEC attraction
of fermions
Fermi-Sea
collapse
BEC density
increase
runaway

23. Collapse Experiments 7Li collapse 85Rb "Bosenova"
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)
Images from:
40K / 87Rb Fermi-Bose collapse
G. Modugno et al., Science 297, 2240 (2002)

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

25. Fermi-Bose Mixtures in the Large Particle Limit: Collapse
but...: is it just losses??  locally high density: enhanced two- and three-body losses??

26. Lifetime Regimes t = 197ms t = 21ms time/frequency scales:
3-body-loss
-> collapse-time
due to trap dynamics
time/frequency scales:
- nr(K) = 394 Hz
- nax(K) = 17 Hz
- thermalization ms
- collapse: ~ 20 ms
- loss processes ms
loss and collapse dynamics can be distinguished!

27. 3-Body Losses measurement of the 3-body KRb decay rate N 1 d r n , t2 , t F
model for 3-body
inelastic
decay in thermal mixture:
integration over time: ln T dt
-2.5 -2
-1.5 -1
-0.5 20 40 60 80
100
120
140
160
180 T ln N T ln N
Result: K K cm 6 K
( /- 0.2)
3.5 10 28 K Rb Rb s
Measurement does not depend on K atom
number calibration
For 87
Rb |2,2> decay, we reproduce the
value from Söding et al.
[Appl. Phys. B69, 257 (1999)] T d 3 r n 2 r , t n r , t dt B F 10 38 m 6 s N t K

28. Fermi-Bose Mixtures in the Large Particle Limit:
Stability Diagram
NBoson
stable mixture
non stable mixture
aKRb=-281 a0
(S. Inouye et al.,
PRL 93, (2004))
NFermion

29. Does a Bose Einstein condensate float in a Fermi sea?
... it depends ...

30. Solitons in Matter Waves
g>0
g<0
dark solitons
filled solitons
bright solitons
quantum pressure
interactions
K.S. Strecker et al., Nature 417, 150 (2002)
B. P. Anderson et al., PRL 86, 2926 (2001)
gap solitons
"negative mass"
L. Khaykovich et al., Science 296, 1290 (2002)
NSoliton< 104
S. Burger et al., PRL 83, 5198 (1999)
quasi-1D regime
collapse for Eint>Eradial
J. Denschlag et al., Science 287, 97 (2000)
B. Eiermann et al. PRL 92, (2004)

31. 1D: Bright Mixed ‘‘Solitons‘‘
Bose-Bose repulsion versus Fermi-Bose attraction
our data
after switching
off the trap:
behaviour in
the trap:
theory
theory by T. Karpiuk, M. Brewczyk, M. Gaida, K. Rzazewski
dynamics:
constant
envelope 
simulation from M. Brewczyk et al.
T. Karpiuk, M. Brewczyk, S. Ospelkaus-Schwarzer, K. Bongs, M. Gajda, and K. Rzążewski, PRL 93, (2004)

32. Collision simulation shows complex dynamics: - repulsive
- shape oscillations
- particle exchange
Simulation from
M. Brewczyk et al.
fermionic character due to the Pauli-principle ?

33. effective interaction
Bose-Fermi Mixtures with Attractive Interactions Physics in the High Density Limit
effective interaction
("density")
bright
mixed
soliton
collapse
attractive
boson-induced BCS ?
repulsive
trap aspect ratio
Influence of loss processes ?

34. Hamburg Team K. Se Kai Bongs - Atom optics V. M. Baev - Fibre lasers
Spinor BEC:
Jochen Kronjäger
Christoph Becker
Thomas Garl
Martin Brinkmann
Stefan Salewski
Ortwin Hellmig Arnold Stark
Sergej Wexler
Oliver Back
Gerald Rapior
Fermi-Bose mixtures K-Rb:
Silke Ospelkaus-Schwarzer
Christian Ospelkaus
Philipp Ernst
Oliver Wille
Manuel Succo
Q. Gu - Theory
BEC in Space:
Anika Vogel
Malte Schmidt
Staff
Victoria Romano
Dieter Barloesius
Reinhard Mielck
Atom guiding in PCF:
Stefan Vorath Peter Moraczewski

35. Hamburg Cold Quantum Gas Group Hamburg is a nice city...
(for physics ) (and for visits!)