Transcript „Fermi-Bose mixtures of K and Rb atoms:

Krynica, June 2005
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
Universität Hamburg
Institut für Laserphysik
Cold Quantum Gas Group
Hamburg
Fermi-Bose-Mixture
BEC ‘in Space‘
Spinor-BEC
Atom-Guiding in PBF
Cold Quantum Gas Group
Hamburg
Fermi-Bose-Mixture
Poster by Silke Ospelkaus
on Tuesday
Spinor-BEC
Poster by Jochen Kronjäger
on Monday
Bose-Einstein Condensation
Bose-Einstein distribution
1
f ( )  (   ) / kT
1
e
critical temperature for BEC
S. N. Bose
T>Tc
A. Einstein
T<Tc
kTc  0.94  N
1
3
N0/N
1
1-(T/Tc)3
Tc
T
Bose-Einstein Condensation
High-temperature effect !!!
Bose-Einstein distribution
1
f ( )  (   ) / kT
1
e
critical temperature for BEC
kTc  0.94  N
T>Tc
T<Tc
1
3
N0/N
1
1-(T/Tc)3
Tc
T
Fermions in a Harmonic Trap
Fermi-Dirac distribution
1
f ( ) 
(   ) / kT
e
1
Fermi temperature
E. Fermi
T>TF
kTF  1,81  N
P.A.M. Dirac
T=0
1
3
f()
T=0
F
T~TF
1
T>TF
F

Fermions in a Harmonic Trap
Fermi-Dirac distribution
Quantum statistical effects also for
T~TF, but more difficult to see...
1
f ( ) 
(   ) / kT
e
1
Fermi temperature
kTF  1,81  N
T>TF
T<TF
1
3
f()
T=0
T~TF
1
T>TF
F

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...)
condensate
fraction
thermal
Bosons
Fermions
e.g.: Momentum Distributions of Fermions and Bosons
P(p)
P(p)
T>>Tc,TF
0
p
P(p)
-pF
0
pF
p
-pF
0
pF
p
-pF
0
pF
p
P(p)
T<Tc,TF
0
p
P(p)
P(p)
T<<Tc,TF
0
p
e.g.: Momentum Distributions of Fermions and Bosons
P(p)
P(p)
T>>Tc,TF
0
p
P(p)
-pF
0
pF
p
-pF
0
pF
p
P(p)
T<Tc,TF
0
p
e.g.: Superfluidity in Quantum Gases: a) Bosons
• drag free motion
MIT
C. Raman et al., PRL. 83, 2502-2505 (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
Superfluidity in Quantum Gases: b) Fermions
Cooper pairs - BCS superfluidity
T0
exponentially difficult to reach
TBCS  0.28TF e


k

2kF a
(valid for kF|a|<<1)

k
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
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
...
• boson mediated superfluidity in a lattice
F. Illuminati and A. Albus, Phys. Rev. Lett. 93, 090406 (2004)
...
 interplay between tunneling and various on-site-interactions
Fermi-Bose Mixtures
there is even more:
• special interest: mixtures in optical lattices
 new phases, composite particles, ...
• composite fermions
M. Lewenstein et al.,
Phys. Rev. Lett. 92, 050401 (2004)
M. Cramer et al.,
Phys. Rev. Lett. 93, 190405 (2004)
IIFD
2
IISF
Ubf 1
Ubb 0
-1
IDM
IIFL
IFL
IDM
IIFL
IIFL
IISF
IIDM
.
-2 0IIDM .
b/Ubb 1
Fermi-Bose Mixtures
effective interactions:
Bose-Bose int.
Bose-Fermi int.
NF
2
2
 ( B )
 2 2 ( B)
( B) ( B)
( B)
( B)
i

   Vtrap   g B N B 
  g BF   i( F )  ( B) ,
t
2m
i 1
bosons
fermions
i
 (j F )
t
2
 2 2 (F )
(F ) (F )
( B)

  j  Vtrap  j  g BF N B 
 (j F )
2m
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, 183201 (2004)
see also:
G. Modugno et al., Science 297, 2240 (2002)
Fermi-Bose Mixtures

detailed understanding of interactions
and also of loss processes is necessary
Bose-Fermi interaction physics
- system boundary conditions
- coupled excitations
6Li/7Li
6Li/23Na
40K/87Rb
(e.g. exp. in Jin group, JILA and Inguscio group, LENS)
Bose-Fermi interactions
interspecies correlations
novel phases
heteronuclear molecules
at Duke U., ENS Paris, Innsbruck U., Rice U.
at MIT
at LENS Florence, Jila Boulder, Hamburg U., ETH Zürich
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 10..20 s
magnetic trap
nax ~ 11 Hz (Rb)
nrad ~ 260 Hz (Rb)
soon: optical lattice
in addition: dipole trap
Hamburg Setup
Mai 2003
laser systems
experimental setup
first BEC 7/2004
first degenerate
Fermi gas 8/2004
Sympathetic Cooling
state of the art
(temperature):
number of K-atoms
state of the art
(particle
numbers):
5x107 6Li at T~0.05 TF
1x106 40K at T~0.15 TF (for K-Rb cooling)
nax=11Hz, nr=330Hz
nax=11Hz, nr=267Hz
only BEC: >5*106
only Fermions: >1*106
number of Rb-atoms
Attractive Boson-Fermion Interaction
effective potential for fermions:
aK-Rb ~ -279 a0
+
=
BEC
experimental signatures:
Fermion cloud without BEC
Fermion cloud with BEC
Mean Field Instability of the System
BEC
BEC attraction
of fermions
Fermi-Sea
BEC density
increase
collapse
runaway
Collapse Experiments
7Li
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)
Images from: http://spot.colorado.edu/~cwieman/Bosenova.html
40K
/ 87Rb Fermi-Bose collapse
G. Modugno et al., Science 297, 2240 (2002)
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
t = 197ms
t = 21ms
time/frequency scales:
3-body-loss
-
nr(K) = 394 Hz
nax(K) = 17 Hz
-> collapse-time
due to trap dynamics
thermalization 10..50 ms
collapse: ~ 20 ms
loss processes 100..200 ms
loss and collapse dynamics can be distinguished!
3-Body Losses
measurement of the 3-body KRb decay rate
NK
NK
model for 3-body inelastic
decay in thermal mixture:
integration over time:
ln N K T
ln N K T
T
ln N K 0
T
ln N K 0
K K Rb
NK
1
Rb
3
2
B
d r n r ,t n F r , t
3
T
KK
Rb Rb
0
dt
2
d r n B r ,t n F r , t
NK t
Result:
0
KK
-0.5
-1
Rb
Rb
( 3.5 +/- 0.2) 10
28
cm 6
s
Measurement does not depend on K atom
number calibration
-1.5
For 87Rb |2,2> decay, we reproduce the
value from Söding et al.
[Appl. Phys. B69, 257 (1999)]
-2
-2.5
0
20
40
3
T
0
60
dt
80
100
120
140
160
2
d r n B r , t n F r ,t
10
NK t
38
6
m s
180
Fermi-Bose Mixtures in the Large Particle Limit:
NBoson
Stability Diagram
stable mixture
non stable mixture
aKRb=-281 a0
(S. Inouye et al.,
PRL 93, 183201 (2004)
NFermion
Does a Bose Einstein condensate
float in a Fermi sea?
... it depends ...
Solitons in Matter Waves
g>0
dark solitons
g<0
filled solitons
bright solitons
quantum pressure
interactions
B. P. Anderson et al., PRL 86, 2926 (2001)
gap solitons
"negative mass"
K.S. Strecker et al., Nature 417, 150 (2002)
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, 230401(2004)
1D: Bright Mixed ‘‘Solitons‘‘
Bose-Bose repulsion versus Fermi-Bose attraction
after switching
off the trap:
behaviour in
the trap:
cr
g B nB  g BF
nF
cr
g BF  g BF
our data
theory
cr
g BF  g BF
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, 100401 (2004)
Collision
simulation shows
complex dynamics:
- repulsive
- shape oscillations
- particle exchange
Simulation from
M. Brewczyk et al.
fermionic character due to the Pauli-principle ?
Bose-Fermi Mixtures with Attractive Interactions
Physics in the High Density Limit
repulsive
attractive
effective interaction
("density")
collapse
boson-induced BCS ?
trap aspect ratio
Influence of loss processes ?
bright
mixed
soliton
Hamburg Team
Kai Bongs - Atom optics
Spinor BEC:
Jochen Kronjäger
Christoph Becker
Thomas Garl
Martin Brinkmann
Fermi-Bose mixtures K-Rb:
Silke Ospelkaus-Schwarzer
Christian Ospelkaus
Philipp Ernst
Oliver Wille
Manuel Succo
BEC in Space:
Anika Vogel
Malte Schmidt
Atom guiding in PCF:
Stefan Vorath
Peter Moraczewski
K. Se
V. M. Baev - Fibre lasers
Stefan Salewski
Ortwin Hellmig
Arnold Stark
Sergej Wexler
Oliver Back
Gerald Rapior
Q. Gu - Theory
Staff
Victoria Romano
Dieter Barloesius
Reinhard Mielck
Cold Quantum Gas Group
Hamburg
Hamburg is a nice city...
(for physics ) (and for visits!)