„Fermi-Bose mixtures of 40 K and 87 Rb atoms: Bose Einstein condensate float in a Fermi Klaus Sengstock ca, June 2005 Quantum Optic 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
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„Fermi-Bose mixtures of 40 K and 87 Rb atoms: Does a Bose Einstein condensate float in a Fermi sea?" Klaus Sengstock Krynica, June 2005 Quantum Optics.
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„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)