Krynica, June 2005 Quantum Optics VI Fermi-Bose mixtures of 40 K and 87 Rb atoms: Does a Bose Einstein condensate float in a Fermi sea?" Mixtures of ultracold Bose- and Fermi-gases Bright Fermi-Bose solitons Dynamics of the system: e.g.: mean field driven collapse Klaus Sengstock Universität Hamburg Institut für Laserphysik
Cold Quantum Gas Group Hamburg Fermi-Bose-Mixture Spinor-BEC BEC in Space Atom-Guiding in PBF
Cold Quantum Gas Group Hamburg Fermi-Bose-Mixture Spinor-BEC Poster by Silke Ospelkaus on Tuesday Poster by Jochen Kronjäger on Monday
Bose-Einstein Condensation Bose-Einstein distribution 1 f ( ε ) = ( ε µ )/ kt 1 e critical temperature for BEC S. N. Bose A. Einstein kt c 0.94 hω N 1 3 T>T c T<T c N 0 /N 1 1-(T/T c ) 3 T c T
Bose-Einstein Condensation High-temperature effect!!! Bose-Einstein distribution 1 f ( ε ) = ( ε µ )/ kt 1 e critical temperature for BEC kt c 0.94 hω N 1 3 T>T c T<T c N 0 /N 1 1-(T/T c ) 3 T c T
Fermions in a Harmonic Trap Fermi-Dirac distribution 1 f ( ε) = ( ε µ ) / kt e + 1 Fermi temperature E. Fermi P.A.M. Dirac kt F 1,81 hω N 1 3 T>T F T=0 f(ε) ε F 1 T=0 T~T F T>TF ε F ε
Fermions in a Harmonic Trap Fermi-Dirac distribution Quantum statistical effects also for T~T F, but more difficult to see... 1 f ( ε) = ( ε µ ) / kt e + 1 Fermi temperature kt F 1,81 hω N 1 3 T>T F T<T F f(ε) 1 T=0 T~T F T>T F ε F ε
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>>T c,t F 0 p -p F 0 p p F P(p) P(p) 0 p T<T c,t F -p F p F 0 p P(p) P(p) 0 p T<<T c,t F -p F p F 0 p
e.g.: Momentum Distributions of Fermions and Bosons P(p) P(p) T>>T c,t F 0 p -p F 0 p p F P(p) P(p) 0 p T<T c,t F -p F p F 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 T60 exponentially difficult to reach k r T BCS 0. 28T F e π 2k F a (valid for k F a <<1) k r e.g.: k F a=-0.2 -> T BCS ~ 10-4 T F (very very small) (very) low-temperature effect
Superfluidity in Quantum Gases: b) Fermions ways out of it: manipulate T BCS 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
there is even more: Fermi-Bose Mixtures 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) 2 U 1 bf U bb 0 II FD II SF II FL IFL I DM II FL I DM II DM -1 II SF II FL. II -2 DM. 0 µ 1 b /U bb
effective interactions: ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (, F j B B BF F j F trap F j F j N i B F i BF B B B B B B trap B B N g V m t i g N g V m t i F ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ 2 2 2 1 2 2 2 2 2 2 + + = + + + = = h h h h 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.: 40 K - 87 Rb mixture: g B > 0 (a BB ~ 100 a 0 ) g BF < 0 (a BF ~ -280 a 0 ) 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. (e.g. exp. exp. in in Jin Jin group, group, JILA JILA and and Inguscio Inguscio group, group, LENS) LENS) - Bose-Fermi interactions - interspecies correlations - novel phases - heteronuclear molecules 6 Li/ 7 Li at Duke U., ENS Paris, Innsbruck U., Rice U. 6 Li/ 23 Na at MIT 40 K/ 87 Rb at LENS Florence, Jila Boulder, Hamburg U., ETH Zürich
soon: optical lattice Hamburg Setup two-species 2D-MOT flux: 87 Rb ~ 5 10 9 s -1 40 K ~ 5 10 6 s -1 two-species 3D-MOT Rb ~ 10 10 K ~ 3 10 7 within 10..20 s magnetic trap ν ax ~ 11 Hz (Rb) ν rad ~ 260 Hz (Rb) in addition: dipole trap
Mai 2003 Hamburg Setup laser systems experimental setup first BEC 7/2004 first degenerate Fermi gas 8/2004
Sympathetic Cooling state of the art (temperature): 5x10 7 6 Li at T~0.05T F 1x10 6 40 K at T~0.15T F (for K-Rb cooling) state of the art (particle numbers): number of K-atoms ν ax =11Hz, ν r =330Hz ν ax =11Hz, ν r =267Hz only BEC: >5*10 6 only Fermions: >1*10 6 number of Rb-atoms
Attractive Boson-Fermion Interaction a K-Rb ~ -279 a 0 effective potential for fermions: + = BEC experimental signatures: Fermion cloud without BEC Fermion cloud with BEC
Mean Field Instability of the System BEC Fermi-Sea BEC attraction of fermions BEC density increase runaway collapse
7 Li collapse Sackett et al., PRL 82, 876 (1999) J.M. Gerton et al., Nature 8, 692 (2000) Collapse Experiments 85 Rb "Bosenova" Donley et al., Nature 412, 295 (2001) Images from: http://spot.colorado.edu/~cwieman/bosenova.html 40 K / 87 Rb 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 τ = 197ms τ = 21ms 3-body-loss time/frequency scales: - ν r (K) = 394 Hz - ν ax (K) = 17 Hz - thermalization 10..50 ms - collapse: ~ 20 ms - loss processes 100..200 ms -> collapse-time due to trap dynamics loss and collapse dynamics can be distinguished!
3-Body Losses measurement of the 3-body KRb decay rate model for 3-body inelastic decay in thermal mixture: integration over time: ln N K T ln N K 0 N K 1 K K Rb Rb N K N K T K K Rb Rb 0 d 3 2 r n B r,t n F r,t T dt d 3 rn B 2 r,t n F r,t N K t ln N K T ln N K 0 0-0.5 T Result: K K Rb Rb 3.5 10 28 cm 6 ( +/- 0.2) s -1-1.5-2 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)] -2.5 0 20 40 60 80 100 120 140 160 180 T dt d 3 rn B 2 r,t n F r,t 0 N K t 10 38 m 6 s
Fermi-Bose Mixtures in the Large Particle Limit: Stability Diagram N Boson stable mixture non stable mixture a KRb =-281 a 0 (S. Inouye et al., PRL 93, 183201 (2004) N Fermion
Does a Bose Einstein condensate float in a Fermi sea?... it depends...
Solitons in Matter Waves g>0 g<0 dark solitons 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) N Soliton < 10 4 S. Burger et al., PRL 83, 5198 (1999) quasi-1d regime J. Denschlag et al., Science 287, 97 (2000) B. Eiermann et al. PRL 92, 230401(2004) collapse for E int >E radial
T. Karpiuk, M. Brewczyk, S. Ospelkaus-Schwarzer, K. Bongs, M. Gajda, and K. Rzążewski, PRL 93, 100401 (2004) 1D: Bright Mixed Solitons Bose-Bose repulsion versus Fermi-Bose attraction behaviour in the trap: our data theory after switching off the trap: g n = B B g cr BF n F cr g BF < g BF cr g BF > g BF theory by T. Karpiuk, M. Brewczyk, M. Gaida, K. Rzazewski dynamics: constant envelope simulation from M. Brewczyk et al.
simulation shows complex dynamics: Collision - 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 effective interaction ("density") attractive collapse bright mixed soliton repulsive boson-induced BCS? trap aspect ratio Influence of ofloss processes?
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 Hamburg Team 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!)