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 ColdCold QuantumQuantum GasGas GroupGroup HamburgHamburg
Fermi-Bose-Mixture Spinor-BEC
BEC ‘in Space‘ Atom-Guiding in PBF ColdCold QuantumQuantum GasGas GroupGroup HamburgHamburg
Fermi-Bose-Mixture Spinor-BEC
Poster by Silke Ospelkaus Poster by Jochen Kronjäger on Tuesday on Monday Bose-Einstein Condensation
Bose-Einstein distribution 1 f (ε) = e(ε −µ )/ kT −1 critical temperature for BEC
1 S. N. Bose A. Einstein 3 kTc ≈ 0.94 hω N
T>Tc T Tc T Bose-Einstein Condensation Bose-Einstein distribution 1 f (ε) = High-temperature effect !!! e(ε −µ )/ kT −1 critical temperature for BEC 1 3 kTc ≈ 0.94 hω N T>Tc T Tc T Fermions in a Harmonic Trap Fermi-Dirac distribution 1 f (ε) = ( ) / e ε −µ kT + 1 Fermi temperature 1 3 E. Fermi P.A.M. Dirac kTF ≈1,81 hω N T>T T=0 F f(ε) T=0 T~TF 1 εF T>TF εF ε Fermions in a Harmonic Trap Fermi-Dirac distribution 1 Quantum statistical effects also for f (ε) = ( ) / ε −µ kT + 1 T~TF, but more difficult to see... e Fermi temperature 1 3 kTF ≈1,81 hω N T>T T T=0 T~TF 1 T>TF εF ε Fermionic Quantum Gases difficulty to reach low temperatures for Fermi gases: no s-wave scattering of identical fermions! Æ no thermalization in evaporative cooling a) Æ use different spin components (D. Jin et al. 98) b) Æ use e.g. a BEC to cool a Fermi sea (and look to the details...) thermal Bosons condensate fraction Fermions e.g.: Momentum Distributions of Fermions and Bosons P(p) P(p) T>>Tc,TF 0 p -pF 0 pF p P(p) P(p) T P(p) P(p) T< P(p) P(p) T>>Tc,TF 0 p -pF 0 pF p P(p) P(p) T 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 r k π − 2kF a TBCS ≈ 0.28TF e r − k (valid for kF|a|<<1) -4 e.g.: kFa=-0.2 -> TBCS ~ 10 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 • ? ... ÆÆFermi-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) ... Æ interplay between tunneling and various on-site-interactions Fermi-Bose Mixtures there is even more: • special interest: mixtures in optical lattices Æ new phases, composite particles, ... • composite fermions II M. Lewenstein et al., FD Phys. Rev. Lett. 92, 050401 (2004) 2 IISF M. Cramer et al., 1 IDM U IIFL Phys. Rev. Lett. 93, 190405 (2004) bf IFL Ubb 0 IIDM IIFL IDM -1 IISF IIFL . IIDM . -201 µb/Ubb Fermi-Bose Mixtures effective interactions: Bose-Bose int. Bose-Fermi int. (B) 2 N ∂ϕ 2 F 2 bosons h 2 (B) (B) (B) (B) (B) (F ) (B) ih = − ∇ ϕ + Vtrap ϕ + gB N B ϕ ϕ + gBF ∑ ϕi ϕ , ∂t 2m i =1 (F ) 2 ∂ϕ 2 fermions j h 2 (F ) (F ) (F ) (B) (F ) ih = − ∇ ϕ j + Vtrap ϕ j + gBF N B ϕ ϕ j ∂t 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 ÆÆ detailed understanding of interactions and also of loss processes is necessary Bose-FermiBose-Fermi interactioninteraction physicsphysics --ssystemystembboundaryoundary conditionsconditions --ccoupledoupled excitationsexcitations (e.g.(e.g.eexp.xp. in inJinJin g group,roup, JILA JILA and andInguscioInguscio group, group, LENS) LENS) --BBose-Fermiose-Fermi interactionsinteractions --interspeciesinterspecies correlationscorrelations --nnovelovel phasesphases --hheteronucleareteronuclear moleculesmolecules 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 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 in addition: dipole trap magnetic trap νax ~ 11 Hz (Rb) νrad ~ 260 Hz (Rb) soon: optical lattice Hamburg Setup Mai 2003 laser systems experimental setup first BEC 7/2004 first degenerate Fermi gas 8/2004 Sympathetic Cooling state of the art 76 5x10 Li at T~0.05TF (temperature): 640 1x10 K at T~0.15TF (for K-Rb cooling) νax=11Hz, νr=330Hz ν =11Hz, ν =267Hz state of the art ax r (particle numbers): f K-atoms o only BEC: >5*106 only Fermions: >1*106 number number of Rb-atoms Attractive Boson-Fermion Interaction aK-Rb ~ -279 a0 Æeffective potential for fermions: + = 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 collapsecollapse 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?? Æ locally high density: enhanced two- and three-body losses?? Lifetime Regimes τ = 197ms τ = 21ms time/frequency scales: -> collapse-time - ν (K) = 394 Hz 3-body-loss r due to trap dynamics - νax(K) = 17 Hz - 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 model for 3-body inelastic N K 1 K K Rb Rb 3 2 decay in thermal mixture: d r nB r,t nF r,t N K N K 3 2 T T d rnB r,t nF r,t integration over time: ln N T ln N 0 K dt K K K Rb Rb 0 N K t T ln N T ln N 0 K K Result: 0 cm 6 K ( 3.5 +/- 0.2) 10 28 -0.5 KRbRb s -1 Measurement does not depend on K atom number calibration -1.5 For 87Rb |2,2> decay, we reproduce the value from Söding et al. -2 [Appl. Phys. B69, 257 (1999)] -2.5 0 20 40 60 80 100 120 140 160 180 3 2 T d rnB r,t nF r,t 38 6 0 dt 10 m s N K t 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 g<0 dark solitons filled solitons bright solitons quantum pressure K.S. Strecker et al., Nature 417, 150 (2002) interactions B. P. Anderson et al., PRL 86, 2926 (2001) gap solitons "negative mass" L. Khaykovich et al., Science 296, 1290 (2002) 4 NSoliton< 10 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‘‘ cr Bose-Bose repulsion versus Fermi-Bose attraction gBnB = gBF nF after switching behaviour in off the trap: cr the trap: 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 9 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 effective interaction ("density") bright collapse mixed soliton attractive boson-induced BCS ? repulsive trap aspect ratio InfluenceInfluenceooffllossoss processesprocesses?? HamburgHamburg TeamTeam K. Se Kai Bongs - Atom optics V. M. Baev - Fibre lasers Spinor BEC: Jochen Kronjäger Stefan Salewski Christoph Becker Ortwin Hellmig Thomas Garl Arnold Stark Martin Brinkmann Sergej Wexler Fermi-Bose mixtures K-Rb: Oliver Back Silke Ospelkaus-Schwarzer Gerald Rapior Christian Ospelkaus Philipp Ernst Oliver Wille Q. Gu -Theory Manuel Succo BEC in Space: Staff Anika Vogel Malte Schmidt Victoria Romano Atom guiding in PCF: Dieter Barloesius Stefan Vorath Reinhard Mielck Peter Moraczewski ColdCold QuantumQuantum GasGas GroupGroup HamburgHamburg HamburgHamburg isis aa nicenice citycity...... ((forfor physicsphysics )) (and(and forfor visitsvisits!)!)