Chromium Bose-Einstein Condensates

Transcription

1 Kioloa, Febuay 8, 6 Choiu ose-einstein Condensates Luis Santos Univesität Stuttgat

2 Choiu EC EC of Choiu atos [Giesaie et al., PRL 94, 64 (5)] Also expeients on Choiu in Pais-Nod It is NOT just anothe EC, because Choiu has a lage agnetic oent, µ=6µ Fist available dipola EC The gound state of 5 C is 7 S 3 Fist available spin-3 EC

3 Outline of the talk Dipola gases C-EC as spin-3 EC =-3 = == =- =- =3

4 Dipola gases In typical expeients up to now the atos inteact via shot-ange isotopic inteactions The inteaction is given by the s-wave scatteing length a 4πh a V ( ) δ( )

5 Dipola gases Recent expeiental developents open a novel eseach aea in cold gases: the analysis of dipola gases Atos with lage agnetic oent, as C Pola olecules Diect cooling of pola olecules Photoassociation of pola olecules in optical lattices Feshbach esonances in binay ixtues [Giesaie et al., PRL 94, 64 (5)] [ethle and Meije, Int. Rev. Phys. Che., 73 (3)] [Jaksch et al., PRL 89, 44 (); Daski et al., PRL 9, 4 (3); Ro et al., PRL 93, 73 (4)] [Stan et al. PRL 93, 43 (4); Inouye et al., PRL 93, 83 (4); Petov et al., cond-at/5] Lase induced dipole-dipole inteaction [O Dell et al., PRL 84, 5687 ()] Rydbeg atos [Jaksch et al., PRL 85, 8 ()]

6 Dipola gases Dipole-dipole inteaction d V( ) = 3 ( 3cos θ ) The inteaction is anisotopic (patially attactive and patially epulsive!) Long-ange inteaction Attactive inteaction Repulsive inteaction

7 Dipola gases At low tepeatues the physics of a dipola EC is given by a nonlocal nonlinea Schödinge equation ), ( ), ( ) 3cos ( ), ( ), ( ), ( 3 t t d g t g t V t t i d h h ψ ψ θ ψ ψ = Nonlocal NLSE g a g d d Nonlocal nonlineaity is also obseved in othe physical systes Plasa physics [Litvak et al., Sov. J. Plasa Phys., 6 (975)] Neatic Liquid Cystals [Peccianti et al., Natue 43, 733 (4)]

8 Dipola gases [Stuhle et al., PRL 95, 546 (5)] The expansion dynaics of a dipola EC is significantly affected by the dipola inteaction [Góal and Santos, PRA 66, 363 (); Yi and You, PRA 67, 456 (3); Giovanai et al., J. Opt. 5, 8 (3)] y aspect atio Ry / R 3.5.5, along y: Fist tace of dipola effects in EC eve!!.5, along : tie of flight [s]

9 Dipola gases Dipola EC pesents any novel chaacteistic featues Tap-dependent stability [Yi and You, PRA 6, 464 (); Góal et al., PRA 6, 56 (); Santos et al., PRL 85, 79 ()] Phonon ε ω h Single paticle (b) OGOLIUOV ql.5.5 Roton Roton-axon excitation spectu [O Dell et al., PRL 9, 4 (3); Santos et al., PRL 9, 543 (3)] D solitons [Pedi and Santos, PRL 95, 546 (5)] Inelastic scatteing Tuly-D otion without distotion!!

10 Outline of the talk Dipola gases C-EC as spin-3 EC =-3 = == =- =- =3

11 Choiu EC as a spino EC F Spin ½ F = F, = = F, = Magnetically tapped 87 Rb [Hall et al., PRL 8, 539 (998)] Spin F Optically tapped Na [Stenge et al.., Natue 396, 345 (998) ] = F, = ±, 87 Rb [Schalljohann et al., PRL 9, 44 (4); Chang et al., PRL 93, 74 (4); Higbie et al., PRL 95, 54 (5)] Spino EC Spin F, = ±, ±, = F 87 Rb [Schalljohann et al., PRL 9, 44 (4); Kuwaoto et al., PRA 69, 6364 (4); Widea et al., PRL 95, 945 (5)]

12 Choiu EC as a spino EC [Santos and Pfau, cond-at/5634] The gound state of 5 C is 7 S 3 =-3 =- =- = Hence, unless we pup into one state (which is what is done up to now), we will have to deal with a spino wavefunction with 7 coponents!!!! Spin-3 EC = = =3 ψ 3 ψ ψ ψ = ψ ψ ψ ψ 3

13 Choiu EC as a spino EC Hˆ = Hailtonian Hˆ Vˆ s Vˆ dd Single paticle physics Shot-ange inteactions Dipole-dipole inteactions H h d ψˆ ( ) U tap ( ) p ˆ = M ψˆ ( ) Zeean effect p = gµ (No quadatic Zeean effect in C-EC)

14 Choiu EC as a spino EC Hˆ = Hailtonian Hˆ Vˆ s Vˆ dd Single paticle physics Shot-ange inteactions Dipole-dipole inteactions n n V ˆ s = d g S S Pˆ S ( ) [Ho, PRL 8, 74 (998)] They conseve the total spin : S= =nn a s-wave scatteing length fo total spin S S Only even S is possible fo osons: S=,,4,6 gs = 4πh as / M This is siila as fo S=, but having S=3 will lead to new physics!! Fo 5 C: [Wene et al., PRL 94, 83 (5)] a =? a = 7()a a = 58(6 4 )a a (4)a 6 =

15 Choiu EC as a spino EC Hˆ = Hailtonian Hˆ Vˆ s Vˆ dd Single paticle physics Shot-ange inteactions Dipole-dipole inteactions They do NOT conseve the total spin Vˆ dd c S n n d d ψˆ ( ) ˆ ( ) ˆ ( ) ˆ ( 3 ψ ψ n ψ n d = n e)( S n 3( S S e) ) This violation of the spin consevation eans that spin can be tansfeed into cente-of-ass angula oentu!! ( S, S S ) S, = ae the spin-3 atices e = ( ') ' x y v v

16 Choiu EC as a spino EC: Gound state Mean-field appoxiation Single-ode appoxiation ψˆ ( ) Nψ ( ) ψ ( ) = Φ( ) ψ Magnetic field in -diection [{ }] ~ p S c~ S c Θ c S S S S S E ψ 3 c = g6 g) /8. 65 ( g c ( g c = g 55g 7g4 5g6) / 33 g = g 6 g4 / 77 g6 /98. / g Θ = ( ) ψ ~ p = p N d Φ( ) ψ 4

17 Choiu EC as a spino EC: Gound state In ode to get a feeling, let s copae with spin- EC [Ciobanu et al., PRA 6, 3367 (); Koashi and Ueda, PRL 84, 66 ()] E 4 5 ~ p S Θ c S c Thesaebutwithout the c 3 te!! Feoagnetic Θ = = S c ~ p / 4 c c / p ~ / 4 =- = = = =- Pola 87 Rb Θ c < c c / > p ~ / 4 =- = = = =- Cyclic Θ = S c > c > ~ / 4 p Relative phases ipotant Fo spin-: only feoagnetic ( 87 Rb) o pola (Sodiu) [Ho, PRL 8, 74 (998)]

18 Choiu EC as a spino EC: Gound state [{ }] ~ p S c~ S c Θ c S S S S S E ψ <.G p~ g POLAR FERROMAGNETIC S,, S OR 3,,,3 4 7 CY 3, CY 3, OR CY, 3 3 6c~ [Diene and Ho, S S CY 3,,, g /g6 Θ S = S ~ / c ~ = p Θ = S = S 6 ~ p / c~ S ~ / c ~ = p Θ = S = S 6 ~ p / c~ = = p c Θ = S o ~ / ~ iaxial neatics cond-at/575] [Madsen et al., PRL 9, 4555 (4); Achaya et al., PRL 9, 4556 (4)]

19 Choiu EC as a spino EC: Dynaics The dipole-dipole inteaction plays a little ole in the gound-state popeties ut it can play a cucial ole in the dynaics! Only shot-ange pat With dipola inteaction Fobidden by spin-consevation =-3 =- =- = = = =3 Spin-elaxation due to the dipola inteaction! =-3 =- =- = = = =3 The loss in spin, ust be gained by the cente of ass angula oentu

20 Choiu EC as a spino EC: Dynaics Density fo the state =- y 5 (a) y 5 (b) x x The state =- stats to otate! It esebles the Einstein-de Haas effect [Kawaguchi et al., cond-at/55] The coheent EH-effect is destoyed if gµ >> hω

21 Choiu EC as a spino EC: Dynaics Also the c 3 tes have a significant ole int he spino dynaics and ay lead to a apid tansfe fo = to =3 and =-3 87 Rb (a) (b) s 5s Fo F= a sequential population is obseved > > > > > 4s 5s (c) [Schalljohann et al., PRL 9, 44 (4] s > > > > > (d) Population 5s =3 = "=" "=" "=" "=3" ωt

22 Suay Popeties of Dipola ECs Nonlocal nonlineaity. Multidiensional solitons C-EC as spino EC =3 D Dipola gases [Sinha and Santos, in pepaation)] =-3 = == =- =- Dipola Lattice gases [Góal et al., PRL 88, 746 ()] Feionic dipola gases [aanov et al., PRL 9, 543 (4)] Rotating dipola gases [aanov et al., PRL 94, 744 (5); Reayi et al., cond-at/5764] Quantu infoation [ennen et al., PRL 8, 6 (999); Jaksch et al., PRL 85, 8 (); DeMille et al., PRL 88, 679 ()]

23 People P. Pedi S. Sinha S. Giovanai R. Nath L. Santos J. Stuhle A. Giesaie T. Koch M. Fattoi T. Pfau M. aanov,. Daski, K. Góal, M. Lewenstein, E. Tieann, G. V. Shlyapnikov, S. Kotochigova P. Julienne, P. Zolle