Atomic Dark-Bright Solitons: Theory and Experiments

A omic Da k-B igh Soli ons: Theo y and Expe imen s D. J. F an zeskakis* Depa men o Physics, Uni e si y o A hens, G eece LENCOS 12, Se ille, July 9-12, 2012 *In collabo a ion wi h: P. G. Ke ekidis, D. Yan (Amhe s ), R. Ca e e o-González (San Diego), M. Hoe e (No h Ca olina), P. Engels, J. Chang., C. Hamne (Washing on), P. Schmelche , S. Middelkamp, J. S ockho e (Hambu g), J. Cue as, A. Al a ez (Se ille) V. Achilleos (A hens), V. Ro hos (Thessaloniki) Ou line Bοse-Eins ein condensa es (BECs) - Bina y BECs - G oss-Pi ae skii mean- ield desc ip ion Da k-b igh soli ons in bina y BECs - Single and mul iple da k-b igh soli ons - SU(2) o a ions: “bea ing” da k-da k soli ons Da k-b igh soli ons a ini e empe a u es - Dissipa i e G oss-Pi ae skii equa ions - Di e en empe a u e-dependen damping egimes Conclusions and ou look Bose-Eins ein condensa es (BECs) BEC: S a e o ma e in which a mac oscopic numbe o pa icles sha e he same quan um s a e Theo e ical p edic ion: Bose-Eins ein (1925) Expe imen al obse a ion: Co nell-Wieman-Ke e le-Hule (1995) in ul acold a oms o 87Rb, 23Na and 7Li. Nobel P ize (2001) Fi s expe imen al obse a ion: magne ically- apped spin s a es o 87Rb BEC (JILA g oup, PRL 1997) Bina y Bose-Eins ein condensa es 2 2 222 2 112 )( 22 2 2 2 1 2 212 2 111 )( 11 2 2 1 2 2 ψψψψψ ψψψψψ        +++∇−=∂        +++∇−=∂ ggV m i ggV m i ex ex     Two coupled G oss-Pi ae skii equa ions ( o di e en hype ine s a es o he same a om species): in a-species a omic collisions in e -species a omic collisions Typically, e.g., o di e en spin s a es o 87Rb: 221211 ggg ≈≈ Bina y BECs in he mean- ield pic u e 2 2 2 2 12 2 2 1 2 2 2 11 2 1 )( 2 1 1)( 2 1 ψµψψψψ ψψψψψ      −+++∂−=∂      −+++∂−=∂ zVi zVi z z 1/ 2 1 )( 22 <<≡Ω Ω= ⊥ ωω z zzV Bina y BECs in highly aniso opic (quasi-1D) ha monic aps Da k-b igh soli ons in homogeneous BECs kD Dkz zzD z i z )]1(2[ 2 1 )(, an)],([ })](exp{i[kzhsec),( ,sin anhcos),( 22 00 2 1 −+−===−= += += µθϕζ θζηψ ϕζϕψ  “Symbio ic” soli ons The b igh soli on (suppo ed only by a ac i e in e ac ions) exis s only due o he in e species in e ac ion wi h he da k soli on b igh soli on da k soli on da k soli on b igh soli on z  Hambu g: Phase-imp in ing o a da k soli on in s a e |1, 0> and illing he densi y dip wi h a oms in s a e |2, 0 >  Washing on: Gene a ion o da k-b igh soli ons by coun e low o wo componen s in he |1, -1> and |2, -2> s a es Obse a ions o da k-b igh soli ons Hambu g expe imen S. S ellme e al., Na . Phys. 2008 Washing on expe imen s C. Hamme e al., PRL 2011 S. Middelkamp e al., PLA 2011 Da k-b igh soli ons in he ap 2 2,1 ψ z Adiaba ic dynamics o da k-b igh soli ons in he ap - s eps o ollow: Find an equa ion o he backg ound wa e unc ion Find a pe u bed NLS sys em o he da k-b igh soli on wa e unc ion Assume: he soli on’s unc ional o m emains he same bu he soli on pa ame e s a e unknown unc ions o ime E olu ion o eno malized Hamil onian  e olu ion o soli on pa ame e s b igh soli on da k soli on apping po en ial backg ound densi y ( )        ∆ −+= −−−++∂+∂= ∫ +∞ ∞− µ ϕ µ ψµψψψψ 223 2 2 22 2 2 1 2 2 2 1 sec 2 1 3 4 ||)1(2)1|||(||||| D N D dzE b zzDB Pe u ba ion heo y – Hamil onian app oach ( ) ( ) ( ) ( ) uVQuu z u u i zdz dV VQu z i b d 2 2 2 2 2 2 2 2 2 2 2 2 1 1 )(|| 2 1 12 2 1 )(1|| 2 1 υ µ υµυ υ υυ µ υυυ υυ −≡=−+− ∂ ∂ + ∂ ∂       ∂ ∂ +−≡=−+− ∂ ∂ + ∂ ∂ App oxima e da k-b igh soli on solu ion o Qd ≠ 0, Qb ≠ 0 as in he unpe u bed case bu wi h: )( an)()(),(),( 0 D z DD ϕϕϕ →→→  Coupled GPEs as coupled pe u bed NLSEs Use o he da k-b igh soli on ene gy o ind he e olu ion o he unknown ime-dependen soli on pa ame e s D, φ, z0 ),()exp()( 1 z iz υµψ −Φ= )(||:ionapp oxima Fe miThomas 2 zV −=Φ− µ BEC wa e unc ion ca ying a da k soli on: da k soli on E olu ion o he da k-b igh soli on ene gy: Oscilla ions o da k-b igh soli ons dz Q QDDNDD d dE b b d db            ∂ ∂ + ∂ ∂ −=++= ∫ +∞ ∞− ∗∗ υυ ϕϕϕ Re2) an(sec4 2   Equa ion o mo ion o he da k-b igh soli on cen e : µ ωω b oscosc N z d z ≡         + − Ω ==+ ; )4/(14 1 2 ,0 d 2/1 2 0 2 2 0 2 22 / Ω osc ω µ / b N S. Middelkamp e al., Phys. Le . A 2011 Busch-Anglin, PRL 2001 D N DDz b µ ϕϕ 2 cos, an 22 0 −==  Dissipa i e dynamics a ini e empe a u es Coupled dissipa i e G oss-Pi ae skii equa ion (DGPEs) (Pi ae skii, So . Phys. JETP 1959) jj k kzj j zVi ψµψψγ        −++∂−=∂− ∑ = 2 1 2 2 )( 2 1 )( )(1),(4;T~ µαµαγ α >>=<<= TkTk BBj Achilleos, Yan, Ke ekidis, F an zeskakis, NJP 2012 ( ) ( ) ( ) ( )       ∂ ∂ +−≡=−+− ∂ ∂ + ∂ ∂         ∂ ∂ + ∂ ∂ +−≡=−+− ∂ ∂ + ∂ ∂ u uVQuu z u u i zdz dV VQu z i bb d d µγυ µ υµυ υ µ γ υ υυ µ υυυ υυ 2 2 2 2 2 2 2 2 2 2 2 2 1 1 )(|| 2 1 12 2 1 )(1|| 2 1 Coupled DGPEs as coupled pe u bed NLSEs Tempe a u e-induced an idamping o soli ons 22 )2/1( V(z) z Ω= Fo adiaba ic pe u ba ion heo y esul s in he ollowing equa ion o mo ion ( o su icien ly deep/slow soli ons): 0 0 2 00 =+− zzaz osc ω  () oscc c osc aaaasass ωω 2, 2 1 0 22 2,1 22 =−±=⇒=+− + ∈⇒> Rsaa c 2,1 + ∈=⇒= Rssaa c 21 Csaa c ∈⇒< 2,1 • Supe -c i ical case : • C i ical case : • Sub-c i ical case : Cockbu n, Nis azakis, Ho ikis, Ke ekidis, P oukakis, F an zeskakis, PRL 2010; PRA2011 Achilleos, Yan, Ke ekidis, F an zeskakis, NJP 2012 2/1 2 2 2 2 )4/(4 1 2 , 8 )4/(6 83 2         + − Ω =        +− + +        −= b b oscb b db b b b b d N NN N NN a µ ωγ µ γγ µ µ γ µ γµ Da k and da k-b igh soli on ajec o ies Supe -c i ical case :Sub-c i ical case : c aa > c aa < Tempe a u e da k soli on b igh soli on b igh soli on da k soli on da k soli on da k-b igh soli on The bi u ca ion diag am is “d i ed” owa ds smalle alues o γ ⇒ da k-b igh soli ons a e mo e obus han da k soli ons Conclusions Da k-b igh soli ons in bina y BECs: - Single- and mul iple-da k-b igh soli ons - SU(2) o a ions: bea ing and egula da k-da k soli ons - Dissipa i e dynamics o da k-b igh soli ons a ini e empe a u es - In all cases connec ion o expe imen s was p o ided Cu en and u u e wo k Vec o soli ons in mul i-componen BECs (including spino BECs) - Sca e ing o ec o soli ons a na ow ba ie s - Dissipa i e dynamics o ec o soli ons in a ious se ings - Vec o soli on dynamics in highe -dimensional se ings “Filled” (wi h he b igh soli on) da k soli ons a e mo e obus han “ba e” da k soli ons in BECs agains :  empe a u e-induced dissipa ion  ans e se ins abili ies (da k-b igh ings) Some ele an e e ences: