Quantum hydrodynamics

Transcription

1 Outline 1 2 Peter vn der Strten Atom Optics nd Ultrfst Dynmics 3 theory experiment 4 Het trnsfer elow T c 5 Summry nd Outlook 1 / 8 2 / 8 Tisz-Lndu two-fluid hydrodynmics ( ) Superfluid: component of liquid which is ssocited with mcroscopic occuption (BEC) of one single-prticle stte. Crries zero entropy, flows without dissiption with n irrottionl velocity. Hydrodynmicl interctions etween superfluid nd norml fluid Tisz Norml fluid: comprised of incoherent therml excittions, ehves like ny fluid t finite tempertures in locl thermodynmic equilirium. This requires strong collisions. Lndu 4 / 8 5 / 8

2 Physics Tody, Octoer 29 First nd second sound in liquid helium First sound Pressure wve In-phse Temperture wve Out-of-phse 6 / 8 nd Bose gses 7 / 8 9 / 8 Current setup Russell J. Donnelly, Physics Tody, Octoer 29 8 / 8

3 Utrecht s sodium BEC setup Hydrodynmic, cold therml cloud Sodium BEC since August 24 Typiclly produce record toms in BEC Cloverlef type mgnetic trp: flexile trp frequencies Spin polriztion of toms efore trnsfer to mg. trp Fully utomted dt collection Shot-to-shot fluctutions less thn 2% Hydrodynmic therml cloud in xil direction Phse contrst imging Rdil trp size < men free pth < xil size Collision rte 1 2 Hz, rdil/xil trp frequencies 1 Hz/1 Hz Lrge tom numer due to suppression of vlnches fter three-ody collisions 1 / 8 Phse contrst imging Setup 11 / 8 Phse contrst imging Imges 12 / 8 13 / 8

4 Motivtion Liquid helium: second sound is out-of-phse Two component system: superfluid BEC, dilute therml cloud Reched hydrodynmic regime in therml cloud Lndu s two-fluid model in dilute gsses Study friction superfluid BEC therml cloud Friction? Sign of superfluidity? 15 / 8 Effects of therml cloud on BEC 16 / 8 Effects of therml cloud on BEC Position therml cloud (um) Frequency:7.783 Hz Time (s) Pull BEC & therml cloud to the left Blue detuned dipole trp Seprtes BEC from therml cloud Turn off dipole trp Therml cloud: collision rte 2 s 1 Position BEC (um) Position difference (um) Time (s) Frequency:7.477 Hz Dmping:2.4 s^ Time (s) 17 / 8 19 / 8

5 Out-of-phse oscilltion Interction therml cloud BEC Therml cloud strts to oscillte, BEC dmps. Friction? Possile mechnisms: Men field pressure on therml cloud Other hydrodynmic effects... Friction independent of trp frequency Hydrodynmic effects strongly depend on trp frequency Position difference BEC nd therml cloud Dmped out-of-phse dipole oscilltion 2 / 8 Interction therml cloud BEC 21 / 8 Lndu dmping 3 Scttering of therml excittions through the men field of the condenste (collisionless) 1.5Hz 4Hz Γ=.85 s 1 Γ=1.6 s 1 Dmping scles with trp frequency! Dmping proly cused y hydrodynmic effects Dmping of BEC y therml cloud 1 2 Discussed for the first time y Lndu for plsm oscilltions Also pplicle for the qurk-gluon plsm, nomlous skin effects in metls, phonons in metls Discussed for trpped Bose gses y Fedichev et l., Phys. Rev. Lett. 8, 2269 (1998). Dmping of superfluid flow y therml cloud, R. Meppelink et l. Phys. Rev. Lett. 13, (29) 22 / 8 23 / 8

6 Dmping rte for different hydrodynmicity 2. Rtio dmping rtes Direct oservtion of second sound Hydrodynmicity Dmping of superfluid flow y therml cloud, R. Meppelink et l. Phys. Rev. Lett. 13, (29) 24 / 8 Speed of sound theory theory Two modes: the norml fluid (n) nd the superfluid (s): n t = (n n v n +n s v s ), (n n v n + n s v s ) t For the superfluid: v s t = µ m. After linerizing (n = n + δn): 2 δs t 2 = n s mn n s 2 2 δt nd = p m, s t = (ns v n ) 2 δn t 2 = 1 m 2 δp. 26 / 8 theory Speed of sound theory (cont.) Two prmeters (n, T ) nd plne wves δa = δa e i( k r ωt) with c = ω/k: ( ) ( ( ) s s c 2 δn + c 2 n ) s s 2 δt = n T mn n T nd ( c 2 1 m Solutions re with c 1 2 = 1 m n ( ) ) p δn 1 ( ) p δt =. n T m T n 2c ± 2 = ( c c 2 2 ) ± (c 1 2 c 2 2 ) 2 + 4δ 4, ( ) p, c 2 2 = n ss 2 T, δ 4 = 4c 2 2 ε 1 c 2 n s mn n c v 1 + ε, ε = c p c v c v 27 / 8 28 / 8

7 Speed of sound theory Motivtion experiment 2 t< Speed of sound [mm/s] only exists for two-fluid system Sound propgtion cn only e oserved under hydrodynmic conditions for dilute Bose gs is density wve in the condenste Effect of the therml toms on second sound is known Dmping rtes unknown t= Temperture [μk] 29 / 8 experiment Generting sound 3 / 8 experiment Detecting sound t> Density difference(r. units) t=5 ms t=6 ms t=7 ms t=8 ms t=9 ms t=1 ms Grow the condenste with lue detuned dipole em in center At t = shut off dipole em Wit & see t=11 ms z/r tf Sound propgtion in Bose-Einstein condenste t finite tempertures, R. Meppelink et l., Phys. Rev. A 8, 4365 (29). 31 / 8 32 / 8

8 experiment Comprison to theory Sound in nother wy T /T c.3 experiment Normlized speed of sound 1.5 Crete nerly pure BEC in mgnetic trp 1. Modulte the rdil trp frequency ωr with frequency close to ωr Due to the coupling etween rdil nd xil motion stnding wve pttern develops fter some time.95 Using the reltion ω = cs k, the sound velocity cs cn e determined with high ccurcy Normlized to Lndu & ZGN speed of sound.9 see lso Engels et l., Phys. Rev. Lett. 98, 9531 (27) Therml density (118 m 3 ) Sound propgtion in Bose-Einstein condenste t finite tempertures, R. Meppelink et l., Phys. Rev. A 8, 4365 (29). experiment 33 / 8 Stnding wve of sound experiment 34 / 8 36 / 8 Experimentl dt, ω vs. k 35 / 8

9 experiment Stnding wve of sound fits experiment Stnding wve of sound speed of sound 4.5 Cs (mm/s) ω/2π (Hz) Scling of the sound velocity with xil trp frequency experiment 37 / 8 From rdil to Frdy modes experiment 38 / 8 Anlysis continuous driving 7 Rdil width (µm) Time (ms) Time Frdy mplitude / Time (ms) 4 / 8

10 experiment Het trnsfer elow Tc Anlysis single pulse 2 FFT mplitude (u) Het trnsfer elow Tc 14 Simultneous detection of first nd second sound Time (ms) 5 Het trnsfer elow Tc / 8 Motivtion Het trnsfer elow Tc 43 / 8 45 / 8 Mesurement setup Detect first nd second sound simultneously First sound is minly temperture wve, second sound is density wve One cn only loclly het the smple, not cool Extend the work ove Tc [Phys. Rev. Lett. 13, 9531 (29)] to elow Tc 44 / 8

11 Het trnsfer elow Tc Het trnsfer elow Tc Results Results 2.3 c τ = 47 ms τ = 38 ms e d τ = 56 ms f BEC τ = 29 ms Aspect rtio therml cloud τ = 74 ms τ = 65 ms h d i Het trnsfer elow Tc c g Stnding wve Qudrupole τ = 2 ms Time (s) 47 / 8 Results -3-4 dens. grd. BEC (.u.) temp. grd. (.u.) τ = 11 ms τ = 2 ms Time (s) Het trnsfer elow Tc 48 / 8 Results.9 BEC frction Center-of-mss (mm) BEC ωs,bec /ωx Γs,BEC /ωx Therml cloud ωs,th /ωx Γs,th/ωx Stnding wve sound mode c d Time (s) T /T c 49 / 8 5 / 8

12 Results Het trnsfer elow T c Results Het trnsfer elow T c.2 Oscillting condenste frction.15 Γfrc/ωx Γoop/ωx.1.5 ωfrc/ωx T /T c ωoop/ωx T /T c 51 / 8 Summry nd Outlook Tke-wy messge 52 / 8 Summry nd Outlook The Crew : Density wve in the condenste BEC Aspectrtio thermlcloud Qudrupole Time(s) Stndingwve Time(s) c d temp. grd. (.u.) dens. grd. BEC (.u.) : proof for persistent flow? Normlizedspeedof sound T/Tc NormlizedtoLndu& ZGNspeedof sound Thermldensity (1 18 m 3 ) Het trnsfer elow T c : proof of two sound modes! Grd. students: Erik vn Ooijen Dries vn Oosten Richrd vn der Stm Roert Meppelink Silvio Koller Alexnder Groot Pieter Bons Technicins: Frits Ditewig Cees de Kok Pul Jurrius Theory: Henk Stoof Remert Duine 54 / 8 55 / 8