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Journal of Research of the National Bureau of Standards Section A Physics and Chemistry

Vortex motions in ideal Bose superfluid

Martin J. Cooper

Published May 1, 1969• 4 citations
Publisher

Abstract

A gene ra l nonlin ea r fi e ld eq u ation is d e ri ved for th e ma c roscopic ord e r parame te r of an id eal cohe re nt Bose gas.It is s hown th a t thi s non int e racti ng sys te m c an su ppo rt s table quantized vortexlike motion s within th e s uperftui d phase.It is s ugges te d th at thi s co he re nt phase of th e id ea l Bose gas describes th e dominant physi ca l feature s of rea l superft uid liquid he lium.Key wo rd s : Cohe re nt Bose gas; s up erftuid ; vort ices.

DOI
10.6028/jres.073a.026

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The method of s e n s itiz e d flu o re sc e n c e was used to d e t e r mine cro ss s e c tio n s f o r th e v ario u s e x c i ta t io n t r a n s f e r p ro cesses 2 2 occuring in K -Rb vapour m ix tu res and f o r ** ^3 /2 ™i%ing and 2 2 2 ^1^2 ^1/ 2 ' ^3 /2 quenching in rubidium induced in c o l l i s i o n s w ith se v e ra l d iatom ic and polyatom ic m olecules in t h e i r ground s t a t e s .The a l k a l i vapour in th e flu o resce n ce c e l l , which was kept a t low p re s s u re s to avoid s e rio u s e f f e c t s o f r a d ia tio n im prisonm ent, was ir r a d i a te d by one component of th e a p p ro p ria te resonance d o u b le t.The r e s u ltin g flu o re s c e n c e , which c o n s is te d o f the w avelength component p re s e n t in th e e x c itin g li g h t (resonance flu o re sc e n c e ) and th o se components which aro se from th e em ission by atoms c o l l i s i o n a l l y p o pulated ( s e n s itiz e d flu o re s c e n c e ), was reso lv ed and observed a t r ig h t an g les to th e d ir e c tio n o f th e in c id e n t beam.Measurements of s e n s itiz e d -to -r e s o n a n c e flu o re s c e n t in t e n s ity r a t i o s in r e l a t i o n to rubidium vapour p re s s u re y ie ld e d the fo llo w in g cro ss s e c tio n s fo r e x c i ta t io n t r a n s f e r in K -Rb vapour m ix tu re s: ^1 2 ' ( ^^^1 /2 = 40 f , Qgg, (K4^P^yg ^ Rb$^P^yg) = 2 ?Q i^,(K 4^Pi/2 -, Rb$2p^yg) = 2 .7 Qg^,(K4^Pgyg -Rb^^P^y^) = 1,9 qJ_2(k4^Pi/2 -K4^P^yj = 260 f , and Q^'(KA^P^y^ -KA^P^y^) = 175 In m ix tu res o f rubidium w ith m olecular g a s e s , measurements o f the i n t e n s ity r a t i o s in r e l a t i o n to gas p re s s u re s gave the fo llo w in g c ro s s s e c tio n s fo r th e mixing and quenching c o l l i s i o n s .

•Jan 1, 1970•0 citations
A gene ra l nonlin ea r fi e ld eq u ation is d e ri ved for th e ma c roscopic ord e r parame te r of an id eal cohe re nt Bose gas.It is s hown th a t thi s non int e racti ng sys te m c an su ppo rt s table quantized vortexlike motion s within th e s uperftui d phase.It is s ugges te d th at thi s co he re nt phase of th e id ea l Bose gas describes th e dominant physi ca l feature s of rea l superft uid liquid he lium.Key wo rd s : Cohe re nt Bose gas; s up erftuid ; vort ices.
c u l a r l y a p p r e c ia te h i s w illin g n e s s to allo w me to conduct my program as I saw f i t , to make my own d is c o v e r ie s and m is ta k e s , and n o t say " I to ld you so" when th in g s ran amuck.I a ls o w ish to than k B i l l Thomason f o r h is in v a lu a b le c o l la b o r a t io n in p o r tio n s o f th e e x p e rim e n ta l work and f o r th e g r e a t i n t e r e s t and p a tie n c e he d is p la y e d th ro u g h o u t o ur a s s o c ia t io n .I w ish to thank P r o f e s s o r Dorr R alph, who i s a n ev er-en d in g so u rce o f ob scu re y e t im p o rtan t in fo rm a tio n , fo r h i s encouragem ent, and a s s is ta n c e in many a s p e c ts o f th e e x p e rim e n ta l work.F u r th e r , I would li k e to thank th e members o f my com m ittee f o r t h e i r i n t e r e s t and s u g g e s tio n s in t h i s work.The te c h n ic a l a s s i s t a n c e , s u g g e s tio n s , and e x p la n a tio n s pro v id ed by Leo Jo rd an and Les E delen have proven in v a lu a b le in th e co m p letio n of t h i s p r o j e c t .O ther members o f th e s t a f f who have done more than t h e i r jo b s r e q u ire d a re th e "gang" i n th e C o lleg e machine shop headed by Joe C ass, and W alter P a tz ig , w ith o u t whose e f f o r t s I would s t i l l be w a itin g f o r new equipment to a r r i v e .My m o th er, f a th e r and b r o th e r a re due s p e c ia l thanks f o r t h e i r c o n tin u ed encouragem ent, love and m oral su p p o rt th ro u g h o u t my educa t i o n a l c a r e e r .I a ls o w ish to thank my b r o t h e r , Buddy, fo r h is a s s is ta n c e in p ro v id in g the p h o to g rap h ic e x p e r t is e n e c e ssa ry to rep ro d u ce many o f th e o s c illo g ra m s ap p ea rin g in t h i s d i s s e r t a t i o n .I a p p r e c ia te th e in v a lu a b le h e l p , lo v e , and encouragem ent of Kathy (G ro ssin ) d u rin g th e co u rse o f t h i s work.I am g r a t e f u l f o r th e f i n a n c i a l a s s is ta n c e in th e p r e p a r a tio n o f t h i s d i s s e r t a t i o n which was p ro v id ed by th e C h arles E. C oates M emorial Fund o f th e L o u isia n a S ta te U n iv e rs ity F o u n d atio n .
in g the o n s e t of d is s ip a tio n at th e ro to n c r i t ic a l v e lo c ity in s u p e r flu id h e liu m .T h is is a c la s s ic a l , c o r r e s p o n d e n c e -p r in c ip le -lim it po in t of v iew and is q u ite an alo g o u s to th e c la s s ic a l d e s c r ip tio n that i s w idely a c c e p te d fo r u n d e rs ta n d in g the e m is s io n of photons by an e le c t r i c c h a rg e th a t m o v e s at a c o n s ta n t v e lo c ity g r e a t e r th a n the sp e e d of lig h t in a d ia le c tr ic m e d iu m .A fte r f i r s t d e riv in g a th e o ry f o r th e w ave e x c ita tio n s and b o u n d a ry -v a lu e p ro b le m s of the c o rre s p o n d e n c e p rin c ip le lim it fo r a co n d en se d -b o so n s y s te m , th is p a p e r show s th a t a w ave r a d i a tio n field f o r m s a ro u n d a fo re ig n body m o v in g th ro u g h the s u p e r fluid m e d iu m w hen the fo re ig n body m o v e s f a s t e r th an the m in im u m p h a se v e lo c ity , {w/k )m jn » w ave e x c ita tio n s in the m e d iu m .M o re o v e r, the sp a tia l d e p e n d e n c e of th is w ave fie ld and the lo s s of e n e rg y r a d ia tin g th ro u g h it a r e c a lc u la te d a s fu n ctio n s of the f r a c tio n a l in c r e a s e of the fo re ig n b o d y 's v e lo c ity above the th r e s h o ld v e lo c ity In s p ite of a p p ro x im a tio n s m a d e in th e c a lc u la tio n s , th e r e s u l t s in d ic a te th a t it is im p o s s ib le , e x p e r i m e n ta lly , to f o r c e an io n c o m p lex to m ove th ro u g h the s u p e rflu id c o m ponent o f h e liu m a t a v e lo c ity o b s e r v a b ly g r e a t e r th an th e ro to n c r i t i c a l v e lo c ity .ACKNOWLEDGMENTS I would lik e to thank P r o f e s s o r R. L. M ills fo r h is c o n trib u tio n s to m y g ra d u a te ed u catio n and fo r h is p e rc e p tiv e c o u n s e l w hile th is r e s e a r c h w a s b e in g c o n d u cted , e s p e c ia lly r e g a r d in g th e re s o lu tio n of s e v e r a l m a th e m a tic a l d iffic u ltie s w hen no so lu tio n s s e e m e d to e x is t.T h e N a tio n a l A e ro n a u tic s and Space A d m in is tr a tio n i s th an k ed f o r i t s fin a n c ia l su p p o rt d u rin g the y e a
The method of s e n s itiz e d flu o re sc e n c e was used to d e t e r mine cro ss s e c tio n s f o r th e v ario u s e x c i ta t io n t r a n s f e r p ro cesses 2 2 occuring in K -Rb vapour m ix tu res and f o r ** ^3 /2 ™i%ing and 2 2 2 ^1^2 ^1/ 2 ' ^3 /2 quenching in rubidium induced in c o l l i s i o n s w ith se v e ra l d iatom ic and polyatom ic m olecules in t h e i r ground s t a t e s .The a l k a l i vapour in th e flu o resce n ce c e l l , which was kept a t low p re s s u re s to avoid s e rio u s e f f e c t s o f r a d ia tio n im prisonm ent, was ir r a d i a te d by one component of th e a p p ro p ria te resonance d o u b le t.The r e s u ltin g flu o re s c e n c e , which c o n s is te d o f the w avelength component p re s e n t in th e e x c itin g li g h t (resonance flu o re sc e n c e ) and th o se components which aro se from th e em ission by atoms c o l l i s i o n a l l y p o pulated ( s e n s itiz e d flu o re s c e n c e ), was reso lv ed and observed a t r ig h t an g les to th e d ir e c tio n o f th e in c id e n t beam.Measurements of s e n s itiz e d -to -r e s o n a n c e flu o re s c e n t in t e n s ity r a t i o s in r e l a t i o n to rubidium vapour p re s s u re y ie ld e d the fo llo w in g cro ss s e c tio n s fo r e x c i ta t io n t r a n s f e r in K -Rb vapour m ix tu re s: ^1 2 ' ( ^^^1 /2 = 40 f , Qgg, (K4^P^yg ^ Rb$^P^yg) = 2 ?Q i^,(K 4^Pi/2 -, Rb$2p^yg) = 2 .7 Qg^,(K4^Pgyg -Rb^^P^y^) = 1,9 qJ_2(k4^Pi/2 -K4^P^yj = 260 f , and Q^'(KA^P^y^ -KA^P^y^) = 175 In m ix tu res o f rubidium w ith m olecular g a s e s , measurements o f the i n t e n s ity r a t i o s in r e l a t i o n to gas p re s s u re s gave the fo llo w in g c ro s s s e c tio n s fo r th e mixing and quenching c o l l i s i o n s .