c-field descriptions of nonequilibrium polariton fluids

Transcription

1 c-feld descrpos of oequlbrum polaro fluds Mchel Wouers Iacopo Carusoo, Vcezo Savoa

2 polaro characerscs Dsperso D / 1D / 0D Ieracos g= ev 1 mm -1 1 mev homogeeous broadeg (bu log lfe me) 0.x mev Polaro lfe me 1-10 s ps oequlbrum g=-0.001? shor rage ( 0.01mm) polarzao depede (b-exco feshbach resoace?) weak: gm/ħ 1 mea feld heory OK [C. Cu e al. PB 1998] [Kwog e al. PB 007] [M.W. PB 007]

3 overvew c-feld models (Gross-Paevsk+ &rucaed Wger) superfludy coherece (BEC)

4 mea feld heory (GPE) ˆ ˆ V g F x ex L, F L usual GPE esoa excao klxl x F e L fe lfe me scales) exeral pumpg laser, creaes a plae wave cohere polaro quaum flud hered from laser super? 0 e k L x depedely uable L equlbrum codesae k x e L m 0 k L m g m where 0

5 superfludy persse curres : rval (drve by laser) scaerg off weak defecs: orval Ladau crero v<v c : flow whou scaerg v>v c : Cerekov radao grea smlary wh equlbrum GPE [Carusoo ad Cu, PL 004; Amo e al. Na. Phys. 009]

6 dyamcal sably x k L L L L e F x F, x k L L e 0 always?? x k x k x k s L L s s e e e 0 paramerc scaerg sgal dler OPO= opcal paramerc oscllaor: occupao of sgal/dler mea feld heory spoaeous U(1) symmery breakg: p s bu s free oequlbrum aalog of BEC phase raso [Houdre e al. PL 000] [Seveso e al. PL 000]

7 dyamcs close o bfurcao Dsperso Im[]? effecve model for sgal dyamcs e[] e[] complex Gzburg Ladau-equao (=complex Gross-Paevsk Equao) a b lear: dsperso ad ga b c d e U(1) symmerc eraco: ga saurao ad eergy shf [Cross & Hoheberg, MP 1993] [Araso&Kramer MP 00] [Keelg & Berloff PL 008]

8 oresoa excao cohere relaxao Sysem eservor excos hermalze wh lace complcaed relaxao process whe polaros are jeced a hgh eergy, bu o chage aure of dyamcal sably also model wh cgle or wh smlar pheomeologcal models aalogy wh lasers (Joaha Keelg)

9 reservor model ex g g V P ga ga saurao exco-polaro eraco polaro feld dyamcs coupled o exco desy dyamcs eservor Sysem

10 applcao: acceleraed codesae experme heory [E. Werz e al. Na. Phys. 010] [M.W. e al PB 010]

11 excao specrum excao specrum real par magary par zero crcal velocy? [M.Szymaska e al. PL 006)] [M. Wouers ad I. Carusoo, PL 007]

12 superfludy : eraco wh a defec v/c s = Force o he defec fe superflud fraco [J. Keelg, PL 011] [M. W. ad I. Carusoo, PL 010]

13 excao specrum II Sac defec exces modes for whch ω k = 0 e(k) Im(k) Codesae perurbao oscllao Spaal decay rae

14 measable flows sgle defec may defecs sparse dese perurbao of he wave fuco, force o defec, bu o decay of superflow Dampg of excaos ehaces sably of superflow! o decay decay

15 log rage order BEC: U(1) broke sae has ODLO: x x' c x x' ˆ ˆ for Wha abou he OPO? descrpo of flucuao eeded go beyod mea feld heory ou of equlbrum o exp[-b H] Bolzma dsrbuo dyamcal heory of ope sysem :, H L[ ] smplfcao eeded!! Hamloa evoluo Ldblad: losses, cohere ga from reservor

16 quaum c-feld map quaum dsspave dyamcs o classcal sochasc process by meas of he Wger (quas-) probably dsrbuo = Trucaed Wger approxmao Observables: e.g. 1-body desy marx P W ˆ P W ˆ x' ˆ x' ˆ x d x P x x' 1 * x W s sampled by fucos ha follow he sochasc process 4 d L, V x g x x F d dw x GPE ose, relaed o losses dw * x, dw x', ' d x, x', '

17 relao o Bolzma eq. for homogeeous sysem: k xx' x x' k e ˆ ˆ formao o LO momeum dsrbuo, ha ca be compued wh Bolzma dk PA o GPE whou ose Bolzma equao whou spoaeous scaerg d d k k PA o GPE wh ose Bolzma equao wh spoaeous scaerg + d d g B k I full usual Bolzma k spurous, should be small wh respec o I B or sasfed f k 1 or γ gk max max see e.g. [Y. Kaga Bose-Ese codesao, Grff, Soke, Srgar eds ]

18 OPO: coherece across hreshold heory experme A hreshold Below hreshold Above hreshold [Carusoo ad Cu, PB 005] [. Spao e al, arxv: ]

19 Noresoa excao: coherece experme heory (reservor+wger) g (1) (x,-x) o uversal [Kasprzak e al. Naure 006] dsorder [M.W. ad V. Savoa, PB 009] [M.H. Szymaska e al PB 008]

20 Dsorder: Bose Glass? equlbrum dsordered Bose gas: heory BG superfludy: qualavely survves wha wh Bose glass?? oequlbrum: experme SF U remember: ω μ o a sgle chemcal poeal! [Fsher e al. PB 1989] [Foaes e al. PL 009] see also [Alma e al. PB 010] [Krzhaovsk e al, PB 009]

21 smulaed saes codesae saes lear egesaes [Krzhaovsk e al, PB 009]

22 physcal pcure ga due o excos should be sauraed everywhere lowes eerges: egesaes, hgher eerges: ew saes (mode lockg) sgle sae develops whe U~ : same scalg as equlbrum for dsorder wh log correlao legh [Malpuech e al PL 006] bu very dffere physcs: o flucuaos eeded for he cohere phase (cf. radom lasers) radom lasers see e.g. [D.S. Wersma Na. Phys. 008]

23 summary mcrocavy polaros challege us o revs well kow pheomea (superfludy, BEC, Bose glass,.) ou of equlbrum GPE+ s a good ool o address hese quesos, especally whe homogeey s mpora

24 wo-reservor model P sgle reservor me scale bu exco lfe me much loger ha ga saurao relaxao me scale o good for pulsed excao I A I I P 1 1 A A I A A I Sysem A κ 1 κ exco lfe me ga me scale

25 applcao: vorex dyamcs experme smulao vorex posos averaged erferrogram [K.G. Lagoudaks e al. PL 010]