Deep sub-doppler cooling of Mg in MOT formed by light waves with elliptical polarization

Transcription

1 Journal of Physcs: Conference Seres PAPER OPEN ACCESS Deep sub-doppler coolng of Mg n MOT formed by lght waves wth ellptcal polarzaton To cte ths artcle: O N Prudnkov et al 2017 J. Phys.: Conf. Ser Vew the artcle onlne for updates and enhancements. Related content - Gray-molasses coolng of 39K to a hgh phase-space densty G. Salomon, L. Fouché, P. Wang et al. - On-Lne Measurement of Sub-Doppler Temperatures n a Rb Magneto-optcal Trap by Trap Centre Oscllatons P. Kohns, P. Buch, W. Süpttz et al. - Radatve forces on atoms wth fnte famles of states P M Vsser and G Nenhus Ths content was downloaded from IP address on 04/09/2018 at 22:25

2 Internatonal Conference on Recent Trends n Physcs 2016 (ICRTP2016) Journal of Physcs: Conference Seres 755 (2016) do: / /755/1/ Deep sub-doppler coolng of Mg n MOT formed by lght waves wth ellptcal polarzaton O N Prudnkov 1, D V Brazhnkov 1,2, A V Tachenachev 1,2, V I Yudn 1,2,3 and A N Goncharov 1,2,3 1 Novosbrsk State Unversty, 2 Progova str., Novosbrsk , Russa 2 Insttute of Laser Physcs SB RAS, 13/3 Acad. Lavrentyev ave., Novosbrsk , Russa 3 Novosbrsk State Techncal Unversty, 20 K. Marx ave., Novosbrsk , Russa E-mal: oleg.nsu@gmal.com Abstract. We study magneto-optcal trap (MOT) of Mg atoms operatng on the closed trplet 3 P 2 3 D 3 ( = nm) transton formed by the lght waves wth ellptcal polarzaton ( confguraton). Compare to well-known trap formed by lght waves wth crcular polarzaton ( + confguraton) the suggested confguraton offer the lower sub- Doppler temperature for trapped Mg atoms, that can t be reached n conventonal + MOT. Mg atoms one of perspectve canddates for realzaton of new-generaton of atomc clock, based on optcal lattces. These atoms have the narrow spectroscopc lnes due to forbdden optcal transton from the ground state 1 S 0 to the lowest excted states 3 P 0,1,2 (see fgure 1). The closed snglet optcal transton 1 S 0 1 P 1 can be used for Doppler coolng of Mg atoms down to the temperature T = 1.2 mk. The ground state of ths optcal transton has angular momentum J g =0 that forbds the possblty of sub-doppler coolng here. In order to get the lower coolng temperature, the coolng on closed trplet 3 P 2 3 D 3 ( =383.3 nm) optcal transton was suggested n [1, 2]. In prncple, the ground state here 3 P 2 s degenerated over angular momentum (J g =2) that should allow sub-doppler coolng [3]. However, the expermental realzaton of laser coolng operatng on 3 P 2 3 D 3 n + MOT dd not brng sgnfcant progress to reachng lower temperature. In partcular, Mg atoms were cooled by laser radaton only down to the temperature 1 mk that much hgher than the Doppler lmt for ths optcal transton T D = 425 K. The recent analyss [2] has revealed the lmtaton of temperature of laser coolng for 24 Mg atoms n + lght feld confguraton and explaned the results of prevous experments [1]. The evoluton of atoms n the resonant lght waves n presence of a statc magnetc feld s descrbed by equaton ˆ H ˆ, ˆ ˆ ˆ (1) t for atomc densty matrx ˆ. Here Ĥ s the Hamltonan and term ˆ ˆ descrbes the relaxaton of atomc levels n the process of spontaneous decay (e.g., see for detals [4, 5]). Nowadays a lots of methods have been developed for solvng ths problem, and they can be separated to semclasscal [4, 6 9] and quantum [10 17] methods. The semclasscal methods requre some condtons to be fulflled [4, 6 9] that allow reducng the quantum equaton for atomc densty matrx to the Fokker- W ( r, p) Tr ˆ( r, p) : Plank type equaton for atomc densty functon Content from ths work may be used under the terms of the Creatve Commons Attrbuton 3.0 lcence. Any further dstrbuton of ths work must mantan attrbuton to the author(s) and the ttle of the work, journal ctaton and DOI. Publshed under lcence by Ltd 1

3 t p W m p F ( r, p) W j 2 p p j D ( r, p) W where F(r,p) and D(r,p) are lght force on movng atom and dffuson coeffcent n lght feld. j (2) Fgure 1. Dagram of low energy levels of 24 Mg. Sold lnes denote coolng transtons, and dashed lnes denote possble clock transtons. The quantum methods as well utlze dfferent approaches and smplfcatons. In partcular, the method descrbed n [16, 17], s so called band theory, use secular approxmaton that assumes enough large detunng = 0 of laser lght wth frequency from atomc resonance frequency 0, U 0 /E R << 36 2 / 2 wth U 0 s depth of optcal potental and E R =ħ 2 k 2 /2M s recol energy (see for detals [16]). Addtonally developed approach s based on smplfed equaton for atomc densty gg matrx of ground state only ˆ that also lmts applcatons of the results [18]. Recently we suggest a new method that allows to fnd soluton of equaton (1) for 1D problem wth taken nto account quantum recol effects wthout lmtatons to feld parameters and confguraton [18, 19]. Our method allows one to compare dfferent feld confguratons to fnd a mnmum temperature of laser coolng. Strctly speakng, the dstrbuton of cold atoms n electromagnetc feld s sgnfcantly non-maxwellan one. However, we defne the temperature here as the average knetc 2 energy that for 1D case results k T p M that s measured n ħ unts (k B T/ħ =1 corresponds T B / 1.28 mk for 3 P 2 3 D 3 optcal transton lnewdth ). 2

4 Fgure 2. Laser coolng temperature of 24 Mg atoms n + feld confguraton (a) and fracton of cold atoms (b) as functon of ntensty of lght waves. k B T/ħ =1 corresponds to T 1.28 mk. Fgure 3. Laser coolng temperature of 24 Mg atoms n ln ln feld confguraton (a) and fracton of cold atoms (b) as functon of ntensty of lght waves. k B T/ħ =1 corresponds to T 1.28 mk. Addtonally, we ntroduce the fracton of cold atoms N p <3ħk,.e. the atoms wth momentum p <3ħk, that for 24 Mg atoms cooled by the lght feld resonance to closed trplet transton 3 P 2 3 D 3 ( = nm) corresponds to an effectve temperature (3ħk) 2 /M 48.4 K. Frst we fnd the temperature of laser coolng 24 Mg atoms on 3 P 2 3 D 3 optcal transtons n conventonal + feld confguraton commonly used n MOT do not reach deep sub-doppler values (see fgure 2a). The ln ln confguraton of lght (formed by counterpropagatng waves wth orthogonal lnear polarzaton) offers much dpper laser coolng temperatures (fgure 3a) and much large fracton of cold atoms N p <3ħk, but cannot be used for MOT, because of zero magneto-optcal trappng force n ln ln feld. Here to get the deep sub-doppler laser coolng temperature for 24 Mg atoms n MOT we suggest lght feld confguraton to use n MOT for Mg atoms (fgure 4). The frst study of MOT n lght feld was done by us n [5], where we dscovered some peculartes of laser coolng 3

5 dealng wth an ellptcal polarzaton of the lght waves, dffer from lnear 0 = 0 and crcular polarzaton 0 = ±/4 [20]. Fgure 5 shows the temperature of laser coolng n feld confguraton as functon of lght ntensty for partcular case of 0 = 0 (lnear polarzaton of counterpropagatng waves). Fgure 6 shows the temperature of laser coolng and the fracton of cold atoms (.e. the atoms wth momentum p <3ħk) n feld confguraton as functon of lght ellptcty parameter 0. As one can see, the temperature dependence s not symmetrcal functon of lght wave ellptcty parameter 0. Fgure 4. feld confguraton formed by counterpropagatng lght waves wth opposte ellptcal polarzaton wth parameters 0 and 0 ( /4< 0 </4 and 0 =0 corresponds to lnear polarzaton and 0 =±/4 corresponds to rght and left crcular polarzatons). The s the mutual orentaton angle between man polarzaton axs of lght waves. Fgure 5. Laser coolng temperature of 24 Mg atoms n ln ln (= /4) feld confguraton (a) and fracton of cold atoms (b) as functon of ntensty of lght waves. k B T/ħ =1 corresponds to T 1.28 mk. 4

6 Fgure 6. Laser coolng temperature of 24 Mg atoms n (= /4) feld confguraton (a) and fracton of cold atoms (b) as functon of ntensty of parameter ellptcty of lght waves 0. The anomaly terms n the frcton force results to mnmum temperature s reached for an ellptcal polarzaton. However, the anomaly force terms domnant for small detunng << only [20], thus for the consdered case of = the anomaly force effect s small and results to temperature of laser coolng get the mnmum values for ellptctes are close to lnear polarzaton: for I = 100 mw/cm 2 mnmum of temperature s reached at o, for I = 200 mw/cm 2 at o, and for I = 300 mw/cm 2 at o. The maxmum fracton of cold atoms N p <3ħk for I = 100 mw/cm 2 s reached at 0 2 o, for I = 200 mw/cm 2 at o, and for I = 300 mw/cm 2 at o. Nonlnear dependence of magneto-optcal trappng force as functon of Zeeman shft H of the ground energy sublevel J g =2,μ g =1 s shown on fgure 7a for conventonal + feld confguraton and fgure 8a for feld confguraton (= /4) at dfferent waves ellptcty parameters 0. The Zeeman shft H = corresponds to magnetc feld H = 12.7 G. Assumng the lnear dependence of magnetc feld on poston near the center of the trap H ( z) z H z for z RW the depth of magneto-optcal trap can be estmated as: ( ) H R W ( H ) RW ( H ) U F ( v 0, H ) d H, (3) ( R ) H W 0 where R W s the radus of the lght beams formng the trap and H (R W ) s the Zeeman shft on the trap boarder (entrance nto the trap). The depth of magneto-optcal trap s determned by the gradent of magnetc feld z H and can be expressed as functon of magnetc feld at the trap boarder (fgure 7b and fgure 8b) for the area of lnear grow of magnetc feld (3). 5

7 Fgure 7. Magneto-optcal trappng force (n ħk unts) on 24 Mg atoms (a) and depth of magnetooptcal potental n ħr W unts (b) as functon of Zeeman shft H n + feld confguraton (I = 100 mw/cm 2 and = ). The depth of magneto-optcal trap, formed by feld confguraton, s sgnfcantly less the depth of magneto-optcal trap formed by conventonal + feld confguraton, but stll much deep to capture cold atoms. As an example, the depth of the trap, formed by feld wth feld confguraton for R W = 0.5 cm and gradent of magnetc feld of H z 12.7 G/cm (that corresponds to H / 0.5 at the trap boarder, fgure 8b) reaches U (H) = ħr W / 1.56 K that much exceed the temperature of cold atoms (T = 124 K for consdered parameters). The ellptcal polarzaton of the lght waves that could results to smaller temperature due to anomaly parts n the frcton force (.e. for 0 < 0 at consdered= /4) unfortunately leads to decrement of the depth of magneto-optcal potental (fgure 8b). As an example for 0 = 3 o the magneto-optcal force reverse when magnetc feld exceeds 9 G ( H / 0.71). For estmaton of number of trapped atoms n MOT one should analyss of nonlnear dependence of magneto-optcal force for slow atoms n magnetc feld. The number N c of trapped atoms N s 4 c v c determned by the crtcal velocty c,.e. the maxmum velocty of slow atom can have and be captured n MOT [21]. By usng the methods we developed n [5], we study magneto-optcal force on slow 24 Mg atoms as functon of magnetc feld. For atoms n + MOT the crtcal velocty c 3.5/k [21] that for magneto-optcal trap formed by waves wth R W = 0.5 cm results to N c atoms. For atoms n MOT at some large values of magnetc feld the magneto-optcal force s reversed (see fgure 9) for some range of velocty of slow atoms. Thus the atoms n ths range of parameters ( v, H ) cannot be captured by the trap, that defne c as a functon of magnetc feld. Here for ln ln feld confguraton (= /4) at large magnetc feld ( H />1.5) the crtcal velocty decreased to c 0.014/k (0.14 m/s) that almost nullfy the number of trapped atoms. Thus for stable work of MOT the low gradents of magnetc feld s requred,.e the magnetc feld wthn the trap area r<r W should never reach the crtcal values H c when the force on the atoms movng wth some velocty range s reversed (fgure 9). As an example, for stable work of MOT for 0 = 1 o magnetc feld should not exceed H c = 9.3 G ( H / 0.73). 6

8 Fgure 8. Magneto-optcal trappng force (n k unts) on 24 Mg atoms (a) and depth of magnetoptcal potental n ħr W unts (b) as functon of Zeeman shft H n feld confguraton for dfferent parameters ellptcty of lght waves 0 (= /4, I =100 mw/cm 2 and = ). Fgure 9. The zones of parameters ( v, H ) where magneto-optcal force on 24 Mg atoms s repulsve force n feld confguraton (= /4) for dfferent parameters ellptcty of lght waves 0 (I =100 mw/cm 2 and = ). 7

9 Fgure 10. Crtcal values of magnetc feld as functon of ntensty of lght waves formng magneto-optcal trap for dfferent detunngs and ellptcty of lght waves for 24 Mg atoms n MOT (= /4). Fgure 10 shows the crtcal values of magnetc feld as functon of ntensty of lght waves formng the trap for dfferent detunngs and ellptcty of lght waves for 24 Mg atoms n MOT (= /4). Concluson In ths paper we have consdered a magneto-optcal trap for 24 Mg atoms operatng on the closed trplet 3 P 2 3 D 3 transton, formed by the lght waves wth ellptcal polarzatons ( confguraton, see fgure 2). In the lmt of a 1D model we have studed the magneto-optcal potental, temperature and fracton of atoms extremely cooled bellow the momentum p=3ħk (12.9 cm/s) as the functons of ntensty, frequency detunng and polarzatons of lght waves that form the MOT. For our smulatons we have used recently suggested method [18, 19] that allows takng nto account the quantum recol effects of nteracton of atoms wth a lght feld and correctly takng nto consderaton the slow atoms localzed n the optcal potental wells as well as the atoms movng above the potental wells. We have found that the lght feld confguraton formed by the waves wth ellptcal polarzatons and orentaton angle = /4 wth parameters ellptcty are close to lnear polarzaton can offer the lowest coolng temperatures on the level T 100 K together wth enough depth of the magneto-optcal potental. In comparson wth the conventonal MOT, formed by waves wth + polarzatons, the suggested MOT should operate wth lower gradent of a statc magnetc feld. Indeed, n comparson wth the + MOT, the proposed MOT s more exactng to the feld parameters, because of strong magnetc feld may reverse magneto-optcal trap force for slow 8

10 atoms n confguraton that lmt the number of atoms captured n the trap. Parameters of the crtcal magnetc felds have been also fgured out. Acknowledgments The work was partally supported by the Russan Scence Foundaton (project no ). A.N. Goncharov thanks the Russan Foundaton for Basc Research for the support (grant no ). References [1] Redmann M et al Physcal Revew A [2] Brazhnkov D V et al Phys. Rev. A [3] Dalbard J and Cohen-Tannoudj C 1989 J. Opt. Soc. Am. B [4] Prudnkov O N et al JETP [5] Prudnkov O N et al Phys. Rev. A [6] Kazantsev A P, Surdutovch G I and Yakovlev V P 1990 Mechancal Acton of Lght on Atoms (Sngapore: World Scentfc) p 392 [7] Dalbard J and Cohen-Tannoudj C 1985 J. Phys. B: At. Mol. Phys [8] Javananen J 1991 Phys. Rev. A [9] Yoo S M and Javananen J 1992 Phys. Rev. A [10] Dum R, Zoller P and Rtsch H 1992 Phys. Rev. A [11] Dalbard J, Castn Y and Mølmer K 1992 Phys. Rev. Lett [12] Mølmer K, Castn Y and Dalbard J 1992 J. Opt. Soc. Am. B [13] Castn Y and Dalbard J 1991 Europhys. Lett [14] Guo J and Berman P 1993 Phys. Rev. A [15] Deutsch I H, Grondalsk J and Alsng P M 1997 Phys. Rev. A 56 R1705 [16] Berg-Sorensen K, Castn Y, Mølmer K and Dalbard J 1993 Europhys. Lett [17] Castn Y, Berg-Sorensen K, Dalbard J and Mølmer K 1994 Phys. Rev. A [18] Prudnkov O N et al JETP [19] Prudnkov O N et al JETP [20] Prudnkov O N et al JETP Lett [21] Monroe C, Swann W, Robnson H and Weman C 1990 Phys. Rev. Lett