TRAPPED ATOMS IN CAVITY QED
Chapter 6 Chapter 6 Cold Atoms and High Finesse Microcavities - Experimental
6.2 Delivering Cold Atoms to the Cavity
6.2.7 Lattice/Cooling Beams I
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state laser (Coherent Verdi) after about 1 year. This was due to bhe large magnetic field generateri by tlie confining magnet around the plasma tube of the iori laser which does not exist in the solid state pump laser.
PGC was iiiiplerner~t,ed and optimized in rr~uch the same way as described for the upstairs hIOTlj and Table 6.4 sumxiarizes the final parameters. Vcrificat,ion that thc atoms were indeed falling vertically towards the cavity gap was accomplished by fluorescence imaging the fallirig cloud. The sequence of p i c t i ~ e s in Fig. 6.11 depicts the fallir~g of the atom cloud towards the cavity as a funct,ion time after the 12 111s PGC cooling cycle has ended. Note that, the end of the rlownstairs PGC cycle, denoted as t = 0 for Fig. 6.11, is assumed to be t = 0 for all future discussior~ of atom transits unless otherwise noted.
Figure 6.11: At seyuer~t,ial delay t,inles after the end of cycle, the atorrl cloud was (destructively) iniaged to er toxvards the gap in the cavity mirrors. Xote that the longer times not only because of the dilution of t,he ator but also because it begins to fall out of the cross-sect,io were also used for the imaging with a 2 rns resonant plds
the downstairs PGC cooling Lsure it was falling vertically fluorescence gets weaker at nic density due to expansion, n of the MOT2 beams which e a t the indicated delay tinie.
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nes. At, t,hese iocat,ions, the atom can be trapped in 2D with a potential depth givc:n by Eq. 6.7 wit11 the spatial dependence in I/I,,, of (cos h-2
+
cos k y j 2 . Furth(:rrnore, an at,oni which h&s up and escapes t,lte trap -will ellcounter severe polarization gradi- ents and xvill coo1 according to the previously discussed Sisyplvpln~s meclla~iism~ as long as tlie lattice is not detuned too fm from resonance. For both cooling and trapping, typical parameters are ( l / I , , , .Y l j 6 / T -7) as for PGC ahove.Figure 6.12: The spatial polarization st,ructure of the optical lattice in the plane of iiitersect,iorl of tlie k vectors of the beams whose t,i~rle phases are locked by 90"
with respect to one anotller. (3:
C
anti-+, +, T. 1)
represent, "pocket,sn of pure (circular and linear) polarizations. Atoris will be trapped at places of pure circular polari~at,ion. Xote the spatial scale with respect to t,he wavelength X indicated in t,he diagram.Pfrith these pararnet,c:rs in hand, we can estirnate tho coolirig rate for ail ator11 wrivi~ig at the latt,ice with a speed of I;O = 31 crrijs: as expected far atonls failing from 1,10T2. ltcwriting Eqs. 6.7 and 6.8 as
for small s , where the saturation parameter s is given by
then the parameters (III,,,
-
l1 6 / r-
-7) give a well tlcptl~ of U'- fir/GO
fors
-
5 x lo-". Asslxnirig that an energy of 2ipproxirnately U' is lost per scattering event, it will take approximately (1/2mvi) /U'-
200 scatteririg (optical pumping) cycles. With an optical pumping time of 1/T1 = 400/r = 13 ps, this will take approxirrlately 2.5 ms, in which time the atom will have moved approximately 0.8 rnm, or approximat,ely all the way tlrrough the cavity. The solution to this perhaps ur~~c(:eptable sitnation is to do the slowing in two stages. In the first, we detune much closer to resonance(III,,,,,
3; S/r-
-112) for a, short period of time (2 ms) to do rrlost of the slowing arid t,iren go fwtller off resonance (I/I,,,-
1 , 6 / r-
-7) to use t,he lattice in much more of a trapping role. Notc that closer t,o resonance, the cooling effect is primarily Doppler cooling, where each scattering everit tends to cool by the acomic recoil of Tft = 100 nKj meaning that. (1/27-,4) /kuTrt-
8000 scattering events are needed. With s = 3, this would take approxiniately 500 ps. Tirliing diagrams will be shown soon in See. 6.2.8 to clarify this protocol, and the cxperimer~tal results will he discussed ill depth in Sec. 7.1.2. Note that. this protocol lias a hiditen cat,cll in that it actually heats t:l~e at,orrls up along the axis orthogonal to the lattice plane (i.e., tire cavity axis) becai~se it relics or1 sporltaileous mriissiori for its coolirig effects.This causes ~moxner~tum ciiffusion diic to t,he randoln nature of the recoil kicks. So far, no nierition has beer1 rxiadc of any cooling protocol along ttris axis, and Sectiori 8.3 will include a very brief discitssiori of rccerit tlieoretical work in tliis area.
The expcrirnental implerrient,ation of this liit,tice proved to be cxtrerriely cl~allerig- ing. Light, for these beams was taken from the unused zerotli order light of the downstairs tra,ppixig li~ser's frequency and irlterrsity control AOM. This was passed through another AOM for filrt,her frerpency control, and then combined with a srnall
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amount of rcpun~ping light into am optical fiber. Tlie lattice light needed to be fo- cused down from thc side througll the 40 prn gap of the pl~ysics cavit,y (inside the vacuum cliarnber). This was aacconiplished 11y ilsing a set of 15 cm focal lengtll cylin- drical lenses n~ount,ed outside the chamber ro nlake 'light sheets" which would pass cleanly through tlic gap. It was necessary to get a little bit creative to allow i n d c pendent steering control of these beams intlepencient of the MOT? light, even though both sets of beirrr~s are spatially very close to one another. In fact; both sets of beams shareti the same retro-reflecting optic. In the end, the rriount,ing of the lenses on a three-axis translation stagc prover1 critical for independent alignmerit of the lattice beams. Once they were aligned and rctro-reflected along the two nominally orthoge nal axes, in a plane itself orthogonal to the cavity axis (see Fig. 6.15 for a clarification of everything that, is going on around the cavity), it was time to satisfy the 90' phase lock reqnirernent,. For this, the retro-refiection from the two arms was re-conlbined on a pliotodiode, and then spatially overlapped to complete a 3ficllelson interferometer.
The photodiode outpnt was used as the input to a servo whose goal was to fix the relative phase of the ~.TVO beams, wit,h one of the retroreflect,ing mirrors piezo-mounted to act as an actuator. This servo bandwidth of about 100 EIz was found to be a d c quat,e, though care liad to be t,aken to turn off the integrating stage when no light fell on the pllot,odiode (the lattice beanis were not on 100% of the time). It must be notecl that the t,lre direct use of the error signal derived from this interferomet,er does not gliarantee a 90' pilase lock tit the position of t l ~ e beam overlap inside t l ~ e cavity (where it matters!) and an atlj~istablc phase offset, knob was incorporated in practice.
As will be discllssed short,ly in Section 7.1.2, there was never any clear evidence that 1-he special lattice arrangement was worth the extra llasslo involved with keeping the time phase locked. Furth~rrnorc:~ it was vc:ry easy to rearrange the optics to change the input polarization st:lierne for the "lattice belnris" froin the l i i ~ i l i i i arra~igemerrt to a ri+ jo- arrangenient. The ri,/n- arrangenrerit has the experimetit,al convenience that these hea,nls can riow share all of the same polarizarion optics as the MOT2 beams. The physical drawhack is that there is no loriger any trapping mechanism in t,his scheme, only cooling. In fact, there is no longer a lattice at all, but two
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indepei~dent ID "optical molasses" beams [153]. Nevertheless, these bean= sho~rld still provide the cooling that is needed in the plane tr2insverse to t,he cavity asis. For the rest of this thesis. the special iritra-cavit3; cooling beants discrissetl in this section arc referred to interchangeably as the "lattice beams" or the "cooling beanls."