MICROSPHERES
Chapter 4 Chapter 4 Cavity QED with High Q Whispering Gallery Modes
4.1 UHV Sphere Apparatus and Data Acquisition
The act,ual setup is depicted in Fig. 4.1 and consists of a grating stabilized diode laser of a few hundred kHz linewidth coupled into LI microsphere via frustrated total internal reflection from a prism [43]. Thc! microspheres, of index n = 1.432, were Eabricat,ed using t l ~ e procedure ontline in 3.1.1 arid then rriorrntcd inside the vacuum system.
grating- stabilized diode laser
saturated absorption
monitor time-averaged cavitv
I I transmission
coilimating optics
peltiel - - - - - - -
..
microspherecesium tempsrature
resewoil heatel, eervo
vacuum chamber
Figure 4.1: A simplified scl~er~:matic of the experimental setup is shown along with a det,ailed discussion in the text. Tile nlicrosphere (shown as a circle up against the prism) is surrounded by a dilute atomic vapor.
The main vacuum cl-lanlt~er is shown in Fig. 4.2 and consisted of a 5 i1tc21 square iioliow piece of fused silica mated (by Glass Inst,rnnients; Pasaderiaj to a 4 112 inch glass to rrletal corrfiat flange on one side and a 1.33 irlcli glass to rrietal "quickflange"
on the other. Tlie microspllere coupling apparatus was lnoilntcd onto a rnatc11i1:mg 4 112 inch conflat flange with a port for electrical fecdti~ronglis, arid this was caref~~lly screived into tile bottom of the main chamber every t,ilne a new sphere was made. The cluickflange led to a six-way cross, from wkricii there were ports for a turbo roughing pump; a cesinm coltl f i r ~ e r , a 20 l,/s ion pump and a window 011 the top.
to 20 11s ion pump
to ion ga<@
: i<
i<ughing pump to cesium source:V
stress relief bellows
'
electrical feedthroughsFigiue 4.2: Tiie va~:ui~rri c:kiarnber design for this experirncnt is sllown schernatically (not to scale). The charnher was fabricat,ed by Glass Instrurilerits (Pilsadcrra; CAI from high grade cjilartz. Its optical prolxrties were found. to bc adequate for tllis asperimer~t, tliougll sspllcre replace~nerit was i~lcoriverlient.
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The sphere was mourited close to the prisrn on a hornerrlade micrrrt,ransltLtioii stage using a specially niade vaciiunl-colllpatible piezo stack (ED0 Corporation, Salt Lake Cit,y) that had 20 prri travel for I kV of bias. It turried out to be very difficult to lriairitairl Q rnilch hig11:;r than about 1 x 10' in these experiments for several reasons.
First, the sphere was inevitably burriped against the prism cluing the process of p r e aligning tile sphere on the translation stage ant1 t,he subsequent bolt,ing of the bottom flange to the main chamber. Secoridl the spheres usually xirere exposed to air for at least 30 llliriutes before thc system could be initially pumped down. Finally, typical spheres iri these experiment-s were 100 jinl diarneter or less (to keep the niode volumes small), which is much smaller tliari the sizes wit,h which the highest d) result,s of Sec.
3.2.1 had been obt,ained.
In any case, t,he range Ql -, Q2 discussed here was acccssecl by using different spheres and various rnodes of the sanle sphere; by loading the bare Q of any individual mode with the prisrn out,coupl~!r~ and by wa,iting for t,lie gradual ciegradatioii of the Q clue to repettted cont'act of the sphere with the prism iiuririg day-to-day process of optimizing the couplirlg in vacuo. In fa,ct, it was necessary to couple to higher order WGM radial rnodes (q
-
3 - 4) in order to rllairitain an acceptable coupling eficiency, as the incoupling ieris was rrioilnted out,side the vacuum chamber. For this experiineiit,, this lens w t . ~ a doublet of focal length 14 em. In atidition, the light was inljected off of the borizortal synnnetry plane of the microsphere by an angle O-
10' - 15' to take advantage of the slight ellipticity of tile splicres (typically-
3%,) and excite thc strcalled precessillg ~rnodes as clcscribc?d in 3.1.2 allowing tlre direct emission from a WGhI to he separated frorti tile reflected exciring beam and collected ordo a PMT. A single travcllirig-wave mode ( q ; l ; r n ) was t,lius exi:ited. It is degenerate ordg with the counter-rotating (q, 1 , -m) rniotie, which for Q
5
5 x 107 is imexcit,ed as evitfenced ci~y the al->sencc of any reso1vc:cl doiiblets in the transmitted intensity 1511.Tht: rriicrospllere assernbly was tllerrllally corit,acted to a Peltier elernent irsirig irrdiurrl solder, and tlie Peltier elerrierlt was heat smik to a copper block with tern- peratwe condrictive epoxy. Temperature changes were rnorlitoreci with a thermistor, cornpared to a manually set referr:r~ce potentiometer and then fed hack to the Peltier
element for active temperature control. The reference potentiorrleter was used to t,-~uie a given cavity resonance w,,,,.itv to the frequency w
,,,,,,,
of the F = 4 c--. F' = 5 hyperfine transit,ion of the Cs D2 line (lifetime T = 1/27 rr 32 ns, see Fig. 6.1) at A,,,,,,, = 852 nrn, relying prinlarily upon the thermally induced change in the sphere's illdcx of refraction. Because there was no active stat-ilization of t,he cavity t,o the atotniC iine pel. se, rcsisidual drifts of the mode--
i 500 kHz over 10 rniriutes with respect t,o t,he atornic line were present, but could be co~npensatetl ruanudly \vit,h very little trouble. The piezucont,rolled translat,iori &age allowed fine coritrol of t,he prism-sphere distance. A picture of this completed systeni is shown in Fig. 4.3.Figure 4.3: A close-up photograph through the quartz chamber at tile micrsophere coupling apparatus. The peltier k~eater and thermistor for the sphere temperature tuning servo are obvious, along with the rnicropositiorGng syst,em and optics.
The heracuum system itself ~vas pumped to a background pressure of torr and contained a thermal Cs reservoir, leading to an atomic density of typically 2 x
lo9
30
atolnis/c~n", as inorlitoreti by optical absorption in t,he vapor. Urider the assumption hhat this background Cs density is a fair represeiitation of the atoinic derlsit,y in t,he eva~iescerit field, the total rrlode volume external to the sphere V,',
-
5 x 10-lo cm3iinplying that iYiT -- 1 atom in this dilute vapor interacts with the mode volurne.
Thie procedure for data acquisition was to scar1 the frequerlcy 31, of rile inciderit, laser while recording the illtelisity transmitted by the microsphere, with averaging r,inles of several rni1111tes required t,o achieve an acceptable signal-t,o-noise ratio.
h
digital storage oscilloscope (Lecroy 9400) was used for the averaging and the res~ilt- ing traces transferred to a PC for analysis. The freqliency of the incident laser is independently monitored via saturated absorption spectroscopy in a separat,e cell.
For small frequency scan.: of 1 2 5 XjIHz, a second method consists of FM locking of 61it: laser to the atorrlic line !52] and freq~iericy scannirlg using a double-passed acousto-optic modulator.