Heterodyne Detection

TRAPPED ATOMS IN CAVITY QED

Chapter 6 Chapter 6 Cold Atoms and High Finesse Microcavities - Experimental

6.4 The Laser System, Cavity Locking and Het- erodyne Detection of the Intracavity Field erodyne Detection of the Intracavity Field

6.4.3 Heterodyne Detection

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Do~vnstream frorn the cavity; dichroic beamsplitters are used t.o separate the beams arid send tlier~i to their respective tlctectors. First? tile 836 ririi liglit is separated arid sent, to the APL) det,ector .sitli am optic ~vllich is apl~roxirnately (85, 15) 7a trarisniis- siori/reflcction at 836 rlln arid better tlia11 99% rcfiectioli at 852 arid 869 nm. The 869 rirrl light is tlicri separated by a second optic wtiicki is approxiriiai-ely (10; 90)

76

traixniission/reflectiori at 869 rim arid (85: 15) % transmissiori]reflecttiori af 852 rim.

The remaining 832 ilrn light, is smit to rhe heterodyne cietectioil set-up.

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beam with the signal probe field arid by maximizing the intririsic detector quantuni efiiciericy

(QE).

Tlie lietcrodyne efficiency q,)<:, for this esperirner~t, was verified in two ways. 111 the firstl a

V

⁼ 88% visibility liornodyne fringe between the LO and sigl~al beams \\as rnadc for identical powers in each bearn. This riumber is scjuared and mnltiplied by both the ciet,ector

QE

of 70% anti the T = 70% tra,nsmissiori fact,or froin the cavity to the detector to give =

(QE)TV2

= 47%.

A

second method is to take a known amount of outpiit power frora the cavit.y arid calibrate this against the signal-tunoise ratio recorded via the heatliote size ⁰¹¹ a calibrated rf spectrum analyzer. The tietails were worked ont by Rob Thon~psori [158j and implemerited by Quentin 1681 in his beat.nicd Matlicad program for the HP70000 spectrum arialy~er used here. With 20.3 nW of optical power; 30 kHz rf bandwidtll, 3.5 rnW of IJO power and tlie m e a s i ~ e d (beatnot,e she, shot noise level and electronic noise levels) of (-18.9 dBm, -80.5 dBm and -85.5 tlBm) respectivelh this program calculates ⁼ 47% for re~narknble agrcelrient witti the measurement based on the homodyne fringe visibility.

Sote that this 1,O level ~rmakes the mei~~urement sliot-noise limited by about 5 dB.

In the data t,o follow, one typica,lly qnotes the average i11tracavit.y photon number 7i at which tlie data was acquired. This nunit~er needs to be compared to tile saturation photon nurriher, no = 4y1;/3yi ( = for an optinially coupled atorn in tlie work here), to decide how "hard" the atom was driven. The coiidition 5i iin,o means the systerli is operating in a linear regime. The meaning of a.n irit,racavit.y photon nunl1)er ii1 can be tleduced fro111 tlie clefinition of 7i = (ZtZ)

,

so that E ii1 riieans that on u.uera,ge the iritracavit,y field is pritiiarily i11 tlie state 10)

.

Note that throrrgliout the rest of tlie work liere,

n

specifies the mcari intracavity plioton in~rriber for the enipty cavity (i.e., no atoriis) at the achral detiirliny 6,,,,.

The relationship of the actual trarisrnitted power to the intraciwity pliotoii riumber requires a slight digression. Assurrririg two identical mirrors of t,ransriission T arid absorptive losses A such tliat, t,he total cavit,y losses are 2

(T +

^A)? then a fraction 211 of the circulating irrtracavity power is al~sorbed. while a fri~ctiori T is trarismitted out of each mirror. Since ^K is a field decay rate? 1/2n is tire energy storage tirne, so that

118

the total iiit,racavity power is Eh,.w\-iir ( 2 ~ ) arid t,he trarisrr~itted power is

It is possiblc to isse this ecluatiori to calibrate the intracavity photon nurriber with t,he size of tlie electronic bcatnote by nsis~g tire know^^ values of T and V ~ s a , arid meas~nirsg P,,,,,, with a calibrated photodet,ector. Once t,his number was calibrated to a specific rf po\Trer level on tile sy~itliesizer creating the probe sideband on TWMKI, periodic checks over a n eight snont,h period sho\ved that it remained valid if the alignment of the detection apparatus was continually t\veakerl.

The tlreoretical 3 dB improvernerit in

SNR

of a balanced heterodyne receiver con- taining two 1natc;hetf tletectors is acl~ieved orlly by careful subtract,ion of the photocur- rents from each of the det,ectors. This was acconiplislied by adjusting t,he arriplitude and phase of the pl~otocurr-eiit from each detector using rf atteriuators and variable cable lerigtiis before the rf 180" splitter. When adjusted correctly, residual arriplitude modulation on the LO meilsincd in the difference phot,ocurrerst at the beat, (detection) frcquericy is ~niriirnized.

6.4.4

Data Acquisition

This chapter coriclndes with a few brief words about the experimcrital data acquisition system used. The prirnury rrietliod of analyzing t,he balanced heterodyne pliotow~r- ront was to IISC a s j ~ e ~ t r u l n analyzer (Iil' 70000 SA) set to the (nominal) +40 hIIIz offset betwecn sigrial arid LO in t11e balanced iit:terodyrse set-up. The exact frequency of tlie SA was tunod rrsarvually by optimi~ing the rf level in zero span on tlie SA's visual display, witti about a 20 kIlz offset typically neccssary. Even with its iriternal oscillator slaved to the master probe frequency synthesizer's oscillator, this manual tuning was necessary. The RP 70000 car1 he externally triggered and has a "video oiit" sigrial wllicli was serit to a digitizing oscilloscope (Lccroy 9400) so that both real-time nionitoririg anti averaging of tlie pliotocisrrent conld be accomplisired. A GPlB interface between the oscilloscope and tho cornputer allowed simple transfer

119

of the dat,a via a LABVIETI' interface and routine analysis was perforrned with ei- ther X'L4TLAB or IGOR. Most of tile data was filtered in hardware at rather low rf bandwidths of about 3 kI-Iz to maxiini~e the signal-to-noise ratio as seen on the oscil- loscope because nl~lcll of tIle optimization of different experimental parameters was performed by visual inspection of this signal. It is expected that future experinlents looking to monitor more carefillly atonlic motion while the at,oms we trapped will require ~ituch greater handwidtl~s approaching 1 MHz (see See. 5.2). The capabilities to tio t,his are already in place in tlit: for11 of either a 100 X~ISar~iplcs/s 12 bit ADC board (Gage Corrlpuscope 6012/A) or a 1 MSample/s 16 bit ADC hoard (National Instruments AT-1CIIO-16E-1).

Chapter 7 Trapping a Single Atom