Comparison of 87Rb N-resonances for D1 and D2 transitions

0.16 MB·English

by  Irina Novikova

Comparison of 87Rb N-resonances for D and D transitions
1 2
∗
Irina Novikova, David F. Phillips, Alexander S. Zibrov , Ronald
L. Walsworth1 and Alexksei V. Taichenachev, Valeriy I. Yudin2
1Harvard-Smithsonian Center for Astrophysics and Department of Physics,
Harvard University, Cambridge, MA, 02138, USA
2Institute of Laser Physics SB RAS and Novosibirsk State University, Novosibirsk, 630090, Russia
6 (Dated: February 2, 2008)
0
We report an experimental comparison of three-photon-absorption resonances (known as “N-
0 resonances”) for the D1 and D2 optical transitions of thermal 87Rb vapor. We find that the D2
2
N-resonance has better contrast, a broader linewidth, and a more symmetric lineshape than the

n D1 N-resonance. Takentogether,thesefactorsimplysuperiorperformanceforfrequencystandards
a operatingonalkaliD2 N-resonances,incontrasttocoherentpopulationtrapping(CPT)resonances
J forwhichtheD2 transitionprovidespoorerfrequencystandardperformancethantheD1 transition.

1
1 PACSnumbers:

]
m-ph aarbeRsoeracpetnipotrlnyo,mreissoiwnnegancadeletsemkrnonnaotswitvnreaatestdo“Nct-ohrheaestorennattnhcrpeeseo”-pp[u6h,loa7tt,oion8n-] (a) FF''==12D1 transitio n D c FF.''=.=.03D 2 transitio n D c
trapping (CPT) resonances[1, 2, 3, 4, 5] for small
o
t atomic frequency standards using thermal alkali vapor. W W D W W W D W
a In this letter, we report an experimental comparison P P P P
s. of N-resonances for the 87Rb D1 (52S1/2 → 52P1/2,
sic λop=tica7l95trannms)itiaonnds.DW2e(fi52nSd1/s2im→ilar52NP-3r/e2s,oλna=nce78q0uanlmity) FF==12 n 0 FF==12 n 0
y
h factors for the D1 and D2 transitions,but a significantly (b) Solenoid Fabry-Perot
p more symmetric lineshape for the D2 transition, which EOM etalon
[ together implies superior performance for a frequency
standard using the D2 N-resonance. Previous work has Laser l /4 PD
1 shown that the quality factor of alkali CPT resonances 6.835GHz Rb cell inside
v frequency magnetic shielding
9 is about an order of magnitude worse for D2 operation synthesizer
7 than for D1.[9, 10] Thus, as currentminiature frequency
0 standards rely on vertical-cavity surface emitting lasers FIG. 1: (a) N-resonance interaction scheme for D1 and D2
1 (VCSELs) that are readily available for the D2 tran- transitions of 87Rb. ΩP and ΩD are probe and drive optical
0 sitions of Rb and Cs but more difficult to acquire for fields that create and interrogate the N-resonance; ν0 is the
6 the D1 transitions, the results reported here provide an splittingoftheground-statehyperfinelevelsF =1andF =2;
0 additional practical advantage for the N-resonance. and ∆c is the one-photon detuning of the probe field from
/ resonance between the F = 2 ground state and the excited
s AnN-resonanceisathree-photon,two-optical-fieldab-
state. (b) Schematic of the experimental setup. See text for
c
sorptive resonance (Fig. 1a). A probe field, Ω , reso-
i P abbreviations.
s nant with the transition between the higher-energy hy-
y
perfine level of the ground electronic state and an elec-
h
tronically excited state, optically pumps the atoms into ference between the resonance mechanisms. The CPT
p
: the lower hyperfine level, leading to increased transmis- transmission maximum appears as a result of optical
v
sion of the probe field through the medium. A drive pumping of atoms into a non-interacting coherent su-
i
X field, ΩD is detuned from the probe field by the atomic perpositionoftwoground-statehyperfine levels(a “dark
r hyperfine frequency, ν0. Together, ΩP and ΩD create state”). However,apuredarkstateexistsonlyfortheD1
a a two-photonRamanresonancethatdrivesatoms coher- transition,thusthe amplitudeandcontrastofCPTreso-
entlyfromthelowertotheupperhyperfinelevel,thereby nances are much higher for D1 operation than for D2.[9]
inducing increased absorption of the probe field ΩP in For N-resonances, the three-photon absorptive process
a narrow resonance with linewidth, ∆ν, set by ground- doesnotrequireadarkstate,withnoresultantadvantage
state hyperfine decoherence. Attractive features of N- ofD1overD2. Furthermore,forcircularlypolarizedlight
resonances for atomic frequency standards include high (commonlyusedinoptically-pumpedatomicclocks)reso-
resonancecontrast,leading-orderlight-shiftcancellation, nantwiththeD1transition,someatomsbecometrapped
and less sensitivity than CPT resonances to high buffer in the Zeeman state with maximum angular momentum
gas pressures.[7, 8] — an “end” state ( F =2,m =±2 for 87Rb) — which
F
Better performance for N-resonances than CPT reso- limits resonance amplitude and contrast on the ground-
nances on the D2 transition is expected due to the dif- state ∆mF = 0 hyperfine clock transition. However, for
2
D2 operation, the end state is coupled to the excited
state through the cycling transition F =2→F′ =3. In on 1.0
si
s
the presence of strong collisional mixing in the excited mi
s
state (inducedby alkali-buffergascollisions),the cycling n
a
transition suppresses optical pumping of atoms into the d tr 0.5
el D transition
eNn-dresstoantae.ncTehsuospwereateixnpgeocnt hthigehDer2retrsaonnsainticoenc.ontrast for obe fi D12 transition
Figure1bshowsaschematicofourN-resonanceappa- Pr 0.0
ratus. We operated the system under conditions identi- -10 -5 0 5 10
Two-photon detuning (kHz)
fiedinourpreviousworktogivegoodfrequencystandard
performance.[7, 8] We derived the two optical fields ΩP FIG.2: Example87RbN-resonancesobservedforD1andD2
and Ω by phase modulating the output of an external
D optical transitions. Laser power is260 µW, corresponding to
cavitydiodelasertunedtoeithertheD1 orD2 transition anintensityof50mW/cm2. Probetransmissionisnormalized
of 87Rb. Laser phase-modulation was performed at the to unityaway from two-photon resonance.
87Rb ground-state hyperfine frequency (ν0 ≃ 6.8 GHz)
by an electro-optic modulator (EOM) driven by an am-
plifiedmicrowavesynthesizerphase-lockedtoahydrogen qcorrespondstobetterfrequencystability.[1]]Asseenin
maser. We used the +1 sideband as the probe field and Figures 2 and 3, the typical measured N-resonance con-
thezerothordercarrierasthedrivefield. Wesetthelaser trast is significantly larger for D2 operation than for the
detuning ∆c and EOM modulation index to match the D1 transition, whereas the linewidth is broader for D2
conditions for leading-order light-shift cancellation: [8] than for D1. The differences in contrast and linewidth
for D1, ∆c ≈+700 MHz from the F =2→F′ =2 tran- largelyoffseteachother,suchthattheN-resonancequal-
sition;forD2,∆c ≈+500MHzfromtheF =2→F′ =3 ityfactorisroughlycomparablefortheD1andD2transi-
transition; in both cases the modulation index ≈ 0.38, tionsoverawiderangeofoperatingconditions. Notethat
corresponding to a probe/drive intensity ratio of about inalkalivaporCPTresonances,thequalityfactorforthe
19%. The laserbeamwas circularlypolarizedby a quar- D2 transitionhasbeenmeasuredtobe aboutanorderof
terwaveplate(λ/4)andweaklyfocusedtoadiameterof magnitude smaller than for the D1 transition.[9, 10]
0.8 mm before entering a Pyrex cell of length 7 cm and Optically-probed atomic frequency standards com-
diameter 2.5 cm containing isotopically enriched 87Rb monly employ slow modulation of the microwave drive
and 100 Torr of Ne buffer gas (which induced excited- and associated phase-sensitive detection as part of the
state collisional broadening ≈ 2 GHz). We heated the crystaloscillatorlock-loop. Henceanasymmetricatomic
cell to ≈ 65◦C, yielding 87Rb density ≈ 4·1011cm−3. resonance lineshape can induce systematic frequency
We isolated the Rb vapor cell from external magnetic shifts proportionaltothe modulationparameters.[11]As
fields using three layers of high-permeability shielding, seen in Fig. 2, 87Rb N-resonances are significantly more
and applied a small (≈ 10 mG) longitudinal magnetic symmetricfortheD2 transitionthanforD1,whichgives
field to lift the degeneracy of the Zeeman sublevels and an important advantage for D2 N-resonance operation.
separate the F = 1, mF = 0 to F = 2, mF = 0 clock The relative asymmetry of the D1 and D2 N-resonance
transition (with first order magnetic field independence) lineshapescanbequantifiedbydescribingeachmeasured
from the m = ±1 transitions with first order magnetic N-resonanceasacombinationofsymmetricandantisym-
F
field sensitivity. The transmitted probe field power was metric Lorentzian functions:
detected by a photodetector (PD); the strong drive field
A∆ν/2 + Bδ
andtheoff-resonantlowersidebandwerefilteredfromthe T =T − (1)
o ∆ν2/4+δ2
transmitted laser beam by a quartz narrow-bandFabry-
Perotetalon (FSR = 20 GHz, finesse = 30) tuned to the
where T is the measured probe field transmission as a
frequency of the probe field.
function of two-photon Raman detuning, δ; and A, B,
Figure 2 shows examples of measured D1 and D2 N- and∆ν arefit parametersthat representthe amplitudes
resonances under identical conditions, with the probe of the symmetric and antisymmetric Lorentzian compo-
field transmission normalized to unity away from two- nentsandtheresonancelinewidth. Fig.4showstheratio
photon resonance. Figure 3 shows the measured de- of antisymmetric and symmetric components, B/A, de-
pendence on laser intensity of the N-resonancecontrast, terminedfromourN-resonancelineshapemeasurements,
linewidth, and quality factor. We define resonance con- asafunctionoflaserintensity,indicatingthattheD1 N-
trast as C = 1 − T /T , where T and T are resonance is typically more than an order of magnitude
min o min o
the transmitted probe field intensities on two-photon more asymmetric than the D2 N-resonance.
resonance and away from resonance, respectively. The In conclusion, N-resonances are three-photon-
linewidth, ∆ν, is the measuredfull-width-half-maximum absorption resonances that are a promising alternative
(FWHM);andtheresonancequalityfactorisq =C/∆ν. to CPTresonancesforsmallatomicfrequencystandards
[The shot-noise limit to atomic clock frequency stability using alkali atoms. Here, we report an experimental
is inversely proportionalto the quality factor; i.e., larger comparison of the D1 and D2 N-resonances in thermal
3
result implies a similar shot-noise-limit to N-resonance
30 (a)
%) frequency standard performance on the D1 and D2
ontrast ( 20 DD12 ttrraannssiittiioonn twrhaincshittiohnesq—ualiintystfaarcktocronistraabsotuwtitahnCorPdTerroesfomnaangcneitsufdoer
e c worse for the D2 transition than for D1. In addition, we
nanc 10 find that the D2 N-resonance lineshape is significantly
eso more symmetric than the D1 lineshape, indicating that
N-r a D2 N-resonance frequency standard will have reduced
0 sensitivity to certain modulation-induced systematic
0 50 100 150
(b) Laser intensity (mW/cm2) frequency shifts. Thus, unlike for CPT resonances,
Hz commercially available diode lasers for the D2 lines of
k
h, 10 Rb and Cs can likely be used without compromising the
widt performance of an N-resonance frequency standard.
e
c
nan 5 The authors are grateful to J. Vanier and M. Cresci-
eso D1 transition manno for useful discussions. This work was supported
N-r D2 transition by ONR, DARPA, ITAMP andthe Smithsonian Institu-
0 tion. A. V. T. and V. I. Y. acknowledge support from
0 (c) 5L0aser intensity 1(m00W/cm2) 150 RFBR (grants no. 05-02-17086, 05-08-01389 and 04-02-
10
-1atio (kHz) 86 DD12 ttrraannssiittiioonn metry B/A 1.5 DD12 ttrraannssiittiioonn
dth r sym 1.0
Contrast/wi 42 sonance a 0.5
0 Re
0 50 100 150 0.0
Laser intensity (mW/cm2) 0 50 100 150
Laser intensity (mW/cm2)
FIG. 3: N-resonance (a) contrast C, (b) linewidth ∆ν, and
(c)qualityfactorq=C/∆ν,asafunctionoftotalinputlaser FIG.4: N-resonanceasymmetry,B/A,asafunctionoflaser
intensity, measured on the 87Rb D1 (solid circles) and D2 intensity, determined from fits of a combination of symmet-
(open diamonds) transitions. Dashed lines are to guide the ric and antisymmetric Lorentzian functions to measured N-
eye. resonance lineshapes; for D1 (solid circles) and D2 (open di-
amonds) transitions. Dashed lines are to guide theeye.
87Rb vapor. We find that the D2 N-resonance has
better contrast but a broader linewidth than the D1
N-resonance, such that the N-resonance quality factor 16488). I.Novikova’se-mailaddress: [email protected].
∗
is comparable for the D1 and D2 transitions. This also at Lebedev Institute of Physics, Moscow, Russia.
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