Absolute Frequency Measurements of the Hg^+ and Ca Optical Clock Transitions with a Femtosecond Laser

6 Pages·0.18 MB·English

by  Th. Udem

Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with
a Femtosecond Laser
∗
Th. Udem , S. A. Diddams, K. R. Vogel, C. W. Oates, E. A. Curtis,
W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg
Time and Frequency Division,
National Institute of Standards and Technology,
325 Broadway, Boulder, Colorado 80305
1
0
The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber
0 is used to phase coherently measure the frequencies of both the Hg+ and Ca optical standards
2
with respect to the SI second as realized at NIST. We find the transition frequencies to be f =
Hg
n 1 064 721 609 899 143(10) Hz and f = 455 986 240 494 158(26) Hz, respectively. In addition to
Ca
a theunprecedentedprecisiondemonstratedhere,thisworkistheprecursortoall-opticalatomicclocks
J based on the Hg+ and Ca standards. Furthermore, when combined with previous measurements,

4 wefindnotimevariationsoftheseatomicfrequencieswithintheuncertaintiesof|(∂fCa/∂t)/fCa|≤
8×10−14 yr−1, and |(∂f /∂t)/f |≤30×10−14 yr−1.
Hg Hg
]
h
p Optical standards based ona single ion or a collection radiatingtheHg+ ionalternatelyattwofrequenciesnear
-
m of laser-cooled atoms are emerging as the most stable the maximum slope of the resonance signal and on op-
and accurate frequency sources of any sort [1, 2, 3, 4, 5]. posite sides of its center. Transitions to the metastable
o
at However,because of their high frequencies (∼500THz), 2D5/2 state are detected with near unit efficiency since
it has proven difficult to count cycles as required for the absorption of a single 282nm photon suppresses the
.
s
building an optical clock and comparing to the cesium scattering of many 194 nm photons on the strongly al-
c
i microwavestandard. Onlyrecently,areliableandconve- lowed 2S1/2−2P1/2 transition[12, 13]. Usually, 48 mea-
s
y nientopticalclockworkfastenoughtocountopticaloscil- surements are made on each side of the resonance prior
h lationshasbeenrealized[6,7,8]. Here,wereportanop- tocorrectingtheaveragefrequencyofthe282nmsource.
p tical clockwork based on a single femtosecond laser that If an asymmetry between the number of excitations de-
[ phase coherently divides down the visible radiation of tected on the high- and low-frequency sides is found,

1 the Hg+ and Ca optical frequency standards to a count- then the frequency of the probe radiation is adjusted to
v able radio frequency. By this means we determine the minimize the asymmetry. In this way, we steer the fre-
9 absolute frequencies of these optical transitions with un- quency of the 282nm source to the center of the S−D
2
paralleled precision in terms of the SI second as realized quadrupoleresonancewithanimprecisionthatdecreases
0
at NIST [9]. Indeed, for the Hg+ standard, the statis- asthe squarerootofthe measurementtime. InFig.1(b)
1
0 tical uncertainty in the measurement is essentially lim- we show an example of a normalized spectrum that was
1 ited by our knowledge of the SI second at ∼ 2×10−15. obtained from multiple bidirectional scans through the
0 The high precision and high demonstrated stability of resonance during the lock-up, where the probe time was
/
s the standards[1, 4] combined with the straightforward 20ms. Mostoften,thefrequencywaslockedtoresonance
c femtosecond-laser-based clockwork suggest Hg+ and Ca witha10msinterrogationperiod,whichprovidedafrac-
si asexcellentreferencesforfutureall-opticalclocks. Addi- tional frequency instability reaching 3×10−15τ−1/2 for
y
tionally, the comparison of atomic frequencies over time an averaging time τ measured in seconds [14].
h
providesconstraintsonthepossibletimevariationoffun-
p
: damentalconstants. Whencombinedwithpreviousmea- Thecalciumstandardisbasedonacollectionof∼107
v surements,thecurrentlevelofprecisionallowsustoplace laser-cooled 40Ca atoms held in a magnetooptic trap.
Xi thetightestconstraintyetonthepossiblevariationofop- The 423 nm 1S0 ↔ 1P1 transition is used for Doppler
r tical frequencies with respect to the cesium standard. cooling and trapping the atoms to a residual tempera-
a ture of ∼ 2 mK, while the 657 nm 1S0(MJ = 0) ↔
TheHg+ andCasystemshaverecentlybeendescribed 3P1(MJ =0) clocktransition(400Hz naturallinewidth)
elsewhere[1, 4, 10, 11], so we summarize only the ba- is used for the frequency standard [Fig 2(a)]. We ex-
sic features. The heart of the mercury optical frequency cite the clocktransitionwith afour-pulseBord´e-Ramsey
standardisasingle,laser-cooled199Hg+ionthatisstored sequence (pulse duration = 1.5 µs) with light from a
in a cryogenic, radio frequency spherical Paul trap. The continuous wave (CW) frequency-stabilized diode laser.
2S (F = 0,M = 0) ↔ 2D (F = 2,M = 0) Using a shelving detection technique similar to that
1/2 F 5/2 F
electric-quadrupole transition at 282 nm [Fig. 1(a)] pro- employed in the Hg+ system, near-resonant 423 nm
vides the reference for the optical standard [1]. We lock pulses (5 µs duration) are used before and after the
thefrequency-doubledoutputofawell-stabilized563nm 657 nm excitation to determine the fraction of atoms
dyelasertothecenterofthequadrupoleresonancebyir- transferred from the ground state. Figure 2(b) shows
2
Bord´e-Ramsey fringes taken at a resolution of 960 Hz. cavity-tuned hydrogen maser. Control of f is achieved
r
This system has demonstrated a fractionalfrequency in- with a cavity folding mirror that is mounted on a piezo
stability of 4×10−15τ−1/2, when probing sub-kilohertz transducer,whilef iscontrolledbyadjustingthe532nm
o
linewidths [4]. For the measurements presented here the pumpbeamintensitywithanelectro-opticmodulator[8].
Ca spectrometer was operated with linewidths ranging When f and f are both phase-locked, the frequency of
o r
from 0.96 to 11.55 kHz which are integer subharmonics everymodeinthecombisknownwiththesameprecision
of the recoil splitting. as the reference maser.
The recent introduction of mode-locked lasers to op- TheCWlightfromtheHg+(563nm)andCa(657nm)
tical frequency metrology greatly simplifies the task of spectrometersistransferredtothemode-lockedlasersys-
opticalfrequency measurements[6,7,8,15, 16,17]. The temviatwosinglemodeopticalfibersthatare130mand
spectrum emitted by a mode locked laser consists of a 10 m long, respectively. Approximately 2 mW of CW
comb of regular spaced continuous waves that are sepa- lightfromeachfiberismode-matchedwiththeappropri-
rated by the pulse repetition rate f . The frequency of ate spectral region of the frequency comb to generate a
r
thenthmodeofthecombisgivenbyf =nf +f [18,19] beatsignalf withanearbymode. Thisbeatnoteisam-
n r o b
where f is the frequency offset common to all modes plifiedandmeasuredwitharadiofrequencycounter. The
o
that is caused by the difference between the group- and opticalfrequencyisthenexpressedasf =f +mf +f ,
opt o r b
the phase-velocity inside the laser cavity. Whereas f where m is a large integer uniquely determined for each
r
can be measured by direct detection of the laser out- system from previous coarse measurements of f .
opt
put with a photodiode, f is measured by heterodyn- We detect cycle slips in both of the phase-locks by
o
ing the harmonic of a mode f = nf + f from the monitoring f and f with additional counters [24]. We
n r o r o
infrared wing of the comb with a mode f2n = 2nfr+fo selectivelydiscardanymeasurementoffopt forwhichthe
from the blue side of the comb [7, 8]. While an oc- measured f or f deviate from the expected value by
o r
tave spanning comb can be produced directly from a more than 1/τ , where τ is the counter gate time
gate gate
mode-locked laser [20], launching the longer pulses from in seconds. We avoid miscounts of f by using an auxil-
b
a commercially-available femtosecond laser into an air- iary counter to record the ratio r between f and f /4,
b b
silica microstructure fiber [21, 22] also produces a fre- where the division by 4 is implemented digitally. Any
quency comb that spans an octave. Via nonlinear pro- measurements of f where the auxiliary counter gives a
b
cesses in the fiber, additional equally spaced and phase- resultthatdoesnotsatisfy(r−4)∗f <10/τ aredis-
b gate
coherent modes are added to the comb. It has been carded. Werelyontheassumptionthatthetwocounters
demonstrated that this process of spectral broadening recording f and r, if in disagreement, do not make the
b
preserves the uniformity of spacing and spectral fidelity same mistake. For each data point the three additional
of the comb to at least a few parts in 1016 [8]. counters(f ,f andr) arestartedbeforethe countingof
r o
Wecoupleapproximately200mWaveragepowerfrom fb, and operated with 50ms longer gate times to ensure
a femtosecond Ti:sapphire ring laser(f ≈ 1 GHz)[23] temporal overlap.
r
into a 15 cm piece of a microstructure fiber that has a Figure 3 summarizes the frequency measurements of
1.7µmcoreandagroupvelocitydispersionthatvanishes Hg+madebetweenAug. 16andAug31,2000,andFig.4
near 770nm[21]. This power is sufficient to increase the summarizes the Ca measurements made fromOct. 26 to
spectral width of the laser from 13 THz to more than Nov. 17, 2000. All measurements are corrected daily
300 THz, spanning from ∼ 520 nm to ∼ 1170 nm. The for the second-order Zeeman shift and for the offset of
infrared part of the comb from the fiber (λ ≈ 1060 nm) the reference maser frequency. The uncertainty for the
is split off by a dichroic mirror and frequency doubled Zeeman correction is < 1× 10−15 for the Hg+ system
into the green portion of the visible spectrum with a and < 2.5×10−15 in the Ca system. The frequency of
2 mm long KNbO3 crystal. Following an adjustable the maser is calibrated by comparing to the local NIST
delay line that matches the optical path lengths, the time scale (5 hydrogen masers and 3 commercial cesium
frequency-doubled light is spatially combined with the clocks), which in turn is calibrated by the local cesium
green part of the original comb using a polarizing beam fountain standard (NIST-F1 [9]) as well as international
splitter. A second rotatable polarizer projects the po- cesium standards. This resulted in a fractional uncer-
larization of the combined beams onto a common axis tainty in the frequency of the reference maser of about
so that they can interfere on a photodiode. This polar- 1.8×10−15 for the measurements.
izer is also used to adjust the relative power of the two The weighted mean of our measurements of the Hg+
beams for optimum signal-to-noise ratio (SNR) in the clock transition is f = 1 064 721 609 899 143 Hz,
Hg
heterodyne signal. A small grating prior to the photodi- where the statistical uncertainty of 2.4 Hz is near the
ode helps to select only that part of the frequency comb fractional frequency instability of the reference maser
thatmatchesthefrequency-doubledlight,therebyreduc- (∼ 2×10−13 at 1s, decreasing to ∼ 4×10−16 at a few
ing noise from unwanted comb lines [19]. We phase-lock days). Since we have not made a full evaluation of the
both f andf to synthesizedfrequencies derivedfroma Hg+-standard,weonlyestimate thetotalsystematicun-
o r
3
certainty to be 10 Hz. The dominant systematic con- gapbetweenf /2theandCastandard[27]. Thisyields
Hg
tribution to the uncertainty of the S−D transition fre- avalue f =455986240494143(40)Hz ingoodagree-
Ca
quency is believed to be the electric-quadrupole shift of ment with the present absolute measurement of f .
Ca
the 2D state arising from coupling with the static po-
5/2 Finally, these results also provide data on the rela-
tentials of the trap. In our spherical Paul trap, where
tive time variability of atomic frequencies. S. Karshen-
the confinement of the ion uses no static applied fields,
boimhasrecentlyreviewedtheimplicationsofsuchcom-
the maximum quadrupole shift should be less than 1Hz
parisons and their contribution toward constraining the
(or a fractional frequency shift < 10−15)[25]. In princi-
possible time variation of fundamental constants [28].
ple, it is possible to eliminate the quadrupole shift by In this regard Hg+ and Ca are two of the most inter-
averagingthe S−D transitionfrequencies for three mu-
esting cases to study. Comparing our present measure-
tually orthogonal orientations of a quantizing magnetic
ment of f to measurements made by PTB in 1997[26]
Ca
field of constant magnitude. In the present experiment, gives (∂f /∂t)/f = (+2 ± 8) × 10−14 yr−1. Sim-
we have measured the S −D frequency for various field Ca Ca
ilarly, combining this result with our May 2000 mea-
values, but we have made no attempt to eliminate the
surement of f with respect to f [27] provides an ini-
Hg Ca
quadrupole shift by using three orthogonal fields of con-
tial baseline constraint on the time variation of f of
Hg
stant magnitude. No shift of the resonance frequency is (∂f /∂t)/f = (−7±30)×10−14 yr−1. Here we use
Hg Hg
observedwithintheprecisionofthesemeasurements. We
thedefinedunitoftimebasedonthefrequencyoftheCs
anticipate that the uncertainties of all systematic shifts
hyperfine interval and assume that any time dependence
inthe Hg+ systemcanbe reducedto values approaching
isslowanddominantlylinearovertherelevanttimescale.
1×10−18 [1, 25].
At our present level of precision we find no evidence of
FortheCadatashown[Fig.4],anadditionalcorrection anyrelativetimevariationbetweenthesethreefrequency
isappliedeachdaytoaccountforafrequencyshiftcaused standards, two optical and one microwave.
by residual phase chirping on the optical Ramsey pulses
producedbyamplitudemodulatinganacoustoopticmod-
The authors are most grateful to T. Parker for pro-
ulator(AOM).Thephasechirpingproducedaresolution
viding the crucial maser calibration and to A. Bartels
dependent frequency shift on the order of 100 Hz for
of GigaOptics for his valuable assistance with the fem-
11.5 kHz wide fringes but only 10 Hz for 0.96 kHz wide
tosecond laser. We are also indebted to R. Windeler of
fringes. Oneachday,the Cafrequencywasmeasuredfor
∼30minutesateachofseveralfringeresolutions,andthe LucentTechnologiesforprovidingthemicrostructureop-
tical fiber. We further acknowledge many illuminating
zero-intercept of a linear fit to the data was used as the
discussions with D. Wineland, J. Hall, S. Karshenboim,
correctedfrequency. Onthelast3daysofmeasurements,
we were able to reduce this shift by a factor of ∼3 with and F. Walls. This research was partially supported by
the Office of Naval Research and through a Cooperative
improvements to the RF pulses that drive the AOM’s.
Research and Development Agreement with Timing So-
The statistical uncertainty for each day’s measurement
lutions, Inc., Boulder, CO.
(typically 8Hz) is smaller than the uncontrolledsystem-
atic uncertainties in the the Ca frequency. The largest
systematicuncertaintystemsfromincompleteknowledge *Present address: Max-Planck-Institut fu¨r Quanten-
of the angular overlap of the counterpropagating beams optik, Hans-Kopfermann-Str.1, 85748 Garching/Germa-
intheCaspectrometer,combinedwithatransversedrift ny.
velocity of the cold Ca ensemble. This leads to a resid-
ual first-order Doppler shift with a magnitude < 15 Hz
(except on Nov. 16 where a large drift velocity led to a
∼52Hz uncertainty). Other significantuncertaintiesin-
cludeourlackofknowledgeorcontrolofelectronicoffsets [1] R. Rafac et al., Phys. Rev.Lett. 85, 2462 (2000).
andbaselineasymmetries(<12Hz),wavefrontcurvature [2] J. E. Bernard et al., Phys.Rev.Lett 82, 3228 (1999).
[3] H. Schnatzet al., Phys.Rev.Lett. 76, 18 (1996).
(< 10 Hz), and cold-atom collisional shifts (< 10 Hz).
[4] C. W. Oates et al., Opt. Lett.25, 1603 (2000).
Taking all knownsystematic uncertainties in quadrature [5] J. von Zanthier et al. Opt.Lett. 25, 1729 (2000).
givesaconfidencelevelof∼26Hzforthemeasuredmean [6] S. A. Diddamset al., Phys.Rev.Lett. 84, 5102 (2000).
value as indicated by the dashed lines in Fig. 4. [7] D. J. Jones et al., Science228, 635 (2000).
Figure 4 also shows the good agreement between our [8] R. Holzwarth et al., Phys.Rev. Lett.85, 2264 (2000).
measurementandthemostrecentvaluemeasuredwitha [9] S. R. Jefferts et al., submitted to Metrologia; S. R.Jef-
fertsetal.,IEEEInternationalFreq.ControlSymp.,714
harmonicfrequencychain[26],whichprovidesadegreeof
(2000).
confidenceinthereproducibilityoftheCastandards. An
[10] C. W. Oates et al., J. Phys.D 7, 449 (1999).
additional measure of the Ca frequency can be made by [11] B. Younget al., Phys. Rev.Lett. 82, 3799 (1999).
using the present absolute measurement of Hg+ and our [12] H. Dehmelt, Bull. Am. Phys.Soc. 20, 60 (1975).
earlier measurement of the 76 374 564 455 429(40) Hz [13] J. C. Bergquist et al., Phys. Rev.A 36, 428 (1987).
4
[14] D. J. Wineland et al., The Hydrogen Atom ed. by T.W. FIG.1: (a)Partiallevelschemefor199Hg+. The194nmradi-
H¨ansch (Springer, Berlin, Heidelberg 1989) pp.123-133. ationisusedforDopplercooling,statepreparationanddetec-
[15] Th. Udem et al., Phys. Rev.Lett. 82, 3568 (1999). tion. The282nmtransitionfromthegroundstate2S (F =
1/2
[16] J. Reichert et al., Phys. Rev.Lett. 84, 3232 (2000). 0,M = 0) to the metastable 2D (F = 2,M = 0) state
F 5/2 F
[17] M. Niering et al., Phys.Rev.Lett. 84, 5496 (2000). provides the reference for the optical clock frequency. (b) A
[18] A.I.Ferguson, J.N.Eckstein,andT. W.H¨ansch,Appl. typicalspectrum of the282nm clock transition obtained un-
Phys.18, 257 (1979). derlockconditionsisshown. Here,theexcitationpulselength
[19] J. Reichert et al., Opt.Comm. 172, 59 (1999). was 20 ms, and the measured linewidth is Fourier transform
[20] F. X.K¨artner et al., Opt. Lett.(in press). limited to about 20Hzat 563nm (40Hzat 282nm).
[21] J. K. Rankaet al., Opt.Lett. 25, 25 (2000).
[22] W. J. Wadsworth et al., Electron. Lett. 36, 53 (2000).
[23] A.Bartels, T. Dekorsy,and H.Kurz, Opt.Lett. 24, 996
(1999).
[24] Th. Udem et al., Opt. Lett.23, 1387 (1998).
[25] W. M. Itano, J. Res. NIST(in press).
[26] F. Riehle et al., Proceedings of EFTF-IEEE IFCS, 700
(1999).
[27] K.R. Vogel et al., Opt. Lett.(in press).
[28] S.Karshenboim, Can. J. Phys. 78, 639 (2000).
1.0
2P1/2FF == 10 2D5/2F = 3 ability 0.9
F = 2 ob
194 nm e pr 0.8 21 Hz
282 nm stat
F = 1 und 0.7
o
(a) F = 0 (b) gr
2S1/2 0.6-60 -40 -20 0 20 40 60
cavity detuning [Hz]
5
1P 22.4
1
3P ms]
1 o
at 22.0
423 nm of
%
657 nm n [
atio 21.6
cit
x
e
(a) 1S0 (b) 21.2
-3 -2 -1 0 1 2 3
cavity detuning [kHz]
FIG. 2: (a) Simplied diagram of the relevant energy levels
in the Ca standard. (b) Optical Bord´e-Ramsey fringes with
a 960 Hz (FWHM) resolution. The total averaging time to
generate this figure was 20s.
30
z
H
2.6 20
4
1
9 10
9
8
9
60 0
1
2
7
4 -10
6
0
1
- g -20
H
f
-30
Aug 16 Aug 21 Aug 26 Aug 31
FIG.3: Achronologicalrecordoftheaveragedailyfrequency
ofthe199Hg+ clocktransitionmeasuredonsixdaysovera15
day period representing 21 651 s of total measurement time.
The error bars represent statistical fluctuations. The dashed
linesrepresentanestimatedsystematicuncertaintyof±10Hz
in theHg+ system in theabsence of a full evaluation.
6
150
z
H
8 100
5
1
4
9 50
4
0
4
2 0
6
8
9
5 -50
5
4
- Ca -100
f
-150
Oct 26 Nov 5 Nov 15
FIG.4: ThefilledsquaresarethemeasuredCafrequencieson
ten days over a 23-day period representing 38 787 s of total
measurement time. The inner and outer error bars for each
day represent the statistical and total uncertainties, respec-
tively. The dashed-lines show the 26 Hz systematic uncer-
tainty assigned to the mean. The open triangle is the PTB
measurement reported in Ref. [26], and theopen circle is the
Cafrequencycalculated fromthepresentHg+ resultandour
previous measurement of the 76 THz gap between Ca and
Hg+ [27].