A sub-40 mHz linewidth laser based on a silicon single-crystal optical cavity

1.4 MB·English

by  T. Kessler

A sub-40 mHz linewidth laser based on a silicon single-crystal optical cavity
T. Kessler,∗ C. Hagemann,∗ C. Grebing, T. Legero, U. Sterr, and F. Riehle
Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
M.J. Martin, L. Chen,† and J. Ye
JILA, National Institute of Standards and Technology and University of Colorado,
Department of Physics, 440 UCB, Boulder, Colorado 80309, USA
State-of-the-art optical oscillators based on lasers frequency stabilized to high finesse optical
cavities are limited by thermal noise that causes fluctuations of the cavity length. Thermal noise
represents a fundamental limit to the stability of an optical interferometer and plays a key role in
2 modern optical metrology. We demonstrate a novel design to reduce the thermal noise limit for
1
opticalcavitiesbyanorderofmagnitudeandpresentanexperimentalrealization ofthisnewcavity
0
system, demonstrating the most stable oscillator of any kind to date. The cavity spacer and the
2
mirror substrates are both constructed from single crystal silicon and operated at 124 K where the

n silicon thermal expansion coefficient is zero and the silicon mechanical loss is small. The cavity
a is supported in a vibration-insensitive configuration, which, together with the superior stiffness
J of silicon crystal, reduces the vibration related noise. With rigorous analysis of heterodyne beat

5 signalsamongthreeindependentstablelasers,thesiliconsystemdemonstratesafractionalfrequency
stability of 1×10−16 at short time scales and supports a laser linewidth of <40 mHz at 1.5 µm,
] representing an optical quality factor of 4×1015.
s
c
i
t INTRODUCTION sitivity of the cavity length to environmental vibration
p
o noise. Also, aging-relatedfrequencydrifts commonlyen-
. Precision optical interferometers are at the heart of countered in conventional glass materials are completely
s
c the world’s most accurate measuring science such as op- absentincrystallinematerials,asdemonstratedby cryo-
si tical atomic clock work [1–4], gravitational wave detec- genic sapphire opticalresonatorsoperatedata tempera-
y tion[5–7], cavityquantumelectrodynamics[8],quantum tureof4.2K[21,22]. Anall-siliconinterferometercanbe
h optomechanics[9,10]andprecisiontestsofrelativity[11]. madeinsensitivetotemperaturefluctuationsasthecoef-
p Theseexperimentsexplorethe nextfrontiersofmeasure- ficientofthermalexpansionofsiliconhasa zerocrossing
[ ment science and open new windows for scientific dis- near 124 K. In this temperature range the Q of silicon
2 coveries. However, the ultimate limit to the sensitivity is orders of magnitude higher than in the conventional
v andstabilityoftheseinterferometrydevicesisnowsetby cavity glass materials such as Ultralow Expansion glass
4 theBrownianthermo-mechanicalnoiseintheinterferom- (ULE) or fused silica [23]. A similar approach has been
5 eter’smirrorsorspacers[12–14]. Thisnoisedirectlyleads usedwithrelativelylow-finesseopticalFabry-Perotinter-
8
tofluctuationsoftheopticallengthoftheinterferometer, ferometers [24] and has recently been proposed for grav-
3
. degrading the frequency stability of any laser stabilized itational wave detection [25]. A remaining issue to be
2 toit[6,15,16,20]andimpedingtheachievementofquan- solved in the future is the thermal noise associated with
1 tum coherence in a macroscopic system. Consequently, opticalcoating,butits contributioncanbe reducedwith
1
different attempts, in both theory [14, 17] and experi- the use of a longer cavity spacer.
1
: ment [18, 19], have been made to lower this limit, which Afterpresentingthedetaileddesignofthesiliconcrys-
v is currently at 3 10−16 fractional instability [16]. tal cavity, we report frequency stabilization of a laser
i ∼ ×
X Here, we present an approachcapable of reducing this to a high finesse silicon interferometer at a wavelength
r thermal noise limit by at least an order of magnitude. of 1.5 µm where the silicon substrate is transparent.
a As a result of the fluctuation-dissipation theorem, the By comparison with two other lasers stabilized to state-
thermal noise of an interferometer made of high me- of-the-art conventional interferometers, we demonstrate
chanical quality factor Q material can be reduced sig- the superiorperformanceofthe siliconinterferometerby
nificantly as compared to conventional glass materials. achieving a laser linewidth of <40 mHz and short-term
For such a high Q material we have selected a silicon stability at 1 10−16. The corresponding optical coher-
single crystal for both the cavity spacer and mirror sub- ence length is×beyond 1 109 m, on the order of the
strates. Silicon has other important advantages: its su- length of the proposed L×aser Interferometer Space An-
perior Young’s modulus effectively suppresses the sen- tenna (LISA). While this performance exceeds any oscil-
lators demonstrated to date in microwave or optical re-
gions, we emphasize that the paradigmshift represented
∗ memberofQUESTInstituteforExperimentalQuantumMetrol- by the use of a crystal cavity instead of more traditional
ogy,Bundesallee100,38116Braunschweig,Germany amorphousmaterials(suchasULE)willenablemuchfur-
† current address: Wuhan Institute of Physics and Mathematics, ther progress for time, frequency, and length metrology.
ChineseAcademyofSciences,Wuhan, 430071, China
2
FIG. 1. Performance of a single-crystal silicon Fabry-Perot interferometer (A) Estimation of frequency noise power spectral
densityarisingfromBrownian-motionthermalnoiseforvariousmirrorsubstrateandspacermaterials. Thenominaldimension
of theoptical cavity hasa spacer length of 210 mm, spacer radius 50 mm, central bore5 mm, radii of curvatureof 1 m/∞ for
thetwomirrors. TherightaxisdisplaysthecorrespondingAllanVarianceforfractionalopticalfrequencyinstability. (B)FEM
simulationofthevibrationsensitivityoftheverticalcavitydesignasafunctionofthepositionofthecentralsupportringfrom
the symmetric plane for ULE and single-crystal silicon as cavity material. The inset shows the strain energy distribution for
thesilicon spacer.
DESIGN OF SILICON CAVITY andthermo-elastic(substrate)noiseisatleasttwoorders
of magnitude below this thermal noise.
Mono-crystalline silicon possesses superior mechanical Toreachthisrecord-lowlevelofthermalnoise,wemust
properties [26] such as high elastic modulus, well above reduce the influence of environmental vibrations on the
that of optical glasses, and large thermal conductivity. resonator of length L = 210 mm. We minimized the
Large, high-purity and low-defect crystals are readily sensitivity ofthe spacerlength to externalappliedforces
available at reasonable cost. Compared to glasses, the via finite element modeling (FEM), taking advantage of
thermalconductivity(500W/mKat124K[27])isabout the full elasticity tensor of silicon. Designs with either
two ordersof magnitude higher (1.31 W/mK), whichas- a vertical [15, 33] or a horizontal optical axis [34, 35]
sures a homogeneous temperature and small local heat- have achieved strong suppression of vibrational sensitiv-
ing from any absorbed laser radiation. Silicon is a cubic ity. After extensive FEM simulations, a verticalconfigu-
crystalwithitslargestYoung’smodulusalongthe<111> rationsimilartothatofRef.[15]waschosen,asitshowed
axis (E = 187.5 GPa) [28, 29], which we have chosen to the smallest sensitivity to the details of the mounting
be the optical axis of the cavity. (e.g., contactareaand contactmaterial). We found that
Figure 1A shows the calculated thermal noise for the ∆L/L < 10−16/µg for a tolerance of the axial position
siliconcavityatitszerocrossingtemperatureof124K,in o|f 0.5 m| m, where g = 9.81 m/s2 is the gravity acceler-
comparisontoroomtemperaturecavitieswithULEspac- ation and ∆L/L is the fractional length change of the
ers and ULE or fused silica mirror substrates. The fre- cavity. This represents a factor of three improvement
quencynoisepowerspectraldensityofthe siliconcavity- over a ULE cavity of the same design.
stabilized laser is reduced partially because of the lower It is important to note that the anisotropic structure
temperature. In addition, the high mechanical quality of silicon leads to a dependence of the sensitivity of the
factor of silicon (Q > 107 [30, 31]) directly reduces the supportpointswithrespecttothecrystalaxes. Wefound
noise contribution from the spacer and the mirror sub- that the <110> directions offered the most optimized
strates. The high Young’s modulus of the mirror sub- supportingconfiguration. Thethreeequivalentdirections
stratecomparedtoULEandfusedsilica(E 67.6GPa) of <110> intersect with our horizontal mounting ring,
≈
alsofurtherreducesthethermalnoiseofthecoating[32]. givingrisetothreesupportingpointsthataresymmetric
Combining these contributions, we estimate that the byaxialrotationof120◦. Forhorizontalaccelerations,we
thermal noise leads to a flicker floor of the fractional findatiltof65nrad/g,comparedto180nrad/gforULE.
optical frequency stability of σ = 7 10−17. In the Finally, for a 10% asymmetry in the elasticity between
y
×
extremely unlikely scenario where the substrate temper- themountingpointswefoundanon-axisfractionallength
ature is set 1 K off from the zero crossing point of the change of 2 10−17/µg (5 10−17/µg for ULE). These
× ×
thermalexpansion,theestimatedthermo-optic(coating) results clearlyillustrate the superior elastic propertiesof
3
placed on an actively controlled vibrationisolationtable
Active shield Vacuum chamber and evacuated to a residual pressure of 1 10−8 mbar.
×
The cavity is surrounded by two massive, cylindrical,
gold-platedcopper-shieldsandsupportedbyatripodma-
Passive shield Silicon cavity chined from teflon. Cooling of the outer shield is accom-
plishedbyevaporatingliquidnitrogenfromadewarusing
a heating resistor. The nitrogen gas flows through su-
Ion
perinsulated vacuum tubes to the outer heat shield and
getter by regulating its flow the shield temperature is stabi-
pump lizedtomaximumdeviationsof 1mKfromthesetpoint.
Cooled ∼
Anadditionalthermallyisolatedpassiveheatshieldsup-
Nitrogen gas
presses radiative heat transfer from the outer shield to
feeding lines
the silicon cavity, resulting in a thermal time constant
of more than 14 days. During continuous operation, the
cryostatexhibitsaccelerationnoiseoflow0.1µg/√Hzin
Vibration isolation platform the frequency range of 1 to 100 Hz.
The cavity length was probed by a commercial Er-
doped fiber laser source. Locking to the cavity reso-
nance was realized via the Pound-Drever-Hall (PDH)
scheme [37]. Phase modulation of the laser was achieved
FIG. 2. Schematic of the vibration-reduced, nitrogen-gas-
by an all-fiber waveguide electro-optical modulator with
based cryostat including the vacuum chamber and the two
an active suppression of the residual amplitude modu-
heat shields centered around the silicon single-crystal cavity.
lation (RAM). Feedback was applied to a fiber-coupled
The thermal time constant of thesystem is 14 days.
acousto-optical modulator with a locking bandwidth of
200 kHz to keep the laser tightly locked to the cavity
∼
silicon compared to low expansion glass. resonance.
The raw material was a high resistivity silicon rod of The coefficient of thermal expansion α of the silicon
100 mm diameter. It was oriented by X-ray diffraction cavity was measured in a region close to its predicted
to define the optical axis to within a few arc minutes. zero-crossing at 124 K by monitoring the frequency of
The crystal was machined to a tapered cylinder shape the laser locked to the cavity as a function of the cav-
with mounting ring and the surface etched to reduce ity temperature measured on its surface with a PT-100
stress induced by the machining [15]. The silicon mirror sensor. The laser frequency was measured in compari-
substrates were machined from the same oriented mate- son to a reference laser system stabilized at room tem-
rialand,afterbeingsuperpolishedandcoatedwithhigh- perature. The minimum cavity length was found at a
reflectivity,low-lossopticalthinfilms,theywereoptically temperature of 124.2 K with a statistical uncertainty
contacted to the spacer. We aligned the substrates and of 5 mK, caused by the delayed response of the cav-
spacercrystalinthesamecrystallographicorientationas ity frequency to a change of its surface temperature.
to best maintain the single crystalproperty of the entire The accuracy of the absolute temperature is limited to
cavity. We wereable to obtain afinesse of 80000for the a value of 0.1 K by the calibration of the tempera-
TEM00 mode of the cavity, and a much higher finesse of ture sensor. We determine a zero-crossing sensitivity of
240 000 for the TEM01 mode. Consequently, for all the dα/dT = 1.71(1) 10−8 K−2. These results are consis-
×
resultsdiscussedinthiswork,theTEM01 modewasused tent with the values given in [36, 38].
for laser stabilization. To determine the cavity length sensitivity to vibra-
tionsinthehorizontalandverticaldirections(k ,k ,and
x y
k , respectively), we analyzed the frequency response of
z
CRYOSTAT DESIGN AND PERFORMANCE the stabilized laser system to applied excitations. We
measured accelerations in all three axes while we simul-
Fractional frequency stability at the level of 1 10−16 taneously recorded the Si cavity-stabilized laser system
×
also places a stringent requirement on cavity tempera- with a second reference laser system. Since we observed
ture stabilization. Thermal fluctuations are suppressed a non-negligible coupling of the movement from the ex-
to first order by operating the cavity at a zero-crossing cited to the non-excited directions, we had to take into
pointofits thermalexpansion,atatemperatureof 124 account amplitude and phase relations of all accelera-
∼
K for silicon [36]. A major challenge for optical cavities tion components in the full calculation [34]. For the
operated at cryogenic temperatures is the reduction of horizontaldirections, a fractionalvibrationsensitivity of
vibrationsinducedbythecoolingmechanism. Thischal- k =6.7(3) 10−17/µg and k =8.4(4) 10−17/µg was
x y
× ×
lenge was overcome in part by a novel and simple cryo- determined. The vertical sensitivity is determined to be
stat design based on nitrogen gas as coolant. A sketch k =5.5(3) 10−17/µg,hencereadilyenablingfractional
z
of the setup is shown in Fig. 2. The vacuum chamber is instabilities×below 10−16. The vibration sensitivity re-
4
a
6
)
z
H 4
(

y
c 2
n
e
u 0
q
e
fr -2 Ref.2-Ref.1
t
a
e -4 Silicon-Ref.1
B
Silicon-Ref.2
-6
0 10 20 30
Time (min)
b c
-15
n n10
o o
ti Ref.2-Ref.1 ti
a -14 a
vi 10 Silicon-Ref.1 vi
e e
d Silicon-Ref.2 d

n n
-16
Alla -15 Alla10 RAM servo on
RAM servo off
10
d d
e e
fi fi
di di
o o
M M
-16 -17
10 10
0.1 1 10 100 0.1 1 10 100
Averaging time (s) Averaging time (s)
FIG. 3. Time record and stability of the optical beat signals between the silicon cavity laser and the two reference lasers. (A)
Traces ofthethreebeatsinvolvedinthethree-cornered hatcomparison afterlineardrift removal(Ref.2−Ref.1: -234.9 mHz/s,
Silicon−Ref.1:-4.7 mHz/s, Silicon−Ref.2: 230.2 mHz/s. (B) Modified Allan deviation of the fractional frequency stability for
thecorrespondingbeatsignalsshowninpanel(A).(C)Fractionalfrequencystability aslimitedbythedriftoftheoffsetofthe
cavity servo error signal, with and without theactive RAMcancelation engaged.
portedhereisthelowestforanyopticalcavitiesdesigned has a finesse of 316 000. The thermal noise of the cavity
completely based on simulations. It is only surpassed is expected to limit the Allan deviation at a flicker floor
by dedicated transportable cavity designs with actively of σ (τ) 6 10−16.
y
≈ ×
tunable degrees of freedom allowing for experimentally
The second reference system (Ref.2) employs another
minimizing the sensitivity [39].
Er-dopedfiberlaserfrequencystabilizedtoaULEcavity.
Themirrorsubstratematerialisfusedsilica,whichlowers
themagnitudeofthethermallydrivenmirrorfluctuations
REFERENCE LASER SYSTEMS in comparison to a system employing ULE mirror sub-
strates. Additionally, the cavity spacer’slength of25cm
reduces the fractional impact of these same fluctuations
To determine the performance of the silicon cavity-
on the frequency stability of the cavity-stabilized laser,
stabilized laser, we utilized two of the best-performing
resultinginanexpectedthermalnoise-limitedflickerfloor
conventional ULE-based optical cavity-stabilized lasers
of 2 10−16. The cavity finesse is 80 000, which led to
from JILA and PTB. Using heterodyne beats between
×
a comparatively increased sensitivity to time-dependent
thesethreeindependentlystabilizedlasers,weperformed
RAMcausedbyparasiticeffects,makingtheactiveRAM
a three-cornered hat comparison [40] at 1.5 µm.
stabilization mandatory.
The first reference laser (Ref.1) is designed as a com-
pact cavity-stabilized system. A distributed feedback To make simultaneous comparisons of the three sys-
fiber laser is stabilized to a horizontally mounted refer- tems,the frequency-stablelightofeachofthe threelaser
ence cavity made of ULE. The cavity is 10 cm long and systems was transferred by single-mode optical fibers to
5
u.)
eat signal (a.--00110.....05005 a eviation10-15 RRSieeliffc..o12n
B 0 5 10 15 20 25 30 n d
a.u.)1.0 b Time (s) Alla
m (0.8 ed
pectru0.6 (49 – 4) mHz Modifi10-16
s0.4
er Thermal noise floor
w0.2
o
P0.0 0.1 1 10 100
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 Averaging time (s)
Optical frequency (Hz)
FIG. 5. Modified Allan deviation of each cavity-stabilized
FIG. 4. Optical heterodyne beat between the silicon cav- laser derived from a three-cornered-hat analysis of the data
ity system and reference laser 2. (A) Beat signal mixed inFig.3. Thedatashowstheaveragestabilityof130data-sets
down to DC and recorded with a digital oscilloscope. (B) with aduration of10 minuteseach. Theerrorbarsrepresent
FastFouriertransform ofthebeatsignalrecorded withaHP the standard deviation of the data averaged for each point.
3561A FFT-Analyzer (37.5 mHzresolution bandwidth, Han- The predicated thermal noise floor of ∼ 5×10−17 for the
ning window). Five consecutive recordings of the beat sig- silicon cavity system is indicated bythe shaded area.
nal are displayed here, demonstrating the robustness of this
record-setting linewidth. The silicon cavity stabilized laser
linewidth has an upperlimit of 35 mHz.
the three systems, modified Allan deviations [45] were
determined from the time records and are shown in
Fig.3B.Theerrorbarshavebeenderivedfollowingaχ2-
a centrally located beat detection unit. A fiber noise
statistics[46,47]. ThetwolaserbeatsinvolvingRef.1are
cancellationsystem[41,42]foreachopticalfiberpathre- limitedbyflickerfrequencynoisetoalevelof 7 10−16,
ducesfiber-noisetobelow10−16at1s. Atthecentralde- ∼ ×
whichis consistentwiththe thermalnoisefloorexpected
tectionunitthelightofallthreelaserswassuperimposed
for this reference laser. The flicker frequency noise of
on 50/50 fiber-splitters. An InGaAs photodiode at the 3.3 10−16 at 0.1 to 1 s averaging time for the beat
output of the last fiber-splitter detected the three beat ∼ ×
between the silicon cavity-stabilized laser and Ref.2 can
signals. The laser beat signals were tracked by phase-
be attributedto alargeextenttothe thermalnoiselimit
locked-loop-basedfilters and subsequently recordedby a
ofRef.2. The effectofactivesuppressionofthe influence
dead-time free counter (K+K Messtechnik: model FXE)
of RAM to the baseline of the servo error signal for the
in phase averaging mode, which corresponds to an over-
silicon cavity system is demonstrated in Fig. 3C.
lappingΛ-modecountingschemeasrequiredforthemea-
The narrowest optical linewidth was observed for the
surementofthemodifiedAllandeviation[43]. Thismea-
beat between the silicon laser and Ref.2. This signal
sure for the stability of the oscillatorswaschosenfor ob-
was analyzed by a digital oscilloscope (Fig. 4A) and a
tainingthehighestpossiblesensitivityataveragingtimes
fast-fourier-transform analyzer (Fig. 4B). We obtain a
greater than 100 ms where we expect to reach the ther-
typical full width at half maximum of 49(4) mHz which
mal noise floor [44].
is the narrowest spectrum of a beat between two lasers
observed. Considering that the silicon cavity-stabilized
laser has the best stability among all three systems, it is
LASER FREQUENCY STABILITY
areasonableestimatethatitslinewidthisbelow35mHz.
The optical coherence time is 10 s.
To characterize the performance of all three lasers, a Toevaluatetheperformanceofeachsinglelaser,rigor-
24 hour long record of the beat signal was taken with a ousthree-corneredhatanalysisincludingcorrelationsbe-
countergatetimeof100ms. Figure3Adocumentsatyp- tweenthe threeoscillatorswascarriedoutfollowing[48].
ical30-minute long trace ofthe beat signalsbetween the Toverifythereproducibilityoftheanalysisthefulldata-
three lasersunder comparisonafter removalofthe linear setwassplitinto130data-setswithadurationof10min-
drift. The best long-term stability was observed for the uteseach. Forthosedata-setsthree-corneredhatanalysis
beatbetweenthe siliconcavity-stabilizedlaserandRef.1 wasperformedincludingtheeffectofpossiblecorrelations
with maximum frequency excursions of 6 Hz over the between the laser systems [48]. The average stability of
full time period. The two beat signals of Silicon Ref.2 eachofthethreelasersisshowninFig.5. Theerrorbars
−
and Ref.2 Ref.1 show correlated fluctuations on a simi- forthesingleoscillatorsrepresentthestandarddeviation
−
lar level at shorter time scales of a few minutes. of the mean values.
For detailed analysis of the frequency stability of At short averaging times the two reference lasers are
6
limited to within a factor of two of their thermal noise excellent long-term stable frequency reference, possibly
floors of 6 10−16 and 2 10−16, respectively. The being competitivewith the stabilityofahydrogenmaser
∼ × ∼ ×
predicted thermal noise for the silicon cavity-stabilized at timescales of 1000 s and beyond. Long-term mea-
laser of 5 10−17 is indicated in the graph. Note that surements against a frequency comb locked to the pri-
∼ ×
instabilitiesarisingfromflickerfrequencynoiseinamod- marycesiumstandard[50]willrevealifthisisindeedthe
ified Allan plot are reduced by 18% in comparison to case. Ourpreliminaryexperimentsarealreadyrecording
∼
the commonly used standard Allan deviation as pointed a long-term optical frequency drift of only a few mHz/s,
outin[44]. Thestabilityofthelaserlockedtothesilicon but longer data sets will be required for detailed anal-
cavityclearlysurpassestheperformanceofthetwoULE- ysis. In combination with an optical frequency comb,
cavity-basedreferencelasersandconsequentlythesilicon which allows the stability of the silicon system to be
data contains the largeststatistical uncertainty. The sil- transferredto any wavelengths within the comb spectral
icon cavity system reaches residual fractional frequency coverage[51, 52], the infrared ultra-stable laser will pro-
instability of 1 10−16 for averaging times of 0.1-1 s videapowerfultoolforhigh-resolutionspectroscopyand
andremainsa∼tthe×low10−16levelforaveragingtimesup optical clocks. With clock instabilities of 1 10−16/√τ
×
to10s,whichisatimescalerelevantforlong-termstabi- that will be possible with such a laser as local oscillator,
lizationtothestrontiumatomicfrequencystandards[49] observationtimes needed to resolvefrequency shifts at a
available at both JILA and PTB. The instability of the level of 10−17 would be at the 100 s level [49].
silicon cavitysystem at shorttime scales(below 0.5 s) is Finally, we note that the thermal noise limit of an op-
limited by the measuredvibration noise floor and RAM. ticalcavitybasedonsingle-crystalsiliconiscurrentlyset
Thislevelofperformanceisthebestfractionalfrequency by the optical coating. We plan to investigate different
stability of any oscillator, optical or microwave, to date. approaches to push down this limit. Possible candidates
Such a stable cavity will have direct impact on optical for the next generation optical coatings are microstruc-
atomic clocks and will also have important implications tured gratings [53] or mirrors based on III/V materials
for quantum metrology and precision measurement sci- suchasgallium-arsenide[54]. Withthesematerialsanin-
ence in general. stability approaching 10−17 and below could be within
reach.
OUTLOOK
ACKNOWLEDGEMENT
Our first investigations of silicon as a material for an
optical reference cavity with ultra-low thermal noise has This silicon cavity work is supported and developed
alreadydemonstratedperformancesthatsurpassanypre- jointly by the Centre for Quantum Engineering and
viously reported optical cavities. At this early stage, a Space-TimeResearch(QUEST),Physikalisch-Technische
number of technicalchallenges are yet to be mastered to Bundesanstalt (PTB), and the JILA Physics Frontier
reach the predicted thermal noise floor of 5 10−17 Center (NSF) and the National Institute of Standards
∼ ×
and to further lower this limit. RAM errors in cavity andTechnology(NIST).WethankR.LalezariandY.Lin
servos can be suppressed to the required level by active of ATF for the coating of the silicon mirrorsand the ini-
feedback. However, at the short time scales the vibra- tialfinessemeasurements. WealsothankM.Notcuttand
tionnoiseofthecryostatshouldbefurtherreduced. The R.Foxforthetechnicalassistancefortheconstructionof
mechanism that limits the stability to 1 10−16 for the second reference cavity. U. Kuetgens and D. Schulze
∼ ×
averaging times of 1–100 s needs further investigations are acknowledgedfor x-ray orientationof the spacer and
basedonadirectcomparisonwithasecondsiliconcavity- the mirrors. G. Grosche is acknowledged for technical
stabilized laser we are currently implementing. assistance on fiber noise cancellation. J. Ye thanks the
Material creep is not expected from a single-crystal Alexander von Humboldt Foundation for financial sup-
cavityagingand therefore the cavity will also serve as an port.
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