Neutral atom frequency reference in the deep ultraviolet with fractional uncertainty = 5.7×10(-15).
ABSTRACT We present an assessment of the (6s2) (1)S0 ↔ (6s6p)(3)P0 clock transition frequency in 199Hg with an uncertainty reduction of nearly 3 orders of magnitude and demonstrate an atomic quality factor Q of ∼10(14). The 199Hg atoms are confined in a vertical lattice trap with light at the newly determined magic wavelength of 362.5697±0.0011 nm and at a lattice depth of 20E(R). The atoms are loaded from a single-stage magneto-optical trap with cooling light at 253.7 nm. The high Q factor is obtained with an 80 ms Rabi pulse at 265.6 nm. We find the frequency of the clock transition to be 1,128,575,290,808,162.0±6.4(syst)±0.3(stat) Hz (i.e., with fractional uncertainty=5.7×10(-15)). Neither an atom number nor second order Zeeman dependence has yet been detected. Only three laser wavelengths are used for the cooling, lattice trapping, probing, and detection.
- [Show abstract] [Hide abstract]
ABSTRACT: We are developing optical lattice clocks with a scope of attaining 10-18 fractional uncertainty. Cryogenic silicon cavity targeting 2×10-17 stability at 1s, will allow full utilization of the potential stability of optical lattice clocks. In order to reduce the blackbody radiation shift, which is the most serious source of uncertainties, Sr clocks in cryogenic environment and Hg clocks are underdevelopment. We discuss prospects for clock comparison, no dead time operation of the clocks and fiber link of the clocks between Riken and the University of Tokyo.Frequency Control Symposium (FCS), 2012 IEEE International; 01/2012
- [Show abstract] [Hide abstract]
ABSTRACT: With Hg199 atoms confined in an optical lattice trap in the Lamb–Dicke regime, we obtain a spectral line at 265.6 nm for which the FWHM is ∼15 Hz. Here we lock an ultrastable laser to this ultranarrow S01−P03 clock transition and achieve a fractional frequency instability of 5.4×10−15/τ for τ≤400 s. The highly stable laser light used for the atom probing is derived from a 1062.6 nm fiber laser locked to an ultrastable optical cavity that exhibits a mean drift rate of −6.0×10−17 s−1 (−16.9 mHz s−1 at 282 THz) over a six month period. A comparison between two such lasers locked to independent optical cavities shows a flicker noise limited fractional frequency instability of 4×10−16 per cavity.Optics Letters 09/2012; 37(17). · 3.39 Impact Factor
- [Show abstract] [Hide abstract]
ABSTRACT: We have measured the absolute frequency of the optical lattice clock based on 87Sr at PTB with an uncertainty of 3.9 × 10−16 using two caesium fountain clocks. This is close to the accuracy of todayʼs best realizations of the SI second. The absolute frequency of the 5 s2 1S0 – 5s5p 3P0 transition in 87Sr is 429 228 004 229 873.13(17) Hz. Our result is in excellent agreement with recent measurements performed in different laboratories worldwide. We improved the total systematic uncertainty of our Sr frequency standard by a factor of five and reach 3 × 10−17, opening new prospects for frequency ratio measurements between optical clocks for fundamental research, geodesy or optical clock evaluation.New Journal of Physics 07/2014; 16(7):073023. · 3.67 Impact Factor
arXiv:1201.3544v1 [physics.atom-ph] 17 Jan 2012
A neutral atom frequency reference in the deep UV with 10−15range uncertainty
J. J. McFerran, L. Yi, S. Mejri, S. Di Manno, W. Zhang, J. Gu´ ena, Y. Le Coq, and S. Bize∗
LNE-SYRTE, Observatoire de Paris, CNRS, UPMC,
61 Avenue de l’Observatoire, 75014, Paris, France
(Dated: January 18, 2012)
We present an assessment of the (6s2)1S0 ↔ (6s7s)3P0 clock transition frequency in199Hg with
an uncertainty reduction of nearly three orders of magnitude and demonstrate an atomic quality
factor, Q, of ∼1014. The199Hg atoms are confined in a vertical lattice trap with light at the newly
determined magic wavelength of 362.5697±0.0011 nm and at a lattice depth of 20ER. The atoms are
loaded from a single stage magneto-optical trap with cooling light at 253.7nm. The high Q factor
is obtained with an 80ms Rabi pulse at 265.6nm. The frequency of the clock transition is found
to be 1 128 575 290 808 162.0 ± 6.4 (sys.) ± 0.3 (stat.)Hz (fractional uncertainty = 5.7×10−15).
Neither an atom number nor second order Zeeman dependence have yet to be detected. Only three
laser wavelengths are used for the cooling, lattice trapping, probing and detection.
PACS numbers:32.30.Jc 37.10.Jk 32.10.Dk 42.62.Fi 37.10.De
The advance in performance of atomic clocks over re-
cent decades is an impressive accomplishment. The ac-
curacy of microwave clocks has improved at a rate of
∼10 per decade and now optical clocks are showing an
improvement at a rate > 102per decade . Optical
clock technology is still relatively young; yet four atomic
species have demonstrated line-center frequency uncer-
tainties at or below 10−16[2–4], with the potential of
several more to follow [5–8]. This will enable further pre-
cision in tests searching for new physics in the low energy
State of the art optical clocks demand an exception-
ally high line-Q, since the attainable frequency stability
of a local oscillator locked to an atomic transition is in-
versely proportional to this quality factor. As Q = ν/∆ν,
where ν is the clock transition frequency and ∆ν is the
excitation linewidth, it is advantageous to have a car-
rier frequency as high as practicality allows. In a neutral
mercury clock this frequency is approximately 1.128PHz,
lying in the deep ultraviolet, hence favourable in this re-
Ion clocks have demonstrated impressive results with
respect to line frequency uncertainties [3, 12, 13] and
progress is expected to continue.
neutral atom clocks is the significantly higher number
of quantum absorbers used for the atom−probe inter-
action. This provides an additional measurement lever
by reducing the integration time required for assessing
various clock shifts. The tightly bound atoms in an op-
tical lattice trap become heavily immune to Doppler and
photon-recoil effects (Lamb-Dicke regime). In the process
of constraining the atoms, one needs to shift the upper
and lower clock state energies by equal amounts by main-
taining the lattice light at the magic wavelength . We
previously reported the measurement of the magic wave-
length in199Hg with 0.21nm uncertainty , making it
the third element to be tested as an optical lattice clock.
Like other alkaline-earth-metal type elements mercury
has a doubly forbidden transition between the ground
A prime driver for
(ns2)1S0 and the excited (nsnp)3P0 levels (n = 6 for
Hg). It has several favourable characteristics for its use
as a primary frequency reference; the most significant be-
ing that its sensitivity to blackbody radiation (BBR) is
more than an order of magnitude lower than that of Sr
and Yb [5, 15]. The uncertainty due to the BBR dom-
inates the frequency uncertainty budgets of these two
clocks [16, 17]. Furthermore, the absence of a high tem-
perature oven for Hg helps to reduce the temperature
variations in the vicinity of the trapped atoms, thus help-
ing to reduce the BBR uncertainty further.
Initial clock transition spectral widths with199Hg were
about 2kHz due to delocalization of atomic states across
lattice sites [6, 18]. Here we have increased the lattice
depth to 20 ER(recoil energy = ?2k2
number; m is the atomic mass) forming more tightly
bound atoms. This has enabled a linewidth reduction to
∼150Hz from which a series of light shift measurements
permitted an improved estimate of the magic wavelength.
In combination with Zeeman shift measurements this has
led to further narrowing, reaching 10Hz. In this letter we
report results pertaining to both the 150Hz and ∼10Hz
wide lines; highlighting the difference where appropri-
ate. Our narrowest lines correspond to a quality factor
of Q = 1014, which has only previously been obtained
in a limited number of systems; e.g., [16, 19–22]. We
have conducted measurements related to various system-
atic shifts, including the first order light shift, Zeeman
shifts and atom number dependence.
The199Hg atoms are loaded into a 1D vertical op-
tical lattice from a single-stage magneto-optical trap
(MOT) that uses laser light at 253.7nm for the cooling
in detail in . Some modifications have been made to
the lattice cavity and to the resonant cavity generating
the 253.7nm ultraviolet light, which we outline here. A
scaled drawing of the apparatus is shown in Fig. 1(a). On
the left hand side appears the combined MOT chamber
and optical lattice cavity. The ports in the horizontal
l/2m; klis the wave
3P1). The MOT and lattice trap are described
and 45◦directions provide access for the MOT beams
(from beneath in the case of the 45◦ports). On the right
hand side is the mercury source chamber, which includes
a 2D MOT set-up. The 2D MOT is not employed in the
measurements described here, but its use is anticipated
in future. Several grams of mercury are maintained at
about −40◦C using a dual Peltier stage. Between 50 and
70mW of 253.7nm light is generated from a frequency
quadrupling scheme for use in the 3D MOT (with the
variation in power occurring over weeks or months).
fl. to CCD
FIG. 1: (Color online) (a) Drawing of the vacuum system showing
the 3D MOT (left side) and 2D MOT chambers. Also visible is
the upper mirror of the optical lattice cavity above the 3D MOT
chamber; fl., fluoresence. (b) Timing sequence for the cooling light,
probe light and 3D MOT magnetic field gradient. The lattice light
remains on continuously throughout the cycle. ∆tl= 80ms and
Tp= 50ms for most measurements here; ∆td= 9ms.
The vertically orientated lattice cavity is comprised of
two spherical mirrors, both with a radius of curvature of
250mm and has a finesse of 210 at 362nm. The waist
size (rad.) is 120µm where the lattice light overlaps the
MOT cloud and produces a maximum lattice depth of
25ER(or 9.2µK). Light at or near the magic wavelength
is coupled into the cavity from below and the transmit-
ted light is used to form a side-lock to maintain constant
intensity. A tunable Ti:sapphire laser has its output fre-
quency doubled in a LiB3O5crystal based resonant cav-
ity to produce the lattice light. In our previous lattice
cavity design there was a 45◦reflector that formed an L-
shaped cavity to lift polarization degeneracy . This
optic was found to degrade rather quickly under vacuum
with the incidence of 362nm light at high power and has
as in the case for the 253.7nm light generation, two fre-
quency doubling stages are employed (see Fig. 2(a) for
the relevant electronic transitions). The infrared-light
(IR) is sourced from a distributed feedback semiconduc-
tor laser, injection locked with light from a fiber laser
tightly locked to an ultrastable optical cavity . About
1mW of 265.6nm light is produced by the frequency
quadrupling scheme. For rapid control of the 265.6nm
probe light level we employ an AOM, which positively
shifts the frequency of the light by 180MHz. Sweeping
the frequency of the 265.6nm light is described in .
An AOM that is used to suppress noise in the fiber link
between the ultrastable laser and the main Hg appara-
tus is used to tune the clock probe frequency. Despite
the drift rate of the ultrastable laser remaining below
+30mHzs−1over the last five months, we still find it
helpful to include a de-drift scheme to keep track of the
clock transition. This is performed using a direct digital
synthesizer (DDS) that steers the frequency of the AOM
in the 1062nm path.
The profile of the clock transition is made via detec-
tion of atoms in the ground state only and with the
timing sequence shown in Fig. 1(b). A broad scan of
the transition spectrum is shown in Fig. 2(b), where
the magnetic bias field is made small enough that the
(1S0) mF = ±1/2 ↔ (3P0) mF = ±1/2 Zeeman com-
ponents overlap one another. The frequency is offset by
the value reported in  for the199Hg transition fre-
quency; i.e., νc = 1128575290808400Hz.
1.5µW of 265.6nm light with a e−2beam radius of
310µm (intensity = 10Wm−2).
maximum (FWHM) is 140Hz and the contrast ∼32%.
We show below that a much narrower transition lies at
the center of this spectrum. We will henceforth refer to
this broad profile as the pedestal. This pedestal may
be an indication that the transverse confinement of the
atoms should be improved. When applying a dc B-field,
this line profile separates into two Zeeman components
[Fig. 2(c)] with slightly lower contrast and FWHM equal
to 120Hz. The Zeeman line separation versus bias field
strength is displayed in Fig. 2(d) (circles) exhibiting a
slope of 11HzµT−1. Since the 265.6nm probe light co-
propagates with the lattice light, its polarization lies or-
thogonal to the axial direction of the lattice (i.e. in the
horizontal plane). The bias B-field is applied in the x-
direction seen in Fig.1(a). The probe light polarization
was confirmed to be mostly linear, but shares a compo-
nent in both x and y-directions, allowing the possibility
for both π and σ transitions. The 11HzµT−1depen-
dence corresponds closely to that expected for σ transi-
tions . Ideally the probe light polarization should be
in the x-direction, but in the present experiment the ul-
3P0 clock transition lies at 265.6nm, so
The full-width half-
tranarrow clock line strength (below) is optimised when
the polarization has shared x and y components. This is
still a matter for investigation.
Ground state fraction
Frequency - νC (Hz)
Ground state fraction
Frequency - νC (Hz)
Zeeman separation (Hz)
Magnetic field strength (µT)
B = 0 μT
B = 35 μT
FIG. 2: (Color online) (a) Partial level scheme for199Hg with hy-
perfine splitting of the ground and excited states. The 265.6nm
radiation is used to probe the1S0 ↔3P0 clock transition, while
253.7nm radiation is used for cooling and detection. (b) A spec-
trum of the199Hg clock transition “pedestal” with mF= ±1/2 →
mF= ±1/2 Zeeman components overlapped. λL=362.573nm and
FWHM = 140Hz. (c) Line profile of the199Hg pedestal show-
ing the separated Zeeman components with FWHM =120Hz. (d)
Frequency separation of the Zeeman components for the ultranar-
row π transition and pedestal versus bias B-field.
3.1 ± 0.3HzµT−1and 11.1 ± 1.7HzµT−1, respectively.
The slope is
Information about the confinement of the atoms in lat-
tice trap is garnered by examining the sideband spec-
tra of the Lamb-Dicke spectrum. Although not shown
here, when we curve-fit to the blue sideband using the
approach outlined in [26, 27] with the only free parame-
ters being the lattice depth and the temperature in the
transverse direction, we find Uo= 18ER(or 6.5µK) and
Tr= 7µK, with associated axial and transverse frequen-
cies of 64kHz and 43Hz, respectively. We estimate the
temperature of the atoms in the axial direction based on
the ratio of the blue and red sidebands to be ∼4µK (with
With the lattice light set at the magic wavelength (dis-
cussion below) and a higher resolution scan made across
the center of the pedestal, we find a much narrower spec-
tral line. Figures 3(a) and (b) show spectra obtained
with Tp= 50ms and 80ms probe pulse durations taken
with approximately 1µW and 0.5µW of 265.6nm probe
light, respectively. The solid lines are the modelled Rabi
spectra with Ω.Tp∼ 1.4π rad for both. In Fig. 3(a) Ω.Tp
was chosen in an attempt to match to the sidebands ob-
served. While the width of the theoretical trace matches
the data, the frequency of the sidebands in general does
not, as seen in 3(b). From a measurement of the probe in-
tensity we estimate the Rabi angle to be Ω.Tp∼ 4.5πrad.
Despite this, we suspect that the sidebands are of a tech-
nical origin and are not due to an overdriven Rabi pulse,
since reducing the probe power does not decrease the
size of the sidebands. For most line-center measurements
Laser frequency detuning
Ground state fraction
FIG. 3: (Color online) Ground state fraction versus probe laser
detuning frequency for: (a) 50ms (Ω.Tp= 1.45π rad) and (b) 80ms
(Ω.Tp= 1.36π rad) Rabi pulses. B=0 and λL≈λm for (a) and (b).
here we use a 50ms probe. With an applied bias B-field
the narrow transition separates into two Zeeman com-
ponents. The 1storder Zeeman dependence is seen in
Fig. 2(d) with a slope of 3.1 ± 0.3HzµT−1. The ratio of
the B-field dependencies for the pedestal versus the nar-
row π transition is ∼3.6, which is close to the σ/π ratio
of 3.3 that one expects when calculated from the differ-
ence in the Land´ e g-factors of the ground and excited
For assessments of the ac Stark shift, the center fre-
quency of the clock transition is measured at a series
of lattice wavelengths and lattice depths. The results
are summarized in Fig. 4(a).
data taken with the 10-15Hz wide spectral lines, while
the inset shows lower resolution data obtained with the
pedestal. From these data we determine the magic fre-
quency to be 826.8546 ± 0.0024THz (λm = 362.5697 ±
0.0011nm). The uncertainty also incorporates the accu-
racy of the wavemeter used for the measurements. From
the line fit we find the strength of the light shift is
(−5.1 ± 0.9)×10−17E−1
of the light shift is shown in Fig. 4(b). Here the line cen-
ter frequency is plotted as a function of the lattice wave-
length while some variation was applied to the lattice
depth as indicated by the color scale. The small vari-
ation in center frequency near 362.570nm is consistent
with the above magic wavelength determination. Here
the strength of the light shift is ∼−6×10−17E−1
A preliminary assessment of other systematic shifts af-
fecting the199Hg clock transition has been conducted
and is summarized in Table I. For a temperature uncer-
The main graph shows
RGHz−1. Another representation
Centre frequency - νC (Hz)
Lattice wavelength - 362 (nm)
Light shift (Hz/ER)
Lattice frequency - 826 (THz)
1.2 1.0 0.80.6
FIG. 4: (Color online) (a) Differential light shift versus lattice
frequency for the199Hg clock transition. The inset shows mea-
surements made over a larger frequency range.
free frequency (wavelength) is 826.8546 ± 0.0024THz (362.5697 ±
0.0011nm) and the slope is −57mHzE−1
sition frequency versus lattice wavelength with changes of lattice
RGHz−1. (b) Clock tran-
tainty of 2K of the chamber surrounding the atoms, and
a 100% uncertainty for the calculated BBR coefficient ,
the shift at 290K is −0.17± 0.20Hz. A measurement of
line center frequency versus Zeeman component separa-
tion showed no variation within a statistical uncertainty
of 1.6Hz. This is expected since the predicted 2ndorder
Zeeman dependence is 2.16×10−9T−2(e.g., B = 10µT
produces a shift of 0.24mHz) .
The frequency dependence on atom number has been
tested by two means: (i) by varying the loading time of
the MOT and (ii) by varying the level of 253.7nm light
used for cooling. Both methods change the number of
atoms loaded into the lattice trap (and also the density
since the size of the MOT cloud changes by less than
5% for the range considered here). The nominal atom
number is N0 = 2.5×103(close to the maximum that
we achieve). Fig. 5(a) shows the line-center frequency,
νHg, versus the relative atom number (N/N0) obtained by
varying the MOT loading time from 0.8 to 2.5s. Fig. 5(b)
shows νHgfor a range of cooling light intensities with a
slope equal to −0.11 ± 0.08Hz per unit s0 (s0 = I/I0,
where I0=102W m−2). The two results suggest a non-
significant density shift at the present resolution. For
daily assessments of line-center frequency (described be-
low) there are between 10 and 30 spectra recorded. From
a plot of center frequency versus relative atom number
we determine the frequency shift at N0, which we show
in Fig. 5(c) for each measurement day where there was
sufficient variation in N/N0. From the weighted mean
the density shift is constrained to 0.26 ± 1.9Hz, consis-
tent with the previous two results. Note, the number
of atoms per site is of order one and in the MOT peak
atomic density is ∼ 6×1010cm−3.
An ac Stark shift may also arise due to the probe light.
In Fig. 5(d) we show the clock transition frequency ver-
sus probe power. At our nominal power level of 1µW
the shift lies within the uncertainty of the measurement.
Shift at N0 (Hz)
MJD - 55800
νHg - νc (Hz)
νHg - νc (Hz)
νHg - νc (Hz)
Probe power (µW)
FIG. 5: Line center frequency versus: (a) relative atom number,
where N0= 2.5×103and (b) MOT cooling light intensity, s0. (c)
Frequency shift at N0 versus measurement day. (d) Line center
frequency versus probe power.
TABLE I: Corrections and uncertainties for the199Hg clock
1st order Zeeman
2nd order Zeeman
Scalar light shift (lattice) < 1
Atom number density
Correction (Hz) Uncertainty (Hz)
We also calculate that the probe light shift is in the
1 − 10mHz range. Tensor Stark and hyperpolarizability
shifts due to the lattice light are omitted from the table
as they are expected to be at least an order of magnitude
Frequency comb accuracy has been verified by com-
paring measurements from two frequency combs (a
Ti:sapphire comb and a Er:fiber based comb), which
are steered by a low noise H-maser reference. The two
combs show agreement to below 0.01Hz. The H-maser
reference is continually compared to the LNE-SYRTE
frequency standard, which has a relative uncertainty of
2.7×10−16. An example of the reproducibility of the
clock transition frequency is shown in Fig. 6, where mea-
surements have been made over a period of three months.
Each point is the mean line center frequency produced
from between 10 and 30 spectra recorded on each day
represented. The measurements were mostly performed
with the two (π-transition) Zeeman components over-
lapped due to the low S/N in the present experiment.
νHg - νc (Hz)
MJD - 55800
FIG. 6: (Color online) Clock transition frequency measured over a
three month period with respect to the SYRTE primary frequency
standard for λm = 362.5697nm. The weighted mean is νc−238.2±
0.3Hz. νc= 1128575290808400 Hz.
The variations in frequency reduce after MJD = 55825
when we began controlling the lattice light frequency to
within 300MHz. The uncertainty of the weighted mean
of this series is 0.3Hz (σ/νHg= 2.5×10−16). Accounting
for the systematic shifts (Table I) we evaluate the199Hg
1S0↔3P0transition frequency to be 1 128 575 290 808
162.0 ± 6.4 (sys.) ± 0.3 (stat.)Hz, where the combined
fractional uncertainty is 5.7×10−15.
This work establishes the potential of199Hg as a high-
accuracy clock.There remain various means for fur-
ther gains in accuracy; e.g., the S/N of the clock sig-
nal should improve as techniques for sideband cooling,
transverse cooling and atom number normalization are
implemented. One also expects that a reliable means of
producing > 150mW of 253.7nm radiation will be found
in which 2D-MOT loading should increase atom numbers
The authors thank the Syst` emes de R´ ef´ erence Temps-
Espace technicians, in particular M. Lours and F. Cornu;
G. Santarelli for the use of lab equipment and D. Ma-
galh˜ aes for assistance. This work is partly funded by
IFRAF and CNES.
 H. Margolis, Contemporary Physics 51, 37 (2010).
 A. Ludlow et al., Science 319, 1805 (2008).
 T. Rosenband et al., Science 319, 1808 (2008).
 C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J.
Wineland, and T. Rosenband,
 H. Hachisu et al., Phys. Rev. Lett. 100, 053001 (2008).
 L. Yi, S. Mejri, J. J. McFerran, Y. Le Coq, and S. Bize,
Phys. Rev. Lett. 106, 073005 (2011).
 C. Tamm, S. Weyers, B. Lipphardt, and E. Peik, Phys.
Rev. A 80, 043403 (2009).
 V. Yudin et al., Phys. Rev. Lett. 107, 030801 (2011).
 S. Blatt et al., Phys. Rev. Lett. 100, 140801 (2008).
 T. Fortier et al., Phys. Rev. Lett. 98, 070801 (2007).
 S. G. Karshenboim and E. Peik, The European Physical
Journal - Special Topics 163, 1 (2008).
 C. W. Chou, D. B. Hume, T. Rosenband, and D. J.
Wineland, Science 329, 1630 (2010).
 C. Tamm et al., IEEE Trans. Instrum. Meas. 56, 601
 H. Katori, M. Takamoto, V. G. Pal’chikov, and V. D.
Ovsiannikov, Phys. Rev. Lett. 91, 173005 (2003).
 S. G. Porsev and A. Derevianko, Phys. Rev. A 74, 020502
 N. D. Lemke et al., Phys. Rev. Lett. 103, 063001 (2009).
 M. Swallows et al., IEEE Trans. Ultrason. Ferroelectr.
Freq. Control 57, 574 (2010).
 S. Mejri, J. J. McFerran, L. Yi, Y. Le Coq, and S. Bize,
Phys. Rev. A 84, 032507 (2011).
 R. Rafac et al., Phys. Rev. Lett. 85, 2462 (2000).
 M. M. Boyd et al., Phys. Rev. Lett. 98, 083002 (2007).
 C. W. Chou, D. B. Hume, M. J. Thorpe, D. J. Wineland,
and T. Rosenband, Phys. Rev. Lett. 106, 160801 (2011).
 N. Huntemann et al.,
 S. T. Dawkins et al., Appl. Phys. B, Lasers Opt. 99, 41
 M. Petersen et al., Phys. Rev. Lett. 101, 183004 (2008).
 M. Petersen,
clock transition,PhD thesis,
strontium: une2` eme
 A. D. Ludlow et al., Phys. Rev. Lett. 96, 033003 (2006).
 BIPM Circular T, 281, May, 2011.
Phys. Rev. Lett. 104,
cooling of Neutral
L’Universit´ e Pierre
` ar´ eseauoptique
` ag´ en´ eration