Recent progress on the NRC 88Sr+ single-ion optical frequency standard
ABSTRACT We report our recent progress made with the NRC 88Sr+ single-ion optical frequency standard. The long-term operation of the standard was improved by actively stabilizing the cooling, repump and clearout laser sources, and by using a femtosecond fiber laser frequency comb to link the probe laser frequency to the microwave time standards. With the femtosecond fiber comb, we have demonstrated continuous operation for a period of eight days and continuous measurement of the probe laser source for three days. Micromotion shifts have been the dominant source of uncertainty in our rf Paul trap because laser beam access is only possible along one axis in the current design. With the aim of reducing to a minimum these shifts, we have constructed an endcap trap designed for minimization of micromotion along three orthogonal axes. We report on the successful trapping of single ions with this endcap trap. Since electrode contamination during trap loading can also induce micromotion shifts as a result of evolving patch potentials, we have increased the trap loading efficiency with photo-ionization.
Conference Proceeding: Mono-Ion Oscillator as Potential Ultimate Laser Frequency StandardThirty Fifth Annual Frequency Control Symposium. 1981; 02/1981
Article: Absolute frequency of the 88-Sr+ 5s 2S1/2- 4d 2D5/2 reference transition at 445 THz and evaluation of systematic shifts
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2010 IEEE International Frequency Control Symposium (FCS), pp. 65-70, 2010-
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Recent progress on the NRC 88Sr+ single-ion optical frequency
Dubé, P.; Madej, A. A.; Bernard, J. E.; Humphrey, G.; Vainio, M.; Jiang, J.;
Jones, D. J.
Recent Progress on the NRC88Sr+Single-Ion
Optical Frequency Standard
P. Dub´ e, A.A. Madej,
J.E. Bernard and G. Humphrey
Institute for National Measurement Standards
NRC, Ottawa, ON, Canada
Center for Metrology and
J. Jiang and D.J. Jones
Department of Physics and Astronomy
University of British Columbia
Vancouver, BC, Canada
Abstract—We report our recent progress made with the
NRC88Sr+single-ion optical frequency standard. The long-term
operation of the standard was improved by actively stabilizing
the cooling, repump and clearout laser sources, and by using a
femtosecond fiber laser frequency comb to link the probe laser
frequency to the microwave time standards. With the femtosec-
ond fiber comb, we have demonstrated continuous operation for
a period of eight days and continuous measurement of the probe
laser source for three days. Micromotion shifts have been the
dominant source of uncertainty in our rf Paul trap because
laser beam access is only possible along one axis in the current
design. With the aim of reducing to a minimum these shifts,
we have constructed an endcap trap designed for minimization
of micromotion along three orthogonal axes. We report on the
successful trapping of single ions with this endcap trap. Since
electrode contamination during trap loading can also induce
micromotion shifts as a result of evolving patch potentials, we
have increased the trap loading efficiency with photo-ionization.
Optical frequency standards based on a trapped and laser-
cooled single ion approximate closely the ideal of an isolated
and unperturbed quantum system and are promising candidates
for attaining the highest frequency accuracies . Several
ion systems have surpassed the microwave time standards in
terms of both stability and reproducibility – and have
the potential of becoming the next generation realization of
At NRC we have developed for a number of years an
optical frequency standard based on the trapped and laser-
cooled88Sr+ion. With the advent of the femtosecond laser
frequency comb technology a decade ago, rapid progress was
made in the characterization, measurement, and reduction of
the systematic shifts that limit the ultimate accuracy of this
frequency standard. For example, we found a method that
cancels the electric quadrupole shift and the tensor parts of
the quadratic Stark shifts . On the other hand, we also
found that micromotion-related shifts, namely the second-
order Doppler shift and the scalar Stark shift, dominate the
error budget of the
apparatus . These shifts are a consequence of micromotion
minimization along only a single trap axis.
88Sr+ion in our current rf Paul trap
For the purpose of minimizing the micromotion shifts, we
have assembled an endcap trap , designed with enough
optical ports for laser beam access along three orthogonal axes
and with trim electrodes for precise ion positioning. This new
trap is presented in Section VI.
The stability and accuracy of any ion frequency standard
depends crucially on the linewidth and stability of its probe
laser system because a single-ion oscillator combined with
Hz-level linewidths imposes severe limitations on the data
collection rate for probe frequency corrections. The 674 nm
probe laser performance is discussed in Section III.
Another important aspect of an optical frequency standard
for its operation as a clockwork and for high-accuracy fre-
quency measurements is its long-term operation. This requires
reliable operation of the probe, cooling, repump, and clearout
lasers, and of the femto-second laser frequency comb if a link
between microwave and optical frequencies is used. We have
demonstrated operation of a fiber comb for a duration of eight
days and have made a new measurement of the88Sr+ion
frequency to confirm the stability of the optical standard over
a period of several years. Stabilization of the trapping laser
sources is described in Section IV and the femto-second fiber
comb measurements are presented in Section V.
Finally, the expected attainable uncertainty in the frequency
of the88Sr+ion is discussed briefly in Section VI in the
context of the new endcap trap.
88Sr+OPTICAL FREQUENCY STANDARD
The energy levels and laser wavelengths of interest for the
88Sr+ion frequency standard are illustrated in the partial
energy level diagram of Fig. 1. This system is described in
detail elsewhere , , so only a brief overview is given
5s2S1/2–4d2D5/2 electric-quadrupole allowed transition at
674 nm (445 THz). This clock transition has a natural
linewidth of 0.407 Hz and its D5/2metastable state has a
lifetime of 0.391 s . The quality factor is thus Q = 1.1 ×
1015. The fractional frequency stability of a laser locked to this
S–D transition can in principle reach a level of ≈ 1 × 10−17
(5 mHz) in less than a day averaging provided that quantum
88Sr+optical frequency standard is based on the
Fig. 1.Energy level diagram of88Sr+.
projection noise (QPN) is the dominant noise process (see
Fig. 2). The narrow linewidth of the clock transition and
the slow data collection rate from the single ion require an
ultra-stable and ultra-narrow laser source to probe the clock
transition without degradation of the ion stability.
The laser at 422 nm, red-detuned from linecenter by about
half the 21.7 MHz linewidth of the 5s2S1/2− 5p2P1/2tran-
sition, is used for cooling the ion. The upper state of the
cooling transition decays to the metastable D3/2state with
a branching ratio of 1:13 . To prevent interruption of the
cooling process, laser radiation at 1092 nm illuminates the ion
during the 422 nm cooling period to repump the ion back into
A typical measurement cycle consists of a cooling pulse of
20 ms followed by an probe pulse of 100 ms. The fluorescence
at 422 nm is monitored with a photo-multiplier tube during
the cooling period to detect whether the ion was promoted
or not to the D5/2metastable state by the preceding probe
laser pulse. When the ion is promoted to the metastable state,
the fluorescence is interrupted. We refer to these events as
quantum jumps. They are used to either record spectra of the
clock transition or to lock the 674 nm laser frequency to the
clock transition linecenter .
The spectrum of the S–D transition is composed of ten
magnetic sensitive Zeeman components, split symmetrically
from the clock transition linecenter ν0. The linear Zeeman shift
is cancelled by measuring a symmetric pair of components and
by taking the average frequency. The electric quadrupole shift
and the tensor parts of the quadratic Stark shifts can also be
cancelled if the average of transitions that sample all of the
Zeeman sub-levels of the D5/2state are averaged , .
Practically this is achieved by averaging the frequencies from
3 pairs of Zeeman components. We use this method when
making measurements of the ion frequency.
The frequency stability of the ion is slightly degraded by
the long natural lifetime of the metastable D5/2state. As soon
as a quantum jump is detected by the fluorescence signal, a
laser at 1033 nm can be used to return the ion back to the
ground state via the short-lived P3/2state. Although we have
tested the clearout laser, this feature was not used in the data
presented in this paper.
All our measurements so far have been performed with an
rf Paul trap apparatus , . Laser beam access is along
a single axis which prevents complete cancellation of the
micromotion. The residual micromotion shifts are −6±13 Hz
(3 × 10−14). They were evaluated in an extensive series of
measurements where the shifts were measured as a function of
the quantization axis defined by an applied magnetic field .
A new endcap trap described in Section VI was built to reduce
these micromotion shifts by several orders of magnitude.
Small micromotion shifts can also appear after minimiza-
tion because of patch potentials created by strontium atoms
deposited on the trap electrodes during loading. These patch
potentials can be reduced significantly if the loading process
is made more efficient. We have found that photo-ionization
loading allowed for a decrease in the strontium flux by
three orders of magnitude compared to electron bombardment
loading. Photo-ionization is realized with a two-step process
where the neutral strontium atoms are first excited to the
5p1P1state from the 5s1S0ground state with laser radiation
at 461 nm, followed by excitation to an auto-ionizing state
with 405 nm laser radiation .
III. PROBE LASER SYSTEM
The probe laser light at 674 nm is produced with a com-
mercial extended-cavity diode laser head driven with low-noise
home-made electronics. The linewidth of the free-running laser
is on the order of 1 MHz. The laser is pre-stabilized on a
Fabry-Perot cavity that has a linewidth of 110 kHz. The error
signal between the laser and the cavity is derived using the
Pound-Drever-Hall (PDH) technique , and applied, after
some signal conditioning, to both the current and the piezo-
electric translator (PZT) of the diode laser. This first stage
reduces the laser linewidth to ≃ 50 Hz relative to a resonance
of the cavity.
The output from this first stage is then stabilized using
an ultra-stable cavity made with ultra-low thermal expansion
coefficient glass (ULE). The spacer length is 25 cm, the cavity
finesse is 160000 and the resonance linewidths are 3.7 kHz
wide. The light emerging from the first cavity is locked to the
ultra-stable cavity using the PDH technique. The conditioned
error signal between the two cavities is fed back to an acousto-
optic modulator (AOM) located after the first cavity output for
fast frequency corrections (150 kHz), and to a PZT-actuated
mirror of the first cavity for drift corrections. The linewidth of
the laser radiation relative to the reference ULE cavity is less
than 1 mHz. The actual linewidth is much larger as a result
of thermal noise in the mirrors and mirror coatings , and
mechanical noise from the environment. We have observed
5 Hz Fourier-transform-limited linewidths in high-resolution
scans of a Zeeman component of the clock transition .
As a measure to reduce to a minimum the frequency drifts,
the reference ULE cavity is stabilized to its temperature of
zero thermal expansion coefficient of 5.45(1)◦C. The present
drift rate of this cavity is only 12 mHz/s (see Fig. 3). This
rate is still slowing down with time.
The stability of the probe laser locked to the ULE cavity
was studied by measuring its frequency with the ion clock
transition. Figure 2 shows an Allan deviation plot of the data.
The stability reaches a level of 5 × 10−16after 3000 s of
averaging time, following closely the expected QPN of the
ion for the present experimental conditions. Note that the
relative stability between the probe laser frequency and the ion
transition is nearly an order of magnitude better than the best
88Sr+ion frequency measurement . With the present QPN
limit, we can expect to find the ion linecenter with a precision
of 1 × 10−16after 19 hours of averaging. The ion stability
can be improved by increasing the quantum jump rate. In our
experiment this can be achieved by selectively pumping the
ion into the lower level of the probed transition, by using the
clearout laser, and by cooling the ion to a lower temperature.
transition as the frequency reference. The short-dashed line is a 1/√τ fit
through the data (2.6 × 10−14/√τ ), the long-dashed line is the theoretical
dependence of the Allan deviation for the present experimental conditions
assuming a purely quantum-projection-noise (QPN) limited measurement
(1.9 × 10−14/√τ ). The solid line represents the Allan deviation limited
by the QPN when all the parameters are optimized (2.6×10−15/√τ ). The
horizontal dotted line is the estimated Allan deviation caused by the thermal
noise level of the 25 cm long Fabry-Perot cavity.
Allan deviation of the probe laser measured by using the ion S–D
The reader is referred to the literature for a more complete
description of this laser system and its performance .
IV. TRAP LASERS STABILIZATION
The lasers at 422 nm, 1092 nm and 1033 nm can be operated
free-running for short periods of time because the linewidths
of the transitions they drive are 22 or 24 MHz wide. For
reliable, long-term operation, and for optimum performance
it is necessary to lock each of these lasers to obtain MHz-
level stability over days. In this Section, we describe the
stabilization methods used to control these laser sources.
A. 422 nm laser
The 422 nm source is a commercial extended cavity GaN
diode laser. It has a free-running linewidth of ≈ 10 MHz.
The linewidth is reduced to 2.4 MHz with stabilization onto a
low-finesse Fabry-Perot cavity. The spectrally-narrowed light
is then stabilized to the Doppler-free 5s2S1/2(F′′= 2) –
6p2P1/2(F′= 3) hyperfine transition in
transition is red-detuned from the88Sr+cooling transition by
440 MHz. A double-pass AOM provides precise tuning of the
422 nm frequency with respect to the cooling transition. The
422 nm laser routinely stays locked to85Rb for a few days,
until a mode-hop occurs.
85Rb . This
B. 1092 nm and 1033 Lasers
The 1092 nm radiation is produced with an ytterbium-
doped, diode-pumped fiber laser while the 1033 nm radiation
is from an extended cavity diode laser. Both lasers are stabi-
lized to a polarization-stabilized He-Ne laser using a Fabry-
Perot transfer cavity . The infrared lasers remain locked
for several days with this robust system which has a capture
range of several hundred MHz. The rms frequency fluctuations
of the stabilized 1092 nm and 1033 nm lasers are, respectively,
0.5 MHz and 1 MHz.
V. FEMTO-SECOND FIBER FREQUENCY COMB
The femto-second fiber comb used in the present series
of measurements is a stretched-pulse erbium-doped ring fiber
oscillator that uses nonlinear polarization rotation as the mode-
locking mechanism. It produces 120-fs pulses at a rate of 100
MHz. There are two external branches, each with a chirped-
pulse erbium-doped fiber amplifier and with a highly nonlinear
fiber. One of the branches is used for offset frequency locking.
The other branch is optimized for super-continuum generation
at 1348 nm for frequency-doubling in a periodically-poled
MgO:LiNbO3 crystal to 674 nm. A detailed description of
this fiber comb is given elsewhere , .
The operation of the fiber comb as a clockwork linking the
microwave time standards to the ion optical frequency was
tested by measuring the 674 nm probe laser frequency over a
period of several days. The results are shown in Fig. 3. The
fiber comb remained locked without adjustment (repetition rate
and offset frequency) to the microwave standards for the entire
duration of the measurement period of eight days. Figure 4
shows the Allan deviation of the probe laser calculated with the
last three days of Fig. 3. The 1/τ dependence reflects the white
phase noise behavior of the maser. Since the measurement
of the probe laser has a 1/τ dependence with values similar
to those of the maser, the probe laser can be considered to
be phase stable relative to the stability level of the maser.
Variations in the ULE drift rate account for the rise in the
Allan deviation at averaging times longer than 1000 s. The
Allan deviation measured with the88Sr+clock transition as
reference shown in Fig. 2 reached lower levels for two reasons;
the ion is a more stable reference than the maser and the ULE
drift rate was removed in the analysis with a piecewise linear
The88Sr+clock transition frequency was measured with
the femtosecond fiber comb in another series of measurements.
As in the long-term measurement described above, the fiber
comb measures the absolute frequency of the probe laser
Frequency Offset (kHz)
frequency comb referenced to the NRC rf atomic clocks. The observed linear
drift of 11.9 mHz/s is caused by the isothermal creep of the reference cavity
ULE spacer. The missing data is due to a loss of lock of the probe laser to
its reference cavity.
Probe laser frequency measured with the erbium-doped fiber laser
Averaging Time (s)
from the final three days of the data shown in Fig. 3 after removal of the
linear drift. The Allan deviation of the reference maser is shown as solid dots
for comparison. Both curves follow the characteristic 1/τ dependence of the
maser phase noise up to an averaging time of τ ≈ 200 s.
The solid line is the Allan deviation of the probe laser calculated
with respect to the microwave time signal from a maser
source. Simultaneously, the offset of the probe laser frequency
from three pairs of Zeeman components is measured. The
average of these component linecenters results in an ion
frequency measurement that is corrected for the linear Zeeman
shift, the electric quadrupole shift and the tensor terms of
the quadratic Stark shifts , , . The absolute ion
frequency is found by combining the comb measurements
with the offset between the probe laser and the ion. A value
of 444779044095477.6 Hz is obtained, with a statistical
uncertainty of 0.8 Hz. The maser uncertainty was 1.1 Hz
for this measurement and the uncertainty associated with the
transfer of the maser signal to the comb is estimated at 0.3 Hz.
The total standard uncertainty estimate is 1.4 Hz . The data
is shown in Fig. 5.
This result obtained in 2009 can be compared to a mea-
an erbium-doped fiber laser frequency comb. A drift of +14 mHz/s, due to
the probe laser reference cavity, was subtracted. The resulting frequency is
444779044095477.6 ± 1.4 Hz. Note that this frequency is not corrected
for ion systematic shifts except the electric quadrupole shift and the tensor
terms of the quadratic Stark shifts.
Measurement of the88Sr+ion S–D clock transition frequency with
surement made in 2005 under similar conditions, that is
before it was corrected for micromotion shifts and blackbody
radiation shifts . This value is f2005(not corrected) =
444779044095478.0±4.3 Hz. The excellent agreement with
the 2009 result, f2009−f2005= −0.4±4.5 Hz, demonstrates a
high level of stability of the standard over a period of several
years despite net micromotion shifts of 6 Hz.
VI. NEW ION TRAP
An endcap trap  was built to give access to the cooling
laser beam along three orthogonal axes for minimization of
the micromotion in three dimensions. The endcap electrodes
are made with 0.50 mm diameter molybdenum wire and are
separated by 0.54 mm. Their end faces were polished to a
mirror finish. The shield electrodes were made from 2.0 mm
diameter tantalum rods. Trim electrodes, including the endcap
electrodes for the axial direction, are provided to control the
ion position along three orthogonal axes. The micromotion
signal will be obtained from the modulation of the 422 nm
fluorescence due to the first order Doppler shift at the rf
potential applied to the electrodes . It is expected that
micromotion shifts will be reduced to a level of 10−17or less
An aspherical lens with a numerical aperture of 0.7 was
mounted inside the vacuum chamber for efficient collection
of the fluorescence sent to a photo-multiplier tube (PMT).
Opposite the PMT, another port is reserved for a photon-
counting camera which will be used for trap diagnostic and
studies involving ion clouds which are not efficiently detected
by the restricted field of view of the PMT. The light collection
systems of the camera and PMT are equipped with a band-
pass interference filter at 422 nm for optimum rejection of
background light from the other laser sources.
We have successfully trapped single ions with this new trap.
Figure 6 shows quantum jumps from a single ion observed in
the fluorescence signal detected by the PMT. The high contrast
between the bright and dark periods ensures that the quantum