CHIN. PHYS. LETT. Vol. 32, No. 5 (2015) 054206
Improvement of Laser Frequency Stabilization for the Optical Pumping Cesium
Beam Standard *
WANG Qing(王青)** , DUAN Jun(段俊), QI Xiang-Hui(齐向晖), ZHANG Yin(张胤), CHEN Xu-Zong(陈徐宗)
School of Electronics Engineering and Computer Science, Peking University, Beijing 100871
(Received 11 November 2014)
A method is presented to improve the laser frequency stabilization for the optical pumping cesium clock. By
comparing the laser frequency stabilization of different schemes, we verify that the light angle is an important
factor that limits the long-term frequency stability. We minimize the drift of the light angle by using a fibercoupled output, and lock the frequency of a distributed-feedback diode laser to the fluorescence spectrum of the
atomic beam. The measured frequency stability is about 3.5 × 10−11 at 1 s and reaches 1.5 × 10−12 at 2000 s.
The Allan variance keeps going down for up to thousands of seconds, indicating that the medium- and longterm stability of the laser frequency is significantly improved and perfectly fulfills the requirement for the optical
pumping cesium clock.
PACS: 42.62.Fi, 42.72.−g, 06.30.Ft
DOI: 10.1088/0256-307X/32/5/054206
Stabilizing the laser frequency to atomic transition lines has played an important part in many
atomic physics applications, such as frequency standards, metrology, laser-cooling and optical communications. A variety of methods have been presented
in the literature.[1−6] Almost all these methods share
the same principle that generating a dispersive signal as the frequency-discrimination error signal, and
electronically locking the laser frequency to its zerocrossing point.
By using the modulation and demodulation technology, this dispersive signal with a high signal-tonoise ratio can usually be obtained from atomic absorption spectra, for example, the saturated absorption spectrum (SAS).[1,2]
Furthermore, the dispersive signal can also be
induced directly without the modulation of light.
These techniques include dichroic atomic vapor laser
lock (DAVLL),[3] polarization spectroscopy (PS)[4]
and atomic non-linearly generated laser locking signal
(ANGELLS).[5] Most of these modulation-free techniques can provide an excellent short-term frequency
stability, however almost all the systems cannot work
continuously for a long period.
Lasers used for optical pumping and detecting in
the Cs atomic clock are required to be stabilized to
atomic transition lines for several years or even longer
without losing the lock. For ensuring the high performance of the Cs atomic clock, the laser frequency
stability needs to be better than 1 × 10−10 at 1 s, and
superior to 5 × 10−12 at 500 s and beyond. In addition, the frequency stabilization system should not be
complicated. To achieve all the requirements for the
optical pumping Cs clock, the SAS with the modula-
tion of light is a normal choice.[6]
The typical saturated absorption setup is shown
in Fig. 1. A distributed feedback (DFB) diode laser
(DL) serves as a light source, operating at 852 nm with
a 3 MHz line-width. An optical isolator (ISO) is used
to prevent the optical feedback from the saturated absorption setup and the main output of the system. By
using a combination of a half-wave plate and a polarizing beam splitter (PBS), a variable part of the laser
power is divided for spectroscopy, and then the light
beam is split into three beams by thick glass. Two
weak reflected light beams of the same intensity serve
as the probe beams, while the strong transmitted light
acts as the pump beam. One of the probe beams coincides with the pump beam in opposite directions in
the Cs vapor cell. The two probe beams are detected
by two balanced photo diodes. In our experiments,
the whole setup was assembled in a physics package
with a volume of 500 cm3 .
If the two counter-propagating light beams coincide with each other without any angle, they will interact with atoms of the same velocity class only when
the laser frequency is scanned to the atomic resonant
frequency, forming the SAS peaks. At other frequencies, they will be absorbed by different atoms separately, generating the SAS background. The subtraction of the two PD outputs forms the saturated absorption spectrum without background. Scanning the
laser frequency, we obtain the SAS (Fig. 2(a)).
For stabilizing the laser frequency, a 10 kHz sinusoidal modulation was added to the laser injection current. The subtraction signal of the two PD outputs
was amplified, filtered, and synchronously demodulated by using a self-made lock-in amplifier. Then,
* Supported by the National Fundamental Research Program of China under Grant No 2011CB921501, and the National Natural
Science Foundation of China under Grant Nos 91336103, 10934010 and 61078026.
** Corresponding author. Email: [email protected]
© 2015 Chinese Physical Society and IOP Publishing Ltd
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CHIN. PHYS. LETT. Vol. 32, No. 5 (2015) 054206
we obtained the dispersive error signal used to adjust
the laser frequency by correcting its injection current
through a proportional-integral controller.
Pump
Probe
PD
Cs cell
Output
ISO
DL
BPS
λ/2
Fig. 1. SAS setup without Doppler background.
(a)
(4,5)
4
(3,5)
(3,4)
0.5
F '=3
2T10-10
5
0
(b)
Allan deviation σy(τ)
Amplitude (V)
1
integration time and fails to fully meet the requirement for the Cs clock. When the integration time is
larger than 1000 s, the Allan variance curve is almost
flat.
To improve the medium- and long-term frequency
stability, the cell temperature needs to be stabilized
better. Other sources of limitations such as the
light beam angle, the light density, the magnetic field
and the background gas contamination in the cell[8,9]
should also be taken into consideration. However, it
is difficult and complicated to control all these sources
based on the setup of the SAS scheme.
To improve the medium- and long-term frequency
stability, instead of SAS, another more stable and robust atomic transition spectrum can be used to stabilize the laser frequency conveniently in the optically
pumped cesium beam standard.
F '=5
1
0.5
0
F '=3
0
F '=4
100
200
300
400
Detuning (MHz)
Fig. 2. Spectroscopic signals used to lock the laser frequency: (a) the saturated absorption spectroscopy, and
(b) the beam fluorescence spectroscopy.
To evaluate the fraction stability of the laser frequency stabilized in the laboratory environment, we
locked two similar diode lasers to the 4–3 and 4–4
transitions of the Cs D2 line separately, and mixed
the outputs of two diode lasers on a fast photodiode.
The beat-note signal was then amplified and counted.
The blue line in Fig. 3 shows the stability in terms of
the Allan variance versus the integration time.
We can see that the laser beat note exhibits a frequency stability of 8 × 10−11 at 1 s, and decreases to
1.7 × 10−11 at 40 s. After that, the stability becomes
worse.
As reported in Ref. [8], the dominating source
of limitation on the frequency stability measured at
short- or medium-term integration times is the cell
temperature. The cell temperature represents the velocity distribution of atoms, which has a strong impact on the background Doppler profile. Moreover,
the light absorption in the cell varies with the atomic
density that depends on the cell temperature.
The fluctuation of the environment temperature is
about 2 K/day. After taking control of the cell temperature and reducing its drift to less than 100 mK/day,
we obtain an improved stability, as shown in Fig. 3 by
the red line. Obviously, the frequency stability becomes better, while the curve still goes up at 200 s
1T10-10
5T10-11
2T10-11
1T10-11
5T10-12
2T10-12
1T10-12





Sampling time τ (s)
Fig. 3. Relative laser frequency stability in terms of the
Allan variance by using SAS. Here triangles with the blue
line represent the stability without controlling the cell
temperature, and squares with the red line represent the
stability after taking control of the cell temperature. The
black line shows the frequency stability requirement for
the Cs clock.
Atomic
beam
Collector
Magnetic
shield
Signal
PD
Tube
Oven G
DL
ISO
G
A
For beat frequency
λ/2
PBS
Fig. 4. Schematic diagram of the fluorescence spectrum
emitted by an atomic beam. G: graphite; and A: aperture.
Figure 4 shows a simplified diagram of the cesiumbeam-tube used in the optical pumping cesium beam
standard. A light beam for spectroscopy interacts perpendicularly with the atomic beam. The atomic beam
sprays out from the collimator of a cesium oven and
passes through a graphite pipe, which is 5 cm in length
and 5 mm in diameter. Before interacting with the
laser, the atomic beam has passed through the pumping and microwave area, which is equivalent to another
aperture to collimate the atomic again. The equiva-
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CHIN. PHYS. LETT. Vol. 32, No. 5 (2015) 054206
lent aperture is also about 5 mm in diameter and a
distance of 30 cm away from the oven. Thus the divergence of the atomic beam is calculated to be less
than 1∘ , which is small enough to be ignored. When
resonances happen, the fluorescence light is collected
by a ball shaped collector, and then led to a photo
diode (PD). Figure 2(b) shows the beam fluorescence
spectrum (BS). Three spectral lines are corresponding to the 𝐹 = 4 → 𝐹 ′ = 3, 4 and 5 transitions of
the Cs D2 line. Due to the fact that the 4–5 line is
a cycling transition and its strength factor is larger
than those of the other two transitions, the signal of
the 4–5 transition line is the largest.
All the above physical components described were
enclosed in a tube covered by three layers of the magnetic shielding material which reduced the residual
magnetic field to less than 1 mG. Moreover, a titanium
sublimation pump was used to maintain the vacuum
degree inside, and the oven temperature was well controlled. In fact, the drift of the oven temperature only
caused variances of the atomic beam flux. Thus, similar to the light intensity, the oven temperature could
not influence the center point of the fluorescence spectrum while it just varied the signal amplitude. In addition, unlike the atoms in the cell, the atomic beam
was always fresh and free from the background gas
contamination.
Therefore, compared with the SAS, almost all the
sources of limitations to the frequency stability are
eliminated except the light beam angle. Furthermore,
the beam spectrum hardly has any Doppler background, and the space between the three peaks is
larger than SAS (see Fig. 2), which is desired to avoid
the harmful influence from each other. Thus it is a
better reference line for locking the laser frequency
used in our atomic clock.
and one of them was shifted 100 MHz by an acoustooptic modulator (AOM) for measuring the beat note
signal. Then we obtained the frequency stability as
shown by the blue line in Fig. 5.
However, the result shows unexpectedly that the
Allan variance still increases when the sampling time
is longer than about 200 s, even though the reference
spectrum is improved. According to the above analysis, we supposed that it was possibly caused by the
drift of the light beam angle, due to the expansion and
contraction of optical apparatuses or other parameters. In fact, the center point used for frequency locking altered greatly while the light beam tilted slightly.
In experiments, the oven was heated to 373 K, thus
the most probable velocity of atoms could be figured
out,
√︂
√︂
2𝑅𝑇
2 × 8.314 × 373
𝜐=
=
= 216 m/s, (1)
𝑀
0.133
where 𝜐 is the most probable velocity of atoms;
𝑅 = 8.314 J·mol−1 ·K−1 is the molar gas constant;
𝑇 = 373 K is the oven temperature; and 𝑀 =
0.133 kg·mol−1 is the molar mass of cesium atoms.
However, the light beam was not strictly perpendicular to the atomic beam; while tilted by a small
angle 𝜃, we could estimate the shift of center point
due to the Doppler Effect
𝜐 sin 𝜃
𝛿𝜔
𝜐 sin 𝜃
= 𝜔0
=
≈ 253 kHz/mrad, (2)
𝜃
𝑐 𝜃
𝜆 𝜃
where 𝑐 is the velocity of light in a vacuum, and 𝜔0 is
the atomic resonance frequency. This rate is slightly
larger than that in SAS (80 kHz/mrad).[8]
Atomic
beam
Collector
Signal
Magnetic
shield
PD
Tube
2T10-10
Oven G
Allan deviation σy(τ)
1T10-10
A
G
5T10-11
2T10-11
1T10-11
DL
5T10-12
For beat frequency
λ/2
PBS
Fig. 6. Improved setup for the laser frequency stabilization. G: graphite; and A: aperture.
2T10-12
1T10-12
ISO





Sampling time τ (s)
Fig. 5. The Allan variance of the laser frequency stabilized by using BS. Here triangles with the blue line represent the stability without controlling the light beam angle,
and squares with the red line represent the stability after
using the fiber-coupled output. The black line shows the
frequency stability requirement for the Cs clock.
For measuring the frequency stability, both the
lasers were stabilized to the 4–5 transition separately,
We found that in experiments, fiber-coupled output could be used conveniently to minimize this angle
drift efficiently. As shown in Fig. 6, the light beam is
first coupled into a long fiber through an adapter with
a collimator, and then is sent into the tube. We just
needed to fix the output coupler to isolate the variation of the light beam angle. After stabilizing the
two laser frequencies, we finally achieved an excellent
stability of the laser frequency shown by the red line
in Fig. 5.
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CHIN. PHYS. LETT. Vol. 32, No. 5 (2015) 054206
√
The Allan variance keeps going down with a 𝜏
slope for up to thousands of seconds, showing that the
stability is less than 4 × 10−11 at 1 s and 1.5 × 10−12 at
2000 s, and then reaches the flicker floor at the level of
about 1–2 × 10−12 . The medium- and long-term stability of the laser frequency is significantly improved
and fulfills the frequency stability requirement for the
optical pumping Cs clock.
The result indicates that the light angle is a second important source to make the frequency stability
bad. As to the SAS, the light beam angle means the
angle between the probe and pump beams. If the two
light beams are not parallel, there will always be a
certain velocity class of atoms that can interact with
the two beams simultaneously. The velocity vectors of
these atoms lie in the plane whose projection coincides
with the angle bisector of the two atomic beams. As
a result, the signal-to-noise ratio of the SAS will be
reduced greatly. In other words, the SAS will rapidly
become worse when the angle becomes larger.
It is noteworthy that in some actual applications,
the desired laser frequency does not lie at the center of
the atomic resonance line, while rather at a displaced
frequency, for instance, laser cooling. When we lock
the laser frequency to the beam spectrum, the locking
point can be tuned conveniently by adjusting the incident angle of the laser according to Eq. (2), which is
another advantage of the atomic beam scheme.
In the optically pumped cesium beam standard, we
just need to lock the laser frequency on the actual peak
of the spectrum, while not the intrinsic atomic transition line. Thus it does not matter that the laser beam
is not perfectly perpendicular to the atomic beam.
In conclusion, we have discussed the major limita-
tion that influences the medium- and long-term stability of the stabilized laser frequency, and presented
a method to improve the laser frequency stabilization
for the optical pumping cesium beam standard. By
locking the laser frequency to the fluorescence spectrum of the atomic beam with the fiber-coupled output, we can improve the stability of the laser frequency
greatly. The stability is about 3.5 × 10−11 at 1 s, and
√
the Allan variance keeps decreasing with a 𝜏 slope
for integration times even up to 2000 s, with a flicker
floor at the level of about 1–2 × 10−12 , which perfectly meets the requirement for the optical pumping
Cs beam standard. We believe that this scheme for
stabilizing laser frequency is also suitable for many
other atomic physical applications requiring long-term
stable optical sources.
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