DTIC ADA477304: Rubidium-Fountain Characterization Using the USNO Clock Ensemble

Rubidium-Fountain Characterization Using
the USNO Clock Ensemble

Steven Peil, Scott Crane, Thomas B. Swanson, Christopher R. Ekstrom
Clock Development Division, U. S. Naval Observatory
Washington, D.C.

Abstract —We have carried out stability comparisons between
our rubidium fountain, built as a prototype for a continuously
operating clock, and the USNO Maser Mean timescale. Long,
continuous runs of the prototype system allow us to demonstrate
fractional frequency-stability comparisons to the Maser Mean
that integrate as white frequency noise, with a stability of
5x10 16 at one day. We have measured the frequency sensitivity
of the rubidium fountain to various experimental parameters in
order to establish the regulation required to reach a long-term
stability of order lxl0~ 16 .

L Introduction

Since their introduction more than 50 years ago, atomic
clocks have revolutionized time and frequency applications.
The advent of laser cooling of atoms brought about dramatic
improvements in atomic-clock performance, particularly in
the area of primary standards, resulting in the transformation
from systems based on beams of atoms to ones that
interrogate a cloud of cold atoms tossed in a fountain
geometry. Atomic-fountain clocks are being operated at
several laboratories throughout the world and have been
contributing to the BIPM for almost a decade. The U. S.
Naval Observatory has a program to construct six operational
rubidium fountains to include in its clock ensemble and
improve its time-keeping capabilities.

One of the challenges introduced by improvements in
clock technology is the determination of the performance of
the (purportedly) best clocks. All frequency and time
measurements are referential, and comparing a state-of-the-
art clock to one that is less precise reveals little about the
performance of the better clock. Typically, the frequency of
a fountain clock is compared to the frequency of a hydrogen
maser, which usually has superior short-term performance.
This enables characterization of the fountain for averaging
times on the order of several hours. Beyond this duration,
maser frequency fluctuations tend to dominate the stability
comparison, making further fountain characterization
difficult.

Because of this difficulty, many timing laboratories build
at least two fountains or other high-stability clocks for
characterization. We carried out a comparison between our
rubidium fountain prototype, NRF1, and our research cesium
fountain, NCF, but because the older cesium system was not

built for continuous operation, the measurement times were
limited to several days [1]. In this paper, we present further
characterization of NRF1 by comparing its continuous phase
output during several long runs to the observatory’s most
stable timescale. We also present measurements of the
stability of various systematic frequency shifts and project the
required regulation of particular operational parameters to
reach our goal of long-term fractional-frequency
reproducibility of order lxlO -16 .

II. Design Improvements

The design of NRF1 has been discussed in detail
previously [2]. Two of the major technical challenges to
building a continuously operating fountain clock are the laser
and optical systems. We use a miniature optical table that is
very robust and stable, which has not been an obstacle to
continuous operation at any point in the past two years [3].
This optical table provides the agile frequency tuning,
intensity modulation, and power division for the fiber outputs
that connect to the physics package. Improved air filtration
and optical isolation have made our Tksapphire laser more
robust, enabling us to carry out long, continuous runs with
NRF1. We successfully demonstrated continuous operation
for a month, at which point we intentionally terminated the
run to pursue other measurements. However, maintaining
operation over this time required occasional (once to several
times a week) adjustments to some part of the Ti: sapphire
laser system.

For a more robust laser solution, we have implemented an
all-semiconductor system, consisting of an external-cavity
diode laser (ECDL) followed by a tapered-diode amplifier.
The ECDL exhibits an intrinsic line width of several hundred
kilohertz for short averaging times and delivers up to 50 mW
of power. The tapered amplifier can generate 1 W of output
power with a gain of 40. The two laser heads, 60 dB of
optical isolation, and fiber launching components are all
located on a small optical breadboard that we intend to rack
mount. Sensitivity of the ECDL to acoustic noise
necessitates isolation of this laser table using a lead-lined
foam box. Several months of experimentation and fountain
operation with the system give us confidence that it will serve
as a suitable laser source for NRF 1 and it will be used in our
friture fountain systems.

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Rubidium-Fountain Characterization Using the USNO Clock Ensemble

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III. Measurement Against Maser Mean

The ability to operate NRF1 continuously allows us to
make comparisons to any clock or timescale at the
observatory. We use a 5 MHz signal from a quartz oscillator
phase-locked to a hydrogen maser to generate the 6.8 GHz
microwave drive for the fountain and also as the reference for
a high-precision frequency synthesizer (or AOG, for
“Auxiliary Output Generator”) [4]. The difference in
frequency between the microwave drive and the atoms’ clock
transition is written via RS232 to the AOG with a gain of
0.28 once every 16 fountain cycles (19.2 seconds), making an
effective time constant of 58 seconds. The AOG’s steered
frequency output is monitored on one channel of a dual-mixer
measurement system. This system measures most of the
observatory’s masers and several physical timescales, using
each of our primary and backup master clocks as a reference.
These data are recorded, allowing for a large array of inter¬
comparisons between clocks as well as providing the
measurements used to generate the observatory’s timescales.
While these phase data are recorded every 20 seconds, we use
a decimated data set with hourly samples for the medium-
and long-term analyses presented here.

The most stable reference for post-processing comparisons
is the developmental USNO Maser Mean [5]. In Fig. 1 we
show the results of measuring the stability of NRF1 against
the Maser Mean over an event-free period of 11 days. After a
single relative frequency and starting phase have been
removed, the peak-to-peak phase deviation between NRF1
and the Maser Mean during this interval is less than 200 ps.
The Allan-deviation plot shows that the relative frequency
fluctuations integrate as white frequency noise at a rate of
1.5x10 _13 /t' 2 for averaging times up to 2.5 days, reaching
5xl0 -16 at one day and ~3xl0 -16 at 2.5 days. While the
fountain ran continuously for intervals as long as one month,
significant humidity and temperature fluctuations in the lab
prevented us from obtaining a more lengthy comparison.

Figure 1. (a) Plot of phase comparison between NRF1 and the Maser Mean
for an 11 -day run. (b) Plot of overlapping Allan deviation versus integration

time.

IV. Systematic Frequency Shifts

Even longer runs - and perhaps even better clocks for
comparison - are required to analyze whether NRF1 will
flicker at this level, and whether it will exhibit random walk,
or drift. It is far more efficient to try to determine the limits
to performance by considering the stability of known
systematic frequency shifts. By measuring the sensitivity of
NRF1 to large changes in experimental parameters we can
infer the required regulation of those parameters to reach our
long-term frequency stability goals. While these systematic
measurements are often made for an accuracy evaluation of
primary standards, we seek to determine the ultimate
frequency reproducibility of our system and are only
interested in the stability of these frequency shifts.

A. Methods

We measure the sensitivity of the fountain to a given
experimental parameter by modulating it between two or
more values. This modulation can be as fast as once every
other fountain cycle, but we typically chose an interval of
once every 30 minutes, during which time the measurement
of the frequency shift from this modulation is still limited by
the fountain rather than a single reference maser. We use
comparisons to the Maser Mean for modulations that can not
be changed rapidly, as detailed later in this paper. Most
measurements of the sensitivity to these modulations reach an
uncertainty of order I x KF 1 in one day. The sensitivity and
uncertainty can be used to ascertain the regulation required to
reach our long-term reproducibility goal of l-3xl0 -16 . In
Table 1, we summarize the results of all of the systematic
frequency-shift stability measurements we have investigated
to date and the regulation necessary to limit each effect to a
contribution of lxlO -16 or less.

B. Magnetic Fields

We run NRF1 with a Magneto-Optical Trap (MOT) for
the atom-collection phase, which requires the application of a
magnetic quadrupole field. This field is applied with coils
that are inside three of the four magnetic shields, resulting in
a frequency shift that depends on the trapping-field strength.
Measuring this shift by modulating the strength of the
trapping field gave results that varied depending on the
frequency of the modulation cycle. We believe this is likely
due to a slow relaxation of the magnetic shields to the
changing MOT field. To obtain a value that corresponds to
the shift we might be susceptible to when running
continuously, we kept a particular value of the field for 2-3
days and measured NRF 1 ’s frequency versus the Maser Mean
over that interval. This measurement for three different
values of current in the MOT coils is shown in Fig. 2. The
measured shift is 1.4(0.6)xl0 _15 /A, and we run at a MOT
current of roughly 2.4 A. This requires a regulation of the
MOT current of 2%, while our current is stable to much
better than 1%.

TABLE I. Table showing results of sensitivity of NRF1 to various parameters. The measured values for the third through sixth

ENTRIES ARE CONSISTENT WITH ZERO FREQUENCY SHIFT. THE REQUIRED REGULATION FOR THESE PARAMETERS ARE THEREFORE WORST-CASE SCENARIOS,
AND MAY BE MUCH LESS STRINGENT. THE LAST ENTRY IS A CALCULATION FOR WHICH NO UNCERTAINTY HAS BEEN INCLUDED.

PARAMETER

SLOPE AND UNCERTAINTY

REGULATION FOR lxl 0~ u

MOT current

1.4(0.6)x10 _15 /A

2%

C-field current

-3.5(0.2)xl0 _15 /|iA at 100 ]iA

0.03% at 100 pA

Atom number

-8(12)xl0 _16 /popn

5%

Microwave power

3.9(4.0)xl0 _15 /nW

2%

Laser power

-0.6(2.2)x10 _15 /W

3%

Inclination

0.4(5.2)xl0 _16 /mrad

0.15 mrad

Microwave power balance

3.6(0.2)xl0 _14 /(tull imbalance)

0.3%

Temperature (blackbody shift)

-1.7xlO“ 16 /°C

1.5% at 32 °C

The size of this shift on the clock transition corresponds
to a change in the magnetic field seen by the atoms of order
40 u(i. This is a small addition to our C-field of 2.3 mG,
therefore it is reasonable to expect a linear dependence of the
frequency shift on MOT current.

In addition, there is a quadratic sensitivity of the clock
frequency with magnetic field in the free-precession region.
We were unable to characterize the magnetic field by running
on the linearly sensitive Zeeman line due to a transverse
magnetic field at the cavity of roughly 300 |J,G and its
associated gradients. We did verify that the quadratic
Zeeman shift has the expected form and magnitude, giving us
confidence in using the theoretical sensitivity in our projected
long-term stability. This projection dictates regulating the
100 |iA current in the C-field to 0.03%. This level of
regulation has been successfully demonstrated in our cesium
research fountain.

C. Atom Number

We attempted to measure an atom number-dependent
frequency shift by modulating the number of launched atoms.
The number was changed by modulating the microwave
power in the state-selection cavity between the nominal
operating power and lower values. We saw no shift,
measuring a statistically limited value of -8(12)xl0 -16 , for a
change from nominal operating conditions (on order of 10 5
detected atoms) to no atoms. This limit would require 5%
regulation in the atom number. We plan on running these
tests longer to reduce the statistical errors because we
anticipate the actual shifts to be negligible for our operating
conditions. Calculations based on parameters realized in our
system and others’ measurements [6,7] indicate a maximum
collision shift of 5xl0 -17 , implying that this systematic shift
should not cause instability at the level of lxlO -16 for any
degree of atom-number fluctuations.

D. Microwave Power

Modulation of the microwave power applied to the clock
cavity between our operating value of-57.5 dBm and several

lower values revealed no frequency shift at the demonstrated
level of precision. The statistical uncertainty allows us to put
a limit on the required power regulation of 3%. The
microwave power was adjusted by amplitude modulating the
IF drive that is mixed with the 6.8 GHz signal to generate the
microwaves for Ramsey interrogation. The reduced
sensitivity to frequency fluctuations at the lower microwave
powers was taken into account.

E. Laser Power

Several measurements were made in which different laser
beams were left on during the free-drift time. These indicate
the required degree of shuttering required for each individual
beam, which is trivial to meet with a physical shutter as long
as it closes completely. We also measured the sensitivity to
stray light on our laser table by modulating the operation of a
shutter before the input fiber. The result is consistent with
zero frequency shift, with a statistically limited uncertainty
corresponding to a requirement that the optical power on the
laser table be stable to 3%. Operating with a shutter before
the input fiber is problematic because of the proximity to the
vibration-sensitive ECDL.

F. Inclination

We measured the frequency sensitivity to changes in the
apparatus angle with respect to the vertical direction. When
the microwave cavity is driven symmetrically from both
sides, the measured change in frequency with tilt angle is
consistent with zero, with a statistical uncertainty
corresponding to a required vertical alignment of 0.15 mrad.
The maximum frequency sensitivity we see for an unbalanced
drive is 3.6(0.2)xl0 -14 for no tilt, and 7.7(0.5)xl0 -14 at a tilt
of 5 mrad. This implies a requirement that the microwave
drive be balanced to 0.3% when the vertical alignment is
better than 0.3 mrad. However, this measurement did not
exhibit the monotonic behavior expected for the distributed
cavity-phase shift [8], most likely due to the magnetic-field
gradient, discussed above, which complicates the atoms’
frequency dependence on cavity position.

Figure 2. Results of measurement of frequency shift introduced by MOT
magnetic field. The shift versus MOT coil current is plotted for three
different values. For each current, the difference between the fountain
frequency and the Maser Mean frequency was averaged for at least 2 days.

G. Blackbody Radiation

The frequency sensitivity to blackbody radiation has not
been explicitly measured, but using known temperature
coefficients for this effect, we determine that a temperature
regulation of 0.5 °C at our operating temperature of 32 °C
will be adequate. Although the uncertainty on the size of the
blackbody shift is one of the largest contributions for primary
standards, the sensitivity to temperature is not a serious
concern for our application. The operational fountains will
be housed in an environment regulated to 0.1 °C.

We are planning to investigate the sensitivity to cavity
temperature due to cavity pulling, and we may improve the
statistical limits on some of the measurements that we have
carried out. The conclusion that can be drawn from all of
these tests so far is that we have not identified any source of
frequency instability that should prevent us from reaching
long-term relative-frequency stability of order lxlO -16 .

V. Conclusion

To summarize, we have demonstrated long, continuous
runs with our engineering-prototype rubidium fountain, and
we have used the long averaging time to characterize the
system against the observatory’s Maser Mean timescale.
These comparisons together with our measurements of the
stability of systematic frequency shifts provide
encouragement that we can meet our long-term frequency
reproducibility goals.

[6] Chad Fertig and Kurt Gibble, Phys. Rev. Lett. 85, p. 1622, 2000.

[7] Y. Sortais, et al., Phys. Rev. Lett. 85, p. 3117, 2000.

[8] F. Chapelet, et al., Proceedings of the 20th Eur. Freq. and Time Forum,
Braunschweig, Germany, p.160, 2006.

References

[1] S. Peil, S. Crane, T. Swanson and C. Ekstrom, Proceedings of the 20th
Eur. Freq. and Time Forum, Braunschweig, Germany, p.194, 2006.

[2] S. Peil, S. Crane, T. Swanson, C. Ekstrom, Proceedings of the 2005
IEEE Freq. Control Symp., Vancouver, Canada, p. 304, 2005.

[3] S. Crane, S. Peil and C. Ekstrom Ibid. p. 301.

[4] USNO does not endorse any commercial product, nor does USNO
permit any use of this document for marketing or advertising.

[5] P. Koppang, J. Skinner, and D. Johns, Proc. 38 th Precise Time and
Time Interval (PTTI) Appl. Planning Meeting, 2006, in press.