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Standards of Time and Frequency at the Outset of the 21st Century
R E V I E W
Standards of Time and Frequency at the
Outset of the 21st Century
S. A. Diddams,* J. C. Bergquist, S. R. Jefferts, C. W. Oates
After 50 years of development, microwave atomic clocks based on cesium have
achieved fractional uncertainties below 1 part in 10
15
, a level unequaled in all of
metrology. The past 5 years have seen the accelerated development of optical
atomic clocks, which may enable even greater improvements in timekeeping. Time
and frequency standards with various levels of performance are ubiquitous in our
society, with applications in many technological fields as well as in the continued
exploration of the frontiers of basic science. We review state-of-the-art atomic time
and frequency standards and discuss some of their uses in science and technology.
As important as
Btime[ might be to those
who are navigators, scientists, or even musi-
cians, it is no more than an arbitrary pa-
rameter that is used to describe dynamics,
or the mechanics of motion. David Mermin
was struck by this as he wondered about
the role that time and space would play in
physics in the next century (1):
How can people talk about spacetime
turning into a foam at the Planck scale
when we barely manage to define space
and time at the atomic scale? Time, for
example, is nothing more than an ex-
tremely convenient and compact way
to characterize the correlations be-
tween objects we can use as clocks,
and clocks tend to be macroscopic. To
be sure, we can generate frequencies
from atoms and correlate them with
macroscopic clocks, but the shorter
the length scale, the more it looks like
you
_re talking about energies divided
by Planck
_s constant. The connections
with clocks become increasingly indi-
rect. There seems to me to be a consid-
erable danger here of imposing on an
utterly alien realm a useful bookkeep-
ing device we
_ve merely invented for
our own macroscopic convenience.
The definition of time can be puzzling
exactly because of the apparent arbitrariness
that Mermin described. It is through the
external or internal periodic dynamics of one
object that we define time, and armed with
that time scale, we can characterize the
dynamics of other objectsan oddly circular
argument. Another conundrum: How do we
determine the period (or its inverse, frequen-
cy) of our time standard, or any clock, to be
uniform? Clearly, time is relative and several
time sources must be compared toward
establishing the most stable and accurate
definition of the second, our base unit of
time in the international system (SI).
In view of this, there is considerable irony
in the fact that the second is the most
accurately realized unit of measurement, with
fractional uncertainty now below 1 part in
10
15
. Moreover, it could be argued that the
technologies based on the arbitrarily defined
second have had an impact like few others in
our modern society. Everyday systems in-
cluding the electric power grid, cell phones,
the Internet, and the Global Positioning
System (GPS) depend critically on time and
frequency standards for continued operation.
Because of its position of metrological
preeminence, the second is also used to
define three other SI units (meter, candela,
and ampere), and several other important
physical quantities are defined or measured
in terms of the second. For example, accept-
ing that the speed of light is a constant, the
meter is defined as the path length traveled
by light in a vacuum during the time interval
of 1/299,792,458 of a second. As a result,
lasers with a known and fixed frequency have
become the standards for length metrology,
where they guide precision measurements of
physical distances (e.g., in the etching and
lithography of semiconductor wafers). An-
other example is the definition of the volt,
which can be obtained via the Josephson
effect in terms of the product of a physical
constant and the frequency. For these and
other reasons, the development and operation
of high-quality time and frequency standards
is an important endeavor at National Metrol-
ogy Institutes (NMI) around the world, with
consequences that reach into our daily lives.
In many research laboratories, the scien-
tific impact of precision time and frequency
measurements has been considerable. Exam-
ples include the prediction of gravitational
radiation from binary pulsars (2) and the
most precise direct measurement of the grav-
itational red shift (3). Additionally, the
development of time and frequency stan-
dards over the past 60 years has gone hand-
in-hand with many scientific advances in the
fields of atomic, molecular, and optical
physics. Modern atomic clocks have their
roots in the microwave spectroscopy experi-
ments of Stern, Rabi, and Ramsey. Many of
the techniques that are used in modern
atomic clocks resulted from the development
of the maser, the laser, and the new field of
laser spectroscopy that followed. These de-
velopments led to laser cooling and trapping
of atoms and ions, which now provide
clockmakers with isolated and nearly mo-
tionless quantum references for what are
now the best clocks in existence.
In labeling the time of a physical event,
one must count the number of cycles (and
perhaps fractions of cycles) of some periodic
occurrence relative to an agreed-upon time
origin. For some situations, the time origin is
of great importance; in other cases, it is only
the interval, or time difference, between two
events that is of interest. In what follows, we
focus on the latter and discuss the issues
surrounding the generation and characteriza-
tion of the source of the periodic events
(often called a frequency standard) with
which time intervals are generated and
measured. As many excellent reviews on
the development of atomic frequency stan-
dards already exist (46), we concentrate on
the most accurate atomic clockthe cesium
fountain clockand then discuss the new
optical clocks, which are anticipated to be
the atomic timepieces of the future.
Historical Background
The best choice for a timekeeping device is
an object whose dynamical period is well
characterized, not easily perturbed, and
(ideally) constant. A natural, macroscopic
candidate that could be used to define the
unit of time is some phenomenon of nature,
whose period is especially uniform. Figure 1
compares the performance of a few impor-
tant clocks from recent history. For many
centuries, the daily rotation of Earth on its
axis seemed to offer a uniform time base, but
as time standards and measurement tech-
niques improved, the length of a day was
found to fluctuate and generally grow longer
(which was attributed in part to tidal
friction). Astronomers seeking a more stable
unit of time chose the period of the orbital
Time & Frequency Division, National Institute of
Standards and Technology, 325 Broadway, Boulder,
CO 80305, USA.
*To whom correspondence should be addressed.
E-mail: sdiddams@boulder.nist.gov
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19 NOVEMBER 2004
VOL 306
SCIENCE
www.sciencemag.org
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PECIAL
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EC
TI
ON motion of Earth about the Sun (nominally
1 year) as the basis for the definition of
the second. In 1956, the Ephemeris Second
(1/31,556,925.9747 of the tropical year
1900) was formally adopted by the General
Conference of Weights and Measures as the
best measure of time.
Although the orbital motion of Earth in the
solar system might be more uniform than the
solar day, its period was impractically long for
most purposes and was likely to suffer un-
predictable changes and aging effects (hence,
the definition of Ephemeris Time based on a
particular solar year). Already when this def-
inition of the second was adopted, scientists
were investigating resonances or transitions in
microscopic atomic systems as a more suitable
means for defining time intervals and frequen-
cy. Many transitions between energy states in
well-isolated atomic systems are highly im-
mune to perturbations that would change the
atomic resonance frequency n
o
, making these
systems ideal candidates for clocks. Quantum
mechanics dictates that the energies of a
bound system (e.g., an electron bound to an
atom) have discrete values. Hence, an atom
or molecule can make a transition between
two energy levels (E
1
and E
2
) by the ab-
sorption or emission of energy in the form of
electromagnetic radiation having the precise
frequency n
o
0 kE
1
E
2
k/h, where h is the
Planck constant. On the
basis of this principle,
most atomic frequency
s t a n d a r d s ( a t o m i c
clocks) work by steer-
ing the frequency of an
external oscillator to
match a particular val-
ue of n
o
.
The first atomic
clocks owe their genesis
to the explosion of ad-
vances in quantum me-
chanics and microwave
electronics before and
during the Second World
War. Much of the semi-
nal work specific to
clock development was
done by Rabi. Although
he may have suggested
using cesium as the ref-
erence for an atomic
clock as early as 1945, it
was the inversion transi-
tion in the ammonia
molecule at È23.8 GHz
that served as the refer-
ence for the first atom-