FOCS 1, a continuous cold caesium fountain atomic clock in Switzerland, started operating in 2004 at an uncertainty of one second in 30 million years.
An atomic clock is a clock device that uses an electronic transition frequency in the microwave, optical, or ultraviolet region of the electromagnetic spectrum of atoms as a frequency standard for its timekeeping element. Atomic clocks are the most accurate time and frequency standards known, and are used as primary standards for international time distribution services, to control the wave frequency of television broadcasts, and in global navigation satellite systems such as GPS.
The principle of operation of an atomic clock is not based on nuclear physics, but rather on atomic physics; it uses the microwave signal that electrons in atoms emit when they change energy levels. Early atomic clocks were based on masers at room temperature. Currently, the most accurate atomic clocks first cool the atoms to near absolute zero temperature by slowing them with lasers and probing them in atomic fountains in a microwave-filled cavity. An example of this is the NIST-F1 atomic clock, one of the national primary time and frequency standards of the United States.
The accuracy of an atomic clock depends on two factors. The first factor is temperature of the sample atoms—colder atoms move much more slowly, allowing longer probe times. The second factor is the frequency and intrinsic width of the electronic transition. Higher frequencies and narrow lines increase the precision.
National standards agencies in many countries maintain a network of atomic clocks which are intercompared and kept synchronized to an accuracy of 10−9 seconds per day (approximately 1 part in 1014). These clocks collectively define a continuous and stable time scale, International Atomic Time (TAI). For civil time, another time scale is disseminated, Coordinated Universal Time (UTC). UTC is derived from TAI, but approximately synchronised, by using leap seconds, to UT1, which is based on actual rotation of the Earth with respect to the solar time.
- 1 History
- 2 Mechanism
- 3 Physics package realisations
- 4 Power consumption
- 5 Evaluated accuracy
- 6 Research
- 7 Applications
- 8 See also
- 9 References
- 10 External links
The idea of using atomic transitions to measure time was suggested by Lord Kelvin in 1879. Magnetic resonance, developed in the 1930s by Isidor Rabi, became the practical method for doing this. In 1945, Rabi first publicly suggested that atomic beam magnetic resonance might be used as the basis of a clock. The first atomic clock was an ammonia maser device built in 1949 at the U.S. National Bureau of Standards (NBS, now NIST). It was less accurate than existing quartz clocks, but served to demonstrate the concept. The first accurate atomic clock, a caesium standard based on a certain transition of the caesium-133 atom, was built by Louis Essen and Jack Parry in 1955 at the National Physical Laboratory in the UK. Calibration of the caesium standard atomic clock was carried out by the use of the astronomical time scale ephemeris time (ET). This led to the internationally agreed definition of the latest SI second being based on atomic time. Equality of the ET second with the (atomic clock) SI second has been verified to within 1 part in 1010. The SI second thus inherits the effect of decisions by the original designers of the ephemeris time scale, determining the length of the ET second.
Since the beginning of development in the 1950s, atomic clocks have been based on the hyperfine transitions in hydrogen-1, caesium-133, and rubidium-87. The first commercial atomic clock was the Atomichron, manufactured by the National Company. More than 50 were sold between 1956 and 1960. This bulky and expensive instrument was subsequently replaced by much smaller rack-mountable devices, such as the Hewlett-Packard model 5060 caesium frequency standard, released in 1964.
In the late 1990s four factors contributed to major advances in clocks:
- Laser cooling and trapping of atoms
- So-called high-finesse Fabry–Pérot cavities for narrow laser line widths
- Precision laser spectroscopy
- Convenient counting of optical frequencies using optical combs.
In August 2004, NIST scientists demonstrated a chip-scale atomic clock. According to the researchers, the clock was believed to be one-hundredth the size of any other. It requires no more than 125 mW, making it suitable for battery-driven applications. This technology became available commercially in 2011. Ion trap experimental optical clocks are more precise than the current caesium standard.
In 2016, NASA plans to deploy the Deep Space Atomic Clock (DSAC), a miniaturized, ultra-precise mercury-ion atomic clock, into outer space. The DSAC is considered much more stable than other current navigational clocks.
Since 1967, the International System of Units (SI) has defined the second as the duration of 9192631770 cycles of radiation corresponding to the transition between two energy levels of the caesium-133 atom. In 1997, the International Committee for Weights and Measures (CIPM) added that the preceding definition refers to a caesium atom at rest at a temperature of 0 K.
This definition makes the caesium oscillator the primary standard for time and frequency measurements, called the caesium standard. The definitions of other physical units, e.g., the volt and the metre, rely on the definition of the second.
The actual time-reference of an atomic clock consists of an electronic oscillator operating at microwave frequency. The oscillator is arranged so that its frequency-determining components include an element that can be controlled by a feedback signal. The feedback signal keeps the oscillator tuned in resonance with the frequency of the electronic transition of caesium or rubidium.
The core of the atomic clock is a tunable microwave cavity containing a gas. In a hydrogen maser clock the gas emits microwaves (the gas mases) on a hyperfine transition, the field in the cavity oscillates, and the cavity is tuned for maximum microwave amplitude. Alternatively, in a caesium or rubidium clock, the beam or gas absorbs microwaves and the cavity contains an electronic amplifier to make it oscillate. For both types the atoms in the gas are prepared in one electronic state prior to filling them into the cavity. For the second type the number of atoms which change electronic state is detected and the cavity is tuned for a maximum of detected state changes.
Most of the complexity of the clock lies in this adjustment process. The adjustment tries to correct for unwanted side-effects, such as frequencies from other electron transitions, temperature changes, and the spreading in frequencies caused by ensemble effects.[clarification needed] One way of doing this is to sweep the microwave oscillator's frequency across a narrow range to generate a modulated signal at the detector. The detector's signal can then be demodulated to apply feedback to control long-term drift in the radio frequency. In this way, the quantum-mechanical properties of the atomic transition frequency of the caesium can be used to tune the microwave oscillator to the same frequency, except for a small amount of experimental error. When a clock is first turned on, it takes a while for the oscillator to stabilize. In practice, the feedback and monitoring mechanism is much more complex.
A number of other atomic clock schemes are in use for other purposes. Rubidium standard clocks are prized for their low cost, small size (commercial standards are as small as 17 cm3) and short-term stability. They are used in many commercial, portable and aerospace applications. Hydrogen masers (often manufactured in Russia) have superior short-term stability compared to other standards, but lower long-term accuracy.
Often, one standard is used to fix another. For example, some commercial applications use a rubidium standard periodically corrected by a global positioning system receiver (see GPS disciplined oscillator). This achieves excellent short-term accuracy, with long-term accuracy equal to (and traceable to) the U.S. national time standards.
The lifetime of a standard is an important practical issue. Modern rubidium standard tubes last more than ten years, and can cost as little as US$50. Caesium reference tubes suitable for national standards currently last about seven years and cost about US$35,000. The long-term stability of hydrogen maser standards decreases because of changes in the cavity's properties over time.
Modern clocks use magneto-optical traps to cool the atoms for improved precision.
Physics package realisations
||This section may be too technical for most readers to understand. (December 2013) (Learn how and when to remove this template message)|
A number of methods exist for utilizing hyperfine atomic transitions. These methods, with their respective benefits and drawbacks, have influenced the development of commercial devices and laboratory standards. By tradition, the hardware that is used to probe the atoms is called the physics package.
Atomic beam standard
The atomic beam standard is a direct extension of the Stern-Gerlach atomic splitting experiment. The atoms of choice are heated in an oven to create gas, which is collimated into a beam. This beam passes through a state-selector magnet A, where atoms of the wrong state are separated out from the beam. The beam is exposed to an RF field at or near the transition. The beam then passes through a space before it is again exposed to the RF field. The RF field and a static homogeneous magnetic field from the C-field coil will change the state of the atoms. After the second RF field exposure the atomic beam passes through a second state selector magnet B, where the atom state being selected out of the beam at the A magnet is being selected. This way, the detected number of atoms will relate to the ability to match the atomic transition. After the second state-selector a mass-spectrometer using an ionizer will detect the rate of atoms being received.
Modern variants of this beam mechanism use optical pumping to transition all atoms to the same state rather than dumping half the atoms. Optical detection using scintillation can also be used.
The frequency errors can be made very small for a beam device, or predicted (such as the magnetic field pull of the C-coil) in such a way that a high degree of repeatability and stability can be achieved. This is why an atomic beam can be used as a primary standard.
Atomic gas cell standard
The atomic gas cell standard builds on a confined reference isotope (often an alkali metal such as Rubidium (87Rb)) inside an RF cavity. The atoms are excited to a common state using optical pumping; when the applied RF field is swept over the hyperfine spectrum, the gas will absorb the pumping light, and a photodetector provides the response. The absorption peak steers the fly-wheel oscillator.
A typical rubidium gas-cell uses a rubidium (87Rb) lamp heated to 108-110 degrees Celsius, and an RF field to excite it to produce light, where the D1 and D2 lines are the significant wavelengths. An 85Rb cell filters out the a component of the D1 and D2 line so that only the b component pumps the 87Rb gas cell in the RF cavity.
Among the significant frequency pulling mechanisms inherent to the gas cell are wall-shift, buffer-gas shift, cavity-shift and light-shift. The wall-shift occurs as the gas bumps into the wall of the glass container. Wall-shift can be reduced by wall coating and compensation by buffer gas. The buffer gas shift comes from the reference atoms which bounce into buffer gas atoms such as neon and argon; these shifts can be both positive and negative. The cavity shift comes from the RF cavity, which can deform the resonance amplitude response; this depends upon cavity centre frequency and resonator Q-value. Light-shift is an effect where frequency is pulled differently depending on the light intensity, which often is modulated by the temperature shift of the rubidium lamp and filter cell.
There are thus many factors in which temperature and ageing can shift frequency over time, and this is why a gas cell standard is unfit for a primary standard, but can become a very inexpensive, low-power and small-size solution for a secondary standard or where better stability compared to crystal oscillators is needed, but not the full performance of a caesium beam standard. The rubidium gas standards have seen use in telecommunications systems and portable instruments.
Active maser standard
The active maser standard is a development from the atomic beam standard in which the observation time was increased by using a bounce-box. By controlling the beam intensity, spontaneous emission provides sufficient energy to provide a continuous oscillation, which is tapped and used as a reference for a flywheel oscillator.
The active maser is sensitive to wall-shift and cavity pulling. The wall-shift is mitigated by using PTFE coating (or other suitable coating) to reduce the effect. The cavity pulling effect can be reduced by automatic cavity tuning. In addition the magnetic field pulls the frequency.
Although the long-term stability of the active maser is not as good as that of a caesium beam, it remains one of the most stable sources available. The inherent pulling effects make repeatability troublesome and prohibit its use as a primary standard, but it makes an excellent secondary standard. It is used as a low-noise flywheel standard for caesium beam standards.
The fountain standard is a development from the beam standard where the beam has been folded back to itself by the Earth's gravity, such that the first and second RF field becomes the same RF cavity. A ball of atoms is laser cooled, which reduces black body temperature shifts. Phase errors between RF cavities are essentially removed. The length of the beam is longer than many beams, but the speed is also much slower such that the observation time becomes significantly longer and hence a higher Q value is achieved in the Ramsey fringes.
Caesium fountains have been implemented in many laboratories, but rubidium has even greater ability to provide stability in the fountain configuration.
Ion trap standard
The ion trap standard is a set of different approaches, but their common property is that a cooled ion is confined in an electrostatic trap. The hyperfine region of the available electron is then being tracked similar to that of a gas cell standard.
Ion traps have been used for numerous ions. 199Hg+ was an early candidate. Quantum logic spectroscopy of a single Al ion became the most precise in 2008. In 2010 an improved setup using a Mg+ logic ion instead of Be was demonstrated
|This section requires expansion. (June 2008)|
The power consumption of atomic clocks varies with their size. Atomic clocks on the scale of one chip require less than 30 milliwatt; Primary frequency and time standards like the United States Time Standard atomic clocks, NIST-F1 and NIST-F2, use far greater quantities of power.
The evaluated accuracy uB reports of various primary frequency and time standards are published online by the International Bureau of Weights and Measures (BIPM). Several frequency and time standards groups in 2015 reported uB values in the 2 × 10−16 to 3 × 10−16 range.
In 2011, the NPL-CsF2 caesium fountain clock operated by the National Physical Laboratory (NPL), which serves as the United Kingdom primary frequency and time standard, was improved regarding the two largest sources of measurement uncertainties — distributed cavity phase and microwave lensing frequency shifts. In 2011 this resulted in an evaluated frequency uncertainty reduction from uB = 4.1 × 10−16 to uB = 2.3 × 10−16;— the lowest value for any primary national standard at the time. At this frequency uncertainty, the NPL-CsF2 is expected to neither gain nor lose a second in about 138 million (138 × 106) years.
The NIST-F2 caesium fountain clock operated by the National Institute of Standards and Technology (NIST), was officially launched in April 2014, to serve as a new U.S. civilian frequency and time standard, along with the NIST-F1 standard. The planned uB performance level of NIST-F2 is 1 × 10−16. "At this planned performance level the NIST-F2 clock will not lose a second in at least 300 million years. NIST-F2 was designed using lessons learned from NIST-F1. The NIST-F2 key advance compared to the NIST-F1 is that the vertical flight tube is now chilled inside a container of liquid nitrogen, at −193 °C (−315.4 °F). This cycled cooling dramatically lowers the background radiation and thus reduces some of the very small measurement errors that must be corrected in NIST-F1.
The first in-house accuracy evaluation of NIST-F2 reported a uB of 1.1 × 10−16. However, a published scientific criticism of that NIST F-2 accuracy evaluation described problems in its treatment of distributed cavity phase shifts and the microwave lensing frequency shift, which is treated significantly differently than in the majority of accurate fountain clock evaluations. In March 2014 and March 2015 the NIST-F2 caesium fountain clock reported a uB of 1.5 × 10−16. These uB reports of evaluation of primary frequency standards are more in line with the scientific criticism on the first accuracy evaluation. At this frequency uncertainty, the NIST-F2 is expected to neither gain nor lose a second in more than 211 million (211 × 106) years.
Secondary representations of the second
A list of frequencies recommended for secondary representations of the second is maintained by the International Bureau of Weights and Measures (BIPM) since 2006 and is available online. The list contains the frequency values and the respective standard uncertainties for the rubidium microwave transition and for several optical transitions. These secondary frequency standards are accurate at the level of parts in 10−18; however, the uncertainties provided in the list are in the range of parts in 10−14 – 10−15 since they are limited by the linking to the caesium primary standard that currently (2015) defines the second.
|relative Allan deviation
|133Caesium||9 192 631 770(*)||10−13|
|87Rubidium||6 834 682 610.904 324||10−15|
|1Hydrogen||1 420 405 751.77||10−15|
|Optical clock (87Strontium)||429 228 004 229 873.4||10−17|
For context, a femtosecond (1 × 10−15 s) is to a second what a second is to about 31.71 million (31.71 × 106) years and an attosecond (1 × 10−18 s) is to a second what a second is to about 31.71 billion (31.71 × 109) years.
21st Century experimental atomic clocks that provide non-caesium-based secondary representations of the second are becoming so precise that they are likely to be used as extremely sensitive detectors for other things besides measuring frequency and time. For example, the frequency of atomic clocks is altered slightly by gravity, magnetic fields, electrical fields, force, motion, temperature and other phenomena. The experimental clocks tend to continue improving, and leadership in performance has been shifted back and forth between various types of experimental clocks.
In March 2008, physicists at NIST described a quantum logic clock based on individual ions of beryllium and aluminium. This clock was compared to NIST's mercury ion clock. These were the most accurate clocks that had been constructed, with neither clock gaining nor losing time at a rate that would exceed a second in over a billion years. In February 2010, NIST physicists described a second, enhanced version of the quantum logic clock based on individual ions of magnesium and aluminium. Considered the world's most precise clock in 2010 with a fractional frequency inaccuracy of 8.6 × 10−18, it offers more than twice the precision of the original. 
The theoretical move from microwaves as the atomic "escapement" for clocks to light in the optical range (harder to measure but offering better performance) earned John L. Hall and Theodor W. Hänsch the Nobel Prize in Physics in 2005. One of 2012's Physics Nobelists, David J. Wineland, is a pioneer in exploiting the properties of single ion held in a trap to develop clocks of the highest stability.
New technologies, such as femtosecond frequency combs, optical lattices, and quantum information, have enabled prototypes of next-generation atomic clocks. These clocks are based on optical rather than microwave transitions. A major obstacle to developing an optical clock is the difficulty of directly measuring optical frequencies. This problem has been solved with the development of self-referenced mode-locked lasers, commonly referred to as femtosecond frequency combs. Before the demonstration of the frequency comb in 2000, terahertz techniques were needed to bridge the gap between radio and optical frequencies, and the systems for doing so were cumbersome and complicated. With the refinement of the frequency comb, these measurements have become much more accessible and numerous optical clock systems are now being developed around the world.
As in the radio range, absorption spectroscopy is used to stabilize an oscillator—in this case a laser. When the optical frequency is divided down into a countable radio frequency using a femtosecond comb, the bandwidth of the phase noise is also divided by that factor. Although the bandwidth of laser phase noise is generally greater than stable microwave sources, after division it is less.
The two primary systems under consideration for use in optical frequency standards are:
These two techniques allow the atoms or ions to be highly isolated from external perturbations, thus producing an extremely stable frequency reference.
The rare-earth element ytterbium (Yb) is valued not so much for its mechanical properties but for its complement of internal energy levels. "A particular transition in Yb atoms, at a wavelength of 578 nm, currently provides one of the world's most accurate optical atomic frequency standards," said Marianna Safronova. The estimated amount of uncertainty achieved corresponds to a Yb clock uncertainty of about one second over the lifetime of the universe so far, 15 billion years, according to scientists at the Joint Quantum Institute (JQI) and the University of Delaware in December 2012.
In 2013 optical lattice clocks (OLCs) were shown to be as good as or better than caesium fountain clocks. Two optical lattice clocks containing about 10 000 atoms of strontium-87 were able to stay in synchrony with each other at a precision of at least 1.5 × 10−16, which is as accurate as the experiment could measure. These clocks have been shown to keep pace with all three of the caesium fountain clocks at the Paris Observatory. There are two reasons for the possibly better precision. Firstly, the frequency is measured using light, which has a much higher frequency than microwaves, and secondly, by using many atoms, any errors are averaged. Using ytterbium-171 atoms, a new record for stability with a precision of 1.6 × 10−18 over a 7-hour period was published on 22 August 2013. At this stability, the two independently from each other working optical lattice clocks the NIST research team used would differ less than a second over the age of the universe ((13.799±0.021 × 109) years); this was 10 times better than previous experiments. The clocks rely on 10 000 ytterbium atoms cooled to 10 microkelvin and trapped in an optical lattice. A laser at 578 nm excites the atoms between two of their energy levels. Having established the stability of the clocks, the researchers are studying external influences and evaluating the remaining systematic uncertainties, in the hope that they can bring the clock's accuracy down to the level of its stability. An improved optical lattice clock was described in a 2014 Nature paper. In 2015 JILA evaluated the absolute frequency uncertainty of their latest strontium-87 optical lattice clock at 2.1 × 10−18, which corresponds to a measurable gravitational time dilation for an elevation change of 2 cm (0.79 in) on planet Earth that according to JILA/NIST Fellow Jun Ye is "getting really close to being useful for relativistic geodesy". At this frequency uncertainty, this JILA optical lattice optical clock is expected to neither gain nor lose a second in more than 15 billion (15 × 109) years.
Optical clocks are currently (2015) still primarily research projects, less mature than rubidium and caesium microwave standards, which regularly deliver time to the International Bureau of Weights and Measures (BIPM) for establishing International Atomic Time. As the optical standards (the best experimental optical clocks have already achieved better stability and absolute frequency uncertainties below 1 × 10−17) move beyond their microwave counterparts in terms of performance this puts them in a position to replace the current standard for time, the caesium fountain clock. In the future this might lead to redefine the caesium microwave based SI second and other new dissemination techniques to transfer clock signals will be required that can be used in both shorter-range and longer-range (frequency) comparisons between attosecond (sub-1 × 10−17 s) accurate clocks without significantly compromising their performance.
Clock comparison techniques
In June 2015 the European National Physical Laboratory (NPL) in Teddington, UK; the French department of Time-Space Reference Systems at the Paris Observatory; the German German National Metrology Institute (PTB) in Braunschweig; and Italy’s National Institute of Metrology Research in Turin labs have started tests to improve the accuracy of current state-of-the-art satellite comparisons by a factor 10, but it will still be limited to one part in 1 × 10−16. These 4 European labs are developing and host a variety of experimental optical clocks that harness different elements in different experimental set-ups and want to compare their optical clocks against each other and check whether they agree. In a next phase these labs strive to transmit comparison signals in the visible spectrum through fibre-optic cables. This will allow their experimental optical clocks to be compared with an accuracy similar to the expected accuracies of the optical clocks themselves. Some of these labs have already established fibre-optic links, and tests have begun on sections between Paris and Teddington, and Paris and Braunschweig. Fibre-optic links between experimental optical clocks also exist between the American NIST lab and its partner lab JILA, both in Boulder, Colorado but these span much shorter distances than the European network and are between just two labs. According to Fritz Riehle, a physicist at PTB "Europe is in a unique position as it has a high density of the best clocks in the world".
The development of atomic clocks has led to many scientific and technological advances such as a worldwide system of precise position measurement (the Global Positioning System and GLObal NAvigation Satellite System), and applications in the Internet, which depend critically on frequency and time standards. Atomic clocks are installed at sites of time signal radio transmitters. They are used at some long wave and medium wave broadcasting stations to deliver a very precise carrier frequency. Atomic clocks are used in many scientific disciplines, such as for long-baseline interferometry in radioastronomy.
The Global Positioning System (GPS) provides very accurate timing and frequency signals. A GPS receiver works by measuring the relative time delay of signals from a minimum of four, but usually more, GPS satellites, each of which has at least two onboard caesium and as many as two rubidium atomic clocks. The relative times are mathematically transformed into three absolute spatial coordinates and one absolute time coordinate. GPS Time (GPST) is a continuous time scale and theoretically accurate to about 14 ns. However, most receivers lose accuracy in the interpretation of the signals and are only accurate to 100 ns. The GPST is related to but differs from TAI (International Atomic Time) and UTC (Coordinated Universal Time). GPST remains at a constant offset with TAI (TAI – GPST = 19 seconds) and like TAI does not implement leap seconds. Periodic corrections are performed to the on-board clocks in the satellites to keep them synchronized with ground clocks. The GPS navigation message includes the difference between GPST and UTC. As of July 2015, GPST is 17 seconds ahead of UTC because of the leap second added to UTC on June 30, 2015. Receivers subtract this offset from GPS Time to calculate UTC and specific timezone values.
The GLObal NAvigation Satellite System (GLONASS) provides an alternative to the Global Positioning System (GPS) system and is the second navigational system in operation with global coverage and of comparable precision. GLONASS Time (GLONASST) is generated by the GLONASS Central Synchroniser and is typically better than 1,000 ns. Unlike GPS, the GLONASS time scale implements leap seconds, like UTC.
Systems under construction
The BeiDou and Galileo satellite navigation systems are under construction in 2015 but both have to add planned extra satellites to achieve their full-scale global coverage constellation goal. BeiDou Time (BDT) is a continuous time scale starting at 1 January 2006 at 0:00:00 UTC and is synchronised with UTC within 100 ns. Galileo System Time (GST) is a continuous time scale which is generated on the ground at the Galileo Control Centre in Fucino, Italy, by the Precise Timing Facility, based on averages of different atomic clocks and maintained by the Galileo Central Segment and synchronised with TAI with a nominal offset below 50 ns. The Galileo navigation message includes the differences between GST, UTC and GPST (to promote interoperability).
Time signal radio transmitters
A radio clock is a clock that automatically synchronizes itself by means of government radio time signals received by a radio receiver. Many retailers market radio clocks inaccurately as atomic clocks; although the radio signals they receive originate from atomic clocks, they are not atomic clocks themselves. They are inexpensive time-keeping devices with an accuracy of about a second. Instrument grade time receivers provide higher accuracy. Such devices incur a transit delay of approximately 1 ms for every 300 kilometres (186 mi) of distance from the radio transmitter. Many governments operate transmitters for time-keeping purposes.
- USNO Master Clock
- McCarthy, Dennis; Seidelmann, P. Kenneth (2009). TIME from Earth Rotation to Atomic Physics. Weinheim: Wiley-VCH. ch. 10 & 11.
- Thomson, William; Tait, Peter Guthrie (1879). Treatise on Natural Philosophy. 1, part 1 (2nd ed.). Cambridge, England: Cambridge University Press. p. 227.
- M.A. Lombardi; T.P. Heavner; S.R. Jefferts (2007). "NIST Primary Frequency Standards and the Realization of the SI Second" (PDF). Journal of Measurement Science. 2 (4): 74.
- Isidor I. Rabi, "Radiofrequency spectroscopy" (Richtmyer Memorial Lecture, delivered at Columbia University in New York, New York, on 20 January 1945).
- "Meeting at New York, January 19 and 20, 1945" Physical Review, vol. 67, pages 199-204 (1945).
- William L. Laurence, "'Cosmic pendulum' for clock planned," New York Times, 21 January 1945, page 34. Reprinted on page 77 of: Lombardi, Michael A.; Heavner, Thomas P.; and Jefferts, Steven R. (December 2007) "NIST primary frequency standards and the realization of the SI second," NCSLI Measure, vol. 2, no. 4, pages 74-89.
- D.B. Sullivan (2001). "Time and frequency measurement at NIST: The first 100 years" (PDF). 2001 IEEE International Frequency Control Symposium. NIST. pp. 4–17.
- Essen, L.; Parry, J. V. L. (1955). "An Atomic Standard of Frequency and Time Interval: A Cæsium Resonator". Nature. 176 (4476): 280. Bibcode:1955Natur.176..280E. doi:10.1038/176280a0.
- W. Markowitz; R.G. Hall; L. Essen; J.V.L. Parry (1958). "Frequency of cesium in terms of ephemeris time". Physical Review Letters. 1 (3): 105–107. Bibcode:1958PhRvL...1..105M. doi:10.1103/PhysRevLett.1.105.
- W. Markowitz (1988). "Comparisons of ET(Solar), ET(Lunar), UT and TDT'". In A.K. Babcock; G.A. Wilkins. The Earth's Rotation and Reference Frames for Geodesy and Geophysics, International Astronomical Union Symposia #128. pp. 413–418.. Pages 413–414, gives the information that the SI second was made equal to the second of ephemeris time as determined from lunar observations, and was later verified in this relation, to 1 part in 1010.
- J. Ye; H. Schnatz; L.W. Hollberg (2003). "Optical frequency combs: From frequency metrology to optical phase control" (PDF). IEEE Journal of Selected Topics in Quantum Electronics. 9 (4): 1041.
- "Chip-Scale Atomic Devices at NIST". NIST. 2007. Archived from the original on 7 January 2008. Retrieved 17 January 2008. Available on-line at: NIST.gov
- "SA.45s CSAC Chip Scale Atomic Clock" (PDF). 2011. Retrieved 12 June 2013.
- Landau, Elizabeth (27 April 2015). "Deep Space Atomic Clock". NASA. Retrieved 29 April 2015.
- "International System of Units (SI)" (PDF) (8th ed.). International Bureau of Weights and Measures (BIPM). 2006.
- "FAQs". Franklin Instrument Company. 2007. Archived from the original on 16 February 2008. Retrieved 17 January 2008.
- P. O. Schmidt; T. Rosenband; C. Langer; W. M. Itano; J. C. Bergquist; D. J. Wineland (2005). "Spectroscopy using quantum logic". Science. 309: 749. Bibcode:2005Sci...309..749S. doi:10.1126/science.1114375.
- Chou, C.; Hume, D.; Koelemeij, J.; Wineland, D.; Rosenband, T. (10 February 2010). "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks". Phys Rev Lett. 104 (7): 070802. arXiv:. Bibcode:2010PhRvL.104g0802C. doi:10.1103/PhysRevLett.104.070802. PMID 20366869.
- Lutwak, Robert (26–29 November 2007). "The Chip-Scale Atomic Clock — Prototype Evaluation". 36th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting.
- "NIST Launches a New U.S. Time Standard: NIST-F2 Atomic Clock". nist.gov.
- Evaluation of the frequency of the H-maser 1401708 by the primary frequency standard NPL-CsF2, National Physical Laboratory, February 2010
- "NPL's atomic clock revealed to be the world's most accurate : News : News + Events : National Physical Laboratory". npl.co.uk.
- "NPL-CsF2: now the atomic clock with the world's best long-term accuracy - Science Codex". sciencecodex.com.
- Improved accuracy of the NPL-CsF2 primary frequency standard: evaluation of distributed cavity phase and microwave lensing frequency shifts, Ruoxin Li, Kurt Gibble, and Krzysztof Szymaniec, August 2011
- NIST Cesium Fountains — Current Status and Future Prospects (PDF)
- "Time gets an upgrade". New Scientist: 7. 12 April 2014.
- "NIST launches a new US time standard: NIST-F2 atomic clock". phys.org. 3 April 2014. Retrieved 3 April 2014.
- "NIST launches a new US time standard: NIST-F2 atomic clock". nist.gov. 3 April 2014. Retrieved 3 April 2014.
- "Background: How NIST-F2 Works". nist.gov. 2 April 2014. Retrieved 4 April 2014.
- Heavner T P, Donley E A , Levi F, Costanzo G, Parker TE, Shirley J H, Ashby N, Barlow S and Jefferts SR, “First accuracy evaluation of NIST-F2,” 2014 Metrologia 51, 174–182, May 2014
- Comment on 'First accuracy evaluation of NIST-F2,' Kurt Gibble, Metrologia 52, 163, January 2015
- "President Piñera Receives ESO's First Atomic Clock". ESO Announcement. 15 November 2013. Retrieved 20 November 2013.
- Laura Ost (4 February 2014). "A New Era for Atomic Clocks". National Institute of Standards and Technology. Retrieved 18 October 2015.
- "Unit of time (second)". SI Brochure. BIPM. 2014 . Retrieved 23 June 2015.
- 87Rubidium BIPM document
- 87Strontium BIPM document
- "NIST 'Quantum Logic Clock' Rivals Mercury Ion as World's Most Accurate Clock" (PDF). PhysOrg.com. 6 March 2008. Retrieved 24 October 2009.
- NIST's Second 'Quantum Logic Clock' Based on Aluminum Ion is Now World's Most Precise Clock, NIST, 4 February 2010
- C.W Chou; D. Hume; J.C.J. Koelemeij; D.J. Wineland & T. Rosenband (17 February 2010). "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks" (PDF). NIST. Retrieved 9 February 2011.
- D. Lindley (20 May 2009). "Coping With Unusual Atomic Collisions Makes an Atomic Clock More Accurate". National Science Foundation. Retrieved 10 July 2009.
- W.H. Oskay; et al. (2006). "Single-atom optical clock with high accuracy" (PDF). Physical Review Letters. 97 (2): 020801. Bibcode:2006PhRvL..97b0801O. doi:10.1103/PhysRevLett.97.020801. PMID 16907426.
- Fritz Riehle. "On Secondary Representations of the Second" (PDF). Physikalisch-Technische Bundesanstalt, Division Optics. Retrieved 22 June 2015.
- 171Ytterbium BIPM document
- "Blackbody Radiation Shift: Quantum Thermodynamics Will Redefine Clocks". Retrieved 5 December 2012.
- Ost, Laura (22 January 2014). "JILA Strontium Atomic Clock Sets New Records in Both Precision and Stability". NIST Tech Beat. National Institute of Standards and Technology. Retrieved 5 December 2014.
- "Precise atomic clock may redefine time". 9 July 2013. Retrieved 24 August 2013.
- "NIST Ytterbium Atomic Clocks Set Record for Stability". 22 August 2013. Retrieved 24 August 2013.
- "New atomic clock sets the record for stability". 27 August 2013. Retrieved 19 January 2014.
- Bloom, B. J.; Nicholson, T. L.; Williams, J. R.; Campbell, S. L.; Bishof, M.; Zhang, X.; Zhang, W.; Bromley, S. L.; Ye, J. (22 January 2014). "An optical lattice clock with accuracy and stability at the 10−18 level". Nature. 506 (7486): 71–5. arXiv:. Bibcode:2014Natur.506...71B. doi:10.1038/nature12941. PMID 24463513.
- T.L. Nicholson; S.L. Campbell; R.B. Hutson; G.E. Marti; B.J. Bloom; R.L. McNally; W. Zhang; M.D. Barrett; M.S. Safronova; G.F. Strouse; W.L. Tew; J. Ye (21 April 2015). "Systematic evaluation of an atomic clock at 2 × 10−18 total uncertainty". Nature Communications. 6: 6896. doi:10.1038/ncomms7896. Retrieved 24 June 2015.
- JILA Scientific Communications (21 April 2015). "About Time". http://jila.colorado.edu. Retrieved 27 June 2015. External link in
- Laura Ost (21 April 2015). "Getting Better All the Time: JILA Strontium Atomic Clock Sets New Record". National Institute of Standards and Technology. Retrieved 17 October 2015.
- James Vincent (22 April 2015). "The most accurate clock ever built only loses one second every 15 billion years". The Verge. Retrieved 26 June 2015.
- N. Huntemann; C. Sanner; B. Lipphardt; Chr. Tamm; E. Peik (8 February 2016). "Single-Ion Atomic Clock with 3 × 10−18 Systematic Uncertainty". Phys. Rev. Lett. 116: 063001. doi:10.1103/PhysRevLett.116.063001. Retrieved 18 June 2016.
- "BIPM Time Coordinated Universal Time (UTC)". BIPM. Retrieved 29 December 2013.
- N. Poli; C. W. Oates; P. Gill; G. M. Tino (13 January 2014). "Optical atomic clocks". arXiv:.
- "Time for a change? Super precise optical lattice clock could 'redefine the second' and be used as a standard for the world's time". Daily Mail. 10 July 2013. Retrieved 10 July 2013.
- "BIPM work programme: Time". BIPM. Retrieved 25 June 2015.
- Helen Margolis (12 January 2014). "Timekeepers of the future". Nature Physics, Vol 10, February 2014, 82-83. doi:10.1038/nphys2834. Retrieved 31 August 2015.
- Elizabeth Gibney (2 June 2015). "Hyper-precise atomic clocks face off to redefine time - Next-generation timekeepers can only be tested against each other.". Nature. 522: 16–17. doi:10.1038/522016a. Retrieved 29 August 2015.
- McCarthy, D. D.; Seidelmann, P. K. (2009). TIME—From Earth Rotation to Atomic Physics. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA. p. 266. ISBN 978-3-527-40780-4.
- "Global Positioning System". Gps.gov. Archived from the original on 30 July 2010. Retrieved June 26, 2010.
- David W. Allan (1997). "The Science of Timekeeping" (PDF). Hewlett Packard. Archived from the original on October 12, 2012.
- "The Role of GPS in Precise Time and Frequency Dissemination" (PDF). GPSworld. July–August 1990. Retrieved April 27, 2014.
- "GPS time accurate to 100 nanoseconds". Galleon. Retrieved October 12, 2012.
- "UTC to GPS Time Correction". qps.nl.
- "NAVSTAR GPS User Equipment Introduction" (PDF). Section 1.2.2
- "Notice Advisory to Navstar Users (NANU) 2012034". GPS Operations Center. May 30, 2012. Retrieved July 2, 2012.
- "Time References in GNSS". navipedia.net.
- GLONASS Interface Control Document, Navigation radiosignal In bands L1, L2 (ICD L1, L2 GLONASS), Russian Institute of Space Device Engineering, Edition 5.1, 2008
- China Satellite Navigation Office, Version 2.0, December 2013
- Definition and Realization of the System Time of COMPASS/BeiDou Navigation Satellite System, Chunhao Han, Beijing Global Information Center,(BGIC), Beijing, China
- European GNSS (Galileo) Open Service Signal-In-Space Operational Status Definition, Issue 1.0, September 2015
- 1 The Definition and Implementation of Galileo System Time (GST). ICG-4 WG-D on GNSS time scales. Jérôme Delporte. CNES – French Space Agency.
- GNSS Timescale Description
- "ESA Adds System Time Offset to Galileo Navigation Message". insidegnss.com.
- Michael A. Lombardi, "How Accurate is a Radio Controlled Clock?, National Institute of Standards and Technology, 2010.
- What is a Cesium atom clock?
- S.R. Jefferts, T.P. Heavner, T.E. Parker and J.H. Shirley (NIST Time and Frequency Division) (2007). "NIST Cesium Fountains − Current Status and Future Prospects" (PDF). Acta Physica Polonica A. 112 (5): 759 ff. Bibcode:2007AcPPA.112..759J.
- National Research Council of Canada, archived content: Optical frequency standard based on a single trapped ion
- United States Naval Observatory Time Service Department
- PTB Braunschweig, Germany - with link in English language
- National Physical Laboratory (UK) time website
- NIST Internet Time Service (ITS): Set Your Computer Clock Via the Internet
- NIST press release about chip-scaled atomic clock
- NIST website
- Web pages on atomic clocks by The Science Museum (London)
- Optical Atomic Clock BBC, 2005
- Optical lattice clock; Journal of the Physical Society of Japan
- The atomic fountain
- National Research Council of Canada, archived content: Optical Frequency Comb – The Measurement of Optical Frequencies