Attosecond Clocks & Future of Time

A.      Introduction

1.     On 25 Feb 1991, a Patriot missile defense system malfunctioned resulting in a Scud missile hitting a US Army barrack, killing 28 soldiers and injuring around 100 other people. The Patriot System was deployed at Dhahran, Saudi Arabia, for Operation Desert Storm. It had accumulated a clock drift of nearly 343 milli-seconds over a 100 hour continuous operation. This led to a tracking error of 687 meters. The error caused the incoming Scud missile (travelling at about 1,676 meters per second) to go outside the "range gate" of the system, which declared it as false alarm. Accurate internal clocks would have prevented this from occurring. The new generation hypersonic weapons travel at about 8000 meters per second and need tracking radars to be synchronized in microseconds and nano seconds. With long deployment times and possibility of GPS denial, these systems will need extremely accurate internal clocks with very low drift over a period of time. The accuracy of these clocks can be further improved by synchronizing them with higher accuracy clocks.

2.     The field of Radars, Telecommunications, Electronic Warfare, electricity grid and navigation are inseparable from the support of high-precision time and frequency. Taking the mobile network as an example, poor accuracy of time synchronization between base stations affects inter-cell handoffs causing call drops. Synchronization error also causes interference between base stations and makes access difficult for users. Future 5G requires time synchronization accuracy in nanoseconds.

3.     More stable and portable clock designs will be a big boon to remote surgery, biological imaging, auto-driven cars, Air Traffic Management Systems, critical defense applications, space travel, telecom networks fault identification, and earthquakes as well as nuclear bomb test monitoring. Astronomers could use them to connect multiple telescopes in ways that dramatically sharpen their images which will be very helpful in search for exo-planets.

4.     The optical atomic clock represented a revolutionary step forward in the evolution of time standards. Its impact has ushered in a new era, where the motion, correlation, and rearrangement of electrons in atoms and molecules can be tracked and even controlled in real time. Such breakthrough promises, not only a deeper understanding of the physical world, such as the implications of our fundamental constants, but also has the potential to significantly advance or even replace technology as significant as our global-positioning system (GPS) with more precise system that can work inside big buildings, enable planes to land using auto pilot, enable laser based radar (LIDAR) to generate sharper 3D images, enable remotely guided unmanned vehicles (e.g., spacecraft, drones, robotic automation), allow faster transactions in financial markets and enable precise calibration of astronomical telescopes upto attoseconds needed for the detection of extra-solar planets.

B.      Emergence of Better Clocks

1.     Better clocks will be enabling tools for many scientific and technical applications. They can extend the frontiers of precision spectroscopy as well as of time and frequency metrology. They will make it possible to precisely synchronize clocks over large distances. In astronomy, such synchronized clocks may allow an extension of large baseline interferometry to infrared and optical wavelengths. Better clocks can improve the performance of remotely piloted aerial/ ground vehicles and the tracking of probes in deep space. Accurate clocks are also needed to synchronize emerging telecommunication networks as the bandwidth increases and latency requirements become more stringent. In fundamental physics, more accurate clocks will permit more rigorous tests of special and general relativity, as well as other fundamental laws.

2.     Scientists have demonstrated the world’s most accurate clock with a total uncertainty of 2 parts in 10^18 , or about 10,000 times better than GPS clocks. This means that if the clock began ticking at the Big Bang nearly 14 billion years ago it would be accurate to better than one second today. These clocks will enable identification of variations in sensitive limits of fundamental constant. The perfection of optical frequency standards has progressed at a rapid pace and the femtosecond laser comb provides a perfect clockwork mechanism.

3.     The technological advances that result from creating such a device are benefiting other fields of technology. Stable lasers evolved as part of the optical clocks can be used to watch chemical reactions in the atmosphere. They can also be used to monitor people’s breath to see if someone’s sick. Extreme timing precision will push forward the world of quantum computing.

C.      Standard Clocks

C.1.         Crystal Oscillators

• A wide temperature range crystal oscillator has a typical f vs. T stability of ~10 to 50 ppm. A Temperature Controlled Crystal Oscillator (TCXO) can reduce that to ~1 ppm or 10^-6. An Oven Controlled Crystal Oscillator (OCXO) can enhance that stability to 1 x 10^-8 or better (but at the cost of much higher power consumption). High-end (SC-cut) OCXOs can stay within 1 x 10^-10 over a wide temperature range.

C.2.         Atomic Clocks

• Since they were first created in the mid-twentieth century, atomic clocks have been the gold standard of timekeeping. All of the primary standard clocks up until now utilize microwave resonance in cesium-133. Inside a cesium beam clock, an oven heats the metal until atoms boil off. These hot particles zip through the microwave cavity at various speeds and angles. The cesium atoms shed their energy by giving off their own microwaves at 9,192,631,770 cycles per second. These microwaves hit a detector, which reads their frequency as “ticks” marking fractions of a second.
•  This method of keeping time with atomic clocks has been refined over the last fifty years to the point that the most accurate clock in the world will only deviate by a second over 200 million years, but the basic principles have remained the same.
• An atomic clock aboard a GPS satellite can develop an error of up to 10 nanoseconds every 24 hours. Without regularly communicating with each other, clocks onboard GPS satellites would gradually desynchronize, resulting in a decrease of precision when triangulating someone's position. At a rate of roughly a foot per nanosecond of error, it would take only a few weeks before Google Maps could no longer tell Main Street from the highway.

C.3.         Nuclear Clocks

• Since protons and neutrons are densely packed in the nucleus and are thus less likely to be disturbed by outside influences, researchers think the nucleus could serve as the basis for an ultra-precise atomic clock in the future. The transitions a nucleus occur at much higher frequencies than electron transitions, which would allow for even more precise measurements of time.
• The difficulty with nuclear excitations, however, is that they require much higher energy levels than electron energy transitions because their protons and neutrons are more densely packed. Exciting an atom’s nucleus requires energy in the x-ray range, where frequencies range from 30 petahertz to 30 exahertz. This high energy requirement was thought to make atomic clocks based on nuclear transitions infeasible.
• According to new research, it should be possible to excite the nucleus of thorium-229 using ultraviolet light. The correct frequency to transition a thorium-229 nucleus from a ground state to an excited state, is still not identified. Simulations show that a thorium-229 nuclei could be excited as result of alpha decay in uranium-233.

C.4.         Chip Scale Atomic Clock (CSAC)

• By using Chip Scale Atomic Clocks (CSAC), developed in part with the Defense Advanced Research Projects Agency (DARPA), a wealth of opportunities open up. Using CSACs, military patrols can travel on foot and still carry backpack-sized jammers that prevent radio-controlled improvised explosive devices from detonating. They can also be used by the military to enable UAVs (“drones”) to fly farther and longer without getting lost if they lose a GPS signal, or if that signal is jammed. A highly stable internal oscillator bridges periods of interference or temporary loss of synchronization with minimal loss of accuracy. Military radios can use it to derive very precise timing to divide up frequencies and create secure channels.
• Soldiers operate inside buildings, they may have to wait minutes to reconnect to GPS satellites to acquire the precise time signal used to synchronize secure communications. A stable internal clock can enable the radios to stay synchronized, and re-acquire an encrypted signal in seconds.
• Stable internal clocks also enhance the discovery of underwater oil and mineral deposits. When a ship surveys the sea floor, it drops an array of sensors with stable clocks and use a technique called reflection seismology. The sensors map underground formations by tracking how long it takes for a sonic pulse to travel through the ocean floor, creating a three-dimensional map of potential oil and gas deposits. For the maps to be accurate, sensor synchronization must be precise. As sensor nets are deployed over wider areas and left unattended for longer periods (with no access to GPS under water), the need for accurate clocks and reduced battery drain becomes important.

D.      Optical Clocks

1.     Atomic clocks “tick” with the oscillations of an electromagnetic wave whose frequency is locked to that of an atomic transition. The superiority of optical clocks over microwave cesium clocks is due to the much higher tick rate of optical waves compared with microwaves. Optical clocks can outperform cesium standards in both fractional-frequency stability and accuracy by up to 2 orders of magnitude.

2.     Optical clock development needed a method for counting high optical frequencies (several hundreds of terahertz in the infrared/visible domains). Advances in the field of high speed laser technology and invention of the frequency combs have enabled the possibility to count the frequency by comparing it to countable microwave frequencies. In 2014, the world’s most accurate optical clock was built at the University of Colorado at Boulder. It will not lose or gain one second in the entire age of the universe. The clock is so precise, that out of every 10 quintillion ticks only 3.5 would be out of sync. Its jitter is in femtosecond range.

3.     An optical clock has three predominant components. The first is an extremely steady “reference” frequency supplied by a optical absorption line in an atom or ion. This “clock transition” will typically have a natural line width of a few hertz or less. The second component is a feedback system (a laser, known as a “local oscillator”) that "binds" the output of a laser to the reference frequency. The third key element of an optical clock offers a very accurate means to measure the frequency of the laser emitted by the trapped atom, typically a “femtosecond comb”.

D.1.         Frequency Reference

•  Critical to the performance of an optical clock is the first element – the clock transition. This needs to be as narrow as possible to make the clock stable. Its frequency should be unaffected by external perturbations such as electric and magnetic fields so that the clock is as accurate as possible. The ideal frequency reference would be a single, motionless atom, unperturbed by any interactions with other atoms or the environment. We can come fairly close to this utopia by trapping a single ion in the tiny gap between the electrodes of an electromagnetic trap (figure 1). This trapping allows the ion to be laser-cooled to a temperature of about 1 mK and be confined to a region of space just a few tens of nanometres across. The clock transition is therefore not broadened by the effects of temperature or motion.
• To probe the clock transition one needs a highly monochromatic laser, which can be achieved by stabilizing the laser frequency to a mode of an environmentally isolated low-drift optical reference cavity. Lasers with line widths that are less than 1 Hz have been achieved.
• Unfortunately, it is not easy to monitor the light being absorbed because narrow transitions are intrinsically very weak. The solution lies with a technique developed by the Nobel laureate Hans Dehmelt, which enables the absorption to be detected with almost 100% efficiency. Known as “electron shelving”, the technique is based on the fact that when the ion absorbs the probe light, it jumps to a long-lived excited state, where it remains for about a second. During this time, the ion cannot be laser-cooled – the process where the ion repeatedly jumps between its ground state and a short-lived excited state, absorbing and re-emitting photons at the cooling wavelength.
• The upshot is that when the ion is “shelved” in the long-lived excited state, no fluorescence photons from the cooling transition are emitted. The absence or presence of this fluorescence tells us whether the probe light has driven the ion to the long-lived state or not. By measuring the probability of the ion jumping to the long-lived state as a function of the frequency of the probe laser, we can observe the narrow spectral profile of the clock transition. The frequency of the laser light can then be stabilized to the centre of this profile, where the transition probability is at a maximum.
• To make certain this absorption occurs, the Strontium/ ytterbium atom is sequestered in a vacuum chamber and cooled to almost absolute zero by creating an 'optical lattice' using red laser beams with "magic wavelength”. This prompts the atom to switch between energy levels, "ticking" 430 trillion times per second. Light is absorbed and reemitted during these tick events, in a manner that reduces its kinetic energy. The clock parts have to be cooled to about -180 degrees Celsius using a special refrigerator, and the insides have to be coated in black to cancel reflections from the light seeping in.

D.2.         Local Oscillator Laser

• The second component of the Optical Clock is the laser based local oscillator. Cavity-stabilized laser systems are a key enabling technology for optical frequency standards and precision measurement. They are limited by fundamental mirror substrate and coating thermal noise. The optical cavity must have sufficiently good short-term stability to permit interrogation of a narrow spectroscopic feature in the quantum reference (i.e., ion, atom, or molecule) with a good Signal to Noise ratio. In the case of the single Strontium atom, the optical transition line width is 2.1 Hz wide (ytterbium atom has a line width of 1 Hz), which requires a local oscillator with a sub-hertz line width resolution. Significant effort has been invested for the reduction of the laser line width down to sub-hertz level. A key aspect in this development has been improved techniques for the mechanical and thermal isolation of the Fabry-Perot optical cavity from the surrounding laboratory environment. A more recent advance in this evolution focuses on reducing the acceleration sensitivity of the cavity through geometrical design and by careful choice of how the cavity is supported.
• For an optical clock, the local oscillator is comprised of a continuous wave (cw) laser that has its emission spectrum narrowed and stabilized to an isolated high-Q Fabry-Perot optical cavity.

D.3.         Frequency Combs

• The third component of the optical clock is the frequency comb. J. Hall and his colleagues developed methods to stabilize mode-locked femtosecond-lasers to such a high degree that they could play the role of a frequency divider. The comb could be used to connect optical frequencies both to other parts of the optical spectrum and to the microwave domain. For this pioneering work, the 2005 Nobel Prize in Physics was awarded to Profs. Ted H?nsch and John Hall.
• Until the late 1990s, ultra-short pulses from mode-locked lasers were know to have unstable underlying carrier frequency and/ or phase. Ultrafast pulse-trains with repetition frequencies of 1 GHz and higher were needed for sampling or exciting high-speed or transient events and making precision measurements across octaves of bandwidth. Simultaneously creating broad spectral coverage, low-noise performance, and timing synchronization into the femtosecond domain and below was a challenge. With improving laser technology through the 1980s and 90s (e.g. shorter pulse laser systems, reduced technical noise, lower noise pump lasers), researchers began to address this question.
• The technique required a laser spectrum that spanned an optical octave (i.e., a frequency comb bandwidth so broad that, if the frequency of the lowest comb components were doubled, they would overlap with those at the higher frequencies). When these doubled frequency components are mixed with the higher frequency components from the same comb, their difference frequency (beat frequency) would be exactly equal to “carrier-envelope offset” (CEO)
• The basic idea behind the frequency comb is the result of the Fourier transform relationship, which relates a signal measured in time to its corresponding frequency distribution.
• Now consider a single light pulse of 2.1 femtosecond duration with a carrier frequency of 474 x 10^12 Hz (474 THz), or a “red” wavelength of 633nm. The corresponding Fourier Transformed frequency spectrum for this pulse is still cantered at 474 THz, but due to the short pulse envelope, the spectrum is very broad.
• Now consider the pair of identical pulses with a time delay between them that is exactly 13 periods of the carrier frequency. Each pulse individually has the same spectral amplitude, however, as one pulse is delayed in time relative to the other, there will be a linear phase shift across the spectrum of the second pulse. The spectral components from each pulse will constructively interfere only when this relative phase shift is an integer multiple.
• Further, instead of a pulse pair we consider an infinite train of equally spaced pulses, the constructive interference peaks will simply become sharper and sharper until each resembles a narrow frequency (of a few Hz) similar to that of a highly monochromatic cw laser used to excite an atomic or molecular transition. We can now compare the frequency of the cw laser with that of a single “tooth” of the femtosecond frequency comb, that is nearest to the superimposed cw laser. The frequency of that comb tooth can be determined by comparing the pulse repetition rate (which is in GHz) with a standard electronic counter based on atomic clock.
•  As long as the teeths of the frequency comb are stable, the measured microwave signal will remain phase coherent with the optical signal.

E.      Applications

E.1.         Telecom Synchronization Needs

• A high quality, stable clock will transform a network that experiences problems 2-3 times a day to a network that maintains timing even through major slips or outages. While there can be some circuit interruptions, a clock system provides a stable frequency source during times of circuit impairments. Connected equipment is not effected until the clock holdover drift results in a slip.
• The frequency-synchronization network supporting time synchronization consists of a primary reference clock (PRC)—a frequency-reference device—and a synchronous Ethernet equipment clock (EEC), which synchronizes and distributes frequency by SyncE. Asynchronous Ethernet switch transmits with an accuracy of ±100ppm, whereas SyncE has an accuracy of ±4.6 ppm. Network wide time synchronization is done using Network Time Protocol (NTP) with accuracy of 5-100 msec or Precision Time Protocol (PTP) with accuracy of upto 100 nsec. In addition, the synchronization-network management system monitors and controls these time- and frequency-synchronization devices.
• TD-LTE (time-division duplexing LTE) requires time-synchronization accuracy of 3 μs. High precision, a minimum of 65 ns is required as a relative time error for carrier aggregation technologies. Strict latency is one of the main targets for some of the applications that need to be supported by 5G, such as automatic traffic control, remote surgery and tactile internet. In this respect, 5G systems should provide end-to-end latency of 1 ms which needs the network to be synchronized down to nano-seconds.
• Time-stamping systems are also required to be enhanced to meet the synchronization needs. When the internal clock frequency of a device is 125 MHz (Ethernet Phy), the error of one time-stamp becomes about 8 nanosecond. This is required to be reduced to sub-nanoseconds. These systems will require highly accurate internal clocks with low jitter and drift.

E.2.         Very Fast Frequency Hopping Radio

• With the availability of fast spectrum analyzers and synthesizers, it is possible to jam frequency hopping systems. If a jammer is fast enough, it can detect the frequency of transmission and tune the jammer to that frequency well before the radio hops to the next frequency. However, with a good enough clock, it is possible to defeat such “follower” jamming.
• Because radio waves travel at the speed of light, the propagation delays are 3.3 μs per km. If the hopping rate is fast enough for the propagation delay difference to be greater than 1/hop-rate, i.e., if the radios can hop to the next frequency before the jamming signal reaches the receiver, then the radios are jamming-proof (for follower jammers). The propagation delays imply that for two radios communicating at a distance of 1 Km (~3.3 μs) and the jammer located 5 Km (~16.5 μs) from each radio respectively, would require a round trip delay of about 30 μs. Since the clock accuracies required by frequency hopping systems are usually 10% to 20% of message duration, the allowed clock error is about 6 μs. Such a system will require internal clock stability of 4x 10^-10 if resynch happens in 4 hours.

E.3.         Identify Friend or Foe

• In a modern battle, when the sky is filled with friendly and enemy aircrafts, and a variety of advanced weapons are ready to fire from both ground and airborne platforms, positive identification of friend and foe is critically important. Fratricide due to identification errors has been a major problem. Current IFF systems use an interrogation/ response method which employs cryptographically encoded spread spectrum signals. The interrogation signal received by a friend is supposed to result in the "correct" code being automatically sent back via a transponder on the friendly platform. The "correct" code must change frequently to prevent a foe from recording and transmitting that code ("repeat jamming"), thereby appearing as a friend.
• The code is changed at the end of what is called the code validity interval (CVI). The better the internal clock accuracy, the shorter can be the CVI. This will make the system more resistant to repeat jamming. More accurate internal clocks will also enable longer autonomy period for users to resynchronize their clocks during a mission.

E.4.         Bistatic Radar

• Conventional (i.e., "monostatic") radar, in which the illuminator and receiver are on the same platform, is vulnerable to a variety of countermeasures. Bistatic radar have the illuminator and receiver widely separated. This greatly reduces the vulnerability to jamming and antiradiation weapons, and can increase slow moving target detection and identification capability via "clutter tuning”mode. In this mode the receiver maneuvers so that its motion compensates for the motion of the illuminator, creating zero Doppler shift for the area being searched.
• The transmitter can remain far from the battle area, in a "sanctuary." The receiver can remain "quiet”. In this deployment, the timing and phase coherence problems can be orders of magnitude more severe, especially when the platforms are moving. The reference oscillators must remain synchronized and syntonized during a mission so that the receiver knows when the transmitter emits each pulse, and the phase variations will be small enough to allow a satisfactory image to be formed. Low noise crystal oscillators are required for short term stability; atomic frequency standards are often required for long term stability.

E.5.         Electronic Warfare

• The ability to locate radio and radar emitters is important in modern warfare. One method of locating emitters is to measure the time difference of arrival of the same signal at widely separated locations. Emitter location by means of this method depends on the availability of highly accurate clocks, and on highly accurate methods of synchronizing clocks that are widely separated. Since electromagnetic waves travel at the speed of light, 30 cm per nanosecond, the clocks of emitter locating systems must be kept synchronized to within nanoseconds in order to locate emitters with high accuracy. Multipath and the geometrical arrangement of emitter locators usually results in a dilution of precision. Without resynchronization, even the best available militarized atomic clocks can maintain such accuracies for periods of only a few hours.
• With the availability of GPS and using the "GPS common view" method of time transfer, widely separated clocks can be synchronized to better than 10 ns (assuming that GPS is not jammed). An even more accurate method of synchronization is "two-way time transfer via communication satellites," which, by means of very small aperture terminals (VSATs) and pseudonoise modems, can attain subnanosecond time transfer accuracies.
• Another important application for low-noise frequency sources is the ELINT (ELectronic INTelligence) receiver. These receivers are used to search a broad range of frequencies for signals that may be emitted by a potential adversary. The frequency source must be as noise free as possible so as not to obscure weak incoming signals. The frequency source must also be extremely stable and accurate in order to allow accurate measurement of the incoming signal's characteristics.

E.6.         Electricity Grid

• Timing in electric substations is becoming more important as more technologies and control schemes become available that rely on accurate time. The grid needs to establish a highly accurate and highly redundant/available substation timing architecture.
• Resolution and precision requirements of the electricity grid is 1 ms for events and faults in substation synchronization. It also requires 1 kilo Pulse Per Second with 250 ns precision in synchrophasor relays for time stamped voltage or current vectors. Traveling wave fault location uses precise time (accurate to within 0.1 μs) to measure high frequency waves generated by faults on transmission lines. Wavefront arrival time is used to calculate fault location to within 500 feet or less.
• Power grids are moving towards better devices and architecture that ensure high accuracy and high availability of precise timing sources.

E.7.         GPS

• The GPS constellation comprises 24 Earth-orbiting satellites, which transmit radio signals that consist of the satellite's position and the time it transmitted the signal. The distance between a satellite and a receiver can be computed by subtracting the time that the signal left the satellite from the time that it arrives at the receiver. If the distance to four or more satellites is measured, then a three-dimensional position on Earth can be determined. GPS positioning capability is provided at no cost to civilian and commercial users worldwide at an accuracy level of 28 m. This accuracy level is known as the standard positioning service (SPS).
• GPS time is theoretically accurate to about 14 nanoseconds. However, most receivers lose accuracy in the interpretation of the signals and are only accurate to 100 nanoseconds. The absolute timing accuracy specification for the GPS SPS is 340 nanoseconds relative to UTC. The U.S. military and its allies, and a select number of other authorized users, receive a specified accuracy level known as the precise positioning service (PPS) that is protected against jamming and is also encrypted.
• GPS is not perfect. Sometimes we lose GPS signal when traveling through tunnels, and sometimes the signal is not nearly as accurate as it should be. For position accuracy to 10 meters, the clock accuracy has to be roughly 10^-8 of a second. A 1-nanosecond error in time equates to an error of approximately 30 centimeters.
• Upcoming technologies such as self-driving cars will probably rely upon a combination of local sensing and GPS signals to navigate independently without incident. So any improvement in GPS accuracy would be hugely advantageous in speeding up and rolling out the era of the autonomous car.
• Clocks are the main instruments required for navigation with satellites. Highly stable and accurate satellite clocks present a large potential for improvements of user positions in real-time. If clocks are stable enough such that epoch-wise clock synchronisation is no longer required for precise positioning involving carrier phase, precise point positioning in real-time becomes possible using only broadcast information from the satellite itself.
• It is, however, necessary to control other error sources such as propagation delays, orbit errors or relativistic corrections at a similar quality level. A large variety of applications could profit from such improved space infrastructure, ranging from precise navigation, e.g., for automatic navigation of ships in ports without reference station installations, tsunami warning systems with sensors at remote locations, space applications such as docking manoeuvres, and finally, distribution of atomic time and a high-precision frequency standard from space.

E.8.         Other Navigation Systems

• Galileo, Europe's own global satellite navigation system, will have 24 satellites plus spares in Medium Earth Orbit (MEO) at an altitude of 23222 kilometres. Eight active satellites will occupy each of three orbital planes inclined at an angle of 56° to the equator. Galileo’s highly-accurate clocks are at the heart of the system. Each satellite emits a signal containing the time it was transmitted and the satellite’s orbital position. Because the speed of light is known, the time it takes for the signal to reach a ground-based receiver can be used to calculate the distance from the satellite. Combined inputs from several satellites simultaneously will pinpoint the receiver’s place in the world.
• Galileo’s passive hydrogen maser clock is made of an atomic resonator. Another clock deployed is the smaller, simpler rubidium clock, with gaseous rubidium atoms released into a vapour cell inside an atomic resonator. Both Galileo’s atomic clocks are very stable over a few hours. It offers a time accuracy of 30 nanoseconds and location accuracy of 1 m for unencrypted and 1 cm for encrypted.
• There are similar systems in place by Russia (GLONASS, time accuracy of 100 nanoseconds and location accuracy of 8 m) and China (COMPASS, time accuracy of 10 nanosecond and location accuracy of 10 m).
• Indian satellite navigation system called Indian Regional Navigation Satellite System (IRNSS) has 7 satellites in orbit and aims to offer a time accuracy of  2 nanoseconds and location accuracy of 10 m for public and 1 m for military.

E.9.         Very Long Baseline Interferometry (VLBI)

• One of the most enabling techniques in radio astronomy is Very Long Baseline Interferometry (VLBI), which is based on the simultaneous observation of a radio sky with many antennas on the Earth surface. Correlation of the signals detected by distant antennas improves the angular resolution of the observations with respect to the single antenna. The magnification equals the ratio of the baseline, i.e. the distance between two antennas, and the single antenna dish diameter, when they are expressed in number of wavelengths of the VLBI receiving frequency, which determines the theoretically ultimate achievable resolution. It usually ranges from 10^4 to 10^6. VLBI is a powerful technique in many fields, from the study of compact radio sources to spectroscopy of the interstellar medium, which may disclose important findings in fundamental physics and in the search for dark matter. In addition, it is one of the most reliable techniques for Earth sciences, enabling, for instance, a better modelling of the Earth surface, of the atmosphere, of climate changes.
• The signals of interest in VLBI range from 100 MHz to 300 GHz: the correlation of signals from distant antennas starts with down-conversion and sampling at each telescope.
• If we use an observing frequency of 10 GHz and want to keep the phase coherent to ~10 degrees (out of the 360 degrees) after 1000 seconds integration then there is a need 10 / (360 * 10 * 10^9 * 1 x 10^3) or a clock stability of about 2.8 x 10^-15. Higher frequencies and longer durations will be even more demanding.
• Currently, astronomy and radio astronomy deal with new observables like: fast radio bursts, extremely high-stability millisecond pulsars and in general a new class of experimental evidences of a very fast transient Universe. Even the recent detection of gravitational waves imposes to perform direct comparisons of atomic and astronomical observables, at an equivalent level of uncertainty, to get independent verifications and deeper insights into the fundamental physical properties of the Universe. All these challenges require a much higher level of timing resolution both at short and long timescales. The mm-level positioning requires delay precision of a few picoseconds (3 ps = 1 mm).
• With better clocks, radio astronomy can achieve the angular resolution needed to investigate compact radio sources or can directly study molecular emissions from the interstellar medium.

E.10.      Gravity Potential Measurement

• According to Einstein's theory of relativity, the passage of time changes in a gravitational field. On Earth, raising a clock by 1 cm increases its apparent tick rate by 1.1 parts in 10^18, allowing chronometric levelling through comparison of optical clocks. Clocks at the top of Mount Everest pull ahead of those at sea level by about 30 microseconds a year. Raising a clock 10 centimeters will change its rate by one part in 10^17. A frequency shift of 10^17 corresponds to a time dilation due to walking speed.
• The gravity potential (geopotential) difference is measured by remote comparison of two precise optical clocks via optical fiber frequency transfer. After synchronization, the signal’s frequency shift is measured based upon the comparison of bidirectional frequency signals from two oscillators connected with two optical atomic clocks via remote optical fiber frequency transfer technique.
• This required transportable optical clocks. Designing optical clocks that are robust enough to operate in the field, as opposed to in the lab, is a significant challenge, particularly because they are generally very sensitive to vibrations and temperature fluctuations in the environment.

E.11.      Search for Extra-Solar Planets

• Searches for extra-solar planets is currently done via the radial velocity method, with a night-to-night relative precisions better than 1 m/s from stellar absorption lines integrated over wavelength ranges of ～100 to 300 nm. Higher precision ?10 cm/s, stable over many-year time-scales is required for detecting Earth-mass extra-solar planets around solar-mass stars.
• This can be achieved by using femtosecond-pulsed mode-locked lasers. Simulations of frequency comb spectra show that the photon-limited wavelength calibration precision achievable with existing echelle spectrographs should be ～1 cm/s when integrated over a 400 nm range. The typical photon-limited precision of ～1 cm/ s is five orders of magnitude smaller than the typical pixel size, which is 15-μm. This corresponds approximately to the size of the silicon atoms making up the charge-coupled device (CCD) substrate.
• The frequency comb will require a pulse repetition rates of 5–30 GHz (current technology supports 1 GHz), given the typical resolving power of existing and possible future spectrographs. Achieving such high repetition rates, represents a significant challenge in the design of a practical system.

E.12.      Measurement of Fundamental Constants

• In the Standard Model, the fine-structure constant is immutable throughout eternity. But in some competing theories (such as certain string theories), alpha could waver slightly or grow as time goes by. In August 2001 a group of astronomers reported preliminary evidence that alpha may have increased by one part in 10,000 during the past six billion years. But the evidence is equivocal, and the question is a hard one to settle. By comparing rubidium clocks to those based on cesium and other elements, scientists may be able to lower the limit on possible alpha fluctuations by a factor of 20.
• An optical clock, as a very precise device, is a very convenient system to test the fundamental postulates of physics. Unification theories beyond the Standard Model propose a possibility of temporal variations of fundamental constants in the expanding Universe.

E.13.      Dark Matter

• Dark matter, together with dark energy, is one of the mysterious problems of science. Observations of gravitational effects on the galaxy scale suggest the existence of dark matter. Rotating galaxies should have shattered a long time ago as their gravity alone cannot hold matter with such velocities. It seems that galaxies have some extra yet undetected mass (dark matter) that helps them to withstand as galaxies.
• It is generally assumed that dark matter is a scalar field which is coupled with general relativity. This scalar field should oscillate and therefore can induce corresponding harmonic variations of the fine structure constant αEM , the mass of fermions mfer and the quantum chromodynamic mass scale. By long-term observations of the locally measured frequency ratio of atomic transitions, it should be possible to observe these oscillations or obtain constraints on the coupling between the dark matter scalar field and the standard matter. Because clocks can be compared locally, a network of clocks used to detect the dark matter, does not need to be connected by phase coherent links but just synchronized like gravitational wave detectors.

E.14.      Special Relativity Theory

• Einstein’s relativity theory changed our understanding of space, time, energy and mass. Einstein based his theory on two tenets. First, the laws of physics are the same for all non-accelerating observers. Second the speed of light has a defined and finite value c which is independent of the motions of observers. He has shown that space and time are coupled that they can be treated as a continuum - space-time. One of the embodiments of Einstein’s theory is the time dilation. It means that clocks do not tick at the same rate for all observers. In special relativity theory, a moving clock runs more slowly with respect to an inertial frame of observation.
• Transporting "perfect" clocks slowly around the surface of the earth along the equator yields ?t = -207 ns eastward and ?t = +207 ns westward (portable clock is late eastward). The effect is due to the earth's rotation. At latitude 40 degree, for example, the rate of a clock will change by 1.091 x 10^-13 per kilometer above sea level. Moving a clock from sea level to 1km elevation makes it gain 9.4 nsec/ day at that latitude. Spacecraft Examples:
• For a space shuttle in a 325 km orbit, ?t = tspace - tground = -25 μsec/day
• For GPS satellites (12 hr period circular orbits), ?t = +38.5 μsec/day

F.      Clocks of the Future

1.     When we speak of “Future Clocks” there are two trends that bear watching. The first is that atomic clocks are evolving from being based on microwave technology to being based on state-of-the-art optical technology. This exploration will continue to lead us to unexpected discoveries and novel advances in science and technology. The second is that atomic clocks are evolving from being large devices, to also being microminiaturized, and hence ubiquitous. The improvements that they can enable in GPS user equipment stands out as “low hanging fruit.” However, we also foresee an upcoming era of innovation where this technology will find additional uses in everyday life.

2.     The remarkable progress of optical clocks has not kept scientists from seeking what might be the next breakthrough in atomic clock technology. The clear path forward would be to base new clocks on atomic transitions with higher frequencies and smaller inherent environmental sensitivities.

G.     Conclusion

1.     A hundred years ago today, Einstein’s theory of gravity was first put to the test when Arthur Eddington observed light “bending” around the sun during a solar eclipse. A century later, scientists are still searching for the limits of the theory. The theory of relativity describes our universe on the large scale, but on the border with the infinitesimally small scale the theory does not jibe and it remains inconsistent with quantum mechanics. Today’s attempts at unifying general relativity and quantum mechanics predict violations of the Einstein’s equivalence principle.

2.     It is interesting to look at the historical evolution of the accuracy of clocks. The clocks in medieval church towers were only good to about 20 min per day. In the 18th century, the nautical clock H4 of the legendary watchmaker John Harrison reached an accuracy of some 100 ms per day. A stable crystal oscillator with a ±0.0000005% (5ppb) drift would deviate by ±432 nanoseconds per day. The best primary cesium fountain clocks of today can be accurate to within 100 ps per day. Optical Clocks could eventually reach 10^-19 total (statistical and systematic) uncertainty, which translates to mm level geodetic accuracy.

3.     It is expected that the most powerful applications will lie in fields that have traditionally exploited precision clocks, such as navigation, communications, and signal synchronization and timing. Given their high performance level, these clocks will probably be used in more extreme cases such as deep-space navigation and ultra-low noise secure communications. The world’s quietest microwave signals are now generated from down-converted optical signals, and referenced optical frequency combs are used for precision calibration of astronomical spectrographs in searches for exo-planets.

4.     The trend of technology evolution plays a very important role to understand how and why products evolve over time and define strategies of further improvements of products. If the history of ticks and tocks tells us anything, it is that each new advance has fired other revolutions – from sea-faring to GPS and mobile telephones. Let us hope that the optical clocks are similarly revolutionary.