1. Optical Clocks for Fundamental Physics in Space
Presentation of some of the ideas we have for potential mission opportunities for fundamental physics tests using optical clocks.
Helen Margolis, Hugh Klein and Patrick Gill
National Physical Laboratory
GAUGE meeting, RAL, 14th November 2006

2. Recent improvements in optical frequency standards
Atomic timekeeping began just over fifty years ago with the development of the first Cs clock by Louis Essen at NPL.
That had an accuracy of about 1 part in 1010, and led to a redefinition of the second in terms of the caesium ground state hyperfine transition frequency in 1967.
Since then the performance of caesium atomic clocks has improved by more than five orders of magnitude, with the best caesium fountain clocks now being accurate to better than 1 part in 1015.
However there has recently been a very rapid improvement in the performance of optical standards, particularly as a result of the development of the femtosecond optical frequency comb technique for measuring optical frequencies.
We have now reached the stage where the best frequency measurements of optical standards are limited by the current definition of the second (and hence frequency).
Further improvement in optical standards is very likely, and indeed long term stability at the parts in 1017 level has already been demonstrated at NIST by comparison of their mercury ion and aluminium ion optical frequency standards.

3. + Optical clocks f 1   f (S/N) instability
So why do optical clocks offer the promise of such exceptional performance?
All other factors being equal, the stability of an atomic clock is proportional to the operating frequency f and inversely proportional to the linewidth f.
This is more typically expressed in terms of the fractional frequency instability , whih also depends on the signal to noise with which the absorption signal is measured. A high stability corresponds to a smaller value of .
Optical frequencies are around 105 times higher than microwave frequencies, and the linewidth-limiting processes in the two domains are similar.
This means that optical frequencies can have Q-factors (the ratio of the transition frequency to the linewidth of 1015 or even higher.
Thus we can see that basing a standard on a transition in the optical rather than the microwave region of the spectrum could in principle lead to n enormous improvement in stability.
So how do you make an optical clock? Well, any clock needs three basic components.
The first of these is some kind of oscillator. In the case of an optical clock this is an ultra-stable laser.
The second is some kind of reference to which the oscillator can be stabilised. This might be either a single laser-cooled ion in an electromagnetic trap, or a collection of cold atoms trapped in an optical lattice. At NPL we are working on two trapped ion optical frequency standards, based on strontium and ytterbium ions, and we have also just begun a project to develop an optical lattice clock.
The third component of the clock is some kind of counter to count the oscillations of the oscillator. Microwave frequencies can be counted directly by electronic means, but for optical frequencies we use a femtosecond optical frequency comb.
Oscillator (Ultra-stable laser)
Counter (Femtosecond comb)
Reference (narrow optical transition in an atom or ion)

4. ESA studies
Optical frequency synthesizer for space-borne optical frequency metrology
18 months (February 2006 – July 2007)
Feasibility and applications of optical clocks as frequency and time references in ESA deep space stations
12 months (July 2006 – June 2007)
Absolute long-distance measurement with (sub)-micrometre accuracy for formation flight applications
15 months (October 2006 – December 2007)
ESA have recognised the potential of this optical clock technology, and at NPL we are currently involved in three separate study projects for them. We are the prime contractor for the first two of these, and a subcontractor on the third.
The main focus of the first study is to look at the issues associated with transferring the femtosecond optical frequency comb technology to a space environment, and to look at the potential applications of such technology across a range of ESA directorates including fundamental science, satellite navigation, telecommunications and earth observation. One very obvious application is in optical clocks in space, and the last parts of the study focus on this aspect.
The second study is looking at the potential of optical clocks to replace and improve upon the current clocks used to provide frequency and time references in ESA ground stations used for deep space navigation. It is also concerned with the problems of time and frequency distribution both within the ground station and between the ground and the spacecraft.
The final study, which has just begun and is being led by Menlo Systems, is looking at a very specific application of the femtosecond comb technology – to make high accuracy absolute long distance measurements for formation flying applications, with particular emphasis on the Darwin and Xeus missions.

5. Cosmic Vision
For the rest of the presentation I have drawn heavily on material supplied to me by Stephan Schiller, who in collaboration with a number of other scientists around Europe has developed a proposal for a gravity explorer satellite mission using optical clocks.
More details can be found in this paper on the Los Alamos preprint server – I just want to outline a few of the ideas here.
S. Schiller, A. Görlitz, J. Koelemeij, B. Roth, A. Nevsky, A. Wicht, U. Düsseldorf
G.Tino, N. Poli, R.E. Drullinger, U. Firenze/LENS
P. Lemonde, LNE-SYRTE Paris U. Sterr, F. Riehle, E. Peik, C. Tamm, PTB Braunschweig C. Salomon, ENS Paris P. Gill, H. Klein, H. Margolis, NPL Teddington
G. Mileti, Obs. Neuchatel
R. Holzwarth, T. Hänsch, MPQ Munich
E. Rasel, W. Ertmer, U. Hannover
H. Dittus, C. Lämmerzahl, ZARM Bremen
A. Peters, H.U. Berlin
E. Samain, Obs. Cote d‘Azur
L. Iorio U. Bari, I. Ciufolini, U. Lecce
S.Schiller et al. arxiv:gr-qc/

6. Mission scope Explore gravity:
Fundamental physics: - high precision tests of fundamental aspects of General Relativity - search for new physics
Geophysics: gravity field and elevation mapping - clock comparison measures difference in U - map out U using movable clocks
Time and frequency distribution on earth and in space (“master clock”):
Terrestrial use of optical clocks requires a reference clock in a well-defined potential U/U = 10-9 (corresponds to h = 1 cm) results in / = 10-18
Precision navigation in space
Space VBLI
Optical link between different clocks
The proposals fall within the ESA Cosmic Vision framework, with the principal aim being to use optical clocks to explore gravity – both fundamental physics aspects and geophysics.
In terms of fundamental physics, one of the most exciting possibilities is to test Einstein’s prediction of the gravitation redshift with extremely high accuracy.
In terms of geophysics, a satellite-borne optical clock would allow very precise mapping of the earth’s gravity field by frequency comparison of transportable terrestrial clocks with the space clock.
The proposed mission would also have significant benefits to time and frequency metrology and the distribution of clock signals. Earth-based operation of optical clocks will ultimately be limited by uncertainties in the value of the gravitational potential at the clock’s locations and in their relative velocity. For example, an uncertainty of 1 cm in the elevation of a clock or an uncertainty in relative velocity of 1 cm / year corresponds to an uncertainty of 1 part in 1018 of the clock transition frequency. For applications requiring the highest time and frequency accuracy it is therefore essential to operate optical clocks in space, where the above effects can be determined with sufficient accuracy by continuously measuring the orbit parameters. An earth-orbiting master clock could be used for a range of applications including the distribution of time and frequency signals on earth and in space and precision spacecraft navigation.
Slide material courtesy of Stephan Schiller

7. Mission scenario Orbital phase I Orbital phase II
Clock ensemble n1 n2 n0
Orbital phase I
Highly elliptic orbit, ~ 1 year duration
Test of Local Position Invariance and gravitational redshift
Orbital phase II
Geostationary, several years duration
Master clock for earth and space users
Geophysics
As currently envisaged, the mission would consist of two different orbital phases.
In the first, lasting approximately 1 year, the satellite would be launched into a highly elliptical orbit for tests of fundamental physics.
In the second phase the satellite would be transferred to a geostationary orbit for the gravity field mapping and to provide a master clock for time and frequency applications.
In concept, the satellite payload would consist of a femtosecond comb stabilized to an ultrastable optical local oscillator (a narrow linewidth laser stabilized to a high finesse optical cavity). The femtosecond comb would be used to stabilise a variety of lasers necessary for the operation of an ensemble of optical clocks.
The optimum choice of optical clocks needs to be considered carefully. They should at least be dissimilar in their dependence on a variety of fundamental constants, but the optimum choice may be different for the different proposed applications. For example for a local position invariance test and a gravitational redshift measurement the most important parameter is the stability of the clock over a 10 hour timescale, while for master clock use, accuracy and longer-term stability are also important.
Slide material courtesy of Stephan Schiller

8. Measurement of the gravitational redshift
A satellite-based measurement of the absolute gravitational redshift could be done in two ways.
The first is to compare clocks on satellites in different circular orbits. Then the gravitational potential difference and thus the gravitational redshift would be approximately constant in time, and it is necessary to achieve a high absolute accuracy of the clocks in space.
The alternative is to place the space clock in a highly elliptical orbit, while the second clock is located on earth. The gravitational shift of the terrestrial clock is not important since it is sufficiently constant on the orbit timescale. The frequency shift between the two clocks is modulated in time at the orbital frequency, and so the requirement on the clocks is a high stability on the timescale of the orbital period. This makes this approach simpler, although an accurate determination of the gravitational potential experienced by the satellite clock is still necessary, for example by laser ranging.
For the proposed orbit, the gravitational potential variation U/c2 would be approximately 2 parts in With clock instabilities and time transfer at the level of 1 part in 1018 on the orbital half period of 7 hours, a test of the redshift with relative accuracy of 1 part in 108 per orbit, and better than 1 part in 109 after averaging over 1 year would be possible.
A second test is a test of the universality of the gravitational redshift, a consequence of the principle of local position invariance. If this holds true then a comparison of the frequencies of two clocks of different nature located in the same satellite should yield the same value, no matter where the satellite is with respect to massive bodies. A test of local position invariance is simpler than an absolute gravitational redshift test because it is performed entirely within the satellite, and an accurate knowledge of the gravitational potential along the orbit is not necessary. Again, the crucial clock requirement is low instability rather than high accuracy.
Clock ensemble
for eccentricty e = 0.4 n1 n2 n0
Gravitational redshift universality test: z1=z2 ? (Local Position Invariance) - Intercomparison of dissimilar on-board clocks
Absolute gravitational redshift measurement - Test of higher-order relativistic corrections (Linet & Teyssandier 2002, Blanchet et al 2001, Ashby 1998) - Comparison with a ground clock (via microwave/optical link) - Requires precise orbit determination (laser ranging)
Slide material courtesy of Stephan Schiller

9. Time distribution and clock comparisons
Time distribution world-wide
Comparison of distant clocks (common view)
In the second phase of the proposed mission, the master clock could play an important role both in time and frequency distribution worldwide, but also in the comparison of remotely optical clocks.
In this context it should be mentioned that accurate time transfer between the satellite clock and the receiver, be it on earth or another satellite, is critical: a level better than 1 part in 1018 for an averaging time of a few hours will be necessary to take full advantage of anticipated optical clock performance. New time transfer technology beyond the advanced microwave link for ACES will have to be developed, and it may be necessary to shift to optical time transfer techniques. U
Satellite
Master clock
Slide material courtesy of Stephan Schiller

10. Gravity (geopotential) measurements
Comparison between master and probe clock (via microwave optical link)
Yields information about gravitational potential
Comparison between the master clock and probe clocks via a microwave or optical link can also be used for geopotential measurements, since it provides information about the gravitational potential at the position of the probe clock.
It is estimated that a clock comparison accuracy of might be achievable in a timescale of about 10 hours, limited by the link.
Geoid measurements with better than 1 mm accuracy could even provide a means of earthquake monitoring, but this would require clocks with fractional accuracy of 1 part in 1019. U
Probe clock (n2)
Master clock (n1)
Slide material courtesy of Stephan Schiller

11. Is there scope to combine cold atom sensors and optical clocks in a mission to test fundamental physics?
What would be the orbit implications?
Are there things that either technology can do better than the other?
What peripheral objectives could add value in either case?
Having outlined a few of our ideas for using optical clocks to test fundamental physics in space, I thought I would end with a few questions for discussion.
Is there scope for combing cold atom sensors and optical clocks in a mission to test fundamental physics?
If so, what would be the orbit implications, and are there things that either technology can do better than the other.
What subsidiary objectives could add value to the mission in either case? For example in the case of optical clocks there could be enormous benefits to time and frequency metrology as I have shown.

12. Slide from Stephan Schiller