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Philosophical transactions. Series A, Mathematical, physical, and engineering sciences logoLink to Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
. 2017 Jun 26;375(2099):20160241. doi: 10.1098/rsta.2016.0241

Optical atomic phase reference and timing

L Hollberg 1,✉, E H Cornell 1, A Abdelrahmann 1
PMCID: PMC5487717  PMID: 28652494

Abstract

Atomic clocks based on laser-cooled atoms have made tremendous advances in both accuracy and stability. However, advanced clocks have not found their way into widespread use because there has been little need for such high performance in real-world/commercial applications. The drive in the commercial world favours smaller, lower-power, more robust compact atomic clocks that function well in real-world non-laboratory environments. Although the high-performance atomic frequency references are useful to test Einstein's special relativity more precisely, there are not compelling scientific arguments to expect a breakdown in special relativity. On the other hand, the dynamics of gravity, evidenced by the recent spectacular results in experimental detection of gravity waves by the LIGO Scientific Collaboration, shows dramatically that there is new physics to be seen and understood in space–time science. Those systems require strain measurements at less than or equal to 10−20. As we discuss here, cold atom optical frequency references are still many orders of magnitude away from the frequency stability that should be achievable with narrow-linewidth quantum transitions and large numbers of very cold atoms, and they may be able to achieve levels of phase stability, ΔΦ/Φtotal ≤ 10−20, that could make an important impact in gravity wave science.

This article is part of the themed issue ‘Quantum technology for the 21st century’.

Keywords: optical atomic clocks, Yb, time transfer, frequency standard, gravity waves

1. Introduction

This paper examines how best to leverage the outstanding performance of cold atom atomic frequency reference to impact problems of basic science and our understanding of the Universe, as well as applications in real-world commerce and industry.

The remarkable advances in the performance of atomic clocks over the past 40 years have come in large part as a result of three advances: highly refined methods for laser cooling and trapping of atoms, robust tunable laser sources that have precise control of their spectral characteristics (single mode, narrow linewidth, sufficient power), and a convenient method for dividing optical frequencies to the microwave range and thus connecting coherently to electronic sources. In terms of the basic performance metrics of frequency stability and accuracy, the cold atom clocks are working very well: respectively approximately σy(τ) ≅ 5 × 10−14τ−1/2 and 1 × 10−16 for microwave transitions and σy(τ) ≅ 5 × 10−16τ−1/2 and 5 × 10−18 for optical [1]. The frequency stability and accuracy of these high-performance atomic clocks are far better than is actually needed for real-world applications. Some evidence for that claim is that those systems do not really function as ‘clocks’ at all—they do not keep time (epoch), although in principle they could. In current practice they serve as extraordinarily good frequency references based on precise measurements of quantum transitions and over relatively short time intervals: 0.1 s to several days.

The technology of the advanced clocks is well established, and although they could be engineered into robust systems, it is difficult to identify applications that actually need 15 digits or more of accurate time or frequency information. Thus, we do not currently see cold atom atomic clocks making a significant impact outside the national standards laboratories. In the meantime, high-performance quantum-based atomic frequency standards will naturally continue to play key roles in scientific experiments such as tests of general relativity, precision spectroscopy and atomic physics, quantum degenerate gases, etc.

2. Time and frequency distribution

The lack of non-science applications that demand the best accuracy and stability is certainly a major reason that we have not developed time/frequency distribution systems that are widely applicable and deliver those high levels of performance. The existing global navigation satellite system (GNSS) systems (GPS, GLONASS) meet most requirements for positioning and navigation very well, and they can provide time synchronized to UTC with uncertainties of 1–30 ns depending upon the system details. Time transfer performance using microwave signals from GNSS satellites and two-way communication signals (two-way satellite time and frequency transfer, TWSTFT) currently achieves frequency instability of about 10−11 to 10−13 at one second; frequency accuracy of about 15 digits can be reached after approximately 1 day of signal averaging. Much better performance is possible where direct fibre optic connections are feasible. The current situation on time and frequency transfer has been nicely summarized in recent references [2–4]. Most importantly, the GNSS signals are available essentially anywhere on the Earth, and there are more to come on the near-term horizon from GALILEO and BEIDOU.

However, compared to the performance of the best atomic frequency references, there are glaring weaknesses of our current worldwide timing systems in transferring very-high-performance time and frequency in a generally applicable manner. To take advantage of the latest atomic clock capabilities, we have been considering alternative and generally applicable approaches for a feasible space–time reference that could provide precise time (epoch) and frequency in a well-defined time scale and reference frame. This approach addresses many of the current limitations. It would be based on a flywheel clock orbiting the Earth in a mid-Earth orbit. The use of two-way laser links (and/or microwave links) between the flywheel clock and the high-performance cold atom clocks at the national standards laboratories could deliver high-performance time (epoch) and frequency to small ground terminals where needed. That approach is discussed and analysed in a recent paper that also provides references to other methods [5]. The two-way laser links would also give range information at the 1 mm level for precise orbit determination and applications in geodesy. With a precise orbit and a synchronized flywheel clock, the system would provide an accurate reference frame and the ability to provide accurate time (epoch) at the 1 ps level essentially anywhere.

3. Optical atomic phase reference and potential use for gravity wave (GW) measurements

It is obvious that state-of-the-art atomic frequency references can and should be used to test the foundations of our best understanding of space and time and general relativity, especially when significant improvements can be made in the experimental constraints. However, from the present vantage point there do not seem to be compelling reasons to expect violations of special relativity in the next several decades of precision measurements. On the other hand, as predicted by general relativity and now detected experimentally by the LIGO Scientific Collaboration, we know that gravitational waves (GW) distort space at the Earth with levels of strain h = ΔL/L ≈ 10−21. Those laser-based GW detectors must make relative phase measurements on optical signals ΔΦ/Φtotal ≤ 10−21 and have achieved that for averaging times comparable to the GW periods detectable on Earth. As we describe below, perhaps cold atom optical atomic phase references could reach levels of performance that could contribute to the measurements of GW signals and astronomy.

The dimensional strain h = ΔL/L sensitivity that is required for GW detection is in the 10−20 range and smaller, so an atomic phase reference needs to support ΔΦ/Φtotal ≤ 10−20 for averaging times comparable to the gravity wave period. Achievement of those levels of stability will require a large number of atoms with a high-Q atomic clock transition and extremely low environmental sensitivities and technical noise levels.

We first started looking at concepts for an optical atomic phase reference for potential use with single-arm gravity wave detectors as part of a conceptual study for NASA (Hollberg L. 2013. Final report on optical clocks and gravity waves, for NASA Goddard, unpublished). More elaborate and detailed systems using optical atomic clocks for GW detection have also been proposed recently [6]. There is also potential synergism between these optical phase reference ideas and new concepts proposed for single-arm gravity wave detectors using atom interferometry on the ground or in space [7–10].

A simple configuration that could be used for gravity wave measurements would use the quantum coherence in a cloud of cold atoms to precisely measure the phase of a laser field at discrete measurement times. Those measurements would be synchronized with measurements of the phase of a laser beam that measured the gravity wave strain h over a long path L between satellites. Differential changes in the optical phase between the optical coherence and the laser field that traversed the long path L would be measured with high precision. The method does not require that all of the residual phase fluctuations from the laser(s) beams be removed, because these will be a sequence of relative phase measurements that provide a comparison of the atomic phase with the propagation phase of the light over the long path L. Combining a phase-stable optical atomic phase reference with atom interferometers or LISA-like traditional optical interferometry could provide significant new capabilities for gravity wave detectors in space or other space/science missions.

4. Atomic phase stability

We can estimate the phase stability that could be achieved with cold neutral atoms at optical frequencies by following the analysis for frequency instability for Bordé--Ramsey spectroscopy in optical atomic clocks [11]. For this simple estimate we assume N0 cold atoms with shot-noise-limited detection, an atomic Ramsey fringe linewidth ΔνRam = 1/2TRam limited by the Ramsey time, measurement cycle time TC, laser optical frequency ν0, and averaging time τ. In this case, the fractional frequency instability, as given by the Allan deviation, is

4. 4.1

For now, we also assume no dead time in the measurement and TC = τ. The fractional frequency instability is then equivalent to a phase measurement uncertainty relative to the total phase that has accumulated δΦ(τ)/Φtotal(τ) in that measurement time τ. The quantum transitions of the optical atomic coherence should then support a phase measurement of a laser beam that traversed the long path between satellites with a dimensional strain measurement of h = δx(τ)/xtotal = δΦ(τ)/Φtotal(τ).

For free-falling atoms a measurement time of 100 ms would be straightforward, and even a 3 s measurement time with cold atoms on the ground is feasible using an optical lattice (with small atom numbers) or with large atom numbers in a tall fountain as demonstrated by Kasevich et al. [12]. A very interesting case would be long measurement times, possible with large numbers of free-floating cold atoms in the micro-gravity environment of space. In space the free-floating cold atoms could have very low velocity and allow long Ramsey times and correspondingly narrow linewidths. It would be straightforward to recapture the cold atoms and probe clock transition again with low dead time.

5. Laser local oscillator, cavities and thermal noise

Present optical reference cavities provide frequency-stabilized lasers that are phase-coherent for times t ≤ 10 s [13–15]. The thermal noise in optical materials causes mirror surfaces to have motions of ≈10−16 m Hz−1/2 corresponding to fractional frequency instabilities for optical reference cavities of about σy(τ) ≅ 2 × 10−16 for 0.1 ≤ τ ≤ 10 s and for a 30–50 cm long cavity [13–15]. As we will show below, that level of performance will not match the stability that could be achieved with cold atoms and that is required for measurements of GWs.

6. Cold Yb

The ytterbium optical clock transition, 1S0 to 3P0, at 578 nm (figure 1) has demonstrated exceptionally high frequency stability out to long averaging times in optical lattices [16]. It provides an excellent example of what might be possible if one aimed for even much higher stability required for GW detection.

Figure 1.

Figure 1.

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Simplified energy level diagram for Yb showing the first-stage cooling transition at 399 nm, the second-stage cooling at 556 nm, and clock transition at 578 nm, with their respective natural linewidths. (Online version in colour.)

With modern methods of laser cooling and trapping it should be possible to load atoms into a three-dimensional magneto-optical trap (3D-MOT) at a rate of ≈1011 atoms per second [17–21]. The basic measurement cycle optical atomic phase reference would be: Zeeman-slowing Yb atoms using the 399 nm transition to load a 3D-MOT at 399 nm, followed by second-stage cooling on the 556 nm transition, and then release of the cloud of cold atoms to free fall. The clock transition would be driven with a sequence of four pulses at 578 nm using the Bordé--Ramsey approach.

To emphasize the potential stability that could be achieved with a free-falling cloud of cold atoms, we take optimistic but conceivable experimental parameters: N = 1010 cold atoms, 100% contrast, a Ramsey measurement time of 50 ms, and a TC = TRam = τ. In this case, equation (4.1) predicts a fractional frequency instability of 4 × 10−20 in a single 50 ms measurement, corresponding to 1 × 10−21/√τ for τ in seconds. These simple estimates of frequency stability are surprisingly good and are encouraging for potential use in gravity wave detectors. Figure 2 illustrates the frequency stability of current optical atomic frequency references and compact optical cavities, and what could be achievable by pushing towards the range of interest for GW detectors.

Figure 2.

Figure 2.

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The two upper curves show the approximate fractional frequency instability of modern state-of-the-art optical atomic frequency references and cavities as a function of averaging time. The lower curve is the projected performance of a free-falling cold Yb system assuming quantum projection noise-limited frequency instability for the parameters given in the text. The transition from τ−1/2 dependence to nearly flat stability on longer times is a very rough estimate of the ability to control variations of systematic shifts and environmental sensitivities. Those effects are well beyond current knowledge and will need to be carefully evaluated and demonstrated in the laboratory. (Online version in colour.)

Ytterbium clock transitions are also interesting candidates as a stable optical phase reference because they have several isotopes with reasonable abundance, including both fermions and bosons. 171Yb has a particularly simple spin-½ nucleus, and the even isotopes with zero nuclear spin (172Yb, 174Yb, 176Yb) have narrow clock transitions with linewidths that can be tuned using the method of magnetic-field-induced forbidden transitions [22].

Arguably, it is unreasonably ambitious to extrapolate so far beyond the current state-of-the-art performance of atomic frequency references, but the fact that there is real new GW science that requires 20+ digits of phase measurement capability means that there is good reason to push the stability to new levels. Perhaps cold atom optical systems can contribute to GW science. In any case, there is a lot of unrealized stability available from cold atoms, and we will certainly learn a great deal pushing towards much higher stability. Thus motivated, we are building an experimental system to test the concepts and explore these new regimes. Figure 3 shows a block diagram of how the system is being realized, and figure 4 is an image of the cold Yb apparatus.

Figure 3.

Figure 3.

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A conceptual diagram of an optical atomic phase reference based on free-falling cold Yb atoms. Two Yb Zeeman-slowers load two 3D-MOTs that capture and cool the Yb atoms with blue (399 nm) and subsequently with green (556 nm). The cooling trapping lasers are then turned off, the atoms released to free fall, and the narrow optical clock transition at 578 nm is probed using a laser locked to a stable optical reference cavity. As illustrated here, AOM modulators generate four pulses of the clock laser (Bordé--Ramsey method) which are sent vertically in opposite directions through the free-floating cloud of cold atoms. Known frequency shifts due to gravitational acceleration would be taken into account by the AOM frequency offsets. (Online version in colour.)

Figure 4.

Figure 4.

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Image of a cold Yb apparatus that is nearing completion for testing the concepts outlined here and evaluation of the stability achievable with cold atom clouds in free fall. Atom loading is along the horizontal axis, cooling beams on 45° diagonals and into the page. The large windows and magnetic coils for the MOT provide access to falling atoms. Clock laser propagation is in the vertical direction.

Several approaches are used to deal with the problematic motion-induced frequency shifts of free-falling atoms. Those include: confining the atoms in optical lattices (relatively small numbers of atoms, 104 to 105, but longer interaction times, 0.1 s to 3 s); measuring quickly before atoms fall out of the probe beams (limited Q, interaction times a few ms, large numbers of atoms); or launching the atoms in an atomic fountain (atom numbers ≈ 106 and good interaction times ≈ 1 s). Each approach has associated frequency shifts, advantages and disadvantages. For simplicity and to evaluate potential performance of a space-based version that might be used for GW measurements, we are focusing on free-falling clouds of cold atoms. The system will use two or more clouds of dropped atoms that are probed either simultaneously or sequentially with clock laser beams propagating in the vertical direction. Multiple horizontal beams are a very viable alternative. With falling atoms, these geometries will allow longer interaction times and hence narrower linewidths and higher Q values. This also brings significant complications and the disadvantage of accelerating atoms and the associated time-dependent optical phases. Since local gravitational acceleration can be known well and is relatively constant, the time-dependent phases of falling atoms can be dealt with in the same manner as is now done in light-pulse atom interferometers configured as gravimeters or in Cs fountain atomic clocks. There will be phase shifts due to the vertical acceleration, but those can be known and subtracted from the measured phase.

7. Dead time and Dick effect

The predicted performance is far beyond the stability now achieved with atoms or short optical reference cavities, and cavities as long as the 4 km LIGO cavities are impracticable elsewhere. To move beyond the thermal noise on the lasers it will be necessary to have multiple cold atom samples to verify that phase measurements of the light can be made at the 10−20 level. Using multiple clouds of cold atoms will also allow us to mitigate the Dick effect [23] where periodically interrogated clock transitions introduce aliasing noise from the LO phase fluctuations on the clock laser and the degradation of the phase stability due to dead time in the measurement. (Because of the time required to cool and trap the atoms, there will be dead time in the measurement of the quantum phase of the clock transition.) By using two or more samples of cold atoms, dead time for cooling, trapping and state preparation can be interleaved between clouds of atoms while probing the clock transition which continues to oscillate in the other cloud(s) of atoms. This interleaved multiple-cloud approach has been used for clocks and atom interferometers with the advantage that the atomic coherence is continuously maintained by atoms [24–29].

8. Beyond the 1/√N0 limit

Even at the standard quantum limit (SQL) given by the quantum projection noise (atom shot noise) limit of frequency instability, the performance is expected to be several orders of magnitude better than the thermal-noise-limited performance of the best (compact) optical reference cavities. At least in principle, the atoms can retain the optical phase as a quantum coherence between two quantum levels with much better stability than can now be achieved with the high-performance physical resonators (quartz crystals and sapphire oscillators for microwaves and super-mirror optical cavities for lasers). In the SQL, the expected frequency instability scales as 1/√N0.

As demonstrated recently by Hosten et al. [30], a powerful complementary approach would be to take advantage of squeezing atomic quantum states to push towards Heisenberg-limited quantum measurements that scale as 1/N atoms. In that case the <10−20 phase measurement could be achieved with far fewer atoms, but with additional constraints and complexity.

9. Outlook

As we have tried to demonstrate here, narrow optical transitions in cold atoms could be used to measure the phase of a laser with fractional uncertainties in the 10−20 range and better for averaging times from 50 ms and longer. If that is actually achieved, it would represent a major advance in phase-stable optical sources and could dramatically change future directions for precision optical measurements. These arguments are meant to emphasize that the quantum coherence in cold atoms could support optical phase measurements several orders of magnitude better than the current state of the art. In the future, perhaps these systems actually could make a significant impact in the growing field of GW measurements and space–time measurements in general.

Acknowledgements

We are grateful to Paul Berceau, Michael T. Taylor and Joseph Kahn for helpful discussions and important contributions to the study of optical links for time transfer to space.

Authors' contributions

L.H. has been involved in all aspects of this project and guiding the research programme, including: basic concepts, analysis, development of experimental hardware and drafting of the article. E.H.C. and A.A. have made major contributions to designing, building and testing the Yb cold atom experimental system and analysing performance limits of key subsystems for the optical atomic phase reference.

Competing interests

We declare we have no competing interests.

Funding

The Keck Foundation supports the majority of this work for a collaborative effort with Mark Kasevich and Peter Graham on advanced methods for gravity wave detection. Early concepts for the optical atomic phase reference, including projections for gravity wave detection, were developed with support from NASA Goddard and were summarized in our final report 2013, unpublished. Funding on related work on ‘optical time transfer’ comes from the NASA, Fundamental Physics Program.

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