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arXiv:0901.2788 · Physical Review A

Reaching the quantum limit in a fountain clock using a microwave oscillator phase locked to an ultrastable laser

S. Weyers, B. Lipphardt, H. Schnatz

Published Mar 11, 2009• 86 citations
arXivHTMLPDF

Abstract

A cesium fountain clock is operated utilizing a microwave oscillator that derives its frequency stability from a stable laser by means of a fiber-laser femtosecond frequency comb. This oscillator is based on the technology developed for optical clocks and replaces the quartz-based microwave oscillator commonly used in fountain clocks. As a result, a significant decrease in the frequency instability of the fountain clock is obtained, reaching $7.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{[\ensuremath{\tau}\text{ }(\text{s})]}^{\ensuremath{-}1/2}$. We could demonstrate that for a significant range of detected atom numbers the instability is limited by quantum projection noise only, and that for the current status of this fountain clock the microwave source poses no limit on the achievable frequency instability.

DOI
10.1103/physreva.79.031803

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A cesium fountain clock is operated utilizing a microwave oscillator that derives its frequency stability from a stable laser by means of a fiber-laser femtosecond frequency comb. This oscillator is based on the technology developed for optical clocks and replaces the quartz-based microwave oscillator commonly used in fountain clocks. As a result, a significant decrease in the frequency instability of the fountain clock is obtained, reaching 7.4\ifmmode×\else\texttimes\fi10\ensuremath−14[\ensuremathτ (s)]\ensuremath−1/27.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{[\ensuremath{\tau}\text{ }(\text{s})]}^{\ensuremath{-}1/2}7.4\ifmmode×\else\texttimes\fi10\ensuremath−14[\ensuremathτ (s)]\ensuremath−1/2. We could demonstrate that for a significant range of detected atom numbers the instability is limited by quantum projection noise only, and that for the current status of this fountain clock the microwave source poses no limit on the achievable frequency instability.
We describe the operation of a laser cooled cesium fountain clock in the quantum limited regime. An ultrastable cryogenic sapphire oscillator is used to measure the short-term frequency stability of the fountain as a function of the number of detected atoms Nat{N}_{\mathrm{at}}Nat​. For Nat{N}_{\mathrm{at}}Nat​ varying from $4\ifmmode\times\else\texttimes\fi{}{10}^{4}$ to $6\ifmmode\times\else\texttimes\fi{}{10}^{5}$ the Allan standard deviation of the frequency fluctuations is in excellent agreement with the ${N}_{\mathrm{at}}^{\ensuremath{-}1/2}$ law of atomic projection noise. With $6\ifmmode\times\else\texttimes\fi{}{10}^{5}$ atoms, the relative frequency stability is $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$, where \ensuremath{\tau} is the integration time in seconds. This is the best short-term stability ever reported for primary frequency standards, a factor of 5 improvement over previous results.
As discussed in the previous chapter, with the present frequency stability of 6 · 10−16 and accuracy of 1.1 · 10−15, microwave frequency standards based on fountains are now in their adulthood. Also, within a few years, further affordable betterments could push the stability into the low 10−16 range (over one-day averaging time) and the accuracy to 1 · 10−16. We have also learnt that, when the quantum projection noise dominates over technical noise sources, the instability of an oscillator which is locked to an atomic transition with frequency ν0 and linewidth ∆ν can be expressed as σ(τ) = ∆ν πν0 √ T Nτ (8.1) where T is the cycle time required to perform a single determination of the line center frequency and N denotes the number of detected atoms [764]. Note that this formula is valid for averaging times τ > T . Also, a signal contrast of 100% and the absence of dead time (between the cycles) are assumed. Now, while the processes that limit the linewidth of an atomic transition in the microwave region are essentially comparable to those in the optical domain, a 5-orders-of-magnitude enhancement is gained by moving from the operating frequency of the cesium primary standard to optical frequencies. Thus, potentially, a dramatic reduction in the instability can be obtained by establishing a frequency standard on an optical transition. At risk of becoming pedantic, before going on, we insist in elucidating the principle of operation of a passive atomic frequency standard (Figure 8.1) [715].
We present experimental work for improved atom loading in the optical molasses of a cesium fountain clock, employing a low-velocity intense source of atoms [Lu et al., Phys. Rev. Lett 77, 3331 (1996)], which we modify by adding a dark-state pump laser. With this modification the atom source has a mean flux of $4\ifmmode\times\else\texttimes\fi{}{10}^{8}$ atoms/s at a mean atom velocity of 8.68.68.6 m/s. Compared to fountain operation using background gas loading, we achieve a significant increase of the loaded and detected atom number by a factor of 40. Operating the fountain clock with a total number of detected atoms ${N}_{\mathrm{at}}=2.9\ifmmode\times\else\texttimes\fi{}{10}^{6}$ in the quantum projection noise-limited regime, a frequency instability ${\ensuremath{\sigma}}_{y}(1s)=2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ is demonstrated.
We demonstrate the construction of the optical system in the atomic clock-beyond atomic fountain based on 87Rb atom. The optical system includes a high-stability laser system and an optical lattice. The high-stability laser system with the new scheme of frequency locking and shift is introduced in detail, which is an important laser source for laser cooling. The optimized frequency and intensity stability are achieved to 4 × 10–14 τ−1/2 ( τ is the averaging time) and 4 × 10–5 τ−1/2 , respectively, which are highly stable. On the basis of the conventional atomic fountain clock, the optical lattice is specially investigated along the direction of gravity and its characteristics are studied systematically. For the optimized and novel exploration, we predict the achievable stability of 3.6×10−14τ−1/2 and it has the potential to be improved to 3.6×10−15τ−1/2 . The realizability of the construction due to the stabilized laser and optical lattice makes the beyond fountain promising candidate for the next-generation high performance microwave atomic clock.
We demonstrate how to realize an optical clock with neutral atoms that is competitive to the currently best single ion optical clocks in accuracy and superior in stability. Using ultracold atoms in a Ca optical frequency standard, we show how to reduce the relative uncertainty to below 10(-15). We observed atom interferences for stabilization of the laser to the clock transition with a visibility of 0.36, which is 70% of the ultimate limit achievable with atoms at rest. A novel scheme was applied to detect these atom interferences with the prospect to reach the quantum projection noise limit at an exceptional low instability of 4 x 10(-17) in 1 s.
Optical atomic clocks with fractional uncertainties around and below 10−17 [1] and fractional instabilities at one second interrogation time of below 10−15 [2] have outperformed the best microwave clocks like the cesium atomic clock. In optical atomic clocks a highly stable laser is used to interrogate optical transitions in laser-cooled atoms, ions, or molecules. The increase in accuracy and stability of the optical atomic clocks results from the increased line quality factor Q= ν/Δν given by the five orders of magnitude higher frequency of optical transitions as compared to the transition relevant in the microwave domain. To utilize this potential it is furthermore necessary to realize a suitable narrow linewidth of the interrogated line. The linewidth of any optical transition is given by the different broadening mechanisms of the respective quantum transition relevant for particular interrogation process as well as by the coherence properties of the interrogating laser.