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Future trends in fundamental physics and applications

Pasquale Maddaloni, Marco Bellini, Paolo De Natale

Published Apr 19, 2016• 0 citations

Abstract

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].

DOI: 10.1201/b14783-13

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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].

8half a century ago and have provided the definition of the second since 1967. The international atomic time (TAI) is currently kept by an ensemble of Cs clocks with a fractional uncertainty of Δν/ν0 ≈ 10 –15 , and some Cs fountain clocks 9,10 operate at even smaller uncertainties. Although Cs atomic clocks operate at the microwave transition of ν0 ≈ 9.2 GHz, using optical transition frequencies of several hundred terahertz should improve the fractional uncertainty Δν/ν0 by 4–5 orders of magnitude, as most measurement uncertainties Δν are independent of ν0 (except the Doppler shift Δ νD = (v/c)ν0, where v is the atomic velocity and c is the speed of light). The invention of the laser and the subsequent improvement of laser frequency stabilities 11 has allowed the realization of optical clocks to become a reality 2,3,12

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.

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.

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

{N}_{\mathrm{at}}

. For

{N}_{\mathrm{at}}

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.

The stability of current state-of-the-art optical atomic clocks [1]-[5] is mostly limited by the frequency noise of the interrogation oscillator through the Dick effect. To achieve the heralded ultimate stability, future optical frequency standards will need to produce light sources with frequency stability at the 10−17fractional level or below at one second of integration time. Recently, a new frontier in cavity stabilized laser sources has pushed the fractional instability to the lower 10−16level at one second of integration time [6]-[8]. However, this instability is limited by thermal noise in the reference cavity elements and may be difficult to reduce further. These state-of-the-art reference cavities are technically challenging to construct and their stability is still at least an order of magnitude too large for lattice clocks to achieve their ultimate performance.

An optical clock or frequency standard based on the interrogation of an atomic transition in the optical domain, operates at ~1014Hz is capable of providing orders of magnitude better accuracy than the present primary standard of frequency or time operating in the microwave range. Optical transitions of an ions, confined within a radio frequency ion trap and laser cooled to ~mK temperature, provides better long term stability since they are free from Coulomb and intra-atomic interactions. Optical frequency standards have been realized with several ions, e.g.,199Hg+,171Yb+,115In+,88Sr+,40Ca+,27Al+and among those171Y+has multiple ultra-narrow optical transitions suitable for serving as frequency standards [1-2].