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Physical Review Letters

Quantum Projection Noise in an Atomic Fountain: A High Stability Cesium Frequency Standard

Giorgio Santarelli, Philippe Laurent, P. Lemonde, Andr  Clairon, Anthony G. Mann, Sheng Chang, Andre Nicholas Luiten, Ch Salomon

Published Jun 7, 1999• 568 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.82.4619

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

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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 $7.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{[\ensuremath{\tau}\text{ }(\text{s})]}^{\ensuremath{-}1/2}$. 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.

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Optical Spectrum Analyzer with Quantum-Limited Noise Floor

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Interactions between atoms and lasers provide the potential for unprecedented control of quantum states. Fulfilling this potential requires detailed knowledge of frequency noise in optical oscillators with state-of-the-art stability. We demonstrate a technique that precisely measures the noise spectrum of an ultrastable laser using optical lattice-trapped 87Sr atoms as a quantum projection noise-limited reference. We determine the laser noise spectrum from near dc to 100 Hz via the measured fluctuations in atomic excitation, guided by a simple and robust theory model. The noise spectrum yields a 26(4) mHz linewidth at a central frequency of 429 THz, corresponding to an optical quality factor of 1.6×10(16). This approach improves upon optical heterodyne beats between two similar laser systems by providing information unique to a single laser and complements the traditionally used Allan deviation which evaluates laser performance at relatively long time scales. We use this technique to verify the reduction of resonant noise in our ultrastable laser via feedback from an optical heterodyne beat. Finally, we show that knowledge of our laser's spectrum allows us to accurately predict the laser-limited stability for optical atomic clocks.

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Article

Marie-Claude Gagné, J.-S. Boulanger, R J W Douglas

The accelerated development of laser methods for manipulating the internal state and motion of atoms, and the recent primary evaluation in France of a cesium frequency standard using cold atoms in an atomic fountain configuration, allow the frontiers of time metrology, accuracy, and stability to be pushed near parts in the 1016 level, a factor of 100 over the present primary laboratory clocks. These positive results revived the development of more accurate cesium atomic clocks, and the Institute of National Measurement Standards (INMS), of the National Research Council of Canada (NRC) is undertaking a cesium-fountain project aimed at reaching these new levels of accuracy and stability. This paper reviews its present status. To appreciate the considerable impact of cold atoms in time and frequency metrology, we begin by recalling the background principles of traditional cesium frequency standards, their typical performance and main limitations. After introducing the important theoretical results essential to understanding the techniques of laser cooling and magneto-optical trapping, we focus on describing the characterization and control of our magneto-optical trap (MOT) and report the parameters that allow us to fill the trap with a few million atoms in less than a second and cool them to a temperature lower than 5 muK using optical molasses. We will describe the specifics of our cesium-fountain prototype, which operates with a 2-dimensional moving molasses. This special configuration is applicable for multipulse operation of the fountain, which can greatly relax the local oscillator requirements for time keeping. Finally, progress toward our objective of launching cooled atoms, at a rate of one ensemble per second, at speeds of 7 m/s, for a fountain with an interrogation time of about 1 s, will be analysed.PACS Nos.: 06.20, 06.30, and 32.80P

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Future trends in fundamental physics and applications

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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].

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Sangmin Lee, Myoung-Sun Heo, Taeg Yong Kwon +6 more

We report on a robust distributed Bragg reflector (DBR) laser system for an atomic fountain clock. To confirm the performance of a DBR laser, the short-term stability of an atomic fountain clock, KRISS-F1, is measured with both DBR laser and an extended-cavity diode laser (ECDL) as a master laser in the fountain laser system. The short-term stability of the fountain clock due to the laser noise is determined to be σy(τ = Tc) = 1.4×10-14when either the ECDL or the DBR laser is used as a master laser. The total stability of the fountain clock with the DBR laser is limited to 3.5 × 10-14at 1 s of averaging time and at the highest atom number in the experiment, which is limited by quantum projection noise. No additional degradation in fountain performance is observed when an ECDL is replaced by the DBR laser. From these results, we conclude that our fountain clock is made much more robust by adopting a DBR laser, which is immune to acoustic and vibrational shocks as well as environmental temperature variations.

IEEE Transactions on Instrumentation and Measurement•Jan 2, 2017•14 citations
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×\else\texttimes\fi1044\ifmmode\times\else\texttimes\fi{}{10}^{4}4\ifmmode×\else\texttimes\fi104 to 6\ifmmode×\else\texttimes\fi1056\ifmmode\times\else\texttimes\fi{}{10}^{5}6\ifmmode×\else\texttimes\fi105 the Allan standard deviation of the frequency fluctuations is in excellent agreement with the Nat\ensuremath−1/2{N}_{\mathrm{at}}^{\ensuremath{-}1/2}Nat\ensuremath−1/2​ law of atomic projection noise. With 6\ifmmode×\else\texttimes\fi1056\ifmmode\times\else\texttimes\fi{}{10}^{5}6\ifmmode×\else\texttimes\fi105 atoms, the relative frequency stability is 4\ifmmode×\else\texttimes\fi10\ensuremath−14\ensuremathτ\ensuremath−1/24\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\ensuremath{\tau}}^{\ensuremath{-}1/2}4\ifmmode×\else\texttimes\fi10\ensuremath−14\ensuremathτ\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.
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.
Interactions between atoms and lasers provide the potential for unprecedented control of quantum states. Fulfilling this potential requires detailed knowledge of frequency noise in optical oscillators with state-of-the-art stability. We demonstrate a technique that precisely measures the noise spectrum of an ultrastable laser using optical lattice-trapped 87Sr atoms as a quantum projection noise-limited reference. We determine the laser noise spectrum from near dc to 100 Hz via the measured fluctuations in atomic excitation, guided by a simple and robust theory model. The noise spectrum yields a 26(4) mHz linewidth at a central frequency of 429 THz, corresponding to an optical quality factor of 1.6×10(16). This approach improves upon optical heterodyne beats between two similar laser systems by providing information unique to a single laser and complements the traditionally used Allan deviation which evaluates laser performance at relatively long time scales. We use this technique to verify the reduction of resonant noise in our ultrastable laser via feedback from an optical heterodyne beat. Finally, we show that knowledge of our laser's spectrum allows us to accurately predict the laser-limited stability for optical atomic clocks.
The accelerated development of laser methods for manipulating the internal state and motion of atoms, and the recent primary evaluation in France of a cesium frequency standard using cold atoms in an atomic fountain configuration, allow the frontiers of time metrology, accuracy, and stability to be pushed near parts in the 1016 level, a factor of 100 over the present primary laboratory clocks. These positive results revived the development of more accurate cesium atomic clocks, and the Institute of National Measurement Standards (INMS), of the National Research Council of Canada (NRC) is undertaking a cesium-fountain project aimed at reaching these new levels of accuracy and stability. This paper reviews its present status. To appreciate the considerable impact of cold atoms in time and frequency metrology, we begin by recalling the background principles of traditional cesium frequency standards, their typical performance and main limitations. After introducing the important theoretical results essential to understanding the techniques of laser cooling and magneto-optical trapping, we focus on describing the characterization and control of our magneto-optical trap (MOT) and report the parameters that allow us to fill the trap with a few million atoms in less than a second and cool them to a temperature lower than 5 muK using optical molasses. We will describe the specifics of our cesium-fountain prototype, which operates with a 2-dimensional moving molasses. This special configuration is applicable for multipulse operation of the fountain, which can greatly relax the local oscillator requirements for time keeping. Finally, progress toward our objective of launching cooled atoms, at a rate of one ensemble per second, at speeds of 7 m/s, for a fountain with an interrogation time of about 1 s, will be analysed.PACS Nos.: 06.20, 06.30, and 32.80P
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 report on a robust distributed Bragg reflector (DBR) laser system for an atomic fountain clock. To confirm the performance of a DBR laser, the short-term stability of an atomic fountain clock, KRISS-F1, is measured with both DBR laser and an extended-cavity diode laser (ECDL) as a master laser in the fountain laser system. The short-term stability of the fountain clock due to the laser noise is determined to be σy(τ = Tc) = 1.4×10-14when either the ECDL or the DBR laser is used as a master laser. The total stability of the fountain clock with the DBR laser is limited to 3.5 × 10-14at 1 s of averaging time and at the highest atom number in the experiment, which is limited by quantum projection noise. No additional degradation in fountain performance is observed when an ECDL is replaced by the DBR laser. From these results, we conclude that our fountain clock is made much more robust by adopting a DBR laser, which is immune to acoustic and vibrational shocks as well as environmental temperature variations.