In this paper, we review several aspects of the frequency stability of optical lattice clocks. We describe a new ultra-stable cavity design with reduced thermal noise and record frequency stability (below 10 −15 ), as well as a non-destructive detection scheme for measuring the clock transition probability. Given the experimental parameters we measured, we simulate different sequence strategies for optimizing the stability. Finally, we report on the development of a second optical lattice clock and simulate several comparison strategies. In particular, we show by a numerical method that a stability as low as 2 × 10 −16 τ −1/2 can be reached with optical lattice clocks, and we show how to demonstrate this stability with a double clock system.
In this paper, we review several aspects of the frequency stability of optical lattice clocks. We describe a new ultra-stable cavity design with reduced thermal noise and record frequency stability (below 10 −15 ), as well as a non-destructive detection scheme for measuring the clock transition probability. Given the experimental parameters we measured, we simulate different sequence strategies for optimizing the stability. Finally, we report on the development of a second optical lattice clock and simulate several comparison strategies. In particular, we show by a numerical method that a stability as low as 2 × 10 −16 τ −1/2 can be reached with optical lattice clocks, and we show how to demonstrate this stability with a double clock system.
This thesis presents the latest achievements regarding the Sr optical lattice clock experiment at LNE-SYRTE, Observatoire de Paris. After having described the general principles for optical lattice clocks and the operation of the clock in question, the emphasis is put on the features that have been added to the experiment since 2007. The most important new elements are an ultra-stable reference cavity for the clock laser, the development of a non-destructive detection technique, and the construction of a second Sr lattice clock. The ultra-stable cavity is constructed from a ULE spacer and fused silica mirrors and has shown a thermal noise floor at 6.5E-16, placing it among the best in the world. The non-destructive detection is effectuated by a phase measurement of a weak probe beam that traverses the atoms placed in one arm of a Mach-Zender interferometer. The non-destructive aspect enables a recycling of the atoms from cycle to cycle which consequently increases the duty cycle, allowing for an increase of the stability of the clock. With these new tools the frequency stability is expected to be 2.2E-16/tau^(1/2) for an optimized sequence. The most recent comparisons between the two Sr clocks reach an accuracy level of 1E-16 after about 1000 s, and this way we have been able to characterize lattice related frequency shifts with an unprecedented accuracy. The measurements ensure a control of lattice related effects at the 1E-18 level even for trap depths as large as 50 Er.
Abstract We present several developments aimed at improving the stability of optical lattice clocks. First, we present our developments of an optical lattice clock using neutral mercury. We mention recent advances made with the fermionic isotope 199Hg. We also mention our work aimed at using bosonic isotopes, which offer the possibility to circumvent the relatively short lifetime of the upper clock state in 199Hg. Second, we present our work on a non-destructive detection in a Sr optical lattice clock. We describe developments that brought the detection scheme from the classical non-destructive regime to the quantum non-destructive regime. Our detection scheme is practical and has the capability to the used beyond proving the principle. Finally, we present our work on laser stabilization using spectral hole burning in a Eu3+:Y2SiO5 crystal at cryogenic temperatures. We describe our development of low noise interrogation based on digital IQ modulation and detection that can probe multiple spectral features simultaneously, as well as several investigations towards fluctuating environmental factors. These advances, individually or combined for example with spectral purity transfer with combs and composite clock approaches, shall bring significant progress in clock stability and accuracy.
We demonstrate the frequency comparison of two optical lattice clocks at the relative stabilities close to the quantum projection noise (QPN) limit of optical lattice clocks. This stable frequency comparison is accomplished by synchronous interrogations of two clocks by a common probe laser, which allows us to cancel out the probe laser's frequency noise. We perform the frequency comparison of a one-dimensional (1D) optical lattice clock with spin-polarized fermions 87Sr and a three-dimensional (3D) optical lattice clock with unity-occupation bosons 88Sr and achieve the Allan standard deviation of σγ(τ)=4×10-16 τ-1/2, which corresponds to the QPN limited stability for N=1,000 atoms and the spectrum linewidth γ=8 Hz. The relative stability reaches 1×10-17 with an averaging time of 1,600 s. Finally, we discuss the prospects to realize 10-18 fractional inaccuracies and the possible application of frequency comparison with synchronous interrogations to remote clocks' comparison for relativistic geodesy.
Optical lattice clocks demonstrate advantages in metrology and frontier physics because of their high stability.Here, we present approaches to enhancing the stability by decoupling the noise related to the short-term and long-term stability.For the short-term stability, we optimize the clock laser by decoupling the frequency noise, and optimize each noise contribution individually until it is below the thermal noise limit.For the long-term stability, we introduce a method to decouple the instability caused by systematic effects.Having identified that the collision frequency shift was the main limiting factor in our systems, we thus optimized the atom number fluctuations in optical lattices.Through targeted optimization, we achieve a synchronous comparison of two clocks with an average stability of 3.2 × 10 -16 = τ p and a long-term stability of 2.4 × 10 -18 at 8000 s.This work provides an analytical framework for enhancing optical clock stability.
Frequency metrology underpins precise measurements. At the forefront of this field are optical clocks which can perform measurements that are accurate to more digits than those in the number representing seconds elapsed from the beginning of the universe. Frequency estimation errors in the operation of optical clocks lead to frequency instability, prohibiting them from reaching high accuracies on short to medium time scales, and limiting access to interesting measurements of the atomic environment and exotic external perturbations such as gravity fields or fields of fundamentally new physical origins. Optical lattice traps are typically employed in state-of-the-art optical clocks to suppress Doppler effects. By carefully tuning the optical lattice to the magic wavelength, unwanted Stark shifts can be suppressed significantly, allowing operation with thousands of atoms and minimising the fundamental source of frequency estimation errors, namely the quantum projection noise, to around 3 × 10−17 at 1 s. In this thesis, the status of the two Strontium optical lattice clocks at NPL, Sr1 and Sr2, is presented going over a few interesting measurement campaigns from the past years involving Sr1 and the latest experimental efforts to re-enable operation of Sr2. A model of clock stability is developed by incorporating known and new frameworks to characterise the relation between the operating parameters of optical clocks and their performance, with relevance to the NPL lattice clocks and beyond. In particular, a method is identified for addressing the main technical noise for optical lattice clocks, the Dick effect, which typically has a magnitude of 10−16 at 1 s and prevents optical lattice clocks from reaching the quantum projection noise level. By taking advantage of dynamical decoupling we can engineer an optimised duty cycle with benefits in general for systems limited by the optical coherence of the clock laser. Moreover, a study of other noise sources in the NPL lattice clocks is conducted using synchronous measurements between Sr1 and Sr2, revealing a large contribution from linear Zeeman shifts, also at the 10−16 level, and a plan to tackle them is detailed. A hybrid clock architecture is discussed showing how optical lattice clocks can improve the optical coherence of ion clocks thanks to their higher servo rate, and a preliminary experimental demonstration is reported. Finally, a new type of spectroscopy is presented which completely avoids aliasing of linear Zeeman shifts by simultaneously driving transitions with opposite Zeeman sensitivities. Such a technique also enables the continuous interrogation of atoms, a crucial missing component in the Dick-free conveyor belt lattice clock concept heralded as the next standard of stable optical clocks.
We consider designs of optical lattice clocks in view of the quantum statistics, relevant atomic spins, and atom-lattice interactions. The first two issues lead to two optimal constructions for the clock: a one-dimensional (1D) optical lattice loaded with spin-polarized fermions and a 3D optical lattice loaded with bosons. By taking atomic multipolar interactions with the lattice fields into account, an "atomic motion insensitive" wavelength is proposed to provide a precise definition of the "magic wavelength." We then present a frequency comparison of these two optical lattice clocks: spin-polarized fermionic 87 Sr and bosonic 88 Sr prepared in 1D and 3D optical lattices, respectively. Synchronous interrogations of these two optical lattice clocks by the same probe laser allowed canceling out its frequency noise as a common mode noise to achieve a relative stability of 3 × 10 −17 for an averaging time of τ = 350 s. The scheme, therefore, provides us with a powerful means to investigate intrinsic uncertainty of the clocks regardless of the probe laser stability. We discuss prospects of the synchronous operation of the clocks on the measurement of the geoid height difference and on the search of constancy of fundamental constants.