arXiv subjects

Andrew D. Ludlow

Publications and source records attributed to Andrew D. Ludlow.

At least 19 recordsLinked to original sources

arXiv2026

Atomic clock frequency ratios with fractional uncertainty $\leq 3.2 \times 10^{-18}$

We report high-precision frequency ratio measurements between optical atomic clocks based on $^{27}$Al$^+$, $^{171}$Yb, and $^{87}$Sr. With total fractional uncertainties at or below $3.2 \times 10^{-18}$, these measurements meet an important milestone criterion for redefinition of the second in the International System of Units. Discrepancies in $^{87}$Sr ratios at approximately $1\times10^{-16}$ and the Al$^+$/Yb ratio at $1.6\times10^{-17}$ in fractional units compared to our previous measurements underscore the importance of repeated, high-precision comparisons by different laboratories. A key innovation in this work is the use of a common ultrastable reference delivered to all clocks via a 3.6 km phase-stabilized fiber link between two institutions. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2 to 3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of $1.3 \times 10^{-16}$ at 1 second. By enabling faster comparisons, this stability will improve sensitivity to non-white noise processes and other underlying limits of state-of-the-art optical frequency standards.

physics.atom-ph↗

arXiv2025

Cryogenic Optical Lattice Clock with $1.7\times 10^{-20}$ Blackbody Radiation Stark Uncertainty

Controlling the Stark perturbation from ambient thermal radiation is key to advancing the performance of many atomic frequency standards, including state-of-the-art optical lattice clocks (OLCs). We demonstrate a cryogenic OLC that utilizes a dynamically actuated radiation shield to control the perturbation at $1.7\times10^{-20}$ fractional frequency, a factor of $\sim$40 beyond the best OLC to date. Our shield furnishes the atoms with a near-ideal cryogenic blackbody radiation (BBR) environment by rejecting external thermal radiation at the part-per-million level during clock spectroscopy, overcoming a key limitation with previous cryogenic BBR control solutions in OLCs. While the lowest BBR shift uncertainty is realized with cryogenic operation, we further exploit the radiation control that the shield offers over a wide range of temperatures to directly measure and verify the leading BBR Stark dynamic correction coefficient for ytterbium. This independent measurement reduces the literature-combined uncertainty of this coefficient by 30%, thus benefiting state-of-the-art Yb OLCs operated at room temperature. We verify the static BBR coefficient for Yb at the low $10^{-18}$ level.

physics.atom-ph↗

arXiv2024

Lattice Light Shift Evaluations In a Dual-Ensemble Yb Optical Lattice Clock

In state-of-the-art optical lattice clocks, beyond-electric-dipole polarizability terms lead to a break-down of magic wavelength trapping. In this Letter, we report a novel approach to evaluate lattice light shifts, specifically addressing recent discrepancies in the atomic multipolarizability term between experimental techniques and theoretical calculations. We combine imaging and multi-ensemble techniques to evaluate lattice light shift atomic coefficients, leveraging comparisons in a dual-ensemble lattice clock to rapidly evaluate differential frequency shifts. Further, we demonstrate application of a running wave field to probe both the multipolarizability and hyperpolarizability coefficients, establishing a new technique for future lattice light shift evaluations.

physics.atom-ph↗

arXiv2024

Clock-line-mediated Sisyphus Cooling

We demonstrate sub-recoil Sisyphus cooling using the long-lived $^{3}\mathrm{P}_{0}$ clock state in alkaline-earth-like ytterbium. A 1388 nm optical standing wave nearly resonant with the $^{3}\textrm{P}_{0}$$\,\rightarrow$$\,^{3}\textrm{D}_{1}$ transition creates a spatially periodic light shift of the $^{3}\textrm{P}_{0}$ clock state. Following excitation on the ultranarrow clock transition, we observe Sisyphus cooling in this potential, as the light shift is correlated with excitation to $^{3}\textrm{D}_{1}$ and subsequent spontaneous decay to the $^{1}\textrm{S}_{0}$ ground state. We observe that cooling enhances the loading efficiency of atoms into a 759 nm magic-wavelength one-dimensional (1D) optical lattice, as compared to standard Doppler cooling on the $^{1}\textrm{S}_{0}$$\,\rightarrow\,$$^{3}\textrm{P}_{1}$ transition. Sisyphus cooling yields temperatures below 200 nK in the weakly confined, transverse dimensions of the 1D optical lattice. These lower temperatures improve optical lattice clocks by facilitating the use of shallow lattices with reduced light shifts, while retaining large atom numbers to reduce the quantum projection noise. This Sisyphus cooling can be pulsed or continuous and is applicable to a range of quantum metrology applications.

physics.atom-ph↗

arXiv2024

Ratchet Loading and Multi-Ensemble Operation in an Optical Lattice Clock

We demonstrate programmable control over the spatial distribution of ultra-cold atoms confined in an optical lattice. The control is facilitated through a combination of spatial manipulation of the magneto-optical trap and atomic population shelving to a metastable state. We first employ the technique to load an extended (5 mm) atomic sample with uniform density in an optical lattice clock, reducing atomic interactions and realizing remarkable frequency homogeneity across the atomic cloud. We also prepare multiple spatially separated atomic ensembles and realize multi-ensemble clock operation within the standard one-dimensional (1D) optical lattice clock architecture. Leveraging this technique, we prepare two oppositely spin-polarized ensembles that are independently addressable, offering a platform for implementing spectroscopic protocols for enhanced tracking of local oscillator phase. Finally, we demonstrate a relative fractional frequency instability at one second of $2.4(1) \times10^{-17}$ between two ensembles, useful for characterization of intra-lattice differential systematics.

physics.atom-ph↗

arXiv2023

Optimal binary gratings for multi-wavelength magneto-optical traps

Grating magneto-optical traps are an enabling quantum technology for portable metrological devices with ultracold atoms. However, beam diffraction efficiency and angle are affected by wavelength, creating a single-optic design challenge for laser cooling in two stages at two distinct wavelengths - as commonly used for loading e.g. Sr or Yb atoms into optical lattice or tweezer clocks. Here, we optically characterize a wide variety of binary gratings at different wavelengths to find a simple empirical fit to experimental grating diffraction efficiency data in terms of dimensionless etch depth and period for various duty cycles. The model avoids complex 3D light-grating surface calculations, yet still yields results accurate to a few percent across a broad range of parameters. Gratings optimized for two (or more) wavelengths can now be designed in an informed manner suitable for a wide class of atomic species enabling advanced quantum technologies.

physics.atom-ph↗

arXiv2020

Optical Atomic Clock Comparison through Turbulent Air

We use frequency comb-based optical two-way time-frequency transfer (O-TWTFT) to measure the optical frequency ratio of state-of-the-art ytterbium and strontium optical atomic clocks separated by a 1.5 km open-air link. Our free-space measurement is compared to a simultaneous measurement acquired via a noise-cancelled fiber link. Despite non-stationary, ps-level time-of-flight variations in the free-space link, ratio measurements obtained from the two links, averaged over 30.5 hours across six days, agree to $6\times10^{-19}$, showing that O-TWTFT can support free-space atomic clock comparisons below the $10^{-18}$ level.

physics.optics↗

arXiv2020

Frequency Ratio Measurements with 18-digit Accuracy Using a Network of Optical Clocks

Atomic clocks occupy a unique position in measurement science, exhibiting higher accuracy than any other measurement standard and underpinning six out of seven base units in the SI system. By exploiting higher resonance frequencies, optical atomic clocks now achieve greater stability and lower frequency uncertainty than existing primary standards. Here, we report frequency ratios of the $^{27}$Al$^+$, $^{171}$Yb and $^{87}$Sr optical clocks in Boulder, Colorado, measured across an optical network spanned by both fiber and free-space links. These ratios have been evaluated with measurement uncertainties between $6\times10^{-18}$ and $8\times10^{-18}$, making them the most accurate reported measurements of frequency ratios to date. This represents a critical step towards redefinition of the SI second and future applications such as relativistic geodesy and tests of fundamental physics.

physics.atom-ph↗

arXiv2020

Coherent Optical Clock Down-Conversion for Microwave Frequencies with 10-18 Instability

Optical atomic clocks are poised to redefine the SI second, thanks to stability and accuracy more than one hundred times better than the current microwave atomic clock standard. However, the best optical clocks have not seen their performance transferred to the electronic domain, where radar, navigation, communications, and fundamental research rely on less stable microwave sources. By comparing two independent optical-to-electronic signal generators, we demonstrate a 10 GHz microwave signal with phase that exactly tracks that of the optical clock phase from which it is derived, yielding an absolute fractional frequency instability of 1*10-18 in the electronic domain. Such faithful reproduction of the optical clock phase expands the opportunities for optical clocks both technologically and scientifically for time-dissemination, navigation, and long-baseline interferometric imaging.

physics.optics↗

arXiv2019

Ramsey-Bordé matter-wave interferometry for laser frequency stabilization at $10^{-16}$ frequency instability and below

We demonstrate Ramsey-Bordé (RB) atom interferometry for high performance laser stabilization with fractional frequency instability $<2 \times 10^{-16}$ for timescales between 10 and 1000s. The RB spectroscopy laser interrogates two counterpropagating $^{40}$Ca beams on the $^1$S$_0$ -- $^3$P$_1$ transition at 657 nm, yielding 1.6 kHz linewidth interference fringes. Fluorescence detection of the excited state population is performed on the (4s4p) $^3$P$_1$ -- (4p$^2$) $^3$P$_0$ transition at 431 nm. Minimal thermal shielding and no vibration isolation are used. These stability results surpass performance from other thermal atomic or molecular systems by one to two orders of magnitude, and further improvements look feasible.

physics.atom-ph↗

arXiv2015

Optical Atomic Clocks

Optical atomic clocks represent the state-of-the-art in the frontier of modern measurement science. In this article we provide a detailed review on the development of optical atomic clocks that are based on trapped single ions and many neutral atoms. We discuss important technical ingredients for optical clocks, and we present measurement precision and systematic uncertainty associated with some of the best clocks to date. We conclude with an outlook on the exciting prospect for clock applications.

physics.atom-ph↗

arXiv2008

Accurate calculations of Sr properties for a high-accuracy optical clock

We have carried out calculations towards the goal of reducing the inaccuracy of the Sr optical atomic clock to 1$\times10^{-17}$ and below. We calculated a.c. polarizabilities of the $5s^2 ^1S_0$ and $5s5p ^3P_0^o$ clock states that are important for reducing the uncertainty of blackbody radiation-induced frequency shifts for the $^1S_0 - ^3P_0^o$ clock transition. We determined four low-lying even-parity states whose total contribution to the static polarizability of the $^3P_0^o$ clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the $^3P_0^o$ state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below 1$\times10^{-17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.

physics.atom-ph↗

arXiv2008

The absolute frequency of the 87Sr optical clock transition

The absolute frequency of the 1S0-3P0 clock transition of 87Sr has been measured to be 429 228 004 229 873.65 (37) Hz using lattice-confined atoms, where the fractional uncertainty of 8.6x10-16 represents one of the most accurate measurements of an atomic transition frequency to date. After a detailed study of systematic effects, which reduced the total systematic uncertainty of the Sr lattice clock to 1.5x10-16, the clock frequency is measured against a hydrogen maser which is simultaneously calibrated to the US primary frequency standard, the NIST Cs fountain clock, NIST-F1. The comparison is made possible using a femtosecond laser based optical frequency comb to phase coherently connect the optical and microwave spectral regions and by a 3.5 km fiber transfer scheme to compare the remotely located clock signals.

physics.atom-ph↗

arXiv2007

Nuclear Spin Effects in Optical Lattice Clocks

We present a detailed experimental and theoretical study of the effect of nuclear spin on the performance of optical lattice clocks. With a state-mixing theory including spin-orbit and hyperfine interactions, we describe the origin of the $^1S_0$-$^3P_0$ clock transition and the differential g-factor between the two clock states for alkaline-earth(-like) atoms, using $^{87}$Sr as an example. Clock frequency shifts due to magnetic and optical fields are discussed with an emphasis on those relating to nuclear structure. An experimental determination of the differential g-factor in $^{87}$Sr is performed and is in good agreement with theory. The magnitude of the tensor light shift on the clock states is also explored experimentally. State specific measurements with controlled nuclear spin polarization are discussed as a method to reduce the nuclear spin-related systematic effects to below 10$^{-17}$ in lattice clocks.

physics.atom-ph↗

arXiv2007

Coherent optical phase transfer over a 32-km fiber with 1-s instability at $10^{-17}$

The phase coherence of an ultrastable optical frequency reference is fully maintained over actively stabilized fiber networks of lengths exceeding 30 km. For a 7-km link installed in an urban environment, the transfer instability is $6 \times 10^{-18}$ at 1-s. The excess phase noise of 0.15 rad, integrated from 8 mHz to 25 MHz, yields a total timing jitter of 0.085 fs. A 32-km link achieves similar performance. Using frequency combs at each end of the coherent-transfer fiber link, a heterodyne beat between two independent ultrastable lasers, separated by 3.5 km and 163 THz, achieves a 1-Hz linewidth.

physics.atom-ph↗

arXiv2006

$^{87}$Sr lattice clock with inaccuracy below 10$^{-15}$

Aided by ultra-high resolution spectroscopy, the overall systematic uncertainty of the $^{1}S_{0}$-$^{3}P_{0}$ clock resonance for lattice-confined $^{87}$Sr has been characterized to $9\times10^{-16}$. This uncertainty is at a level similar to the Cs-fountain primary standard, while the potential stability for the lattice clocks exceeds that of Cs. The absolute frequency of the clock transition has been measured to be 429,228,004,229,874.0(1.1) Hz, where the $2.5\times10^{-15}$ fractional uncertainty represents the most accurate measurement of a neutral-atom-based optical transition frequency to date.

physics.atom-ph↗

arXiv2006

Optical atomic coherence at the one-second time scale

Highest resolution laser spectroscopy has generally been limited to single trapped ion systems due to rapid decoherence which plagues neutral atom ensembles. Here, precision spectroscopy of ultracold neutral atoms confined in a trapping potential shows superior optical coherence without any deleterious effects from motional degrees of freedom, revealing optical resonance linewidths at the hertz level with an excellent signal to noise ratio. The resonance quality factor of 2.4 x 10^{14} is the highest ever recovered in any form of coherent spectroscopy. The spectral resolution permits direct observation of the breaking of nuclear spin degeneracy for the 1S0 and 3P0 optical clock states of 87Sr under a small magnetic bias field. This optical NMR-like approach allows an accurate measurement of the differential Lande g-factor between the two states. The optical atomic coherence demonstrated for collective excitation of a large number of atoms will have a strong impact on quantum measurement and precision frequency metrology.

physics.atom-ph↗

arXiv2005

Systematic study of the $^{87}$Sr clock transition in an optical lattice

With ultracold $^{87}$Sr confined in a magic wavelength optical lattice, we present the most precise study (2.8 Hz statistical uncertainty) to-date of the $^1S_0$ - $^3P_0$ optical clock transition with a detailed analysis of systematic shifts (20 Hz uncertainty) in the absolute frequency measurement of 429 228 004 229 867 Hz. The high resolution permits an investigation of the optical lattice motional sideband structure. The local oscillator for this optical atomic clock is a stable diode laser with its Hz-level linewidth characterized across the optical spectrum using a femtosecond frequency comb.

physics.atom-ph↗