arXiv subjects

M. D. Barrett

Publications and source records attributed to M. D. Barrett.

At least 19 recordsLinked to original sources

arXiv2026

Measurement of the reduced dipole matrix element in Ba$^+$

We present a high-precision measurement of the reduced electric-dipole matrix element $\langle P_{1/2}\|r\|S_{1/2}\rangle$ in $^{138}\mathrm{Ba}^+$. By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be $3.322\,7(12)$, corresponding to a $P_{1/2}$ excited-state radiative lifetime of $7.866\,3(56)$~ns. Combining our experimental results with a prior model for the differential scalar polarizability $\Delta\alpha_0(\omega)$, we extract the static value $\Delta\alpha_0(0) = -73.09(12)$a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature $\mathrm{Ba}^+$ optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.

physics.atom-ph↗

arXiv2026

Absolute frequency measurement of the $^{176}$Lu$^+\,(^{3}\mathrm{D}_1)$ standard against the NRC-FCs2 fountain with $2.6\times10^{-16}$ uncertainty

We report an improved absolute frequency measurement of the $^{176}$Lu$^+\,(^{3}\mathrm{D}_1)$ optical frequency standard, evaluated via a remote link to the NRC-FCs2 caesium fountain primary frequency standard. Operating a single ion clock with 94.2% uptime over 10 days, and using an ambiguity-resolved precise point positioning (PPP-AR) link over the Global Positioning System (GPS), we determine an absolute frequency of $353\,638\,794\,073\,800.33(9)\,$Hz at a fractional uncertainty of $2.6 \times 10^{-16}$. This agrees with our previous result, which underpins the CIPM recommended frequency value, and reduces the uncertainty by a factor of 3.6.

physics.atom-ph↗

arXiv2025

Optical clocks with accuracy validated at the 19th digit

We report a comprehensive evaluation of all known sources of systematic uncertainty for two independent $^{176}$Lu$^+$ single-ion optical references, finding total systematic uncertainty of $1.1\times10^{-19}$ and $1.4\times10^{-19}$ for the two individual systems and $9.6\times10^{-20}$ for the difference. Through direct comparison via correlation spectroscopy, we demonstrate a relative frequency agreement of $-2.4\pm(5.7)_\mathrm{stat}\pm(1.0)_\mathrm{sys}\times10^{-19}$, where `stat' and `sys' indicate the statistical and systematic uncertainty, respectively. The comparison uncertainty is statistically limited after approximately 200 hours of averaging with a measurement instability of $4.8\times10^{-16}(\tau/\mathrm{s})^{-1/2}$.

physics.atom-ph↗

arXiv2025

Analysis of collision shift assessments in ion-based clocks

We consider back-ground gas collision shifts in ion-based clocks. We give both a classical and quantum description of a collision between an ion and a polarizable particle with a simple hard-sphere repulsion. Both descriptions give consistent results, which shows that a collision shift bound is determined by the classical Langevin collision rate reduced by a readily calculated factor describing the decoupling of the clock laser from the ion due to the recoil motion. We also show that the result holds when using a more general Lennard-Jones potential to describe the interaction between the ion and its collision partner. This leads to a simple bound for the collision shift applicable to any single ion clock without resorting to large-scale Monte-Carlo simulations or determination of molecular potential energy curves describing the collision. It also provides a relatively straightforward means to measure the relevant collision rate.

physics.atom-ph↗

arXiv2025

Precision measurement of the $^{176}\mathrm{Lu}^+$ $^3D_1$ microwave clock transitions

We report precision measurement of the unperturbed ${^{3}}D_1$ microwave transition frequencies in $^{176}\mathrm{Lu}^+$ to a fractional uncertainty of $4\times10^{-14}$. We find the $|F,m_F\rangle=|8,0\rangle$ to $|7,0\rangle$ hyperfine transition frequency to be $10\,491\,519\,945.228\,82(38)\,$Hz and the $|7,0\rangle$ to $|6,0\rangle$ transition frequency to be $11\,290\,004\,289.881\,61(36)\,$ Hz. At this precision we are able to observe the hyperfine-mediated effects in the ratio of the quadrupole shifts, from which we can directly infer the residual quadrupole moment after $^3D_1$ hyperfine averaging. We find a residual quadrupole moment of ${-2.48(23)\times10^{-4}}\,e a_0^2$, consistent with a previous assessment using a different and less direct method. With the unperturbed microwave frequencies accurately known, the residual quadrupole shift for a $^{176}\mathrm{Lu}^+$ ($^3D_1$) optical frequency standard can henceforth be readily evaluated to $<10^{-20}$ uncertainty by routine ${^{3}}{D}_1$ microwave spectroscopy.

physics.atom-ph↗

arXiv2025

Zeeman Degenerate Sideband Cooling in $^{176}$Lu$^+$

We explore degenerate Raman sideband cooling in which neighboring Zeeman states of a fixed hyperfine level are coupled via a two-photon Raman transition. The degenerate coupling between $|F,m_F\rangle\rightarrow |F,m_F-1\rangle$ facilitates the removal of multiple motional quanta in a single cycle. This method greatly reduces the number of cooling cycles required to reach the ground state compared to traditional sideband cooling. We show that near ground state cooling can be achieved with a pulse number as low as $\bar{n}$ where $\bar{n}$ is the average phonon number in the initial thermal state. We demonstrate proof-of-concept in $^{176}\mathrm{Lu}^+$ by coupling neighboring Zeeman levels on the motional sideband for the $F=7$ hyperfine level in $^3D_1$. Starting from a thermal distribution with an average phonon number of 6, we demonstrate near ground-state cooling with $\sim10$ pulses. A theoretical description is given that applies to any $F$ level and demonstrates how effective this approach can be.

quant-ph↗

arXiv2025

Lande g-factor measurements for the 5d6s 3D2 hyperfine levels of 176Lu+

We report measurements of the Lande g-factors for the 5d6s $^3$D$_2$ hyperfine levels of $^{176}$Lu$^+$ to a fractional inaccuracy of $5\times 10^{-7}$. Combining these measurements with theoretical calculations allows us to estimate hyperfine-mediated modifications to the quadrupole moments for each state and infer a value of $\delta\Theta = 1.59(34)\times 10^{-4} \,ea_0^2$ for the residual quadrupole moment of the $^1S_0\leftrightarrow{^3}D_2$ hyperfine-averaged clock transition.

physics.atom-ph↗

arXiv2025

Absolute frequency measurement of a Lu$^+$ $(^{3}\rm D_1)$ optical frequency standard via link to international atomic time

We report on an absolute frequency measurement of the ${\rm Lu}^{+}\,(^{3}\rm D_1)$ standard frequency which is defined as the hyperfine-average of $^{1}\rm S_0$ to $^{3}\rm D_1$ optical clock transitions in $^{176}{\rm Lu}^{+}$. The measurement result of $353\,638\,794\,073\,800.35(33)$Hz with a fractional uncertainty of $9.2 \times 10^{-16}$ was obtained by operating a single-ion $^{176}{\rm Lu}^{+}$ frequency standard intermittently over 3 months with a total uptime of 162 hours. Traceability to the International System of Units (SI) is realized by remote link to International Atomic Time. This is the first reported absolute frequency value for a ${\rm Lu}^{+}\,(^{3}\rm D_1)$ optical frequency standard.

physics.atom-ph↗

arXiv2024

An extrapolation method for polarizability assessments of ion-based optical clocks

We present a numerical method for extrapolating polarizability measurements to dc as done in the assessment of blackbody radiation shifts for ion-based clocks. The method explicitly accounts for the frequency dependence of relevant atomic transitions without introducing an ad hoc modelling function. It incorporates \emph{a priori} atomic structure calculations, which allows measurements to be augmented by calculations if there is insufficient data to make a purely measurement based estimate. The method also provides indicators of inconsistencies between theory and experiment or inadequacies of the data for making an extrapolation. We use results from Al$^+$, Lu$^+$, and Yb$^+$ to illustrate features of the method.

physics.atom-ph↗

arXiv2024

Enhanced micromotion compensation using a phase modulated light field

We investigate sideband spectroscopy of a trapped ion using a probe laser phase modulated at the trap drive frequency. The enhanced sensitivity of our technique over traditional sideband spectroscopy allows us to detect stray fields of $0.01\,\mathrm{V/m}$ on a timescale of a few minutes and detect differential phases of $5\,μ\mathrm{rad}$ between applied ac potentials. We also demonstrate the ability suppress Doppler shifts from excess motion to well below the limit imposed by the intrinsic motion of the ion in the vibrational ground-state. The technique we introduce can be readily implemented in any ion trap system that utilizes sideband spectroscopy for micromotion compensation and can be seamlessly integrated into experiments in a fully automated way

physics.atom-ph↗

arXiv2022

$^{176}$Lu$^+$ clock comparison at the $10^{-18}$ level via correlation spectroscopy

We experimentally demonstrate agreement between two $^{176}$Lu$^+$ frequency references using correlation spectroscopy. From a comparison at different magnetic fields, we obtain a quadratic Zeeman coefficient of $-4.89264(88)\,\mathrm{Hz/mT^2}$, which gives a corresponding fractional frequency uncertainty contribution of just $2.5\times 10^{-20}$ for comparisons at typical operating fields of 0.1\,mT. A subsequent comparison with both systems at 0.1\,mT, demonstrates a fractional frequency difference of $(-2.0\pm(3.7)_\mathrm{stat}\pm(0.9)_\mathrm{sys})\times10^{-18}$, where `stat' and `sys' indicate statistical and systematic uncertainty, respectively.

quant-ph↗

arXiv2020

Hyperfine-mediated effects in a Lu$^+$ optical clock

We consider hyperfine-mediated effects for clock transitions in $^{176}$Lu$^+$. Mixing of fine structure levels due to the hyperfine interaction bring about modifications to Landé $g$-factors and the quadrupole moment for a given state. Explicit expressions are derived for both $g$-factor and quadrupole corrections, for which leading order terms arise from the nuclear magnetic dipole coupling. High accuracy measurements of the $g$-factors for the $^1S_0$ and $^3D_1$ hyperfine levels are carried out, which provide an experimental determination of the leading order correction terms.

physics.atom-ph↗

arXiv2020

Precision measurement of the $^3D_1$ and $^3D_2$ quadrupole moments in Lu$^+$

Precision measurements of the Lu$^+$ $^3D_1$ and $^3D_2$ quadrupole moments have been carried out giving $Θ(^3D_1)=0.63862(74)\,e a_0^2$ and $Θ(^3D_2)=0.8602(14)\,e a_0^2$, respectively. The measurements utilize the differential shift between ions in a multi-ion crystal so that effects of external field gradients do not contribute leaving only the well defined Coulomb interaction. At this level of precision, hyperfine-mediated corrections will likely be important.

physics.atom-ph↗

arXiv2020

Magic wavelength of the $^{138}$Ba$^+$ $6s\;{}^2S_{1/2}-5d\;{}^2D_{5/2}$ clock transition

The zero crossing of the dynamic differential scalar polarizability of the $S_{1/2}-D_{5/2}$ clock transition in $^{138}$Ba$^+$ has been determined to be $459.1614(28)\,$THz. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ($\gtrsim 700\,$nm). In particular it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.

physics.atom-ph↗

arXiv2020

Branching fractions for $P_{3/2}$ decays in Ba$^+$

Branching fractions for decays from the $P_{3/2}$ level in $^{138}$Ba$^+$ have been measured with a single laser-cooled ion. Decay probabilities to $S_{1/2}$, $D_{3/2}$ and $D_{5/2}$ are determined to be $0.741716(71)$, $0.028031(23)$ and $0.230253(61)$, respectively, which are an order of magnitude improvement over previous results. Our methodology only involves optical pumping and state detection, and is hence relatively free of systematic effects. Measurements are carried out in two different ways to check for consistency. Our analysis also includes a measurement of the $D_{5/2}$ lifetime, for which we obtain 30.14(40)\,s.

physics.atom-ph↗

arXiv2019

Measurements of the branching ratios for $6P_{1/2}$ decays in $^{138}$Ba$^+$

Measurement of the branching ratios for $6P_{1/2}$ decays to $6S_{1/2}$ and $5D_{3/2}$ in $^{138}$Ba$^+$ are reported with the decay probability from $6P_{1/2}$ to $5D_{3/2}$ measured to be $p=0.268177\pm(37)_\mathrm{stat}-(20)_\mathrm{sys}$. This result differs from a recent report by $12σ$. A detailed account of systematics is given and the likely source of the discrepancy is identified. The new value of the branching ratio is combined with a previous experimental results to give a new estimate of $τ=7.855(10)\,\mathrm{ns}$ for the $6P_{1/2}$ lifetime. In addition, ratios of matrix elements calculated from theory are combined with experimental results to provide improved theoretical estimates of the $6P_{3/2}$ lifetime and the associated matrix elements.

physics.atom-ph↗

arXiv2019

Polarizability assessments of ion-based optical clocks

It is shown that the dynamic differential scalar polarisability of the $S_{1/2}-D_{5/2}$ transition in $^{138}$Ba$^+$ can be determined to an inaccuracy below $0.5\%$ across a wide wavelength range ($λ>700\,\mathrm{nm}$). This can be achieved using measurements for which accurate determination of laser intensity is not required, and most of the required measurements are already in the literature. Measurement of a laser-induced ac-stark shift of the clock transition would then provide an \emph{in situ} measurement of the laser's intensity to the same $0.5\%$ level of inaccuracy, which is not easily achieved by other means. This would allow accurate polarisability measurements for clock transitions in other ions, through comparison with $^{138}$Ba$^+$. The approach would be equally applicable to Sr$^+$ and Ca$^+$, with the latter being immediately applicable to Al$^+$/Ca$^+$ quantum logic clocks.

physics.atom-ph↗

arXiv2019

Hyperfine averaging by dynamic decoupling in a multi-ion lutetium clock

We propose and experimentally demonstrate a scheme which effects hyperfine averaging during a Ramsey interrogation of a clock transition. The method eliminates the need to average over multiple optical transitions, reduces the sensitivity of the clock to its environment, and reduces inhomogeneous broadening in a multi-ion clock. The method is compatible with auto-balanced Ramsey spectroscopy, which facilitates elimination of residual shifts due to imperfect implementation and ac Stark shifts from the optical probe. We demonstrate the scheme using correlation spectroscopy of the $^1S_0$-to-$^3D_1$ clock transition in a three-ion Lu+ clock. From the demonstration we are able to provide a measurement of the $^3D_1$ quadrupole moment, $Θ(^3D_1)=0.634(9)ea_0^2$.

quant-ph↗