arXiv subjects

Steven Hoekstra

Publications and source records attributed to Steven Hoekstra.

At least 19 recordsLinked to original sources

arXiv2026

High-voltage generation system for a traveling-wave Stark decelerator

In this paper we describe the high-voltage generation system we have developed for a traveling-wave Stark decelerator (TWSD). The TWSD can reduce the forward velocity of a molecular beam of heavy neutral polar molecules such as strontium monofluoride (SrF) and barium monofluoride (BaF) from $\sim$ 200 m/s down to $\sim$ 6 m/s. The main motivation for the development of this device is the increased sensitivity from precision spectroscopy of the decelerated molecules to test fundamental physics. The high-voltage generation system can produce eight pulsed sinusoidal waveforms with a maximum amplitude of 10 kV and a linear frequency sweep from 16.7 kHz down to 500 Hz over the span of 40 ms at a repetition rate of 10 Hz. The eight waveforms are phase-offset to each other by 45 degrees. To slow down the heavy molecules, the decelerator is required to have a length of $\sim$ 4 m, which results in a significant capacitive coupling between adjacent channels of $\sim$ 160 pF. As a consequence, the control and stability of the waveforms is extra challenging. We designed a method that compensates for the frequency-dependent coupling between the eight channels. Allowing for amplitude and phase-offsets that do not deviate more than 1% and 2 degrees, respectively, from their design values during the frequency sweep. The system outperforms commercially available options in terms of stability, output voltage amplitude, cost and ease of maintenance. This approach is also relevant for other fields where precise control of high-voltage waveforms is required, such as particle accelerator physics, plasma physics and mass spectroscopy.

physics.atom-ph↗

arXiv2025

A cold beam of BaOH molecules using a water-vapour seeded neon gas

In this paper we report on the production and characterization of a cold beam of BaOH molecules using a cryogenic buffer-gas beam source. BaOH is a highly suitable molecule for studies of the violation of fundamental symmetries, such as the search for the electron's electric dipole moment. BaOH molecules are synthesised inside the cold source through laser ablation of a barium metal target while water vapor is seeded into the neon buffer gas. The BaOH flux is significantly enhanced ($\sim$11 times) when laser-exciting the barium atoms inside the buffer-gas cell on the $^1\mathrm S_0 - ^3\mathrm P_1$ transition. A similar enhancement has been reported for other alkaline-earth(-like) monohydroxides. For typical source conditions, the molecular beam has an average velocity of $\approx180$ m/s and an intensity of $\sim 10^{9}$ molecules s$^{-1}$ in $N=1$, which is comparable to that of cryogenic BaF beams.

physics.atom-ph↗

arXiv2025

Single-photon loading of polar molecules into an optical trap

We propose a scheme to transfer molecules from a slow beam into an optical trap using only a single photon absorption and emission cycle. The efficiency of such a scheme is numerically explored for BaF using realistic experimental parameters. The technique makes use of the state-dependent potential in an external electric field to trap molecules from an initial velocity of order 10 m/s. A rapid optical transition at the point where the molecules come to a standstill in the electric field potential irreversibly transfers them into a ~7 mk optical lattice trap. For a pulsed Stark decelerated beam, we estimated the per-shot efficiency to be ~0.52% or up to ~10$^4$ molecules, with a potential factor 2 improvement when the fields are synchronously modulated with the arriving velocity components. The irreversibility of the scheme allows for larger numbers to be built up over time. Since this scheme does not rely on a closed cycling transition for laser cooling, it broadens the range of molecules that can be used for research on cold molecular chemistry, quantum information, and fundamental interactions in optical traps.

physics.atom-ph↗

arXiv2025

2D transverse laser cooling of a hexapole focused beam of cold BaF molecules

A cryogenic buffer gas beam, an electrostatic hexapole lens, and 2D transverse Doppler laser cooling are combined to produce a bright beam of barium monofluoride ($^{138}$Ba$^{19}$F) molecules. Experimental results and trajectory simulations are used to study the laser cooling effect as a function of laser detuning, laser power, laser alignment, and interaction time. A scattering rate of 6.1(1.4) $\times 10^{5}$ s$^{-1}$ on the laser cooling transition is obtained; this is $14 \%$ of the expected maximum, which is attributed to limited control of the magnetic field used to remix dark states. Using 3 tuneable lasers with appropriate sidebands and detuning, each molecule scatters approximately 400 photons during 2D laser cooling, limited by the interaction time and scattering rate. Leaks to dark states are less than 10$\%$. The experimental results are used to benchmark the trajectory simulations to predict the achievable flux 3.5 m downstream for a planned $e$EDM experiment.

physics.atom-ph↗

arXiv2024

Prospects for measuring the electron's electric dipole moment with polyatomic molecules in an optical lattice

We present the conceptual design of an experiment to measure the electron's electric dipole moment (eEDM) using $^{138}$BaOH molecules in an optical lattice. The BaOH molecule is laser-coolable and highly sensitive to the eEDM, making it an attractive candidate for such a precision measurement, and capturing it in an optical lattice offers potentially very long coherence times. We study possibilities and limitations of this approach, identify the most crucial limiting factors and ways to overcome them. The proposed apparatus can reach a statistical error of $10^{-30}\,e\,$cm by measuring spin precession on a total number of $5 \times 10^9$ molecules over a span of 120 days.

physics.atom-ph↗

arXiv2024

$\mathcal{P,T}$-odd effects in YbCu, YbAg and YbAu

In this work, the molecular enhancement factors of the $\mathcal{P,T}$-odd interactions involving the electron electric dipole moment ($W_\mathrm{d}$) and the scalar-pseudoscalar nucleon-electron couplings ($W_\mathrm{s}$) are computed for the ground state of the bimetallic molecules YbCu, YbAg and YbAu. These systems offer a promising venue for creating cold molecules by associating laser cooled atoms. The relativistic coupled-cluster approach is used in the calculations and a thorough uncertainty analysis is performed to give accurate and reliable uncertainties to the obtained values. Furthermore, an in-depth investigation of the different electronic structure effects that determine the magnitude of the calculated enhancement factors is carried out, and two different schemes for computing $W_\mathrm{d}$ are compared. The recommended values for the enhancement factors are $(13.24\pm0.03)\times10^{24}\frac{h\,\text{Hz}}{e\,\text{cm}}$, $(12.15\pm0.08)\times10^{24}\frac{h\,\text{Hz}}{e\,\text{cm}}$ and $(2.13\pm0.28)\times10^{24}\frac{h\,\text{Hz}}{e\,\text{cm}}$ for $W_\mathrm{d}$, and $(-48.36\pm0.18)\;h\,\text{kHz}$, $(-45.51\pm0.43)\;h\,\text{kHz}$ and $(5.31\pm1.80)\;h\,\text{kHz}$ for $W_\mathrm{s}$, for YbCu, YbAg and YbAu, respectively.

physics.chem-ph↗

arXiv2024

Manipulating a beam of barium fluoride molecules using an electrostatic hexapole

An electrostatic hexapole lens is used to manipulate the transverse properties of a beam of barium fluoride molecules from a cryogenic buffer gas source. The spatial distribution of the beam is measured by recording state-selective laser-induced fluorescence on an emccd camera, providing insight into the intensity and transverse position spread of the molecular beam. Although the high mass and unfavorable Stark shift of barium fluoride pose a considerable challenge, the number of molecules in the low-field seeking component of the N=1 state that pass a 4 mm diameter aperture 712 mm behind the source is increased by a factor of 12. Furthermore, it is demonstrated that the molecular beam can be displaced by up to +/-5 mm by moving the hexapole lens. Our measurements agree well with numerical trajectory simulations. We discuss how electrostatic lenses may be used to increase the sensitivity of beam experiments such as the search for the electric dipole moment of the electron.

physics.atom-ph↗

arXiv2024

A novel method to determine the phase-space distribution of a pulsed molecular beam

We demonstrate a novel method to determine the longitudinal phase-space distribution of a cryogenic buffer gas beam of barium-fluoride molecules based on a two-step laser excitation scheme. The spatial resolution is achieved by a transversely aligned laser beam that drives molecules from the ground state $X^2\Sigma^+$ to the $A^2\Pi_{1/2}$ state around 860 nm, while the velocity resolution is obtained by a laser beam that is aligned counter-propagating with respect to the molecular beam and that drives the Doppler shifted $A^2\Pi_{1/2}$ to $D^2\Sigma^+$ transition around 797 nm. Molecules in the $D$-state are detected virtually background-free by recording the fluorescence from the $D-X$ transition at 413 nm. As molecules in the ground state do not absorb light at 797 nm, problems due to due to optical pumping are avoided. Furthermore, as the first step uses a narrow transition, this method can also be applied to molecules with hyperfine structure. The measured phase-space distributions, reconstructed at the source exit, show that the average velocity and velocity spread vary significantly over the duration of the molecular beam pulse. Our method gives valuable insight into the dynamics in the source and helps to reduce the velocity and increase the intensity of cryogenic buffer gas beams. In addition, transition frequencies are reported for the $X-A$ and $X-D$ transitions in barium fluoride with an absolute accuracy below 0.3 MHz.

physics.atom-ph↗

arXiv2023

Mass and Shape Determination of Optically Levitated Nanoparticles

When introducing a nanoparticle into an optical trap, its mass and shape are not immediately apparent. We combine a charge-based mass measurement with a shape determination method based on light scattering and an analysis of the damping rate anisotropy, all on the same set of silica nanoparticles, trapped using optical tweezers in vacuum. These methods have previously only been used separately, and the mass determination method has not been applied to asymmetric particles before. We demonstrate that the combination of these classification techniques is required to distinguish particles with similar mass but different shape, and vice versa. The ability to identify these parameters is a key step for a range of experiments on precision measurements and sensing using optically levitated nanoparticles.

physics.optics↗

arXiv2023

Opportunities for Fundamental Physics Research with Radioactive Molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

nucl-ex↗

arXiv2022

Molecular enhancement factors for P, T-violating eEDM in BaCH$_3$ and YbCH$_3$ symmetric top molecules

High-precision tests of fundamental symmetries are looking for the parity- (P), time-reversal- (T) violating electric dipole moment of the electron (eEDM) as proof of physics beyond the Standard Model. Particularly, in polyatomic molecules, the complex vibrational and rotational structure gives the possibility to reach high enhancement of the P, T-odd effects in moderate electric fields. Additionally, it is possible to increase the statistical sensitivity by using laser cooling. In this work, we calculate the P, T-odd electronic structure parameters $W_\mathrm{d}$ and $W_\mathrm{s}$ for the promising candidates BaCH$_3$ and YbCH$_3$ for the interpretation of future experiments. We employ high-accuracy relativistic coupled cluster methods and systematically evaluate the uncertainties of our computational approach. Compared to other Ba- and Yb-containing molecules, BaCH$_3$ and YbCH$_3$ exhibit larger $W_\mathrm{d}$ and $W_\mathrm{s}$ associated to increased covalent character of the M--C bond. The calculated values are $3.22\pm 0.11 \times 10^{24}\frac{h\text{Hz}}{e\text{cm}}$ and $13.80\pm 0.35 \times 10^{24}\frac{h\text{Hz}}{e\text{cm}}$ for $W_\mathrm{d}$, and $8.42\pm0.29$~$h$kHz and $45.35\pm1.15$~$h$kHz for $W_\mathrm{s}$, in BaCH$_3$ and YbCH$_3$, respectively. The robust, accurate, and cost-effective computational scheme reported in this work makes our results suitable for extracting the relevant fundamental properties from future measurements and also can be used to explore other polyatomic molecules sensitive to various violations of fundamental symmetries.

physics.chem-ph↗

arXiv2022

Electric dipole moments and the search for new physics

Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework.

hep-ph↗

arXiv2022

Benchmarking of the Fock space coupled cluster method and uncertainty estimation: Magnetic hyperfine interaction in the excited state of BaF

We present an investigation of the performance of the relativistic multi-reference Fock-space coupled cluster (FSCC) method for predicting molecular hyperfine structure (HFS) constants, including a thorough computational study to estimate the associated uncertainties. In particular, we considered the $^{19}$F HFS constant in the ground and excited states of BaF. Due to a larger basis set dependence, the uncertainties on the excited state results (16-85%) were found to be significantly larger than those on the ground state constants ($\sim$2%). The ab initio values were compared to the recent experimental results, and good overall agreement within the theoretical uncertainties was found. This work demonstrates the predictive power of the FSCC method and the reliability of the established uncertainty estimates, which can be crucial in cases where the calculated property cannot be directly compared to experiment.

physics.atom-ph↗

arXiv2021

Systematic study and uncertainty evaluation of $P,T$-odd molecular enhancement factors in BaF

A measurement of the magnitude of the electric dipole moment of the electron (eEDM) larger than that predicted by the Standard Model (SM) of particle physics is expected to have a huge impact on the search for physics beyond the SM. Polar diatomic molecules containing heavy elements experience enhanced sensitivity to parity ($P$) and time-reversal ($T$)-violating phenomena, such as the eEDM and the scalar-pseudoscalar (S-PS) interaction between the nucleons and the electrons, and are thus promising candidates for measurements. The NL-\textit{e}EDM collaboration is preparing an experiment to measure the eEDM and S-PS interaction in a slow beam of cold BaF molecules [Eur. Phys. J. D, 72, 197 (2018)]. Accurate knowledge of the electronic structure parameters, $W_d$ and $W_s$, connecting the eEDM and the S-PS interaction to the measurable energy shifts is crucial for the interpretation of these measurements. In this work we use the finite field relativistic coupled cluster approach to calculate the $W_d$ and $W_s$ parameters in the ground state of the BaF molecule. Special attention was paid to providing a reliable theoretical uncertainty estimate based on investigations of the basis set, electron correlation, relativistic effects and geometry. Our recommended values of the two parameters, including conservative uncertainty estimates, are 3.13 $\pm$ $0.12 \times 10^{24}\frac{\text{Hz}}{e\cdot \text{cm}}$ for $W_d$ and 8.29 $\pm$ 0.12 kHz for $W_s$.

physics.atom-ph↗

arXiv2019

High accuracy theoretical investigations of CaF, SrF, and BaF and implications for laser-cooling

The NL-eEDM collaboration is building an experimental setup to search for the permanent electric dipole moment of the electron in a slow beam of cold barium fluoride molecules [Eur. Phys. J. D, 72, 197 (2018)]. Knowledge of molecular properties of BaF is thus needed to plan the measurements and in particular to determine an optimal laser-cooling scheme. Accurate and reliable theoretical predictions of these properties require incorporation of both high-order correlation and relativistic effects in the calculations. In this work theoretical investigations of the ground and the lowest excited states of BaF and its lighter homologues, CaF and SrF, are carried out in the framework of the relativistic Fock-space coupled cluster (FSCC) and multireference configuration interaction (MRCI) methods. Using the calculated molecular properties, we determine the Franck-Condon factors (FCFs) for the $A^2\Pi_{1/2} \rightarrow X^2\Sigma^{+}_{1/2}$ transition, which was successfully used for cooling CaF and SrF and is now considered for BaF. For all three species, the FCFs are found to be highly diagonal. Calculations are also performed for the $B^2\Sigma^{+}_{1/2} \rightarrow X^2\Sigma^{+}_{1/2}$ transition recently exploited for laser-cooling of CaF; it is shown that this transition is not suitable for laser-cooling of BaF, due to the non-diagonal nature of the FCFs in this system. Special attention is given to the properties of the $A'^2\Delta$ state, which in the case of BaF causes a leak channel, in contrast to CaF and SrF species where this state is energetically above the excited states used in laser-cooling. We also present the dipole moments of the ground and the excited states of the three molecules and the transition dipole moments (TDMs) between the different states.

physics.atom-ph↗

arXiv2018

Mesoscopic Interference for Metric and Curvature (MIMAC) & Gravitational Wave Detection

A compact detector for space-time metric and curvature is highly desirable. Here we show that quantum spatial superpositions of mesoscopic objects, of the type which would in principle become possible with a combination of state of the art techniques and taking into account the known sources of decoherence, could be exploited to create such a detector. By using Stern-Gerlach (SG) interferometry with masses much larger than atoms, where the interferometric signal is extracted by measuring spins, we show that accelerations as low as $5\times10^{-15}\textrm{ms}^{-2}\textrm{Hz}^{-1/2}$ or better, as well as the frame dragging effects caused by the Earth, could be sensed. Constructing such an apparatus to be non-symmetric would also enable the direct detection of curvature and gravitational waves (GWs). The GW sensitivity scales differently from the stray acceleration sensitivity, a unique feature of MIMAC. We have identified mitigation mechanisms for the known sources of noise, namely Gravity Gradient Noise (GGN), uncertainty principle and electro-magnetic forces. Hence it could potentially lead to a meter sized, orientable and vibrational noise (thermal/seismic) resilient detector of mid (ground based) and low (space based) frequency GWs from massive binaries (the predicted regimes are similar to those targeted by atom interferometers and LISA).

gr-qc↗

arXiv2018

Measuring the electric dipole moment of the electron in BaF

We investigate the merits of a measurement of the permanent electric dipole moment of the electron ($e$EDM) with barium monofluoride molecules, thereby searching for phenomena of CP violation beyond those incorporated in the Standard Model of particle physics. Although the BaF molecule has a smaller enhancement factor in terms of the effective electric field than other molecules used in current studies (YbF, ThO and ThF$^+$), we show that a competitive measurement is possible by combining Stark-deceleration, laser-cooling and an intense primary cold source of BaF molecules. With the long coherent interaction times obtainable in a cold beam of BaF, a sensitivity of $5\times10^{-30}$ e$\cdot$cm for an $e$EDM is feasible. We describe the rationale, the challenges and the experimental methods envisioned to achieve this target.

physics.atom-ph↗

arXiv2014

Preparation of an ultra-cold sample of ammonia molecules for precision measurements

We present experiments in which an ultra-cold sample of ammonia molecules is released from an electrostatic trap and recaptured after a variable time. It is shown that, by performing adiabatic cooling before releasing the molecules and adiabatic re-compression after they are recaptured, we are able to observe molecules even after more than 10 ms of free expansion. A coherent measurement performed during this time will have a statistical uncertainty that decreases approximately as the inverse of the square root of the expansion time. This offers interesting prospects for high-resolution spectroscopy and precision tests of fundamental physics theories.

physics.chem-ph↗