arXiv subjects

Kirk W. Madison

Publications and source records attributed to Kirk W. Madison.

At least 19 recordsLinked to original sources

arXiv2026

Invariance of quantum scattering rate coefficients to anisotropy of atom-molecule interactions

Quantum scattering calculations for strongly interacting molecular systems are computationally demanding due to the large number of molecular states coupled by the anisotropy of atom - molecule interactions. We demonstrate that thermal rate coefficients for total (elastic + inelastic) atom - molecule scattering are insensitive to the interaction anisotropy of the underlying potential energy surface. In particular, we show that the rate coefficients for Rb-H$_2$ and Rb-N$_2$ scattering at room temperature can be computed to 1% accuracy with anisotropy set to zero, reducing the complexity of coupled channel quantum scattering calculations to numerical solutions of a single differential equation. Our numerical calculations and statistical analysis based on Gaussian process regression elucidate the origin and limitations of the invariance of the total scattering rate coefficients to changes in atom - molecule interaction anisotropy.

physics.chem-ph↗

arXiv2024

Boundaries of universality of thermal collisions for atom-atom scattering

Thermal rate coefficients for some atomic collisions have been observed to be remarkably independent of the details of interatomic interactions at short range. This makes these rate coefficients universal functions of the long-range interaction parameters and masses, which was previously exploited to develop a self-defining atomic sensor for ambient pressure. Here, we employ rigorous quantum scattering calculations to examine the response of thermally averaged rate coefficients for atom-atom collisions to changes in the interaction potentials. We perform a comprehensive analysis of the universality, and the boundaries thereof, by treating the quantum scattering observables as probabilistic predictions determined by a distribution of interaction potentials. We show that there is a characteristic change of the resulting distributions of rate coefficients, separating light, few-electron atoms and heavy, polarizable atoms. We produce diagrams that illustrate the boundaries of the thermal collision universality at different temperatures and provide guidance for future experiments seeking to exploit the universality.

physics.atom-ph↗

arXiv2024

Revising the Universality Hypothesis for Room-temperature Collisions

Atoms constitute promising quantum sensors for a variety of scenarios including vacuum metrology. Key to this application is knowledge of the collision rate coefficient of the sensor atom with the particles being detected. Prior work demonstrated that, for room-temperature collisions, the total collision rate coefficient and the trap depth dependence of the sensor atom loss rate from shallow traps are both universal, independent of the interaction potential at short range. It was also shown that measurements of the energy transferred to the sensor atom by the collision can be used to estimate the total collision rate coefficient. However, discrepancies found when comparing the results of this and other methods of deducing the rate coefficient call into question its accuracy. Here the universality hypothesis is re-examined and an important correction is presented. We find that measurements of the post-collision recoil energy of sensor atoms held in shallow magnetic traps only provide information about the interaction potential at the very largest inter-atomic distances (e.g.~the value of $C_6$ for a leading order term of $C_6/r^6$). As other non-negligible terms exist at medium and long ranges, the total collision rate coefficient, even if universal, can differ from that computed solely from the value of $C_6$. By incorporating these other long-range terms into a simple semi-classical (SC) calculation, we find the SC prediction matches that of full, multi-channel, quantum mechanical scattering calculations using the complete potential. This work resolves the discrepancies, demonstrates the simplicity of estimating the rate coefficients for universal collision partners, and provides guidance for using atoms as a self-calibrating primary quantum pressure standard.

physics.atom-ph↗

arXiv2024

Demonstration of magnetically silent optically pumped magnetometers for the TUCAN electric dipole moment experiment

We report the performance of a magnetically silent optically pumped cesium magnetometer with a statistical sensitivity of 3.5 pT/rtHz at 1~Hz and a stability of 90 fT over 150 seconds of measurement. Optical pumping with coherent, linearly-polarized, resonant light leads to a relatively long-lived polarized ground state of the cesium vapour contained in a measurement cell. The state precesses at its Larmor frequency in the magnetic field to be measured. Nonlinear magneto-optical rotation then leads to the rotation of the plane of polarization of a linearly polarized probe laser beam. The rotation angle is modulated at twice the Larmor frequency. A measurement of this frequency constitutes an absolute measurement of the magnetic field magnitude. Featuring purely optical operation, non-magnetic construction, low noise floor, and high stability, this sensor will be used for the upcoming TUCAN electric dipole moment experiment and other highly sensitive magnetic applications. Novel aspects of the system include commercial construction and the ability to operate up to 24 sensors on a single probe laser diode.

physics.ins-det↗

arXiv2024

Competing excitation quenching and charge exchange in ultracold Li-Ba$^+$ collisions

Hybrid atom-ion systems are a rich and powerful platform for studying chemical reactions, as they feature both excellent control over the electronic state preparation and readout as well as a versatile tunability over the scattering energy, ranging from the few-partial wave regime to the quantum regime. In this work, we make use of these excellent control knobs, and present a joint experimental and theoretical study of the collisions of a single $^{138}$Ba$^+$ ion prepared in the $5d\,^2D_{3/2,5/2}$ metastable states with a ground state $^6$Li gas near quantum degeneracy. We show that in contrast to previously reported atom-ion mixtures, several non-radiative processes, including charge exchange, excitation exchange and quenching, compete with each other due to the inherent complexity of the ion-atom molecular structure. We present a full quantum model based on high-level electronic structure calculations involving spin-orbit couplings. Results are in excellent agreement with observations, highlighting the strong coupling between the internal angular momenta and the mechanical rotation of the colliding pair, which is relevant in any other hybrid system composed of an alkali-metal atom and an alkaline-earth ion.

quant-ph↗

arXiv2024

Trapped particle evolution driven by residual gas collisions

We present a comprehensive mathematical model and experimental measurements for the evolution of a trapped particle ensemble driven by collisions with a room-temperature background vapor. The model accommodates any trap geometry, confining potential, initial trapped distribution, and other experimental details; it only depends on the the probability distribution function $P_t(E)$ for the collision-induced energy transfer to the trapped ensemble. We describe how to find $P_t(E)$ using quantum scattering calculations and how it can be approximated using quantum diffractive universality. We then compare our model to experimental measurements of a $^{87}$Rb ensemble energy evolution exposed to a room temperature background gas of Ar by means of a single parameter fit for the total collision rate $Γ$. We extracted a collision rate of $Γ= 0.646(1)\ \text{s}^{-1}$. This is compared to a value of $0.664(4)\ \text{s}^{-1}$ found by the commonly used method of zero-trap depth extrapolation, a $2.8\%$ correction that is a result of our model fully taking ensemble loss and heating into account. Finally, we report a five-fold increase in the precision of our collision rate extraction from the experimental data.

physics.atom-ph↗

arXiv2024

Cross-calibration of atomic sensors for pressure metrology

Atomic sensors have shown great promise for density and pressure metrology in the high, ultra-high, and extremely-high vacuum regimes. Specifically, the density of background gas particles in vacuum can be determined by measuring the collision rate between the particles and an ensemble of sensor atoms. This requires preparing the sensor atoms in a particular quantum state, observing the rate of changes of that state, and using the cross section coefficient for state-changing collisions to convert the rate into a corresponding density. The cross section can be known by various methods including by quantum scattering calculations using an ansatz for the interaction potential between the collision pair, by measurements of the post-collision sensor-atom momentum recoil distribution, or by empirical calibration of the sensor atom at a known density. Identifying systematic errors in the results of these methods can be aided by direct comparisons between them. Alternatively, measurements of different sensor atoms exposed to the same background gas offers another point of comparison free of the systematic errors inherent in creating a background gas at a known density. Here, we present such measurements for two sensor atoms, $^{87}$Rb and $^6$Li, and a variety of atomic and molecular background gases including H$_2$, N$_2$, Ar, Ne, Kr, and Xe. We find results consistent with, yet statistically different at the level of 3.5(5)%, from recent theoretical and experiment measurements. This work demonstrates a model-free method for transferring the primacy of one atomic standard to another sensor atom and highlights the utility of sensor-atom cross-calibration experiments to check the validity of direct measurements and theoretical predictions.

physics.atom-ph↗

arXiv2022

Cross-calibration of atomic pressure sensors and deviation from quantum diffractive collision universality for light particles

The total room-temperature, velocity-averaged cross section for atom-atom and atom-molecule collisions is well approximated by a universal function depending only on the magnitude of the leading order dispersion coefficient, $C_6$. This feature of the total cross section together with the universal function for the energy distribution transferred by glancing angle collisions ($P_{\rm{QDU}6}$) can be used to empirically determine the total collision cross section and realize a self-calibrating, vacuum pressure standard. This was previously validated for Rb+N$_2$ and Rb+Rb collisions. However, the post-collision energy distribution is expected to deviate from $P_{\rm{QDU}6}$ in the limit of small $C_6$ and small reduced mass. Here we observe this deviation experimentally by performing a direct cross-species loss rate comparison between Rb+H$_2$ and Li+H$_2$ and using the \textit{ab initio} value of $\langle σ_{\rm{tot}} \, v \rangle_{\rm{Li+H}_2}$. We find a velocity averaged total collision cross section ratio, $R = \langle σ_{\rm{tot}} \, v \rangle_{\rm{Li+H}_2} : \langle σ_{\rm{tot}} \, v \rangle_{\rm{Rb+H}_2} = 0.83(5)$. Based on an \textit{ab initio} computation of $\langle σ_{\rm{tot}} \, v \rangle_{\rm{Li+H}_2} = 3.13(6)\times 10^{-15}$ m$^3$/s, we deduce $\langle σ_{\rm{tot}} \, v \rangle_{\rm{Rb+H}_2} = 3.8(2) \times 10^{-15}$ m$^3$/s, in agreement with a Rb+H$_2$ \textit{ab initio} value of $\langle σ_{\mathrm{tot}} v \rangle_{\mathrm{Rb+H_2}} = 3.57 \times 10^{-15} \mathrm{m}^3/\mathrm{s}$.By contrast, fitting the Rb+H$_2$ loss rate as a function of trap depth to the universal function we find $\langle σ_{\rm{tot}} \, v \rangle_{\rm{Rb+H}_2} = 5.52(9) \times 10^{-15}$ m$^3$/s. Finally, this work demonstrates how to perform a cross-calibration of sensor atoms to extend and enhance the cold atom based pressure sensor.

physics.atom-ph↗

arXiv2022

Measurement of Rb-Rb van der Waals coefficient via Quantum Diffractive Universality

Collisions between trapped atoms or trapped molecules with room temperature particles in the surrounding vacuum induce loss of the trapped population at a rate proportional to the density of the background gas particles. The total velocity-averaged loss rate coefficient $\langle σ_\mathrm{tot} v \rangle$ for such collisions and the variation of the loss rate with trap depth has been shown to depend only on the long range interaction potential between the collision partners. This collision universality was previously used to realize a self-calibrating, atom-based, primary pressure standard and was validated by indirect comparison with an orifice flow standard. Here, we use collision universality to measure $\langle σ_\mathrm{tot} v \rangle = 6.44(11)(5) \times 10^{-15}~\rm{m^3/s}$ for Rb-Rb collisions and deduce the corresponding $C_6 = 4688(198)(95)~E_ha_0^6$, in excellent agreement with predictions based upon $\textit{ab initio}$ calculated and previously measured $C_6$ values.

physics.atom-ph↗

arXiv2022

The Precision nEDM Measurement with UltraCold Neutrons at TRIUMF

The TRIUMF Ultra-Cold Advanced Neutron (TUCAN) collaboration aims at a precision neutron electric dipole moment (nEDM) measurement with an uncertainty of $10^{-27}\,e\cdot\mathrm{cm}$, which is an order-of-magnitude better than the current nEDM upper limit and enables us to test Supersymmetry. To achieve this precision, we are developing a new high-intensity ultracold neutron (UCN) source using super-thermal UCN production in superfluid helium (He-II) and a nEDM spectrometer. The current development status of them is reported in this article.

physics.ins-det↗

arXiv2019

Universality of Diffractive Collisions and the Quantum Pressure Standard

This work demonstrates that quantum diffractive collisions, those that result in very small momentum and energy transfer, are universal. Specifically, the cumulative energy distribution transferred to an initially stationary sensor particle by a quantum diffractive collision follows a universal function that depends only on the sensor particle mass and the thermally-averaged, total collision cross section. The characteristic energy scale corresponds to the localization length associated with the collision-induced quantum measurement, and the shape of the universal function is determined {\it only} by the analytic form of the interaction potential at long range. Using cold $^{87}$Rb sensor atoms confined in a magnetic trap, we observe experimentally the universal function specific to van der Waals collisions, and realize a \emph{self-defining} particle pressure sensor that can be used for any ambient gas. This provides the first primary and quantum definition of the Pascal, applicable to any species and therefore represents a key advance for vacuum and pressure metrology. The quantum pressure standard realized here was compared with a state-of-the-art orifice flow standard transferred by an ionization gauge calibrated for N$_2$. The pressure measurements agreed at the 0.5\% level.

physics.atom-ph↗

arXiv2017

The performance and limitations of FPGA-based digital servos for atomic, molecular, and optical physics experiments

In this work we address the advantages, limitations, and technical subtleties of employing FPGA-based digital servos for high-bandwidth feedback control of lasers in atomic, molecular, and optical (AMO) physics experiments. Specifically, we provide the results of benchmark performance tests in experimental setups including noise, bandwidth, and dynamic range for two digital servos built with low and mid-range priced FPGA development platforms. The digital servo results are compared to results obtained from a commercially available state-of-the-art analog servo using the same plant for control (intensity stabilization). The digital servos have feedback bandwidths of 2.5 MHz, limited by the total signal latency, and we demonstrate improvements beyond the transfer function offered by the analog servo including a three pole filter and a two pole filter with phase compensation to suppress resonances. We also discuss limitations of our FPGA-servo implementation and general considerations when designing and using digital servos.

physics.ins-det↗

arXiv2015

An Adaptable Dual Species Effusive Source and Zeeman Slower Design Demonstrated with Rb and Li

We present a dual-species effusive source and Zeeman slower designed to produce slow atomic beams of two elements with a large mass difference and with very different oven temperature requirements. We demonstrate this design for the case of $^6$Li and $^{85}$Rb and achieve MOT loading rates equivalent to that reported in prior work on dual species (Rb+Li) Zeeman slowers operating at the same oven temperatures. Key design choices, including thermally separating the effusive sources and using a segmented coil design to enable computer control of the magnetic field profile, ensure that the apparatus can be easily modified to slow other atomic species. By performing the final slowing using the quadruple magnetic field of the MOT, we are able to shorten our Zeeman slower length making for a more compact system without compromising performance. We outline the construction and analyze the emission properties of our effusive sources. We also verify the performance of the source and slower, and we observe sequential loading rates of $8 \times 10^8$ atoms/s for a Rb oven temperature of $120\,^{\circ}$C and $1.5 \times 10^8$ atoms/s for a Li reservoir at $450\,^{\circ}$C, corresponding to reservoir lifetimes for continuous operation of 10 and 4 years respectively.

physics.atom-ph↗

arXiv2015

A method for independent and continuous tuning of $N$ lasers phase-locked to the same frequency comb

We present a method of phase-locking any number of continuous-wave lasers to an optical frequency comb (OFC) that enables independent frequency positioning and control of each laser while still maintaining lock to the OFC. The scheme employs an acousto-optic modulator (AOM) in a double pass configuration added to each laser before its light is compared by optical heterodyne with the comb. The only requirement is that the tuning bandwidth of the double pass AOM setup be larger than half the OFC repetition rate. We demonstrate this scheme and achieve an arbitrary frequency tuning precision, a tuning rate of 200~MHz/s and a readout precision at the 1~kHz level.

physics.atom-ph↗

arXiv2015

Transparent Electrodes for High E-Field Production Using A Buried ITO Layer

We present a design and characterization of optically transparent electrodes suitable for atomic and molecular physics experiments where high optical access is required. The electrodes can be operated in air at standard atmospheric pressure and do not suffer electrical breakdown even for electric fields far exceeding the dielectric breakdown of air. This is achieved by putting an ITO coated dielectric substrate inside a stack of dielectric substrates, which prevents ion avalanche resulting from Townsend discharge. With this design, we observe no arcing for fields of up to 120 kV/cm. Using these plates, we directly verify the production of electric fields up to 18~kV/cm inside a quartz vacuum cell by a spectroscopic measurement of the dc Stark shift of the $5^2S_{1/2} \rightarrow 5^2P_{3/2}$ transition for a cloud of laser cooled Rubidium atoms. We also report on the shielding of the electric field and residual electric fields that persist within the vacuum cell once the electrodes are discharged. In addition, we discuss observed atom loss that results from the motion of free charges within the vacuum. The observed asymmetry of these phenomena on the bias of the electrodes suggests that field emission of electrons within the vacuum is primarily responsible for these effects and may indicate a way of mitigating them.

physics.ins-det↗

arXiv2015

Transforming a 4th year Modern Optics Course Using a Deliberate Practice Framework

We present a study of active learning pedagogies in an upper division physics course. This work was guided by the principle of deliberate practice for the development of expertise, and this principle was used in the design of the materials and the orchestration of the classroom activities of the students. We present our process for efficiently converting a traditional lecture course based on instructor notes into activities for such a course with active learning methods. Ninety percent of the same material was covered and scores on common exam problems showed a 15 % improvement with an effect size greater than 1 after the transformation. We observe that the improvement and the associated effect size is sustained after handing off the materials to a second instructor. Because the improvement on exam questions was independent of specific problem topics and because the material tested was so mathematically advanced and broad (including linear algebra, Fourier Transforms, partial differential equations, vector calculus), we expect the transformation process could be applied to most upper division physics courses having a similar mathematical base.

physics.ed-ph↗

arXiv2013

Chemical reactions of ultracold alkali-metal dimers in the lowest-energy $^3Σ$ state

We show that the interaction of polar alkali dimers in the quintet spin state leads to the formation of a deeply bound reaction complex. The reaction complex can decompose adiabatically into homonuclear alkali dimers (for all molecules except KRb) and into alkali trimers (for all molecules). We show that there are no barriers for these chemical reactions. This means that all alkali dimers in the $a^3Σ^+$ state are chemically unstable at ultracold temperature, and the use of an optical lattice to segregate the molecules and suppress losses may be necessary. In addition, we calculate the minimum energy path for the chemical reactions of alkali hydrides. We find that the reaction of two molecules is accelerated by a strong attraction between the alkali atoms, leading to a barrierless process that produces hydrogen atoms with large kinetic energy. We discuss the unique features of the chemical reactions of ultracold alkali dimers in the $a^3Σ^+$ electronic state.

physics.atom-ph↗

arXiv2013

High resolution photoassociation spectroscopy of the $^{6}$Li$_2$ $1^{3}Σ_{g}^{+}$ state

We present experimental observations of seven vibrational levels $v'=20-26$ of the $1^{3}Σ_{g}^{+}$ excited state of Li$_2$ molecules by the photoassociation (PA) of a degenerate Fermi gas of $^6$Li atoms. For each vibrational level, we resolve the rotational structure using a Feshbach resonance to enhance the PA rates from p-wave collisions. We also, for the first time, determine the spin-spin and spin-rotation interaction constants for this state. The absolute uncertainty of our measurements is $\pm 0.00002$ cm$^{-1}$ ($\pm 600$ kHz). We use these new data to further refine an analytic potential for this state.

physics.atom-ph↗