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An activity fundamental to science is building mathematical models. These models are used to both predict the results of future experiments and gain insight into the structure of the system under study. We present an algorithm that automates the model building process in a scientifically principled way. The algorithm can take observed trajectories from a wide variety of mechanical systems and, without any other prior knowledge or tuning of parameters, predict the future evolution of the system. It does this by applying the principle of least action and searching for the simplest Lagrangian that describes the system's behaviour. By generating this Lagrangian in a human interpretable form, it also provides insight into the working of the system., Comment: 9 pages, 6 figures

We describe an experiment in which cold rubidium atoms, confined in an elongated magnetic trap, are excited by transverse oscillation of the trap centre. The temperature after excitation exhibits resonance as a function of the driving frequency. We measure these resonances at several different trap frequencies. In order to interpret the experiments, we develop a simple model that incorporates both collisions between atoms and the anharmonicity of the real three-dimensional trapping potential. As well as providing a precise connection between the transverse harmonic oscillation frequency and the temperature resonance frequency, this model gives insight into the heating and loss mechanisms, and into the dynamics of driven clouds of cold trapped atoms., Comment: 7 pages, 8 figures

We demonstrate slowing and longitudinal cooling of a supersonic beam of CaF molecules using counter-propagating laser light resonant with a closed rotational and almost closed vibrational transition. A group of molecules are decelerated by about 20 m/s by applying light of a fixed frequency for 1.8 ms. Their velocity spread is reduced, corresponding to a final temperature of about 300 mK. The velocity is further reduced by chirping the frequency of the light to keep it in resonance as the molecules slow down., Comment: 6 pages, 6 figures

High-precision measurements benefit from lock-in detection of small signals. Here we discuss the extension of lock-in detection to many channels, using mutually orthogonal modulation waveforms, and show how the the choice of waveforms affects the information content of the signal. We also consider how well the detection scheme rejects noise, both random and correlated. We address the particular difficulty of rejecting a background drift that makes a reproducible offset in the output signal and we show how a systematic error can be avoided by changing the waveforms between runs and averaging over many runs. These advances made possible a recent measurement of the electron's electric dipole moment., Comment: 11 pages, 3 figures

We propose an experiment to measure the electric dipole moment of the electron using ultracold YbF molecules. The molecules are produced as a thermal beam by a cryogenic buffer gas source, and brought to rest in an optical molasses that cools them to the Doppler limit or below. The molecular cloud is then thrown upward to form a fountain in which the electric dipole moment of the electron is measured., Comment: 18 pages, 8 figures, 53 references

We recently reported a new measurement of the electron's electric dipole moment using YbF molecules [Nature 473, 493 (2011)]. Here, we give a more detailed description of the methods used to make this measurement, along with a fuller analysis of the data. We show how our methods isolate the electric dipole moment from imperfections in the experiment that might mimic it. We describe the systematic errors that we discovered, and the small corrections that we made to account for these. By making a set of additional measurements with greatly exaggerated experimental imperfections, we find upper bounds on possible uncorrected systematic errors which we use to determine the systematic uncertainty in the measurement. We also calculate the size of some systematic effects that have been important in previous electric dipole moment measurements, such as the motional magnetic field effect and the geometric phase, and show them to be negligibly small in the present experiment. Our result is consistent with an electric dipole moment of zero, so we provide upper bounds to its size at various confidence levels. Finally, we review the prospects for future improvements in the precision of the experiment., Comment: 35 pages, 15 figures

The fluorescence spectrum resulting from laser excitation of the A^{2}\Pi_{1/2} - X^{2}\Sigma^{+} (0,0) band of ytterbium monofluoride, YbF, has been recorded and analyzed to determine the Franck-Condon factors. The measured values are compared with those predicted from Rydberg-Klein-Rees (RKR) potential energy curves. From the fluorescence decay curve the radiative lifetime of the A^{2}\Pi_{1/2} state is measured to be 28\pm2 ns, and the corresponding transition dipole moment is 4.39\pm0.16 D. The implications for laser cooling YbF are discussed., Comment: 5 pages, 5 figures

We report the Stark deceleration of CaF molecules in the strong-field seeking ground state and in a weak-field seeking component of a rotationally-excited state. We use two types of decelerator, a conventional Stark decelerator for the weak-field seekers, and an alternating gradient decelerator for the strong-field seekers, and we compare their relative merits. We also consider the application of laser cooling to increase the phase-space density of decelerated molecules., Comment: 10 pages, 8 figures

We discuss an experiment underway at Imperial College London to measure the permanent electric dipole moment (EDM) of the electron using a molecular beam of YbF. We describe the measurement method, which uses a combination of laser and radiofrequency resonance techniques to detect the spin precession of the YbF molecule in a strong electric field. We pay particular attention to the analysis scheme and explore some of the possible systematic effects which might mimic the EDM signal. Finally, we describe technical improvements which should increase the sensitivity by more than an order of magnitude over the current experimental limit., Comment: 6 pages, 2 figures

We produce YbF molecules with a density of 10^18 m^-3 using laser ablation inside a cryogenically-cooled cell filled with a helium buffer gas. Using absorption imaging and absorption spectroscopy we study the formation, diffusion, thermalization and optical pumping of the molecules. The absorption images show an initial rapid expansion of molecules away from the ablation target followed by a much slower diffusion to the cell walls. We study how the time constant for diffusion depends on the helium density and temperature, and obtain values for the YbF-He diffusion cross-section at two different temperatures. We measure the translational and rotational temperatures of the molecules as a function of time since formation, obtain the characteristic time constant for the molecules to thermalize with the cell walls, and elucidate the process responsible for limiting this thermalization rate. Finally, we make a detailed study of how the absorption of the probe laser saturates as its intensity increases, showing that the saturation intensity is proportional to the helium density. We use this to estimate collision rates and the density of molecules in the cell., Comment: 20 pages, 11 figures, minor revisions following referee suggestions

We demonstrate Doppler-free saturated absorption spectroscopy of cold molecular radicals formed by laser ablation inside a cryogenic buffer gas cell. By lowering the temperature, congested regions of the spectrum can be simplified, and by using different temperatures for different regions of the spectrum a wide range of rotational states can be studied optimally. We use the technique to study the optical spectrum of YbF radicals with a resolution of 30 MHz, measuring the magnetic hyperfine parameters of the electronic ground state. The method is suitable for high resolution spectroscopy of a great variety of molecules at controlled temperature and pressure, and is particularly well-suited to those that are difficult to produce in the gas phase., Comment: 11 pages, 4 figures

An alternating gradient electric guide provides a way to transport a wide variety of polar molecules, including those in high-field seeking states. We investigate the motion of polar molecules in such a guide by measuring the transmission of CaF molecules in their high-field seeking ground state, with the guide operating at a variety of switching frequencies and voltages. We model the guide using analytical and numerical techniques and compare the predictions of these models to the experimental results and to one another. The analytical results are approximate, but provide simple and useful estimates for the maximum phase-space acceptance of the guide and for the switching frequency required. The numerical methods provide more accurate results over the full range of switching frequencies. Our investigation shows that, even when the fields are static, some high-field seeking molecules are able to pass through the guide on metastable trajectories. We show that the maximum possible transmission requires accurate alignment within the guide and between the guide and detector., Comment: 10 pages, 5 figures; revised following referee suggestions

Heavy polar molecules can be used to measure the electric dipole moment of the electron, which is a sensitive probe of physics beyond the Standard Model. The value is determined by measuring the precession of the molecule's spin in a plane perpendicular to an applied electric field. The longer this precession evolves coherently, the higher the precision of the measurement. For molecules in a trap, this coherence time could be very long indeed. We evaluate the sensitivity of an experiment where neutral molecules are trapped electrically, and compare this to an equivalent measurement in a molecular beam. We consider the use of a Stark decelerator to load the trap from a supersonic source, and calculate the deceleration efficiency for YbF molecules in both strong-field seeking and weak-field seeking states. With a 1s holding time in the trap, the statistical sensitivity could be ten times higher than it is in the beam experiment, and this could improve by a further factor of five if the trap can be loaded from a source of larger emittance. We study some effects due to field inhomogeneity in the trap and find that rotation of the electric field direction, leading to an inhomogeneous geometric phase shift, is the primary obstacle to a sensitive trap-based measurement., Comment: 22 pages, 7 figures, prepared for Faraday Discussion 142

Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the invariant formalism of quantum mechanics. I first describe the essential mathematical features of the Hilbert-space invariant formalism. This is followed by a formal characterisation of all possible algebraic expressions in this formalism. This characterisation is provided in the form of a set of terms. Rewrite rules over this set of terms are then developed that correspond to allowed manipulations of the algebraic expressions. This approach is contrasted with current attempts to build invariant quantum mechanics calculations into computer algebra systems., Comment: 16 pages, 1 table

A circuit capable of measuring nanoampere currents while floating at voltages up to at least 25kV is described. The circuit relays its output to ground potential via an optical fiber. We particularly emphasize the design and construction techniques which allow robust operation in the presence of high voltage spikes and discharges., Comment: 5 pages, 2 figures

We describe a method for determining the radiative decay properties of a molecule by studying the saturation of laser-induced fluorescence and the associated power broadening of spectral lines. The fluorescence saturates because the molecules decay to states that are not resonant with the laser. The amplitudes and widths of two hyperfine components of a spectral line are measured over a range of laser intensities and the results compared to a model of the laser-molecule interaction. Using this method we measure the lifetime of the A(v'=0) state of CaF to be tau=19.2 \pm 0.7 ns, and the Franck-Condon factor for the transition to the X(v=0) state to be Z=0.987 (+0.013 || -0.019). In addition, our analysis provides a measure of the hyperfine interval in the lowest-lying state of A(v'=0), Delta_e=4.8 \pm 1.1 MHz., Comment: 10 pages, 6 figures. Minor revisions following referee suggestions

This paper is a chapter from an upcoming book on cold molecule physics. In it we describe techniques for the preparation and manipulation of cold molecules. We further describe techniques for applying said cold molecules to tests of fundamental physics., Comment: 22 pages, 18 figures

We describe a technique for mapping the spatial variation of static electric, static magnetic, and rf magnetic fields using a pulsed atomic or molecular beam. The method is demonstrated using a beam designed to measure the electric dipole moment of the electron. We present maps of the interaction region, showing sensitivity to (i) electric field variation of 1.5 V/cm at 3.3 kV/cm with a spatial resolution of 15 mm; (ii) magnetic field variation of 5 nT with 25 mm resolution; (iii) radio-frequency magnetic field amplitude with 15 mm resolution. This new diagnostic technique is very powerful in the context of high-precision atomic and molecular physics experiments, where pulsed beams have not hitherto found widespread application., Comment: 6 pages, 12 figures. Figures heavily compressed to comply with arxiv's antediluvian file-size policy

We have developed a source of cold LiH molecules for Stark deceleration and trapping experiments. Lithium metal is ablated from a solid target into a supersonically expanding carrier gas. The translational, rotational and vibrational temperatures are 0.9(0.1) K, 5.9(0.5) K and 468(17) K respectively. Although they have not reached thermal equilibrium with the carrier gas, we estimate that 90% of the LiH molecules are in the ground state, X^{1} \Sigma^{+} (v=0, J=0). With a single 7 ns ablation pulse, the number of molecules in the ground state is 4.5(1.8)*10^{7} molecules per steradian. A second, delayed, ablation pulse produces another LiH beam in a different part of the same gas pulse, thereby almost doubling the signal. A long pulse, lasting 150 microseconds, can make the beam up to 15 times more intense., Comment: 8 pages, 6 figures

We present progress towards a new measurement of the electron electric dipole moment using a cold supersonic beam of YbF molecules. Data are currently being taken with a sensitivity of $10^{-27}\textrm{e.cm}/\sqrt{\textrm{day}}$. We therefore expect to make an improvement over the Tl experiment of Commins' group, which currently gives the most precise result. We discuss the systematic and statistical errors and comment on the future prospect of making a measurement at the level of $10^{-29}\textrm{e.cm}/\sqrt{\textrm{day}}$., Comment: 8 pages, 6 figures, proceedings of ICAP 2006

We present our progress towards a new measurement of the electron electric dipole moment using a beam of YbF molecules. Data are currently being taken with a sensitivity of 10^{-27} e.cm / \sqrt{day}., Comment: 8 pages, presented at ICOLS 2005

We have measured the Stark shift of the $A^2\Pi_{1/2} - X^2\Sigma^+$ transition in YbF. We use a molecular beam triple resonance method, with two laser transitions acting as pump and probe, assisted by an rf transition that tags a single hyperfine transition of the X state. After subtracting the known ground state Stark shift, we obtain a value of $70.3(1.5) $Hz/(V/cm)$^2$ for the static electric polarizability of the state $A^2\Pi_{1/2}(J=1/2,f)$. From this we calculate a value $\mu_e=2.46(3)$D for the electric dipole moment of the $A^2\Pi_{1/2}(v=0)$ state., Comment: 3 pages, 2 figures

Cold supersonic beams of molecules can be slowed down using a switched sequence of electrostatic field gradients. The energy to be removed is proportional to the mass of the molecules. Here we report deceleration of YbF, which is 7 times heavier than any molecule previously decelerated. We use an alternating gradient structure to decelerate and focus the molecules in their ground state. We show that the decelerator exhibits the axial and transverse stability required to bring these molecules to rest. Our work significantly extends the range of molecules amenable to this powerful method of cooling and trapping., Comment: 4 pages, 5 figures

The most sensitive measurements of the electron electric dipole moment d_e have previously been made using heavy atoms. Heavy polar molecules offer a greater sensitivity to d_e because the interaction energy to be measured is typically 10^3 times larger than in a heavy atom. We report the first measurement of this kind, for which we have used the molecule YbF. Together, the large interaction energy and the strong tensor polarizability of the molecule make our experiment essentially free of the systematic errors that currently limit d_e measurements in atoms. Our first result d_e = (- 0.2 \pm 3.2) x 10^-26 e.cm is less sensitive than the best atom measurement, but is limited only by counting statistics and demonstrates the power of the method., Comment: 4 pages, 4 figures. v2. Minor corrections and clarifications made in response to referee comments