arXiv subjects
Publications and source records attributed to M. R. Tarbutt.
We demonstrate coherent microwave control of the rotational, hyperfine and Zeeman states of ultracold CaF molecules, and the magnetic trapping of these molecules in a single, selectable quantum state. We trap about $5\times 10^{3}$ molecules for 2 s at a temperature of 65(11) $μ$K and a density of $1.2 \times 10^{5}$ cm$^{-3}$. We measure the state-specific loss rate due to collisions with background helium.
Experiments with cold molecules usually begin with a molecular source. We describe the construction and characteristics of a cryogenic buffer gas source of CaF molecules. The source emits pulses with a typical duration of 240 $μ$s, a mean speed of about 150 m/s, and a flux of $5\times 10^{10}$ molecules per steradian per pulse in a single rotational state.
We present the properties of a magneto-optical trap (MOT) of CaF molecules. We study the process of loading the MOT from a decelerated buffer-gas-cooled beam, and how best to slow this molecular beam in order to capture the most molecules. We determine how the number of molecules, the photon scattering rate, the oscillation frequency, damping constant, temperature, cloud size and lifetime depend on the key parameters of the MOT, especially the intensity and detuning of the main cooling laser. We compare our results to analytical and numerical models, to the properties of standard atomic MOTs, and to MOTs of SrF molecules. We load up to $2 \times 10^4$ molecules, and measure a maximum scattering rate of $2.5 \times 10^6$ s$^{-1}$ per molecule, a maximum oscillation frequency of 100 Hz, a maximum damping constant of 500 s$^{-1}$, and a minimum MOT rms radius of 1.5 mm. A minimum temperature of 730 $μ$K is obtained by ramping down the laser intensity to low values. The lifetime, typically about 100 ms, is consistent with a leak out of the cooling cycle with a branching ratio of about $6 \times 10^{-6}$. The MOT has a capture velocity of about 11 m/s.
We theoretically investigate the damping and trapping forces in a three-dimensional magneto-optical trap (MOT), by numerically solving the optical Bloch equations. We focus on the case where there are dark states because the atom is driven on a "type-II" system where the angular momentum of the excited state, $F'$, is less than or equal to that of the ground state, $F$. For these systems we find that the force in a three-dimensional light field has very different behaviour to its one dimensional counterpart. This differs from the more commonly used "type-I" systems ($F'=F+1$) where the 1D and 3D behaviours are similar. Unlike type-I systems where, for red-detuned light, both Doppler and sub-Doppler forces damp the atomic motion towards zero velocity, in type-II systems in 3D, the Doppler force and polarization gradient force have opposite signs. As a result, the atom is driven towards a non-zero equilibrium velocity, $v_{0}$, where the two forces cancel. We find that $v_{0}^{2}$ scales linearly with the intensity of the light and is fairly insensitive to the detuning from resonance. We also discover a new magneto-optical force that alters the normal MOT force at low magnetic fields and whose influence is greatest in the type-II systems. We discuss the implications of these findings for the laser cooling and magneto-optical trapping of molecules where type-II transitions are unavoidable in realising closed optical cycling transitions.
The ability to cool atoms below the Doppler limit -- the minimum temperature reachable by Doppler cooling -- has been essential to most experiments with quantum degenerate gases, optical lattices and atomic fountains, among many other applications. A broad set of new applications await ultracold molecules, and the extension of laser cooling to molecules has begun. A molecular magneto-optical trap has been demonstrated, where molecules approached the Doppler limit. However, the sub-Doppler temperatures required for most applications have not yet been reached. Here we cool molecules to 50 uK, well below the Doppler limit, using a three-dimensional optical molasses. These ultracold molecules could be loaded into optical tweezers to trap arbitrary arrays for quantum simulation, launched into a molecular fountain for testing fundamental physics, and used to study ultracold collisions and ultracold chemistry.
Using frequency-chirped radiation pressure slowing, we precisely control the velocity of a pulsed CaF molecular beam down to a few m/s, compressing its velocity spread by a factor of 10 while retaining high intensity: at a velocity of 15~m/s the flux, measured 1.3~m from the source, is 7$\times$10$^{5}$ molecules per cm$^{2}$ per shot in a single rovibrational state. The beam is suitable for loading a magneto-optical trap or, when combined with transverse laser cooling, improving the precision of spectroscopic measurements that test fundamental physics. We compare the frequency-chirped slowing method with the more commonly used frequency-broadened slowing method.
We explore a technique for decelerating molecules using a static magnetic field and optical pumping. Molecules travel through a spatially varying magnetic field and are repeatedly pumped into a weak-field seeking state as they move towards each strong field region, and into a strong-field seeking state as they move towards weak field. The method is time-independent and so is suitable for decelerating both pulsed and continuous molecular beams. By using guiding magnets at each weak field region, the beam can be simultaneously guided and decelerated. By tapering the magnetic field strength in the strong field regions, and exploiting the Doppler shift, the velocity distribution can be compressed during deceleration. We develop the principles of this deceleration technique, provide a realistic design, use numerical simulations to evaluate its performance for a beam of CaF, and compare this performance to other deceleration methods.
We describe the design, construction and operation of a versatile dual-species Zeeman slower for both Cs and Yb, which is easily adaptable for use with other alkali metals and alkaline earths. With the aid of analytic models and numerical simulation of decelerator action, we highlight several real-world problems affecting the performance of a slower and discuss effective solutions. To capture Yb into a magneto-optical trap (MOT), we use the broad $^1S_0$ to $^1P_1$ transition at 399 nm for the slower and the narrow $^1S_0$ to $^3P_1$ intercombination line at 556 nm for the MOT. The Cs MOT and slower both use the D2 line ($6^2S_{1/2}$ to $6^2P_{3/2}$) at 852 nm. We demonstrate that within a few seconds the Zeeman slower loads more than $10^9$ Yb atoms and $10^8$ Cs atoms into their respective MOTs. These are ideal starting numbers for further experiments on ultracold mixtures and molecules.
We model sympathetic cooling of ground-state CaF molecules by ultracold Li and Rb atoms. The molecules are moving in a microwave trap, while the atoms are trapped magnetically. We calculate the differential elastic cross sections for CaF-Li and CaF-Rb collisions, using model Lennard-Jones potentials adjusted to give typical values for the s-wave scattering length. Together with trajectory calculations, these differential cross sections are used to simulate the cooling of the molecules, the heating of the atoms, and the loss of atoms from the trap. We show that a hard-sphere collision model based on an energy-dependent momentum transport cross section accurately predicts the molecule cooling rate but underestimates the rates of atom heating and loss. Our simulations suggest that Rb is a more effective coolant than Li for ground-state molecules, and that the cooling dynamics are less sensitive to the exact value of the s-wave scattering length when Rb is used. Using realistic experimental parameters, we find that molecules can be sympathetically cooled to 100$μ$K in about 10s. By applying evaporative cooling to the atoms, the cooling rate can be increased and the final temperature of the molecules can be reduced to 1$μ$K within 30s.
We demonstrate a scheme for magneto-optically trapping strontium monofluoride (SrF) molecules at temperatures one order of magnitude lower and phase space densities three orders of magnitude higher than obtained previously with laser-cooled molecules. In our trap, optical dark states are destabilized by rapidly and synchronously reversing the trapping laser polarizations and the applied magnetic field gradient. The number of molecules and trap lifetime are also significantly improved from previous work by loading the trap with high laser power and then reducing the power for long-term trapping. With this procedure, temperatures as low as 400 $μ$K are achieved.
Magneto-optical trapping forces for molecules are far weaker than for alkali atoms because the photon scattering rate is reduced when there are multiple ground states, and because of optical pumping into dark states. The force is further reduced when the upper state has a much smaller Zeeman splitting than the lower state. We use a rate model to estimate the strength of the trapping and damping forces in a magneto-optical trap (MOT) of CaF molecules, using either the A$^{2}Π_{1/2}$ - X$^{2}Σ^{+}$ transition or the B$^{2}Σ^{+}$ - X$^{2}Σ^{+}$ transition. We identify a new mechanism of magneto-optical trapping that arises when, in each beam of the MOT, two laser components with opposite polarizations and different detunings address the same transition. This mechanism produces a strong trapping force even when the upper state has little or no Zeeman splitting. It is the main mechanism responsible for the trapping force when the A$^{2}Π_{1/2}$ - X$^{2}Σ^{+}$ transition is used.
We describe an apparatus designed to trap and cool a Yb and Cs mixture. The apparatus consists of a dual species effusive oven source, dual species Zeeman slower, magneto-optical traps in a single ultra-high vacuum science chamber, and the associated laser systems. The dual species Zeeman slower is used to load sequentially the two species into their respective traps. Its design is flexible and may be adapted for other experiments with different mixtures of atomic species. The apparatus provides excellent optical access and can apply large magnetic bias fields to the trapped atoms. The apparatus regularly produces 10${}^{8}$ Cs atoms at 13.3 $μ$K in an optical molasses, and 10${}^{9}$ Yb atoms cooled to 22 $μ$K in a narrowband magneto-optical trap.
Laser cooling and magneto-optical trapping of molecules typically involves multiple transitions driven by several laser frequencies. We analyze how magneto-optical trapping forces depend on the angular momenta, $F_l$ and $F_u$, and the g-factors, $g_l$ and $g_u$, of the lower and upper states. When $F_l > F_u$ the polarizations must be reversed relative to cases where $F_u \ge F_l$. The correct choice of circular polarization depends on the sign of $g_{u}$ but not on the sign of $g_{l}$. If $g_{u}$ is zero there is no trapping force, and the trapping force is very weak whenever $g_u$ is small compared to $g_l$, which it usually is when the cooling transition is the $^{2}Σ$ to $^{2}Π_{1/2}$ transition of a molecule. For some molecules, mixing of the excited $^{2}Π_{1/2}$ state with a nearby $^{2}Σ$ excited state can greatly increase $g_u$, leading to stronger trapping forces. A strong trapping force can also be produced by rapidly and synchronously reversing both the magnetic field and the laser polarizations. We simulate a recent experiment on magneto-optical trapping of SrF molecules, and suggest that an alternative choice of laser beam polarizations will strengthen the trapping force.
We characterize a Fabry-Perot microwave cavity designed for trapping atoms and molecules at the antinode of a microwave field. The cavity is fed from a waveguide through a small coupling hole. Focussing on the compact resonant modes of the cavity, we measure how the electric field profile, the cavity quality factor, and the coupling efficiency, depend on the radius of the coupling hole. We measure how the quality factor depends on the temperature of the mirrors in the range from 77 to 293K. The presence of the coupling hole slightly changes the profile of the mode, leading to increased diffraction losses around the edges of the mirrors and a small reduction in quality factor. We find the hole size that maximizes the intra-cavity electric field. We develop an analytical theory of the aperture-coupled cavity that agrees well with our measurements, with small deviations due to enhanced diffraction losses. We find excellent agreement between our measurements and finite-difference time-domain simulations of the cavity.
The simple structure of the BH molecule makes it an excellent candidate for direct laser cooling. We measure the branching ratios for the decay of the ${\rm A}^{1}Π(v'=0)$ state to vibrational levels of the ground state, ${\rm X}^{1}Σ^{+}$, and find that they are exceedingly favourable for laser cooling. We verify that the branching ratio for the spin-forbidden transition to the intermediate ${\rm a}^{3}Π$ state is inconsequentially small. We measure the frequency of the lowest rotational transition of the X state, and the hyperfine structure in the relevant levels of both the X and A states, and determine the nuclear electric quadrupole and magnetic dipole coupling constants. Our results show that, with a relatively simple laser cooling scheme, a Zeeman slower and magneto-optical trap can be used to cool, slow and trap BH molecules.
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.
The Lambda-doublet transitions in CH at 3.3 and 0.7 GHz are unusually sensitive to variations in the fine-structure constant and the electron-to-proton mass ratio. We describe methods used to measure the frequencies of these transitions with Hz-level accuracy. We produce a pulsed supersonic beam of cold CH by photodissociation of CHBr3, and we measure the microwave transition frequencies as the molecules propagate through a parallel-plate transmission line resonator. We use the molecules to map out the amplitude and phase of the standing wave field inside the transmission line. We investigate velocity-dependent frequency shifts, showing that they can be strongly suppressed through careful timing of the microwave pulses. We measure the Zeeman and Stark effects of the microwave transitions, and reduce systematic shifts due to magnetic and electric fields to below 1 Hz. We also investigate other sources of systematic uncertainty in the experiment.
We excite YbF molecules to low-lying vibrational levels of the $A^2Π_{1/2}$ state, and of the nearby perturber state sometimes called [18.6]0.5. By dispersing the fluorescence, we measure branching ratios for the radiative decay to vibrational levels of the $X^2Σ^+$ state. These ratios help to determine the optimum laser cooling scheme for the molecule. Our results establish the practicality of a scheme that was previously suggested [Tarbutt et al., New J. Phys. 15 (2013) 053034] and show how the scheme can be modified to provide a stronger radiative cooling force.