The use of electrostatic ion beam traps require to set many potentials on the electrodes (ten in our case), making the tuning much more difficult than with quadrupole traps. In order to obtain the best trapping conditions, an analytical formula giving the electrostatic potential inside the trap is required. In this paper, we present a general method to calculate the analytical expression of the electrostatic potential in any axisymmetric set of electrodes. We use conformal mapping to simplify the geometry of the boundary. The calculation is then performed in a space of simple geometry. We show that this method, providing excellent accuracy, allows to obtain the potential on the axis as an analytic function of the potentials applied to the electrodes, thus leading to fast, accurate and efficient calculations. We conclude by presenting stability maps depending on the potentials that enabled us to find the good trapping conditions for oxygen 4+ at much higher energies than what has been achieved until now.
We study the ions dynamics inside an Electrostatic Ion Beam Trap (EIBT) and show that the stability of the trapping is ruled by a Hill's equation. This unexpectedly demonstrates that an EIBT, in the reference frame of the ions works very similar to a quadrupole trap. The parallelism between these two kinds of traps is illustrated by comparing experimental and theoretical stability diagrams of the EIBT. The main difference with quadrupole traps is that the stability depends only on the ratio of the acceleration and trapping electrostatic potentials, not on the mass nor the charge of the ions. A…
We present a detailed description on how to build a Thin WIre electroStatic Trap (TWIST) for ultracold polar molecules. It is the first design of an electrostatic trap that can be superimposed directly onto a magneto optical trap (MOT). We can thus continuously produce ultracold polar molecules via photoassociation from a two species MOT and instantaneously trap them in the TWIST without the need for complex transfer schemes. Despite the spatial overlap of the TWIST and the MOT, the two traps can be operated and optimized completely independently due to the complementary nature of the utilized…
We describe the realization of a dc electric-field trap for ultracold polar molecules, the thin-wire electrostatic trap (TWIST). The thin wires that form the electrodes of the TWIST allow us to superimpose the trap onto a magneto-optical trap (MOT). In our experiment, ultracold polar NaCs molecules in their electronic ground state are created in the MOT via photoassociation, achieving a continuous accumulation in the TWIST of molecules in low-field seeking states. Initial measurements show that the TWIST trap lifetime is limited only by the background pressure in the chamber.
Beams of neutral polar molecules in a low-field seeking quantum state can be slowed down using a Stark decelerator, and can subsequently be loaded and confined in electrostatic quadrupole traps. The efficiency of the trap loading process is determined by the ability to couple the decelerated packet of molecules into the trap without loss of molecules and without heating. We discuss the inherent difficulties to obtain ideal trap loading, and describe and compare different trap loading strategies. A new "split-endcap" quadrupole trap design is presented that enables improved trap loading efficie…
A pulsed beam of ground state OH radicals is slowed down using a Stark decelerator and is subsequently loaded into an electrostatic trap. Characterization of the molecular beam production, deceleration and trap loading process is performed via laser induced fluorescence detection inside the quadrupole trap. Depending on details of the trap loading sequence, typically $10^5$ OH ($X^2Π_{3/2}, J=3/2$) radicals are trapped at a density of around $10^7$ cm$^{-3}$ and at temperatures in the 50-500 mK range. The 1/e trap lifetime is around 1.0 second.
We present experimental results, as well as numerical simulations, for the transverse velocity distribution of ions stored in an electrostatic ion beam trap. The measurements indicate that the transverse velocity spread is about 1% of the longitudinal velocity, and that the ions fill the whole transverse stable phase space. We also demonstrate that ion losses from the trap due to multiple scattering with molecules from the residual gas is an important factor limiting the lifetime of the beam.
We report on the Stark deceleration and electrostatic trapping of $^{14}$NH ($a ^1Δ$) radicals. In the trap, the molecules are excited on the spin-forbidden $A ^3Π\leftarrow a ^1Δ$ transition and detected via their subsequent fluorescence to the $X ^3Σ^-$ ground state. The 1/e trapping time is 1.4 $\pm$ 0.1 s, from which a lower limit of 2.7 s for the radiative lifetime of the $a ^1Δ, v=0,J=2$ state is deduced. The spectral profile of the molecules in the trapping field is measured to probe their spatial distribution. Electrostatic trapping of metastable NH followed by optical pumping of the t…
We analyze the dynamics of a paramagnetic, dipolar molecule in a generic "magneto-electrostatic'' trap where both magnetic and electric fields may be present. The potential energy that governs the dynamics of the molecules is found using a reduced molecular model that incorporates the main features of the system. We discuss the shape of the trapping potentials for different field geometries, as well as the possibility of nonadiabatic transitions to untrapped states, i.e., the analog of Majorana transitions in a quadrupole magnetic atomic trap. Maximizing the lifetime of molecules in a trap is …
We have trapped cesium atoms over many minutes in the focus of a CO$_2$-laser beam employing an extremely simple laser system. Collisional properties of the unpolarized atoms in their electronic ground state are investigated. Inelastic binary collisions changing the hyperfine state lead to trap loss which is quantitatively analyzed. Elastic collisions result in evaporative cooling of the trapped gas from 25 $μ$K to 10 $μ$K over a time scale of about 150 s.
We consider how trapped molecules can be sympathetically cooled by ultracold atoms. As a prototypical system, we study LiH molecules co-trapped with ultracold Li atoms. We calculate the elastic and inelastic collision cross sections of LiH + Li with the molecules initially in the ground state and in the first rotationally excited state. We then use these cross sections to simulate sympathetic cooling in a static electric trap, an ac electric trap, and a microwave trap. In the static trap we find that inelastic losses are too great for cooling to be feasible for this system. The ac and microwav…
Beams of helium atoms in Rydberg-Stark states with principal quantum number $n=48$ and electric dipole moments of 4600~D have been decelerated from a mean initial longitudinal speed of 2000~m/s to zero velocity in the laboratory-fixed frame-of-reference in the continuously moving electric traps of a transmission-line decelerator. In this process accelerations up to $-1.3\times10^{7}$~m/s$^2$ were applied, and changes in kinetic energy of $ΔE_{\mathrm{kin}}=1.3\times10^{-20}$~J ($ΔE_{\mathrm{kin}}/e = 83$~meV) per atom were achieved. Guided and decelerated atoms, and those confined in stationar…
Measurements of interactions between cold molecules and ultracold atoms can allow for a detailed understanding of fundamental collision processes. These measurements can be done using various experimental geometries including where both species are in a beam, where one species is trapped, or when both species are trapped. Simultaneous trapping offers significantly longer interaction times and an associated increased sensitivity to rare collision events. However, there are significant practical challenges associated with combining atom and molecule systems, which often have competing experiment…
We report the magnetic confinement of neutral, ground state hydroxyl radicals (OH) at a density of $\sim3\times10^{3}$ cm$^{-3}$ and temperature of $\sim$30 mK. An adjustable electric field of sufficient magnitude to polarize the OH is superimposed on the trap in either a quadrupole or homogenous field geometry. The OH is confined by an overall potential established via molecular state mixing induced by the combined electric and magnetic fields acting on the molecule's electric dipole and magnetic dipole moments, respectively. An effective molecular Hamiltonian including Stark and Zeeman terms…
Quadrupole ion traps can be transformed into nonlinear traps with integrable motion by adding special electrostatic potentials. This can be done with both stationary potentials (electrostatic plus a uniform magnetic field) and with time-dependent electric potentials. These potentials are chosen such that the single particle Hamilton-Jacobi equations of motion are separable in some coordinate systems. The electrostatic potentials have several free adjustable parameters allowing for a quadrupole trap to be transformed into, for example, a double-well or a toroidal-well system. The particle motio…
We report on the first storage of ion beams in the Double ElectroStatic Ion Ring ExpEriment; DESIREE, at Stockholm University. We have produced beams of atomic carbon anions and small carbon anion molecules (C$_n^-$, $n=1,2,3,4$) in a sputter ion source. The ion beams were accelerated to 10 keV kinetic energy and stored in an electrostatic ion storage ring enclosed in a vacuum chamber at 13 K. For 10 keV C$_2^-$ molecular anions we measure the residual-gas limited beam storage lifetime to be 448 s $\pm$ 18 s with two independent detector systems. Using the measured storage lifetimes we estimat…
We introduce, analyze, and compare two novel methods of Single Photon Cooling that generically cool and compress molecular gases. The first method compresses the molecular gas density by three orders of magnitude and increases collision frequency in trapped samples. The second method compresses the phase space density of the gas by at least two orders of magnitude. Designed with combinations of electric and magnetic fields these methods cool the molecules from ~100mK to 1mK using a single irreversible state change. They can be regarded as generic cooling schemes applicable to any molecule with…
A detailed treatment of an electro-optical trap for polar molecules, realized by embedding an optical trap within a uniform electrostatic field, is presented and the trap's properties analyzed and discussed. The electro-optical trap offers significant advantages over an optical trap that include an increased trap depth and conversion of alignment of the trapped molecules to marked orientation. Tilting the polarization plane of the optical field with respect to the electrostatic field diminishes both the trap depth and orientation and lifts the degeneracy of the $\pm M$ states of the trapped mo…
Electric deflection measurements on liquid helium nanodroplets doped with individual polar molecules demonstrate that the cold superfluid matrix enables full orientation of the molecular dipole along the external field. This translates into a deflection force which is increased enormously by comparison with typical deflection experiments, and it becomes possible to measurably deflect neutral doped droplets with masses of tens to hundreds of thousands of Daltons. This approach permits preparation and study of continuous fluxes of fully oriented polar molecules and is broadly and generally appli…
Electrostatic quadrupole lens for focusing a cryogenic $^{205}$TlF molecular beam
Columbia University（哥伦比亚大学）；Argonne National Laboratory（阿贡国家实验室）；Johns Hopkins University（约翰斯·霍普金斯大学）；Yale University（耶鲁大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；University of Chicago（芝加哥大学）
Supersonic beams of hydrogen atoms, prepared selectively in Rydberg-Stark states of principal quantum number $n$ in the range between 25 and 35, have been deflected by 90$^\circ$, decelerated and loaded into off-axis electric traps at initial densities of $\approx 10^6$ atoms/cm$^{-3}$ and translational temperatures of 150 mK. The ability to confine the atoms spatially was exploited to study their decay by radiative and collisional processes. The evolution of the population of trapped atoms was measured for several milliseconds in dependence of the principal quantum number of the initially pre…
An electrostatic lens with three focusing elements in an alternating-gradient configuration is used to focus a fountain of cesium atoms in their ground (strong-field-seeking) state. The lens electrodes are shaped to produce only sextupole plus dipole equipotentials which avoids adding the unnecessary nonlinear forces present in cylindrical lenses. Defocusing between lenses is greatly reduced by having all of the main electric fields point in the same direction and be of nearly equal magnitude. The addition of the third lens gave us better control of the focusing strength in the two transverse …
We demonstrate an optical bottle beam trap created by interfering two fundamental Gaussian beams with different waists. The beams are derived from a single laser source using a Mach-Zehnder interferometer whose arms have unequal magnifications. Destructive interference of the two beams from the Mach-Zehnder leads to a three dimensional intensity null at the mutual focus of the beams. We demonstrate trapping of cold Cesium atoms in a blue detuned bottle beam trap.
We propose and analyze an electrostatic-optical nano-scale trap for cold diatomic polar molecules. The main ingredient of our proposal is an square-array of ferroelectric nano-rods {with alternating polarization}. We show that, in contrast to electrostatic traps using the linear Stark effect, a quadratic Stark potential supports long-lived trapped states. The molecules are kept at a fixed height from the nano-rods by a standing-wave optical dipole trap. For the molecules and materials considered, we find that nano-traps with trap frequency up to 1MHz, ground-state width $\sim20$nm with lattice…
Focusing optics for neutral molecules finds application in shaping and steering molecular beams. Here we present an electrostatic elliptical mirror for polar molecules consisting of an array of microstructured gold electrodes deposited on a glass substrate. Alternating positive and negative voltages applied to the electrodes create a repulsive potential for molecules in low-field-seeking states. The equipotential lines are parallel to the substrate surface, which is bent in an elliptical shape. The mirror is characterized by focusing a beam of metastable CO molecules and the results are compar…
We apply near-threshold laser photodetachment to characterize the rotational quantum level distribution of OH$^-$ ions stored in the cryogenic ion-beam storage ring, DESIREE, at Stockholm University. We find that the stored ions relax to a rotational temperature of 13.4$\pm$0.2 K with 94.9$\pm$0.3 % of the ions in the rotational ground state. This is consistent with the storage ring temperature of 13.5$\pm$0.5 K as measured with eight silicon diodes, but in contrast to all earlier studies in cryogenic traps and rings where the rotational temperatures were always much higher than those of the s…
We report on the loading of atoms contained in a magneto-optic trap into multiple optical traps formed within the focused beam of a CO_{2} laser. We show that under certain circumstances it is possible to create a linear array of dipole traps with well separated maxima. This is achieved by focusing the laser beam through lenses uncorrected for spherical aberration. We demonstrate that the separation between the micro-traps can be varied, a property which may be useful in experiments which require the creation of entanglement between atoms in different micro-traps. We suggest other experiments …
We demonstrate trapping and quantum state control of single Cesium atoms in a 532 nm wavelength bottle beam trap. The three dimensional trap is formed by crossing two unit charge vortex beams. Single atoms are loaded with 50% probability directly from a magneto-optical trap. We achieve a trapping lifetime of up to 6 s, and demonstrate fast Rabi oscillations with a coherence time of $T_2\sim 43 \pm 9\rm ms$.
The current best upper limit for electron electric dipole moment (EDM), $|d_e|<1.1\times10^{-29}\,$e$\cdot$cm ($90$% confidence), was set by the ACME collaboration in 2018. The ACME experiment uses a spin-precession measurement in a cold beam of ThO molecules to detect $d_e$. An improvement in statistical uncertainty would be possible with more efficient use of molecules from the cryogenic buffer gas beam source. Here, we demonstrate electrostatic focusing of the ThO beam with a hexapole lens. This results in a factor of $16$ enhancement in the molecular flux detectable downstream, in a beamli…
A diffractive optical element (DOE) has been fabricated for creating blue detuned atomic bottle beam traps. The DOE integrates several diffractive lenses for trap creation and imaging of atomic fluorescence. We characterize the performance of the DOE and demonstrate trapping of cold Cesium atoms inside a bottle beam.
A new beamline for Resonant Excitation of Beams with Electromagnetic fields and Lasers (REBEL) and Stopping and Trapping of Radioactive Isotopes for Precision Experiments (STRIPE)
We have realised a 4-beam pyramidal magneto-optical trap ideally suited for future microfabrication. Three mirrors split and steer a single incoming beam into a tripod of reflected beams, allowing trapping in the four-beam overlap volume. We discuss the influence of mirror angle on cooling and trapping, finding optimum efficiency in a tetrahedral configuration. We demonstrate the technique using an ex-vacuo mirror system to illustrate the previously inaccessible supra-plane pyramid MOT configuration. Unlike standard pyramidal MOTs both the pyramid apex and its mirror angle are non-critical and…
We present an optical trap for atoms that we have developed for precision spectroscopy measurements. Cold atoms are captured in a dark region of space inside a blue-detuned hollow laser beam formed by an axicon. We analyze the light potential in a ray optics picture and experimentally demonstrate trapping of laser-cooled metastable xenon atoms.
The performance of a newly built omega type electrostatic analyzer designed to act as an in-line charge-state purification system for ions in the keV energy range is reported. The analyzer consists of a set of four consecutive electrostatic 140° concentric cylindrical electrodes enclosed by Matsuda electrodes. This setup was recently tested and validated using $O^{5+}$ , $Ar^{9+}$ and $Xe^{20+}$ ion beams at an energy of 14 qkeV at the ARIBE facility. A resolving power of 10.5 and a transmission of 100 % of the desired charge state are measured allowing a good purification of incoming ion beam…
We demonstrate a technique for producing a cold pulsed beam of atoms by transferring a cloud of atoms trapped in a three dimensional magneto-optic trap (MOT). The MOT is loaded by heating a getter source of Rb atoms. We show that it is advantageous to transfer with two beams (with a small angle between them) compared to a single beam, because the atoms stop interacting with the beams in the two-beam technique, which results in a Gaussian velocity distribution. The atoms are further cooled in optical molasses by turning off the MOT magnetic field before the transfer beams are turned on.
We demonstrate a simple scheme to reach Bose-Einstein condensation (BEC) of metastable triplet helium atoms using a single beam optical dipole trap with moderate power of less than 3 W. Our scheme is based on RF-induced evaporative cooling in a quadrupole magnetic trap and transfer to a single beam optical dipole trap that is located below the magnetic trap center. We transfer 1x10^6 atoms into the optical dipole trap, with an initial temperature of 14 μK, and observe efficient forced evaporative cooling both in a hybrid trap, in which the quadrupole magnetic trap operates just below the levit…
We describe a new type of blue detuned optical lattice for atom trapping which is intrinsically two dimensional, while providing three-dimensional atom localization. The lattice is insensitive to optical phase fluctuations since it does not depend on field interference between distinct optical beams. The array is created using a novel arrangement of weakly overlapping Gaussian beams that creates a two-dimensional array of dark traps which are suitable for magic trapping of ground and Rydberg states. We analyze the spatial localization that can be achieved and demonstrate trapping and detection…
We present the creation of a lithium-cesium slow beam using a two-dimensional magneto-optical trap. The two-species atomic beam is directed to load a three-dimensional magneto-optical trap in ultrahigh vacuum. We achieve a loading rate of 1.3$\times$10$^{7}$ lithium atoms/s with the lithium oven temperature at 370~$^{\circ}$C and 2.2$\times$10$^{7}$ cesium atoms/s with the Cs oven temperature at 20~$^{\circ}$C. The maximum numbers of lithium and cesium atoms in the trap are 1.0$\times$10$^{9}$ and 1.4$\times$10$^{8}$, respectively. Our results show that the simple and compact two-dimensional m…
We demonstrate three-dimensional trapping of individual Rydberg atoms in holographic optical bottle beam traps. Starting with cold, ground-state $^{87}$Rb atoms held in standard optical tweezers, we excite them to $nS_{1/2}$, $nP_{1/2}$, or $nD_{3/2}$ Rydberg states and transfer them to a hollow trap at 850 nm. For principal quantum numbers $60 \leqslant n \leqslant 90$, the measured trapping time coincides with the Rydberg state lifetime in a 300~K environment. We show that these traps are compatible with quantum information and simulation tasks by performing single qubit microwave Rabi flopp…
