Cold, neutral hydroxyl radicals are Stark decelerated and confined within a magnetic trap consisting of two permanent ring magnets. The OH molecules are trapped in the ro-vibrational ground state at a density of $\sim10^{6}$ cm$^{-3}$ and temperature of 70 mK. Collisions between the trapped OH sample and supersonic beams of atomic He and molecular D$_{2}$ are observed and absolute collision cross sections measured. The He--OH and D$_{2}$--OH center-of-mass collision energies are tuned from 60 cm$^{-1}$ to 230 cm$^{-1}$ and 145 cm$^{-1}$ to 510 cm$^{-1}$, respectively, yielding evidence of reduced He--OH inelastic cross sections at energies below 84 cm$^{-1}$, the OH ground rotational level spacing.
We describe the design, assembly, and testing of a magnet intended to deflect beams of paramagnetic nanoclusters, molecules, and atoms. It is energized by high-grade permanent neodymium magnets. This offers a convenient option in terms of cost, portability, and scalability of the construction, while providing field and gradient values (1.1 T, 330 T/m) which are fully comparable with commonly used electromagnet deflectors.
We report on a surface-electrode trap with SmCo magnets arranged in a quadrupole configuration underneath the trap electrode. Because the distance between the magnets and the trapped ions can be as little as several hundred micrometers, a large magnetic field is produced without any heat management. The magnetic-field gradient was measured using the Zeeman splitting of a single trapped $^{40}$Ca$^+$ ion at several positions, and a field gradient of 36 T/m was obtained. Such a field gradient is useful for the generation of a state-dependent force, which is important for quantum simulation and/o…
We show that combined permanent and induced electric dipole interactions of polar and polarizable molecules with collinear electric fields lead to a sui generis topology of the corresponding Stark energy surfaces and of other observables - such as alignment and orientation cosines - in the plane spanned by the permanent and induced dipole interaction parameters. We find that the loci of the intersections of the surfaces can be traced analytically and that the eigenstates as well as the number of their intersections can be characterized by a single integer index. The value of the index, distinc…
We present designs for Ioffe-Pritchard type magnetic traps using planar patterns of hard magnetic material. Two samples with different pattern designs were produced by spark erosion of 40 $μ$m thick FePt foil. The pattern on the first sample yields calculated axial and radial trap frequencies of 51 Hz and 6.8 kHz, respectively. For the second sample the calculated frequencies are 34 Hz and 11 kHz. The structures were used successfully as a magneto-optical trap for $^{87}$Rb and loaded as a magnetic trap. A third design, based on lithographically patterned 250 nm thick FePt film on a Si substra…
A newly constructed apparatus at the National Institute of Standards and Technology (NIST) is designed for the isolation, manipulation, and study of highly charged ions. Highly charged ions are produced in the NIST electron-beam ion trap (EBIT), extracted through a beamline that selects a single mass/charge species, then captured in a compact Penning trap. The magnetic field of the trap is generated by cylindrical NdFeB permanent magnets integrated into its electrodes. In a room-temperature prototype trap with a single NdFeB magnet, species including Ne10+ and N7+ were confined with storage ti…
We report on the loading and trapping of ultracold atoms in a one dimensional permanent magnetic lattice of period 10 micron produced on an atom chip. The grooved structure which generates the magnetic lattice potential is fabricated on a silicon substrate and coated with a perpendicularly magnetized multilayered TbGdFeCo/Cr film of effective thickness 960 nm. Ultracold atoms are evaporatively cooled in a Z-wire magnetic trap and then adiabatically transferred to the magnetic lattice potential by applying an appropriate bias field. Under our experimental conditions trap frequencies of up to 90…
We present models for a heteronuclear diatomic molecular ion in a linear Paul trap in a rigid-rotor approximation, one purely classical, the other where the center-of-mass motion is treated classically while rotational motion is quantized. We study the rotational dynamics and their influence on the motion of the center-of-mass, in the presence of the coupling between the permanent dipole moment of the ion and the trapping electric field. We show that the presence of the permanent dipole moment affects the trajectory of the ion, and that it departs from the Mathieu equation solution found for a…
A Cryogenic Penning Trap Based on Permanent Magnets
Heinrich Heine Universität Düsseldorf（杜塞尔多夫海因里希·海涅大学）；Institut für Physik, Johannes Gutenberg-Universität（美因茨约翰内斯·古腾堡大学物理研究所）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（达姆施塔特重离子研究中心）；Institut für Quantenoptik, Leibniz Universität Hannover（汉诺威莱布尼茨大学量子光学研究所）；Physikalisch-Technische Bundesanstalt（德国联邦物理技术研究院）；RIKEN, Fundamental Symmetries Laboratory（理化学研究所基本对称性实验室）；Graduate School of Arts and Sciences, University of Tokyo（东京大学大学院人文社会系研究科）；CERN（欧洲核子研究中心）
We propose and numerically study two permanent magnetic micro-structures for creating Ioffe-Pritchard microtraps. A bias magnetic field is used to vary the depth, trap frequencies and the minimum of each microtrap. After the Bose-Einstein condensation achievement, the bias magnetic field can be slowly removed to increase the trap barrier heights for more efficiently holding the Bose-Einstein condensates. Even without the external magnetic field, it is possible to hold ultracold atoms in the microtraps. These microtraps may also be useful for single atom experiments for quantum information proc…
The influence of large permanent dipoles on molecular orbital tomography via high-order harmonic generation (HHG) is investigated in this work. It is found that, owing to the modification of the angle-dependent ionization rate resulting from the Stark shift, the one-side-recollision condition for the tomographic imaging can not be satisfied even with the few-cycle driving pulses. To overcome this problem, we employ a tailored driving pulse by adding a weak low-frequency pulse to the few-cycle laser pulse to control the HHG process and the recollision of the continuum electrons are effectively …
We observe that when an ultracold ground state cesium (Cs) atom becomes bound within the electronic cloud of an extended Cs electronic orbit, ultralong-range molecules with giant (kilo-Debye) permanent electric dipole moments form. Large molecular permanent electric dipole moments are challenging to experimentally realize. Meeting this challenge has garnered significant interest because permanent electric dipole moments are important for understanding symmetry breaking in molecular physics, control of chemical reactions and realization of strongly correlated many-body quantum systems. These ne…
We report the design and experimental demonstration of a compact, reconfigurable Penning ion trap constructed with rare-earth permanent magnets placed outside of a trap vacuum enclosure. We describe the first observation of Doppler laser cooling of ions in a permanent magnet Penning trap. We detail a method for quantifying and optimizing the trap magnetic field uniformity in situ using a thermal beam of neutral $^{40}$Ca precursor atoms. Doppler laser cooling of $^{40}$Ca$^+$ is carried out at 0.65~T, and side-view images of trapped ion fluorescence show crystalline order for both two- and thr…
We demonstrate a simple technique for molecular ion spectroscopy. BaCl$^+$ molecular ions are trapped in a linear Paul trap in the presence of a room-temperature He buffer gas and photodissociated by driving an electronic transition from the ground X$^1Σ^+$ state to the repulsive wall of the A$^1Π$ state. The photodissociation spectrum is recorded by monitoring the induced trap loss of BaCl$^+$ ions as a function of excitation wavelength. Accurate molecular potentials and spectroscopic constants are determined. Comparison of the theoretical photodissociation cross-sections with the measurement…
The direct photodissociation of trapped $^{85}$Rb$_2^+$ (rubidium) molecular ions by the cooling light for the $^{85}$Rb magneto-optical trap (MOT) is studied, both experimentally and theoretically. Vibrationally excited Rb$_{2}^{+}$ ions are created by photoionization of Rb$_{2}$ molecules formed photoassociatively in the Rb MOT and are trapped in a modified spherical Paul trap. The decay rate of the trapped Rb$_{2}^{+}$ ion signal in the presence of the MOT cooling light is measured and agreement with our calculated rates for molecular ion photodissociation is observed. The photodissociation…
It is shown that a superposition of static and rapidly oscillating electric {\it monopole} (source) fields is capable of trapping particles with a permanent electric dipole moment. Thus, the new trapping mechanism differs fundamentally from saddle-point traps that use static and oscillating higher-multipole fields. An analytical stability analysis together with detailed molecular dynamics trajectory calculations prove that the trap is stable. Thin rods of barium titanate (BaTiO$_3$) provide an illustrative example for the working principle of the new trap. The effects of gravity are considered…
We report the sympathetic cooling and Coulomb crystallization of molecular ions above the surface of an ion-trap chip. N$_2^+$ and CaH$^+$ ions were confined in a surface-electrode radiofrequency ion trap and cooled by the interaction with laser-cooled Ca$^{+}$ ions to secular translational temperatures in the millikelvin range. The configuration of trapping potentials generated by the surface electrodes enabled the formation of planar bicomponent Coulomb crystals and the spatial separation of the molecular from the atomic ions on the chip. The structural and thermal properties of the Coulomb …
We present a realistic molecular-dynamics treatment of laser-cooled ions in radiofrequency ion traps which avoids previously made simplifications such as modeling laser cooling as a friction force and combining individual heating mechanisms into a single effective heating force. Based on this implementation, we show that infrequent energetic collisions of single ions with background gas molecules lead to pronounced heating of the entire ion ensemble and a time-varying secular ensemble temperature which manifests itself in a superstatistical time-averaged velocity distribution of the ions. The …
We study the quantum properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap which is superimposed by a homogeneous electric field. Trapped Rydberg atoms can be created in long-lived electronic states exhibiting a permanent electric dipole moment of several hundred Debye. The resulting dipole-dipole interaction in conjunction with the radial confinement is demonstrated to give rise to an effectively one-dimensional ultracold Rydberg gas with a macroscopic interparticle distance. We derive analytical expressions for the electric dipole moment and the critical linear density of Rydberg at…
The parity of atomic wave functions prevents neutral atoms from having permanent electric-dipole moment. Electric-dipole moment is induced in an atom when exposed to strong light, the electric field of the light. Hence the optical trapping of neutral atoms relies on the induced dipole moment. Here we present the calculated numerical values of the detuning, potential depth, minimum laser power required to trap $^{87}$Rb ($D_2$ line) atoms using lasers of wavelength 1064 nm, 850 nm, 820 nm and 800 nm and beam waists 50$μ$m, 100$μ$m and 200$μ$m.
Multipole radiofrequency ion traps are a highly versatile tool to study molecular ions and their interactions in a well-controllable environment. In particular the cryogenic 22-pole ion trap configuration is used to study ion-molecule reactions and complex molecular spectroscopy at temperatures between few Kelvin and room temperatures. This article presents a tutorial on radiofrequency ion trapping in multipole electrode configurations. Stable trapping conditions and buffer gas cooling, as well as important heating mechanisms, are discussed. In addition, selected experimental studies on cation…
We demonstrate the implementation of a simple time-of-flight (ToF) mass spectrometer with medium-mass resolution ($m/Δm\sim50$) geared towards the demands of atomic, molecular, and chemical physics experiments. By utilizing a novel radial ion extraction scheme from a linear quadrupole trap, a device with large trap capacity and high optical access is realized without sacrificing mass resolution. Here we describe the construction and implementation of the device as well as present representative ToF spectra. We conclude by demonstrating the flexibility of the device with proof-of-principle expe…
We describe an array of microscopic atom traps formed by a pattern of magnetisation on a piece of videotape. We describe the way in which cold atoms are loaded into one of these micro-traps and how the trapped atom cloud is used to explore the properties of the trap. Evaporative cooling in the micro-trap down to a temperature of 1 microkelvin allows us to probe the smoothness of the trapping potential and reveals some inhomogeneity produced by the magnetic film. We discuss future prospects for atom chips based on microscopic permanent-magnet structures.
We describe experiments demonstrating efficient transfer of molecules from a magneto-optical trap (MOT) into a conservative magnetic quadrupole trap. Our scheme begins with a blue-detuned optical molasses to cool SrF molecules to $\sim\!50$ $μ$K. Next, we optically pump the molecules into a strongly-trapped sublevel. This two-step process reliably transfers $64\%$ of the molecules initially trapped in the MOT into the magnetic trap, comparable to similar atomic experiments. Once loaded, the magnetic trap is compressed by increasing the magnetic field gradient. Finally, we demonstrate a magneti…
We report on a study of cold reactive collisions between sympathetically-cooled molecular ions and laser-cooled atoms in an ion-atom hybrid trap. Chemical reactions were studied at average collision energies <Ecoll>/k > 20 mK, about two orders of magnitude lower than has been achieved in previous experiments with molecular ions. Choosing N2+ +Rb as a prototypical system, we find that the reaction rate is independent of the collision energy, but strongly dependent on the internal state of Rb. Highly efficient charge exchange about four times faster than the Langevin rate was observed with Rb in…
Trapped diatomic molecular ions could prove to be a sensitive probe for a permanent electron electric dipole moment (eEDM). We propose to use a ground or metastable $^3Δ_1$ level, due to its high polarizability and large EDM enhancement factor. Ions allow for simple trapping and long interrogation times, but require a time-varying electric bias field in order to probe the eEDM. We discuss experimental design as well as challenges in performing a precision spectroscopic measurement in rapidly time-varying electric fields.
State-selected Coulomb-crystallized molecular ions were employed for the first time in ion-molecule reaction studies using the prototypical charge-transfer process $\mathrm{N_2^++N_2\rightarrow N_2+N_2^+}$ as an example. By preparing the reactant ions in a well-defined rovibrational state and localizing them in space by sympathetic cooling to millikelvin temperatures in an ion trap, state- and energy-controlled reaction experiments with sensitivities on the level of single ions were performed. The experimental results were interpreted with quasi-classical trajectory simulations on a six-dimens…
We present various planar magnetic designs that create points above the plane where the magnitude of the static magnetic field is a local minimum. Structures with these properties are of interest in the disciplines of neutral atom confinement, magnetic levitation, and magnetic resonance imaging. Each planar permanent magnet design is accompanied by the equivalent planar single non-crossing conductor design. Presented designs fall into three categories producing: a) zero value magnetic field magnitude point minima, b) non-zero magnetic field magnitude point minima requiring external bias magnet…
We perform hole burning with a low drift stabilized laser within the zero phonon line of the 4f-5d transition in Ce$^{3+}$:Y$_2$SiO$_5$ at 2K. The narrowest spectral holes appear for small applied magnetic fields and are $6\pm4$ MHz wide (FWHM). This puts an upper bound on the homogeneous linewidth of the transition to $3\pm2$ MHz, which is close to lifetime limited. The spin level relaxation time is measured to $72\pm21$ ms with a magnetic field of 10 mT. A slow permanent hole burning mechanism is observed. If the excitation frequency is not changed the fluorescence intensity is reduced by mo…
Molecules are the most demanding quantum systems to be simulated by quantum computers because of their complexity and the emergent role of quantum nature. The recent theoretical proposal of Huh et al. (Nature Photon., 9, 615 (2015)) showed that a multi-photon network with a Gaussian input state can simulate a molecular spectroscopic process. Here, we report the first experimental demonstration of molecular vibrational spectroscopy of SO$_{2}$ with a trapped-ion system. In our realization, the molecular scattering operation is decomposed to a series of elementary quantum optical operations, whi…
We present a full quantal study on the dissociation of a weakly bound molecular ion in the presence of an external time-dependent electric field. We focus on the dissociation dynamics of a molecular ion in a Paul trap relevant for atom-ion hybrid traps. Our results show that a weakly bound molecular ion survives in a Paul trap giving a theoretical ground to previous experimental findings [A. Krükow et al. Phys. Rev. Lett. 116, 193201 (2016) and A. Mohammadi et al. Phys. Rev. Research 3, 013196 (2021)]. In particular, we find that weakly bound molecular ions are more likely to survive in traps …
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…
We discuss the design and optimisation of two types of junctions between surface-electrode radiofrequency ion-trap arrays that enable the integration of experiments with sympathetically cooled molecular ions on a monolithic chip device. A detailed description of a multi-objective optimisation procedure applicable to an arbitrary planar junction is presented, and the results for a cross junction between four quadrupoles as well as a quadrupole-to-octupole junction are discussed. Based on these optimised functional elements, we propose a multi-functional ion-trap chip for experiments with transl…
We consider the practical feasibility of using the direct, electric dipole-dipole interaction between co-trapped molecular ions for robust quantum logic without the need for static polarizing fields. The use of oscillating dipole moments, as opposed to static electric dipoles, dynamically decouples the dipoles from laboratory fields, including the electric fields of the trap itself. Further, this implementation does not require quantum control of motion, potentially removing a major roadblock to ion trap quantum computing scalability. Since the polarizing field is electromagnetic radiation, ev…
The interaction between the electric dipole moment of a trapped molecular ion and the configuration of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this interaction to initialize, process, and read out quantum information encoded in molecular ion qubits without optically illuminating the molecules. We present two schemes wherein a molecular ion can be entangled with a co-trapped atomic ion qubit, providing, among other things, a means for molecular state preparation and measurement. We also show that vir…
We discuss a candidate solution for the controlled trapping and manipulation of two individual Rydberg atoms by means of a magnetic Ioffe-Pritchard trap that is superimposed by a constant electric field. In such a trap Rydberg atoms experience a permanent electric dipole moment that can be of the order of several hundred Debye. The interplay of electric dipolar repulsion and three dimensional magnetic confinement leads to a well controllable equilibrium configuration with tunable trap frequency and atomic distance. We thoroughly investigate the trapping potentials and analyze the interaction-i…
We demonstrate simultaneous deceleration and trapping of a cold atomic and molecular mixture. This is the first step towards studies of cold atom-molecule collisions at low temperatures as well as application of sympathetic cooling. Both atoms and molecules are cooled in a supersonic expansion and are loaded into a moving magnetic trap which brings them to rest via the Zeeman interaction from an initial velocity of 375 m/s. We use a beam seeded with molecular Oxygen, and entrain it with Lithium atoms by laser ablation prior to deceleration. The deceleration ends with loading of the mixture int…
Recent work with laser-cooled molecules in attractive optical traps has shown that the differential AC Stark shifts arising from the trap light itself can become problematic, limiting collisional shielding efficiencies, rotational coherence times, and laser-cooling temperatures. In this work, we explore trapping and laser-cooling of CaF molecules in a ring-shaped repulsive optical trap. The observed dependences of loss rates on temperature and barrier height show characteristic behavior of repulsive traps and indicate strongly suppressed average AC Stark shifts. Within the trap, we find that $…
Trapping cold, chemically important molecules with electromagnetic fields is a useful technique to study small molecules and their interactions. Traps provide long interaction times that are needed to precisely examine these low density molecular samples. However, the trapping fields lead to non-uniform molecular density distributions in these systems. Therefore, it is important to be able to experimentally characterize the spatial density distribution in the trap. Ionizing molecules in different locations in the trap using resonance enhanced multiphoton ionization (REMPI) and detecting the re…
We describe a simple Zeeman slower design using permanent magnets. Contrary to common wire-wound setups no electric power and water cooling are required. In addition, the whole system can be assembled and disassembled at will. The magnetic field is however transverse to the atomic motion and an extra repumper laser is necessary. A Halbach configuration of the magnets produces a high quality magnetic field and no further adjustment is needed. After optimization of the laser parameters, the apparatus produces an intense beam of slow and cold 87Rb atoms. With a typical flux of 1 - 5 \times 10^10 …
We investigate the electronic structure and properties of Rydberg atoms exposed to a magnetic quadrupole field. It is shown that the spatial as well as generalized time reversal symmetries lead to a two-fold degeneracy of the electronic states in the presence of the external field. A delicate interplay between the Coulomb and magnetic interactions in the inhomogeneous field leads to an unusual weak field splitting of the energy levels as well as complex spatial patterns of the corresponding spin polarization density of individual Rydberg states. Remarkably the magnetic quadrupole field induces…
Magneto-optical trapping (MOT) is a key technique on the route towards ultracold molecular ensembles. However, the realization and optimization of magneto-optical traps with their wide parameter space is particularly difficult. Here, we present a very general method for the optimization of molecular magneto-optical trap operation by means of Bayesian optimization (BO). As an example for a possible application, we consider the optimization of a calcium fluoride (CaF) MOT for maximum capture velocity. We find that both the $X^2Σ^+\,$ to $A^2Π_{1/2}\,$ and the $X^2Σ^+\,$ to $B^2Σ^+\,$ transition …
In optical dipole traps, the excited rotational states of a molecule may experience a very different light shift than the ground state. For particles with two polarizability components (parallel and perpendicular), such as linear $^1Σ$ molecules, the differential shift can be nulled by choice of elliptical polarization. When one component of the polarization vector is $\pm i\sqrt{2}$ times the orthogonal component, the light shift for a sublevel of excited rotational states approaches that of the ground state at high optical intensity. In this case, fluctuating trap intensity need not limit co…
We propose an approach for studying quantum information and performing high resolution spectroscopy of rotational states of trapped molecular ions using an on-chip superconducting microwave resonator. Molecular ions have several advantages over neutral molecules. Ions can be loaded into deep (1 eV) RF traps and are trapped independent of the electric dipole moment of their rotational transition. Their charge protects them from motional dephasing and prevents collisional loss, allowing 1 s coherence times when used as a quantum memory, with detection of single molecules possible in <10 ms. An a…
Trapped atoms and ions are among the best controlled quantum systems which find widespread applications in quantum information, sensing and metrology. For molecules, however, a similar degree of control is currently lacking owing to their complex energy-level structure. Quantum-logic protocols in which atomic ions serve as probes for molecular ions are a promising route for achieving this level of control, especially with homonuclear molecules that decouple from black-body radiation. Here, a quantum-non-demolition protocol on single trapped N$_2^+$ molecules is demonstrated. The spin-rovibroni…
We study a hybrid quantum system composed of an ion and an electric dipole. We show how a trapped ion can be used to measure the small electric field generated by a classical dipole. We discuss the application of this scheme to measure the electric dipole moment of cold polar molecules, whose internal state can be controlled with ultrafast laser pulses, by trapping them in the vicinity of a trapped ion.
Magnetic trapping of bromine atoms at temperatures in the milliKelvin regime is demonstrated for the first time. The atoms are produced by photodissociation of Br$_2$ molecules in a molecular beam. The lab-frame velocity of Br atoms is controlled by the wavelength and polarization of the photodissociation laser. Careful selection of the wavelength results in one of the pair of atoms having sufficient velocity to exactly cancel that of the parent molecule, and it remains stationary in the lab frame. A trap is formed at the null point between two opposing neodymium permanent magnets. Dissociatio…
We investigate the properties of two interacting ultracold polar molecules described as distinguishable quantum rigid rotors, trapped in a one-dimensional harmonic potential. The molecules interact via a multichannel two-body contact potential, incorporating the short-range anisotropy of intermolecular interactions including dipole-dipole interaction. The impact of external electric and magnetic fields resulting in Stark and Zeeman shifts of molecular rovibrational states is also investigated. Energy spectra and eigenstates are calculated by means of the exact diagonalization. The importance a…
Radiative emission during cold collisions between trapped laser-cooled Rb atoms and alkaline-earth ions (Ca$^+$, Sr$^+$, Ba$^+$) and Yb$^+$, and between Li and Yb$^+$, are studied theoretically, using accurate effective-core-potential based quantum chemistry calculations of potential energy curves and transition dipole moments of the related molecular ions. Radiative association of molecular ions is predicted to occur for all systems with a cross section two to ten times larger than the radiative charge transfer one. Partial and total rate constants are also calculated and compared to availabl…
