In this chapter we review the field of radio-frequency dressed atom trapping. We emphasise the role of adiabatic potentials and give simple, but generic models of electromagnetic fields that currently produce traps for atoms at microkelvin temperatures and below. The paper aims to be didactic and starts with general descriptions of the essential ingredients of adiabaticity and magnetic resonance. As examples of adiabatic potentials we pay attention to radio-frequency dressing in both the quadrupole trap and the Ioffe-Pritchard trap. We include a description of the effect of different choices of radio-frequency polarisation and orientations or alignment. We describe how the adiabatic potentials, formed from radio-frequency fields, can themselves be probed and manipulated with additional radio-frequency fields including multi-photon-effects. We include a description of time-averaged adiabatic potentials. Practical issues for the construction of radio-frequency adiabatic potentials are addressed including noise, harmonics, and beyond rotating wave approximation effects.
In this article, we have theoretically studied the time averaged adiabatic potential (TAAP) scheme for realizing different atom trapping geometries. It is shown that by varying time orbiting potential (TOP) fields and radio frequency (rf) fields parameters, controlled manipulation of trapping potentials, and conversion from one trapping geometry to another, is possible. The proposed trapping geometries can be useful for studying various atom-optic phenomena such as Bose-Einstein condensation (BEC) in low dimensions, super-fluidity, tunnelling, atom interferometry, etc.
Optical trapping of selected species of radioactive atoms has great potential in precision measurements for testing fundamental physics such as EDM, PNC and parity violating beta-decay asymmetry correlation coefficients. We report trapping of 10^4 radioactive ^{82}Rb atoms (t_{1/2}=75 s) with a trap lifetime of ~55 seconds in an optical dipole trap. Transfer efficiency from the magneto-optical trap was ~14%. We further report the evidence of spontaneous spin polarization of the atoms in optical dipole trap loading. This advancement is an important step towards a new generation of precision J-b…
The molecular association process in a thermal gas of $^{85}$Rb is investigated where the effects of the envelope of the radio-frequency field are taken into account. For experimentally relevant parameters our analysis shows that with increasing pulse length the corresponding molecular conversion efficiency exhibits low-frequency interference fringes which are robust under thermal averaging over a wide range of temperatures. This dynamical interference phenomenon is attributed to Stückelberg phase accumulation between the low-energy continuum states and the dressed molecular state which exhibi…
Quantum vacuum forces dictate the interaction between individual atoms and dielectric surfaces at nanoscale distances. For example, their large strengths typically overwhelm externally applied forces, which makes it challenging to controllably interface cold atoms with nearby nanophotonic systems. Here, we show that it is possible to tailor the vacuum forces themselves to provide strong trapping potentials. The trapping scheme takes advantage of the attractive ground state potential and adiabatic dressing with an excited state whose potential is engineered to be resonantly enhanced and repulsi…
Isolating neutral and charged particles from the environment is essential in precision experiments. For decades, this has been achieved by trapping ions with radio-frequency (rf) fields and neutral particles with optical fields. Recently, trapping of ions by interaction with light has been demonstrated. This might permit combining the advantages of optical trapping and ions. For example, by superimposing optical traps to investigate ensembles of ions and atoms in absence of any radiofrequency fields, as well as to benefit from the versatile and scalable trapping geometries featured by optical …
We demonstrate significantly improved magneto-optical trapping of molecules using a very slow cryogenic beam source and RF modulated and DC magnetic fields. The RF MOT confines $1.1(3) \times 10^5$ CaF molecules at a density of $4(1) \times 10^6$ cm$^{-3}$, which is an order of magnitude greater than previous molecular MOTs. Near Doppler-limited temperatures of $340(20)$ $μ$K are attained. The achieved density enables future work to directly load optical tweezers and create optical arrays for quantum simulation.
Non-adiabatic decay rates for a radio-frequency dressed magnetic trap are calculated using Fermi's Golden Rule: that is, we examine the probability for a single atom to make transitions out of the dressed trap and into a continuum in the adiabatic limit, where perturbation theory can be applied. This approach can be compared to the semi-classical Landau-Zener theory of a resonant dressed atom trap, and it is found that, when carefully implemented, the Landau-Zener theory overestimates the rate of non-adiabatic spin flip transitions in the adiabatic limit. This indicates that care is needed whe…
We consider the stability of systems subjected to periodic parametric driving such that their equations of motion are ordinary differential equations with periodic coefficients and carry out a detailed analysis of important aspects of such systems in the context of the confinement of ions by oscillating electric fields. We show how they can be understood in terms of a pseudopotential approximation and resonances arising from the parametric excitation and investigate the properties of a novel linear Paul trap configuration operating with two radio-frequencies to simultaneously confine two speci…
The method of operation of an atomic magnetometer based on coherent population trapping (CPT) without any requirement of radio frequency scanning is demonstrated. Using a hybrid approach comprising of polarization rotation and tailored transmission due to CPT states, the simultaneous operation of the device as atomic frequency standard as well as atomic magnetometer is investigated. The magnetometer sensitivity can be further improved by utilizing the inherent option of magnetic field assisted synchronized radio frequency scanning.
We have studied magneto-optical traps (MOTs) for efficient on-line trapping of radioactive atoms. After discussing a model of the trapping process in a vapor cell and its efficiency, we present the results of detailed experimental studies on Rb MOTs. Three spherical cells of different sizes were used. These cells can be easily replaced, while keeping the rest of the apparatus unchanged: atomic sources, vacuum conditions, magnetic field gradients, sizes and power of the laser beams, detection system. By direct comparison, we find that the trapping efficiency only weakly depends on the MOT cell …
For several decades, ions have been trapped by radio frequency (RF) and neutral particles by optical fields. We implement the experimental proof-of-principle for trapping an ion in an optical dipole trap. While loading, initialization and final detection are performed in a RF trap, in between, this RF trap is completely disabled and substituted by the optical trap. The measured lifetime of milliseconds allows for hundreds of oscillations within the optical potential. It is mainly limited by heating due to photon scattering. In future experiments the lifetime may be increased by further detunin…
We investigate theoretically the application of Sawtooth Wave Adiabatic Passage (SWAP) in a 1D magneto-optical trap (MOT). As opposed to related methods that have been previously discussed, our approach utilizes repeated cycles of stimulated absorption and emission processes to achieve both trapping and cooling, thereby reducing the adverse effects that arise from photon scattering. Specifically, we demonstrate this method's ability to cool, slow, and trap particles with fewer spontaneously emitted photons, higher forces and in less time when compared to a traditional MOT scheme that utilizes …
High-fidelity entangled Bell states are of great interest in quantum physics. Entanglement of ultracold neutral atoms in two spatially separated optical dipole traps is promising for implementation of quantum computing and quantum simulation and for investigation of Bell states of material objects. We propose a new method to entangle two atoms via long-range Rydberg-Rydberg interaction. Alternatively to previous approaches, based on Rydberg blockade, we consider radiofrequency-assisted Stark-tuned Förster resonances in Rb Rydberg atoms. To reduce the sensitivity of the fidelity of Bell states …
A novel protocol of interrogation based on coherent population trapping in an N-level scheme atomic system leads to dark resonances involving three different photons. An ensemble of several hundreds of radiofrequency-trapped ions is probed by three lasers simultaneously locked onto the same optical frequency comb, resulting in high-contrast spectral lines referenced to an atomic transition in the THz domain. We discuss the cause of uncertainties and limitations for this method and show that reaching a sub-kHz resolution is experimentally accessible via this interrogation protocole.
Adiabatic dressed state potentials are created when magnetic sub-states of trapped atoms are coupled by a radio frequency field. We discuss their theoretical foundations and point out fundamental advantages over potentials purely based on static fields. The enhanced flexibility enables one to implement numerous novel configurations, including double wells, Mach-Zehnder and Sagnac interferometers which even allows for internal state-dependent atom manipulation. These can be realized using simple and highly integrated wire geometries on atom chips.
Recent advances in quantum information processing with trapped ions have demonstrated the need for new ion trap architectures capable of holding and manipulating chains of many (>10) ions. Here we present the design and detailed characterization of a new linear trap, microfabricated with scalable complementary metal-oxide-semiconductor (CMOS) techniques, that is well-suited to this challenge. Forty-four individually controlled DC electrodes provide the many degrees of freedom required to construct anharmonic potential wells, shuttle ions, merge and split ion chains, precisely tune secular mode…
The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher dimensional systems. Here, we report on the trappin…
We explore properties of atoms whose magnetic hyperfine sub-levels are coupled by an external magnetic radio frequency (rf) field. We perform a thorough theoretical analysis of this driven system and present a number of systematic approximations which eventually give rise to dressed adiabatic radio frequency potentials. The predictions of this analytical investigation are compared to numerically exact results obtained by a wave packet propagation. We outline the versatility and flexibility of this new class of potentials and demonstrate their potential use to build atom optical elements such a…
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 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…
Using a Direct Simulation Monte Carlo technique, we have studied the time evolution of a cold atom cloud interacting with a time dependent radio frequency (rf) dressed state potential. Exposure of a cloud of $^{87}Rb$ atoms, trapped in a quadrupole magnetic trap, to a time dependent rf-field with increasing amplitude and decreasing frequency, shows a variation in the number of trapped atoms and the overall shape of the atom cloud. It is shown by simulations that, initially at lower rf-field strength, the rf-field results in ejection of atoms from the trap, leading to evaporative cooling of the…
Ultralong-range Rydberg molecules provide an exciting testbed for molecular physics at exaggerated scales. In the so-called trilobite and butterfly Rydberg molecules, the Born-Oppenheimer approximation can fail due to strong non-adiabatic couplings arising from the combination of radial oscillations and rapid energy variations in the adiabatic potential energy curves. We utilize an accurate coupled-channel treatment of the vibronic system to observe the breakdown of Born-Oppenheimer physics, such as non-adiabatic trapping and decay of molecular states found near pronounced avoided crossings in…
We have realized optical excitation, trapping and detection of the radioisotope $^{81}$Kr with an isotopic abundance of 0.9 ppt. The 124 nm light needed for the production of metastable atoms is generated by a resonant discharge lamp. Photon transport through the optically thick krypton gas inside the lamp is simulated and optimized to enhance both brightness and resonance. We achieve a state-of-the-art $^{81}$Kr loading rate of 1800 atoms/h, which can be further scaled up by adding more lamps. The all-optical approach overcomes the limitations on precision and sample size of radiokrypton dati…
We study experimentally and theoretically structural defects which are formed during the transition from a laser cooled cloud to a Coulomb crystal, consisting of tens of ions in a linear radio frequency trap. We demonstrate the creation of predicted topological defects (`kinks') in purely two-dimensional crystals, and also find kinks which show novel dynamical features in a regime of parameters not considered before. The kinks are always observed at the centre of the trap, showing a large nonlinear localized excitation, and the probability of their occurrence surprisingly saturates at ~0.5. Si…
For conventional ion traps, the trapping potential is close to independent of the electronic state, providing confinement for ions dependent primarily on their charge-to-mass ratio $Q/m$. In contrast, storing ions within an optical dipole trap results in state-dependent confinement. Here we experimentally study optical dipole potentials for $^{138}\mathrm{Ba}^+$ ions stored within two distinctive traps operating at 532 nm and 1064 nm. We prepare the ions in either the $6\mathrm{S}_{\mathrm{1/2}}$ electronic ground or the $5\mathrm{D}_{\mathrm{3/2}}$/ $5\mathrm{D}_{\mathrm{5/2}}$ metastable exc…
Atom chips made of superconducting material can generate magnetic traps with significantly reduced noise. Recently, several designs for superconducting chips have been theoretically analyzed and experimentally tested, for cases with many vortices considered as an average vortex density. Here we show theoretically, for the first time, how the magnetic field of a $\it single$ vortex, pinned by a superconducting nano-disc of radius $\sim$100 nm and combined with an external bias field parallel to the disc surface, yields a closed 3D trap for cold atoms. The size of the trap, and its height above …
Many important physical processes have dynamics that are too complex to completely model analytically. Optimisation of such processes often relies on intuition, trial-and-error, or the construction of empirical models. Machine learning based on artificial neural networks has emerged as an efficient means to develop empirical models of complex systems. We implement a deep artificial neural network to optimise the magneto-optic cooling and trapping of neutral atomic ensembles. Cold atomic ensembles have become commonplace in laboratories around the world, however, many-body interactions give ris…
We present a scheme for creating tight and adiabatic time-averaged atom-traps through the piezoelectric actuation of nanomagnetic structures. We show that potentials formed by the circular translation of magnetic structures have several advantages over conventional rotating-field techniques, particularly for high trap frequencies. As the magnitude of the actuation is changed the trapping potential can be changed adiabatically between harmonic 3D confinement and a toroidal trap.
We evaluate the impact that nonlinear Zeeman shifts have on resonant radio-frequency (RF) dressed traps in an atom-chip configuration. The degeneracy of the resonance between Zeeman levels is lifted at large intensities of a static field, modifying the spatial dependence of the atomic adiabatic potential. In this context, we find effects that are important for the next generation of atom chips with tight trapping: in particular, that the vibrational frequency of the atom trap is sensitive to the RF frequency and, depending on the sign of the Landé factor, can produce significantly weaker, or t…
We implement and demonstrate the effectiveness of a cooling scheme using a moving, all-optical, one-way barrier to cool a sample of $^{87}$Rb atoms, achieving nearly a factor of 2 reduction in temperature. The one-way barrier, composed of two focused, Gaussian laser beams, allows atoms incident on one side to transmit, while reflecting atoms incident on the other. The one-way barrier is adiabatically swept through a sample of atoms contained in a far-off-resonant, single-beam, optical dipole trap that forms a nearly harmonic trapping potential. As the barrier moves longitudinally through the p…
Confinement of single ions in a novel radio-frequency (RF) quadrupole ion trap with spherical shape is investigated. An optimization of this spherical ion trap (SIT) is carried out in order to suppress its nonlinearity substantially by eliminating the electric octupole moment. Hence, a trapping potential and consequently an electric field very similar to the ideal quadrupole ion trap (QIT) are obtained. Afterwards, three stability regions for the optimized SIT are numerically computed. The regions coincide well with those reported in the literature for the ideal QIT. The reason is attributed t…
We report a vapor-cell magneto-optical trapping of Hg isotopes on the ${}^1S_0-{}^3P_1$ intercombination transition. Six abundant isotopes, including four bosons and two fermions, were trapped. Hg is the heaviest non-radioactive atom trapped so far, which enables sensitive atomic searches for ``new physics'' beyond the standard model. We propose an accurate optical lattice clock based on Hg and evaluate its systematic accuracy to be better than $10^{-18}$. Highly accurate and stable Hg-based clocks will provide a new avenue for the research of optical lattice clocks and the time variation of t…
The radiofrequency quadrupole linear ion trap is a widely used device in physics and chemistry. When used for trapping of large ion clouds, the presence of anharmonic terms in the radiofrequency potential limits the total number of stored ions. In this paper, we have studied the anharmonic content of the trapping potential for different implementations of a quadrupole trap, searching for the geometry best suited for the trapping of large ion clouds. This is done by calculating the potential of a real trap using SIMION8.0, followed by a fit, which allows us to obtain the evolution of anharmonic…
We report on the successful commissioning of the Francium Trapping Facility at TRIUMF. Large laser-cooled samples of francium are produced from a francium ion beam delivered by the ISAC radioactive ion beam facility. The ion beam is neutralized on an yttrium foil, which is subsequently heated to transfer the atoms into the magneto-optical trapping region. We have successfully trapped $^{207}$Fr, $^{209}$Fr and $^{221}$Fr, with a maximum of $2.5 \times 10^5$ $^{209}$Fr atoms. The neutral cold atoms will be used in studies of the weak interaction through measurements of atomic parity non-conserv…
We load a Bose-Einstein condensate into a one-dimensional (1D) optical lattice altered through the use of radiofrequency (rf) dressing. The rf resonantly couples the three levels of the $^{87}$Rb $F=1$ manifold and combines with a spin-dependent "bare" optical lattice to result in adiabatic potentials of variable shape, depth, and spatial frequency content. We choose dressing parameters such that the altered lattice is stable over lifetimes exceeding tens of ms at higher depths than in previous work. We observe significant differences between the BEC momentum distributions of the dressed latti…
We demonstrate loading of SrF molecules into an optical dipole trap (ODT) via in-trap $Λ$-cooling. We find that this cooling can be optimized by a proper choice of relative ODT and $Λ$ beam polarizations. In this optimized configuration, we observe molecules with temperatures as low as 14(1) $μ$K in traps with depths up to 570 $μ$K. With optimized parameters, we transfer $\!\sim\!5$% of molecules from our radio-frequency magneto-optical trap into the ODT, at a density of $\sim\!2\times 10^{9}$ cm$^{-3}$, a phase space density of $\sim\!2\times 10^{-7}$, and with a trap lifetime of $\!\sim\!1$ …
The scope of this book is on providing insight into the recently emerged field of optical trapping of ions. Since the ground-breaking introduction of light fields as tools for exerting trapping forces on matter in 1970 by Ashkin, optical dipole traps have enabled an unprecedented level of control over neutral atoms and molecules both at the level of quantum ensembles as well as individual particles. It was found recently that in some situations it is highly advantageous to confine atomic and molecular ions without employing any radiofrequency-based Paul traps or strong external magnetic fields…
A theoretical investigation for implementing a scheme of forced evaporative cooling in radio-frequency (rf) adiabatic potentials is presented. Supposing the atoms to be trapped by a rf field RF1, the cooling procedure is facilitated using a second rf source RF2. This second rf field produces a controlled coupling between the spin states dressed by RF1. The evaporation is then possible in a pulsed or continuous mode. In the pulsed case, atoms with a given energy are transferred into untrapped dressed states by abruptly switching off the interaction. In the continuous case, it is possible for en…
