The evanescent field surrounding nano-scale optical waveguides offers an efficient interface between light and mesoscopic ensembles of neutral atoms. However, the thermal motion of trapped atoms, combined with the strong radial gradients of the guided light, leads to a time-modulated coupling between atoms and the light mode, thus giving rise to additional noise and motional dephasing of collective states. Here, we present a dipole force free scheme for coupling of the radial motional states, utilizing the strong intensity gradient of the guided mode and demonstrate all-optical coupling of the cesium hyperfine ground states and motional sideband transitions. We utilize this to prolong the trap lifetime of an atomic ensemble by Raman sideband cooling of the radial motion, which has not been demonstrated in nano-optical structures previously. Our work points towards full and independent control of internal and external atomic degrees of freedom using guided light modes only.
We dispersively interface an ensemble of one thousand atoms trapped in the evanescent field surrounding a tapered optical nanofiber. This method relies on the azimuthally-asymmetric coupling of the ensemble with the evanescent field of an off-resonant probe beam, transmitted through the nanofiber. The resulting birefringence and dispersion are significant; we observe a phase shift per atom of $\sim$\,1\,mrad at a detuning of six times the natural linewidth, corresponding to an effective resonant optical density per atom of 0.027. Moreover, we utilize this strong dispersion to non-destructively…
We experimentally study the ground state coherence properties of cesium atoms in a nanofiber-based two-color dipole trap, localized 200 nm away from the fiber surface. Using microwave radiation to coherently drive the clock transition, we record Ramsey fringes as well as spin echo signals and infer a reversible dephasing time $T_2^\ast=0.6$ ms and an irreversible dephasing time $T_2^\prime=3.7$ ms. By theoretically modelling the signals, we find that, for our experimental parameters, $T_2^\ast$ and $T_2^\prime$ are limited by the finite initial temperature of the atomic ensemble and the heatin…
Trapping and optically interfacing laser-cooled neutral atoms is an essential requirement for their use in advanced quantum technologies. Here we simultaneously realize both of these tasks with cesium atoms interacting with a multi-color evanescent field surrounding an optical nanofiber. The atoms are localized in a one-dimensional optical lattice about 200 nm above the nanofiber surface and can be efficiently interrogated with a resonant light field sent through the nanofiber. Our technique opens the route towards the direct integration of laser-cooled atomic ensembles within fiber networks, …
We demonstrate an optical tweezer based single atom trapping on an optical nanofiber cavity. We show that the fluorescence of single atoms trapped on the nanofiber cavity can be readily observed in real-time through the fiber guided modes. The photon correlation measurements further clarify the atom number and the dynamics of the trap. The trap lifetime is measured to be 52$\pm$5 ms. From the photon statistics measured for different cavity decay rates, the effective coupling rate of the atom-cavity interface is estimated to be 34$\pm$2 MHz. This yields a cooperativity of 5.4$\pm$0.6 and a cavi…
We present experimental techniques and results related to the optimization and characterization of our nanofiber-based atom trap [Vetsch et al., Phys. Rev. Lett. 104, 203603 (2010)]. The atoms are confined in an optical lattice which is created using a two-color evanescent field surrounding the optical nanofiber. For this purpose, the polarization state of the trapping light fields has to be properly adjusted. We demonstrate that this can be accomplished by analyzing the light scattered by the nanofiber. Furthermore, we show that loading the nanofiber trap from a magneto-optical trap leads to …
We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Green's function, which determines the scattering of light by atoms in the presence of the fi…
Single particle-resolved fluorescence imaging is an enabling technology in cold-atom physics. However, so far, this technique was not available for nanophotonic atom-light interfaces. Here, we image single atoms that are trapped and optically interfaced using an optical nanofiber. Near-resonant light is scattered off the atoms and imaged while counteracting heating mechanisms via degenerate Raman cooling. We detect trapped atoms within 150 ms and record image sequences of given atoms. Building on our technique, we perform two experiments which are conditioned on the number and position of the …
We demonstrate optical transport of cold cesium atoms over millimeter-scale distances along an optical nanofiber. The atoms are trapped in a one-dimensional optical lattice formed by a two-color evanescent field surrounding the nanofiber, far red- and blue-detuned with respect to the atomic transition. The blue-detuned field is a propagating nanofiber-guided mode while the red-detuned field is a standing-wave mode which leads to the periodic axial confinement of the atoms. Here, this standing wave is used for transporting the atoms along the nanofiber by mutually detuning the two counter-propa…
We report on a controllable, hybrid quantum system consisting of cold Rydberg atoms and an optical nanofiber interface. Using a two-photon ladder-type excitation in $^{87}$Rb, we demonstrate both coherent and incoherent Rydberg excitation at submicron distances from the nanofiber surface. The 780 nm photon, near resonant to the $5S \rightarrow 5P$ transition, is mediated by the cooling laser, while the 482 nm light, near resonant to the $5P \rightarrow 29D$ transition, is mediated by the guided mode of the nanofiber. The population loss rate of the cold atom ensemble is used to measure the Ryd…
We propose and demonstrate a new method for Doppler cooling trapped-ion crystals where the distribution of micromotion amplitudes may be large and uneven. The technique uses pulses of Doppler cooling light synchronized with the trap RF that selectively target ions when their velocity is near a node, leading to more uniform cooling across a crystal by a single tone of cooling light. We lay out a theoretical framework that describes where this technique is practical, and provide a simple experimental demonstration.
We demonstrate an ultraviolet diode laser system for cooling of trapped ytterbium ions. The laser power and linewidth are comparable to previous systems based on resonant frequency doubling, but the system is simpler, more robust, and less expensive. We use the laser system to cool small numbers of ytterbium ions confined in a linear Paul trap. From the observed spectra, we deduce final temperatures < 270 mK.
We demonstrated sympathetic cooling of a single ion in a buffer gas of ultracold atoms with small mass. Efficient collisional cooling was realized by suppressing collision-induced heating. We attempt to explain the experimental results with a simple rate equation model and provide a quantitative discussion of the cooling efficiency per collision. The knowledge we obtained in this work is an important ingredient for advancing the technique of sympathetic cooling of ions with neutral atoms.
Using a laser polarization gradient, we realize 3D Sisyphus cooling of $^{171}$Yb$^+$ ions confined in and near the Lamb-Dicke regime in a linear Paul trap. The cooling rate and final mean motional energy of a single ion are characterized as a function of laser intensity and compared to semiclassical and quantum simulations. Sisyphus cooling is also applied to a linear string of four ions to obtain a mean energy of 1-3 quanta for all vibrational modes, an approximately order-of-magnitude reduction below Doppler cooled energies. This is used to enable subsequent, efficient sideband laser coolin…
Spectroscopic studies of few-body systems at ultracold temperatures provide valuable information that often cannot be extracted in a hot environment. Considering a pair of atoms, we propose a cooling mechanism that makes use of a scattering Feshbach resonance. Application of a series of time-dependent magnetic field ramps results in the situation in which either zero, one, or two atoms remain trapped. If two atoms remain in the trap after the field ramps are completed, then they have been cooled. Application of the proposed cooling mechanism to optical traps or lattices is considered.
Doppler cooling with lasers is essential to ions' trapping and also a preliminary step towards achievement of ultracold ions. Due to lack of effective tools, experimentally monitoring the ions' temperature and the laser-ion coupling is difficult in Doppler cooling. Here we analytically explore the Doppler cooling process of trapped ions, exemplified by $^{40}$Ca$^{+}$, by solving the friction coefficient in the Doppler cooling with respect to a thermal bath, particularly, to a bath with large heating rate. We show four regions for cooling and heating induced by the three-level electromagnetica…
We study, both experimentally and theoretically, electromagnetically induced transparency cooling of the drumhead modes of planar 2-dimensional arrays with up to $N\approx 190$ Be${}^+$ ions stored in a Penning trap. Substantial sub-Doppler cooling is observed for all $N$ drumhead modes. Quantitative measurements for the center-of-mass mode show near ground state cooling with motional quantum numbers of $\bar{n} = 0.3\pm0.2$ obtained within $200~μs$. The measured cooling rate is faster than that predicted by single particle theory, consistent with a quantum many-body calculation. For the lower…
Sympathetic cooling of trapped ions through collisions with neutral buffer gases is critical to a variety of modern scientific fields, including fundamental chemistry, mass spectrometry, nuclear and particle physics, and atomic and molecular physics. Despite its widespread use over four decades, there remain open questions regarding its fundamental limitations. To probe these limits, here we examine the steady-state evolution of up to ten barium ions immersed in a gas of three-million laser-cooled calcium atoms. We observe and explain the emergence of nonequilibrium behavior as evidenced by bi…
We implement three-dimensional polarization gradient cooling of trapped ions. Counter-propagating laser beams near $393\,$nm impinge in lin$\,\perp\,$lin configuration, at a frequency below the S$_{1/2}$ to P$_{3/2}$ resonance in $^{40}$Ca$^+$. We demonstrate mean phonon numbers of $5.4(4)$ at a trap frequency of $2π\times 285\,$kHz and $3.3(4)$ at $2π\times480\,$kHz, in the axial and radial directions, respectively. Our measurements demonstrate that cooling with laser beams detuned to lower frequencies from the resonance is robust against an elevated phonon occupation number, and thus works w…
We propose and analyze a scheme for sympathetic cooling of the translational motion of polar molecules in an optical lattice, interacting one by one with laser-cooled ions in a radio-frequency trap. The energy gap between the excitation spectra of the particles in their respective trapping potentials is bridged by means of a parametric resonance, provided by the additional modulation of the RF field. We analyze two scenarios: simultaneous laser cooling and energy exchange between the ion and the molecule, and a scheme when these two processes take place separately. We calculate the lowest fina…
We investigate how the nonlinearity of the Zeeman shift for strong magnetic fields affects the dynamics of rf field induced evaporative cooling in magnetic traps. We demonstrate for the 87-Rb and 23-Na F=2 trapping states with wave packet simulations how the cooling stops when the rf field frequency goes below a certain limit (for the 85-Rb F=2 trapping state the problem does not appear). We examine the applicability of semiclassical models for the strong field case as an extension of our previous work [Phys. Rev. A 58, 3983 (1998)]. Our results verify many of the aspects observed in a recent …
Magnetically trapped neutral atoms can be cooled with the evaporation technique. This is typically done by using a radiofrequency (rf) field that adiabatically couples trapped and untrapped internal atomic states for atoms with kinetic energies above a value set by the field frequency. The rf-field can also induce nonadiabatic changes of internal atomic spin states (F,M) that lead to heating and enhanced loss of atoms. In this paper we use wave packet simulations to show that the evaporation process can induce these nonadiabatic transitions which change the internal spin state of doubly spin-p…
We analyze the ac Stark shift of a cesium atom interacting with far-off-resonance guided light fields in the nanofiber-based two-color optical dipole trap realized by Vetsch \textit{et al.} [Phys. Rev. Lett. \textbf{104}, 203603, (2010)]. Particular emphasis is given to the fictitious magnetic field produced by the vector polarizability of the atom in conjunction with the ellipticity of the polarization of the trapping fields. Taking into account the ac Stark shift, the atomic hyperfine interaction, and a magnetic interaction, we solve the stationary Schrödinger equation at a fixed point in sp…
We report on a scheme to cool and compress trapped clouds of highly magnetic 52Cr atoms. This scheme combines sequences of gray molasses, which freeze the velocity distribution, and free evolutions in the (close to) harmonic trap, which periodically exchange the spatial and velocity degrees of freedom. Taken together, the successive gray molasses pulses cool all external degrees of freedom, which leads to an increase of the phase-space density (PSD) by a factor of about 250, allowing to reach a high final PSD of about 1.7*10^-3. These experiments are performed within an optical dipole trap, in…
We propose a scheme that combines velocity-selective coherent population trapping (CPT) and Raman sideband cooling (RSC) for subrecoil cooling of optically trapped atoms outside the Lamb-Dicke regime. This scheme is based on an inverted $\mathsf{Y}$ configuration in an alkali-metal atom. It consists of a $Λ$ formed by two Raman transitions between the ground hyperfine levels and the $D$ transition, allowing RSC along two paths and formation of a CPT dark state. Using state-dependent difference in vibration frequency of the atom in a circularly polarized trap, we can tune the $Λ$ to make only t…
Recently, laser cooling methods have been extended from atoms to molecules. The complex rotational and vibrational energy level structure of molecules makes laser cooling difficult, but these difficulties have been overcome and molecules have now been cooled to a few microkelvin and trapped for several seconds. This opens many possibilities for applications in quantum science and technology, controlled chemistry, and tests of fundamental physics. This article explains how molecules can be decelerated, cooled and trapped using laser light, reviews the progress made in recent years, and outlines…
Resolved sideband cooling is a standard technique for cooling trapped ions below the Doppler limit to near their motional ground state. Yet, the most common methods for sideband cooling implicitly rely on low Doppler-cooled temperatures and tightly confined ions, and they cannot be optimized for different experimental conditions. Here we introduce a framework which calculates the fastest possible pulsed sideband cooling sequence for a given number of pulses and set of experimental parameters, and we verify its improvement compared to traditional methods using a trapped $^{171}$Yb$^+$ ion. Afte…
Atoms trapped in the evanescent field around a nanofiber experience strong coupling to the light guided in the fiber mode. However, due to the intrinsically strong positional dependence of the coupling, thermal motion of the ensemble limits the use of nanofiber trapped atoms for some quantum tasks. We investigate the thermal dynamics of such an ensemble by using short light pulses to make a spatially inhomogeneous population transfer between atomic states. As we monitor the wave packet of atoms created by this scheme, we find a damped oscillatory behavior which we attribute to sloshing and dis…
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.
Trapped ions are a promising candidate for large scale quantum computation. Several systems have been built in both academic and industrial settings to implement modestly-sized quantum algorithms. Efficient cooling of the motional degrees of freedom is a key requirement for high-fidelity quantum operations using trapped ions. Here, we present a technique whereby individual ions are used to cool individual motional modes in parallel, reducing the time required to bring an ion chain to its motional ground state. We demonstrate this technique experimentally and develop a model to understand the e…
This book chapter gives an introduction to, and an overview of, methods for cooling trapped ions. The main addressees are researchers entering the field. It is not intended as a comprehensive survey and historical account of the extensive literature on this topic. We present the physical ideas behind several cooling schemes, outline their mathematical description, and point to relevant literature useful for a more in-depth study of this topic.
We present the results of simulations of optical sideband cooling of atomic ions in a trap with a shallow potential well. In such traps, an ion cannot be Doppler cooled near to the Lamb-Dicke regime ($η^2(2n+1) \ll 1$). Outside the Lamb-Dicke regime, the sideband cooling dynamics are altered by the existence of various Fock states where the cooling becomes very slow. A calcium ion trapped in our Penning trap realises such a situation, hence single stage cooling is inefficient to prepare the ion in the motional ground state. For these systems, it is necessary to study the cooling dynamics in de…
Cooling of particles to mK-temperatures is essential for a variety of experiments with trapped charged particles. However, many species of interest lack suitable electronic transitions for direct laser cooling. We study theoretically the remote sympathetic cooling of a single proton with laser-cooled $^9$Be$^+$ in a double-Penning-trap system. We investigate three different cooling schemes and find, based on analytical calculations and numerical simulations, that two of them are capable of achieving proton temperatures of about 10 mK with cooling times on the order of 10 s. In contrast, establ…
We present a novel optical cooling scheme that relies on hyperfine dark states to enhance loading and cooling atoms inside deep optical dipole traps. We demonstrate a seven-fold increase in the number of atoms loaded in the conservative potential with strongly shifted excited states. In addition, we use the energy selective dark-state to efficiently cool the atoms trapped inside the conservative potential rapidly and without losses. Our findings open the door to optically assisted cooling of trapped atoms and molecules which lack the closed cycling transitions normally needed to achieve low te…
We present a scheme to embed molecular anions in a gas of ultracold rubidium atoms as a route towards the preparation of cold molecular ions by collisional cooling with ultracold atoms. Associative detachment as an important loss process in collisions between OH- molecules and rubidium atoms is studied. The density distribution of trapped negative ions in the multipole radiofrequency trap is measured by photodetachment tomography, which allows us to derive absolute rate coefficients for the process. We define a regime where translational and internal cooling of molecular ions embedded into the…
A mixed system of cooled and trapped, ions and atoms, paves the way for ion assisted cold chemistry and novel many body studies. Due to the different individual trapping mechanisms, trapped atoms are significantly colder than trapped ions, therefore in the combined system, the strong binary ion$-$atom interaction results in heat flow from ions to atoms. Conversely, trapped ions can also get collisionally heated by the cold atoms, making the resulting equilibrium between ions and atoms intriguing. Here we experimentally demonstrate, Rubidium ions (Rb$^+$) cool in contact with magneto-optically …
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…
Calcium monofluoride (CaF) molecules are loaded into an optical dipole trap (ODT) and subsequently laser cooled within the trap. Starting with magneto-optical trapping, we sub-Doppler cool CaF and then load $150(30)$ CaF molecules into an ODT. Enhanced loading by a factor of five is obtained when sub-Doppler cooling light and trapping light are on simultaneously. For trapped molecules, we directly observe efficient sub-Doppler cooling to a temperature of $60(5)$ $μ\text{K}$. The trapped molecular density of $8(2)\times10^7$ cm$^{-3}$ is an order of magnitude greater than in the initial sub-Dop…
We investigate the temporal dynamics of Doppler cooling of an initially hot single trapped atom in the weak binding regime using a semiclassical approach. We develop an analytical model for the simplest case of a single vibrational mode for a harmonic trap, and show how this model allows us to estimate the initial energy of the trapped particle by observing the fluorescence rate during the cooling process. The experimental implementation of this temperature measurement provides a way to measure atom heating rates by observing the temperature rise in the absence of cooling. This method is techn…
We report a detailed investigation on near-ground state cooling of one and two trapped atomic ions. We introduce a simple sideband cooling method for confined atoms and ions, using RF radiation applied to bare ionic states in a static magnetic field gradient, and demonstrate its application to ions confined at secular trap frequencies, $ω_z \approx 2π\times 117 $kHz. For a single \ybplus ion, the sideband cooling cycle reduces the average phonon number, $\left\langle\,n\,\right\rangle$ from the Doppler limit to $\left\langle\,n\,\right\rangle =$ 0.30(12). This is in agreement with the theoreti…
We report on the realization of a stable mixture of ultracold lithium and ytterbium atoms confined in a far-off-resonance optical dipole trap. We observe sympathetic cooling of 6Li by 174Yb and extract the s-wave scattering length magnitude |a6Li-174Yb| = (13 \pm 3)a0 from the rate of inter-species thermalization. Using forced evaporative cooling of 174Yb, we achieve reduction of the 6Li temperature to below the Fermi temperature, purely through inter-species sympathetic cooling.
The two most widely used ion cooling methods are laser cooling and sympathetic cooling by elastic collisions (ECs). Here we demonstrate another method of cooling ions that is based on resonant charge exchange (RCE) between the trapped ion and the ultracold parent atom. Specifically, trapped Cs$^{+}$ ions are cooled by collisions with co-trapped, ultracold Cs atoms and, separately, by collisions with co-trapped, ultracold Rb atoms. We observe that the cooling of Cs$^{+}$ ions by Cs atoms is more efficient than cooling of Cs$^{+}$ ions by Rb atoms. This signals the presence of a cooling mechanis…
We report the electromagnetically-induced-transparency (EIT) cooling of a large trapped $^{171}$Yb$^+$ ion chain to the quantum ground state. Unlike conventional EIT cooling, we engage a four-level tripod structure and achieve fast sub-Doppler cooling over all motional modes. We observe simultaneous ground-state cooling across the complete transverse mode spectrum of up to $40$ ions, occupying a bandwidth of over $3$ MHz. The cooling time is observed to be less than $300\,μ$s, independent of the number of ions. Such efficient cooling across the entire spectrum is essential for high-fidelity qu…
Efficient cooling of trapped charged particles is essential to many fundamental physics experiments, to high-precision metrology, and to quantum technology. Until now, sympathetic cooling has required close-range Coulomb interactions, but there has been a sustained desire to bring laser-cooling techniques to particles in macroscopically separated traps, extending quantum control techniques to previously inaccessible particles such as highly charged ions, molecular ions and antimatter. Here we demonstrate sympathetic cooling of a single proton using laser-cooled Be+ ions in spatially separated …
We investigate theoretically the possibility for robust and fast cooling of a trapped atomic ion by transient interaction with a pre-cooled ion. The transient coupling is achieved through dynamical control of the ions' equilibrium positions. To achieve short cooling times we make use of shortcuts to adiabaticity by applying invariant-based engineering. We design these to take account of imperfections such as stray fields, and trap frequency offsets. For settings appropriate to a currently operational trap in our laboratory, we find that robust performance could be achieved down to $6.3$ motion…
