We report an improved measurement of the Landé g factor of the 5D5/2 state of singly ionized barium. Measurements were performed on single Doppler-cooled 138Ba+ ions in linear Paul traps using two similar, independent apparatuses. Transitions between Zeeman sublevels of the 6S1/2 and 5D5/2 states were driven with two independent, stabilized radio-frequency synthesizers using a dedicated electrode within each ion trap chamber. State detection within each Zeeman manifold was achieved with a frequency-stabilized fiber laser operating at 1.76 microns. By calculating the ratio of the two Zeeman splittings, and using the measured Landé g factor of the 6S1/2 state, we find a value of 1.200371(4stat)(6sys) for g of 5D5/2.
Laser spectroscopy studies are being prepared to measure the 1s ground state hyperfine splitting in trapped cold highly charged ions. The purpose of such experiments is to test quantum electrodynamics in the strong electric field regime. These experiments form part of the HITRAP project at GSI. A brief review of the planned experiments is presented.
We present a novel method for reducing the inhomogeneous frequency broadening in the hyperfine splitting of the ground state of optically trapped atoms. This reduction is achieved by the addition of a weak light field, spatially mode-matched with the trapping field and whose frequency is tuned in-between the two hyperfine levels. We experimentally demonstrate the new scheme with Rb 85 atoms, and report a 50-fold narrowing of the rf spectrum.
We develop a method for extracting the physical parameters of interest for a dipole trapped cold atomic ensemble. This technique uses the spatially dependent ac-Stark shift of the trap itself to project the atomic distribution onto a light-shift broadened transmission spectrum. We develop a model that connects the atomic distribution with the expected transmission spectrum. We then demonstrate the utility of the technique by deriving the temperature, trap depth, lifetime, and trapped atom number from data that was taken in a single shot experimental measurement.
We present the first terrestrial measurement of the Lande g factor of the 5D5/2 state of singly ionized barium. Measurements were performed on single Doppler-cooled 138Ba+ ions in a linear Paul trap. A frequency-stabilized fiber laser with nominal wavelength 1.762 um was scanned across the 6S1/2<->5D5/2 transition to spectroscopically resolve transitions between Zeeman sublevels of the ground and excited states. From the relative positions of the four narrow transitions observed at several different values for the applied magnetic field, we find a value of 1.2020+/-0.0005 for g of 5D5/2.
We study the feasibility of nearly-degenerate two-photon rovibrational spectroscopy in ensembles of trapped, sympathetically cooled hydrogen molecular ions using a resonance-enhanced multiphoton dissociation (REMPD) scheme. Taking advantage of quasi-coincidences in the rovibrational spectrum, the excitation lasers are tuned close to an intermediate level to resonantly enhance two-photon absorption. Realistic simulations of the REMPD signal are obtained using a four-level model that takes into account saturation effects, ion trajectories, laser frequency noise and redistribution of population b…
We present precision measurements of the hyperfine intervals in the 5D3/2 manifold of a single trapped Barium ion, 137 Ba+ . Measurements of the hyperfine intervals are made between mF = 0 sublevels over a range of magnetic fields allowing us to interpolate to the zero field values with an accuracy below a few Hz, an improvement on previous measurements by three orders of magnitude. Our results, in conjunction with theoretical calculations, provide a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants. In addition, we obtain the magne…
Direct frequency comb spectroscopy of trapped ions is demonstated for the first time. It is shown that the 4s^2S_(1/2)-4p^2P_(3/2) transition in calcium ions can be excited directly with a frequency comb laser that is upconverted to 393 nm. Detection of the transition is performed using a shelving scheme to suppress background signal from non-resonant comb modes. The measured transition frequency of f=761 905 012.7(0.5) MHz presents an improvement in accuracy of more than two orders of magnitude.
Polar molecules are desirable systems for quantum simulations and cold chemistry. Molecular ions are easily trapped, but a bias electric field applied to polarize them tends to accelerate them out of the trap. We present a general solution to this issue by rotating the bias field slowly enough for the molecular polarization axis to follow but rapidly enough for the ions to stay trapped. We demonstrate Ramsey spectroscopy between Stark-Zeeman sublevels in 180Hf19F+ with a coherence time of 100 ms. Frequency shifts arising from well-controlled topological (Berry) phases are used to determine mag…
We perform spectroscopy on the hyperfine splitting of $^{85}$Rb atoms trapped in far-off-resonance optical traps. The existence of a spatially dependent shift in the energy levels is shown to induce an inherent dephasing effect, which causes a broadening of the spectroscopic line and hence an inhomogeneous loss of atomic coherence at a much faster rate than the homogeneous one caused by spontaneous photon scattering. We present here a number of approaches for reducing this inhomogeneous broadening, based on trap geometry, additional laser fields, and novel microwave pulse sequences. We then sh…
We present precision spectroscopy on electrically trapped formaldehyde (H$_2$CO), demonstrating key attributes which will enable molecular spectroscopy with unprecedented precision. Our method makes use of a microstructured electric trap with homogeneous fields in the trap center and rotational transitions with minimal Stark broadening at a 'magic' offset electric field. Using molecules cooled to the low millikelvin temperature regime via optoelectrical Sisyphus cooling, we reduce Stark broadening on the $J=5\leftarrow4$ ($K=3$) transition at 364 GHz to well below 1 kHz, observe Doppler-limite…
We demonstrate a method for precision spectroscopy on trapped ions in the limit of unresolved motional sidebands. By sympathetic cooling of a chain of crystallized ions we suppress adverse temperature variations induced by the spectroscopy laser that usually lead to a distorted line profle and obtain a Voigt profile with negligible distortions. We applied the method to measure the absolute frequency of the astrophysically relevant D2 transition in single 24-Mg+ ions and find 1072082934.33(16)MHz, a nearly 400fold improvement over previous results. Further, we find the excited state lifetime to…
As an important step towards an atomic parity violation experiment in one single trapped Ra$^+$ ion, laser spectroscopy experiments were performed with on-line produced short-lived $^{212,213,214}$Ra$^+$ ions. The isotope shift of the $6\,^2$D$_{3/2}$\,-\,$7\,^2$P$_{1/2}$ and $6\,^2$D$_{3/2}$\,-\,$7\,^2$P$_{3/2}$ transitions and the hyperfine structure constant of the $7\,^2$S$_{1/2}$ and $6\,^2$D$_{3/2}$ states in $^{213}$Ra$^+$ were measured. These values provide a benchmark for the required atomic theory. A lower limit of $232(4)$ ms for the lifetime of the metastable $6\,^2$D$_{5/2}$ state…
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…
Sympathetic cooling of trapped ions has been established as a powerful technique for manipulation of non-laser-coolable ions (Raizen1992,Waki1992,Bowe1999,Barrett2003). For molecular ions, it promises vastly enhanced spectroscopic resolution and accuracy. However, this potential remains untapped so far, with the best resolution achieved being not better than $5\times10^{-8}$ fractionally, due to residual Doppler broadening being present in ion clusters even at the lowest achievable translational temperatures (Bressel2012). Here we introduce a general and accessible approach that enables Dopple…
We investigate the dephasing of ultra cold ^{85}Rb atoms trapped in an optical dipole trap and prepared in a coherent superposition of their two hyperfine ground states by interaction with a microwave pulse. We demonstrate that the dephasing, measured as the Ramsey fringe contrast, can be reversed by stimulating a coherence echo with a pi-pulse between the two pi/2 pulses, in analogy to the photon echo. We also demonstrate that the failure of the echo for certain trap parameters is due to dynamics in the trap, and thereby that ''echo spectroscopy'' can be used to study the quantum dynamics in …
We propose a new spectroscopic method for measuring weak transitions in cold and trapped atoms, which exploits the long interaction times and tight confinement offered by dark optical traps together with an electron shelving technique to achieve extremely high sensitivity. We demonstrate our scheme by measuring a 5S_{1/2}-> 5D_{5/2} two-photon transition in cold Rb atoms trapped in a new single-beam dark optical trap, using an extremely weak probe laser power of 25 micro-Watt. We were able to measure transitions with as small excitation rate as 0.09 sec^(-1).
We present an experimental scheme to perform spectroscopy of the $^2$S$_{1/2}-^2$P$_{1/2}$ and $^2$D$_{3/2}-^2$P$_{1/2}$ transitions in \Ca. By rapidly switching lasers between both transitions, we circumvent the complications of both dark resonances and Doppler heating. We apply this method to directly observe the micromotion modulated fluorescence spectra of both transitions and measure the dependence of the micromotion modulation index on the trap frequency. With a measurement time of 10 minutes, we can detect the center frequencies of both dipole transitions with a precision on the order o…
We demonstrate a general method for state detection of trapped ions that can be applied to a large class of atomic and molecular species. We couple a "spectroscopy" ion (Al+) to a "control" ion (Mg+) in the same trap and perform state detection through off-resonant laser excitation of the spectroscopy ion that induces coherent motion. The motional amplitude, dependent on the spectroscopy ion state, is measured either by time-resolved photon counting, or by resolved sideband excitations on the control ion. The first method provides a simplified way to distinguish "clock" states in Al+, which av…
Rapid progress in cooling and trapping of molecules has enabled first experiments on high resolution spectroscopy of trapped diatomic molecules, promising unprecedented precision. Extending this work to polyatomic molecules provides unique opportunities due to more complex geometries and additional internal degrees of freedom. Here, this is achieved by combining a homogeneous-field microstructured electric trap, rotational transitions with minimal Stark broadening at a 'magic' offset electric field, and optoelectrical Sisyphus cooling of molecules to the low millikelvin temperature regime. We …
A Bose-Einstein condensate (BEC) with periodically modulated interactions (PMI) has emerged as a novel kind of periodic superfluid, which has been recently experimentally created using optical Feshbach resonance. In this paper, we are motivated to investigate the superfluidity of a BEC with PMI trapped in an optical lattice (OL). In particular, we explore the effects of PMI on the sound speed and the dynamical structure factor of the model system. Our numerical results, combined with the analytical results in both the weak-potential limit and the tight-binding limit, have shown that the PMI ca…
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…
$^{133}\text{Ba}^+$ has been identified as an attractive ion for quantum information processing due to the unique combination of its spin-1/2 nucleus and visible wavelength electronic transitions. Using a microgram source of radioactive material, we trap and laser-cool the synthetic $A$ = 133 radioisotope of barium II in a radio-frequency ion trap. Using the same, single trapped atom, we measure the isotope shifts and hyperfine structure of the $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $6^2 \text{S}_{1/2}$ and $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $5^2 \text{D}_{3/2}$ electronic transitions that…
We demonstrate spectroscopy and thermometry of individual motional modes in a mesoscopic 2D ion array using entanglement-induced decoherence as a method of transduction. Our system is a $\sim$400 $μ$m-diameter planar crystal of several hundred $^9$Be$^+$ ions exhibiting complex drumhead modes in the confining potential of a Penning trap. Exploiting precise control over the $^9$Be$^+$ valence electron spins, we apply a homogeneous spin-dependent optical dipole force to excite arbitrary transverse modes with an effective wavelength approaching the interparticle spacing ($\sim$20 \nolinebreak$μ$m…
We present a quantum logic scheme to detect atomic and molecular ions in different states of angular momentum based on their magnetic $g$-factors. The state-dependent magnetic $g$-factors mean that electronic, rotational or hyperfine states may be distinguished by their Zeeman splittings in a given magnetic field. Driving motional sidebands of a chosen Zeeman splitting enables reading out the corresponding state of angular momentum with an auxillary logic ion. As a proof-of-principle demonstration, we show that we can detect the ground electronic state of a ${^{174}}$Yb$^+$ ion using ${^{171}}…
The text below was written during two visits that Daniel Segal made at Universit{é} Paris 13. Danny stayed at Laboratoire de Physique des Lasers the summers of 2008 and 2009 to participate in the exploration of a novel lead in the field of ultra-high resolution spectroscopy. Our idea was to probe trapped molecular ions using Quantum Logic Spectroscopy (QLS) in order to advance our understanding of a variety of fundamental processes in nature. At that time, QLS, a ground-breaking spectroscopic technique, had only been demonstrated with atomic ions. Our ultimategoals were new approaches to the o…
Both the 1S-2S transition and the ground state hyperfine spectrum have been observed in trapped antihydrogen. The former constitutes the first observation of resonant interaction of light with an anti-atom, and the latter is the first detailed measurement of a spectral feature in antihydrogen. Due to the narrow intrinsic linewidth of the 1S-2S transition and use of two-photon laser excitation, the transition energy can be precisely determined in both hydrogen and antihydrogen, allowing a direct comparison as a test of fundamental symmetry. The result is consistent with CPT invariance at a rela…
We use Rabi spectroscopy to explore the low-energy excitation spectrum of a finite-temperature Bose gas of rubidium atoms across the phase transition to a Bose-Einstein condensate (BEC). To record this spectrum, we coherently drive the atomic population between two spin states. A small relative displacement of the spin-specific trapping potentials enables sideband transitions between different motional states. The intrinsic non-linearity of the motional spectrum, mainly originating from two-body interactions, makes it possible to resolve and address individual excitation lines. Together with s…
Spectroscopy is an essential tool in understanding and manipulating quantum systems, such as atoms and molecules. The model describing spectroscopy includes a multipole-field interaction, which leads to established spectroscopic selection rules, and an interaction that is quadratic in the field, which is often neglected. However, spectroscopy using the quadratic (ponderomotive) interaction promises two significant advantages over spectroscopy using the multipole-field interaction: flexible transition rules and vastly improved spatial addressability of the quantum system. For the first time, we…
We discuss a recently demonstrated type of microwave spectroscopy of trapped ultra-cold atoms known as "echo spectroscopy" [M.F. Andersen et. al., Phys. Rev. Lett., in press (2002)]. Echo spectroscopy can serve as an extremely sensitive experimental tool for investigating quantum dynamics of trapped atoms even when a large number of states are thermally populated. We show numerical results for the stability of eigenstates of an atom-optics billiard of the Bunimovich type, and discuss its behavior under different types of perturbations. Finally, we propose to use special geometrical constructio…
A mixed-species geometric phase gate has been proposed for implementing quantum logic spectroscopy on trapped ions that combines probe and information transfer from the spectroscopy to the logic ion in a single pulse. We experimentally realize this method, show how it can be applied as a technique for identifying transitions in currently intractable atoms or molecules, demonstrate its reduced temperature sensitivity, and observe quantum-enhanced frequency sensitivity when it is applied to multi-ion chains. Potential applications include improved readout of trapped-ion clocks and simplified err…
Regarding trapped-ion microwave-frequency standards, we report on the determination of hyperfine splittings and Landé $g_J$ factors of $^{111,113}$Cd$^+$. The hyperfine splittings of the $5p~^2P_{3/2}$ state of $^{111,113}$Cd$^+$ ions were measured using laser-induced fluorescence spectroscopy. The Cd$^+$ ions were confined in a linear Paul trap and sympathetically cooled by Ca$^+$ ions. Furthermore, the hyperfine splittings and Landé $g_J$ factors of the $5s~^2S_{1/2}$ and $5p~^2P_{1/2,3/2}$ levels of $^{111,113}$Cd$^+$ were calculated with greater accuracy using the multiconfiguration Dirac-…
We study the spectroscopy of atoms dressed by a resonant radiofrequency (RF) field inside an inhomogeneous magnetic field and confined in the resulting adiabatic potential. The spectroscopic probe is a second, weak, RF field. The observed line shape is related to the temperature of the trapped cloud. We demonstrate evaporative cooling of the RF-dressed atoms by sweeping the frequency of the second RF field around the Rabi frequency of the dressing field.
We investigate the crossover of the impurity-induced dynamics, in trapped one-dimensional Bose polarons subject to radio frequency (rf) pulses of varying intensity, from an adiabatic to a diabatic regime. Utilizing adiabatic pulses for either weak repulsive or attractive impurity-medium interactions, a multitude of polaronic excitations or mode-couplings of the impurity-bath interaction with the collective breathing motion of the bosonic medium are spectrally resolved. We find that for strongly repulsive impurity-bath interactions, a temporal orthogonality catastrophe manifests in resonances i…
Efficient preparation and detection of the motional state of trapped ions is important in many experiments ranging from quantum computation to precision spectroscopy. We investigate the stimulated Raman adiabatic passage (STIRAP) technique for the manipulation of motional states in a trapped ion system. The presented technique uses a Raman coupling between two hyperfine ground states in $^{25}$Mg$^+$, implemented with delayed pulses, which removes a single phonon independent of the initial motional state. We show that for a thermal state the STIRAP population transfer is more efficient than a …
A method is described for estimating effective scattering lengths via spectroscopy on a trapped pair of atoms. The method relies on the phenomena that the energy levels of two atoms in a harmonic trap are shifted by their collisional interaction. The amount of shift depends on the strength of the interaction (i.e. scattering length). By combining the spectra of the trap state energy levels and a suitable model for the effective scattering length, an estimate for the latter may be inferred. Two practical methods for measuring the trap spectra are proposed and illustrated in examples. The accura…
Laser spectroscopy of cold and trapped molecular ions is a powerful tool for fundamental physics, including the determination of fundamental constants, the laboratory test for their possible variation, and the search for a possible electric dipole moment of the electron. Optical clocks based on molecular ions sensitive to some of these effects are expected to achieve uncertainties approaching the $10^{-18}$ level. While the complexity of molecular structure facilitates these applications, the absence of cycling transitions poses a challenge for direct laser cooling, quantum state control, and …
Trapped ions are ideally suited for precision spectroscopy, as is evident from the remarkably low systematic uncertainties of single-ion clocks. The major weakness of these clocks is the long averaging time, necessitated by the low signal of a single atom. An increased number of ions can overcome this limitation and allow for the implementation of novel clock schemes. However, this presents the challenge to maintain the excellent control over systematic shifts of a single particle in spatially extended and strongly coupled many-body systems. We measure and deduce systematic frequency uncertain…
Precision optical spectroscopy of exotic ions reveals accurate information about nuclear properties such as charge radii and magnetic and quadrupole moments. Thorium ions exhibit unique nuclear properties with high relevance for testing symmetries of nature. We report loading and trapping of single $^{232}$Th$^+$ ions in a linear Paul trap, embedded into and sympathetically cooled by small crystals of trapped $^{40}$Ca$^+$ ions. Trapped Th ions are identified in a non-destructive manner from the voids in the laser-induced Ca fluorescence pattern emitted by the crystal, and alternatively, by me…
We perform Ramsey spectroscopy on the ground state of ultra-cold 87Rb atoms magnetically trapped on a chip in the Knudsen regime. Field inhomogeneities over the sample should limit the 1/e contrast decay time to about 3 s, while decay times of 58 s are actually observed. We explain this surprising result by a spin self-rephasing mechanism induced by the identical spin rotation effect originating from particle indistinguishability. We propose a theory of this synchronization mechanism and obtain good agreement with the experimental observations. The effect is general and susceptible to appear i…
A complete set of spectroscopic data is indispensable when using Rydberg states of trapped ions for quantum information processing. We carried out Rydberg series spectroscopy for $nS_{1/2}$ states with $38 \leq n \leq 65$ and for $nD_{5/2}$ states with $37\leq n \leq 50$ on a single trapped $^{40}$Ca$^+$ ion. From a nonlinear regression to resonance frequencies, we determined the ionization energy of 2 870 575.582(15) GHz, measured 60 times more accurately as compared to the accepted value and contradicting it by 7.5 standard deviations. We confirm quantum defect values of $δ_{S_{1/2}}=1.80299…
Ion traps are a versatile tool to study nonequilibrium statistical physics, due to the tunability of dissipation and nonlinearity. We propose an experiment with a chain of trapped ions, where dissipation is provided by laser heating and cooling, while nonlinearity is provided by trap anharmonicity and beam shaping. The collective dynamics are governed by an equation similar to the complex Ginzburg-Landau equation, except that the reactive nature of the coupling leads to qualitatively different behavior. The system has the unusual feature of being both oscillatory and excitable at the same time…
