Preliminary frequency measurement of the electric quadrupole transition in a single laser-cooled 40Ca+ ion

The trapping and laser cooling of ⁴⁰Ca⁺ ion on the way toward optical frequency standards have been developed. A single ⁴⁰Ca⁺ ion is trapped in the miniature Paul trap and laser cooled by two frequency-stabilized diode lasers. A commercial Ti:Sapphire laser system at 729 nm is referenced to a high-finesse cavity to meet the requirements of ultra narrow linewidth of the 4s²S_1/2-3d²D_5/2 electric quadrupole transition. Its center frequency is preliminarily measured to be 411 042 129 686.1 (2.6) kHz. The attempt to finally lock the 729-nm laser system to atomic transition is made. Further work to improve the accuracy of measurement and the stabilization of system locking is in consideration and preparation.      

A 729 nm laser with ultra-narrow linewidth for probing 4S1/2-3D5/2 clock transition of Ca

A Coherent Inc. Ti:sapphire laser MBR-110 is locked to a temperature-controlled high finesse Fabry-Perot cavity supported on an isolated platform. The linewidth is measured by locking the laser to another similar super-cavity at the same time and the heterodyne beatnote between two laser beams that locked to different cavities determines the linewidth. The result shows that the laser's linewidth is suppressed to be 41 Hz. The long-term drift is measured with a femtosecond comb and determined to be ~ 0.1 Hz/s. This laser is used to probe the 4S_1/2-3D_5/2 clock transition of a single ⁴⁰Ca⁺ ion. The Zeeman components of the clock transition with a linewidth of 160 Hz have been observed.     

Isotope-selective trapping of rare calcium ions using high-power incoherent light sources for the second step of photo-ionization

Rare calcium isotope ⁴⁸Ca⁺ (0.187%) has been selectively loaded in a linear Paul trap using two ultraviolet light emitting diodes with the output power of 85 mW for the second excitation in a two-step photo-ionization process. Isotope selectivity has been achieved by utilizing the isotope shifts for the 4s^{2 1} S ₀–4s4p¹ P ₁ transition of neutral calcium atom. Sympathetic cooling of ⁴⁸Ca⁺ ions has been demonstrated using ⁴⁰Ca⁺ ions as refrigerant ions. Purification of rare isotope ⁴²Ca⁺ ions (0.647%) from a mixture of ⁴⁰Ca⁺ (96.9%) and ⁴²Ca⁺ ions has been performed by adjusting the detuning of the cooling laser frequency, which overcomes the imperfect selectivity for some rare isotopes having close resonance frequencies to that of ⁴⁰Ca in the 4s^{2 1} S ₀–4s4p¹ P ₁ transition. The methods can be applied to ⁴³Ca⁺ ion (0.135%) that has been considered as one of the attractive candidates for quantum information processing as well as for an optical frequency standard. PACS 32.80.Fb; 32.80.Pj; 32.80.Rm     

Rb atomic absorption line reference for single Sr+ laser cooling systems

85 Rb, 5s²S_1/2(F”=2)→6p²P_1/2(F’=2,3) absorption resonance with the ⁸⁸Sr⁺, 5s²S_1/2→5p²P_1/2 transition is exploited to provide a simple, effective frequency reference for a laser cooling/fluorescence excitation source applied to single Sr⁺ ions. A modulation-free frequency stabilization system has been designed which uses the differential signal from two frequency-displaced beams traversing a Rb cell and which probe the Doppler-broadened Rb S–P lineshape at microwatt power levels. The method is applied to frequency lock a 422-nm frequency-doubled diode laser system that is used for excitation of a single ⁸⁸Sr⁺ ion. Stable, long-term laser cooling and fluorescence are achieved using the frequency-stabilized 422-nm source resulting in observed ion confinement times without adjustment of over 8 h, together with an improvement in single-ion loading efficiency. Received: 12 February 1998     

Laser cooling of a single Ca+ ion: Observation of quantum jumps

This paper describes trapping and laser cooling of a Ca⁺ ion in an rf quadrupole ion trap. A single Ca⁺ ion is laser cooled to below 130 mK and quantum jumps are observed by exciting the ion into the metastable D _5/2 state via the P _3/2 state. The lifetime of the metastable D _5/2 state is estimated from the distribution of the dark periods of the quantum-jump signal. Collision-induced jumps between the metastable D _3/2 state and the D _5/2 state in a background gas are also directly observed.     

Measurement of the coherence time of the ground-state Zeeman states in <Superscript>40</Superscript>Ca<Superscript>+</Superscript>

The transition between the two Zeeman sublevels of ²S_1/2 in a single trapped ⁴⁰Ca⁺ ion is directly excited by a radio-frequency magnetic field. A coherence time of 29.4±2.5 ms is measured by Ramsey interferometry. The ratio of the maximum Rabi frequency of the Zeeman transition (∼250 kHz) to the inverse of the coherence time is 7.3×10³, which is considered to be a figure of merit for Zeeman states when they are used as a quantum bit. Several applications of the Zeeman qubit to quantum information processing are also discussed.     

Hyperpolarizabilities of alkaline-earth metal ions Be+, Mg+, and Ca+

The knowledge of the hyperpolarizabilities of atoms and ions is helpful for the analysis of the high order effects of the frequency shifts in precision spectroscopy experiments. Liu et al. [Phys. Rev. Lett. 114, 223001(2015)] proposed to establish all-optical trapped ion clocks using laser at the magic wavelength for clock transition. To evaluate the high-order frequency shifts in this new scheme of optical clocks, hyperpolarizabilities are needed, but absent. Using the finite field method based on the B-spline basis set and model potentials, we calculated the electric-field-dependent energy shifts of the ground and low-lying excited states in Be+, Mg+, and Ca+ in the field strength range of 0.0-6×10.5 a.u.. The scalar and tensor polarizabilities(α0, α2) and hyperpolarizabilities(γ0, γ2, γ4) were deduced. The results of the hyperpolarizabilities for Be+ showed good agreement with the values in literature, implying that the present method can be applied for the effective estimation of the atomic hyperpolarizabilities,which are rarely reported but needed in experiments. The feasibility of optical trapping of Ca+ is discussed, and the contributions of hyperpolarizabilities to the transition frequency shift for Ca+ in the optical dipole trap are estimated using quasi-electrostatic approximation.     

All-diode-laser cooling of single Ca+ ions

+ ions. The Ca⁺ ions are trapped in a miniature rf Paul trap and irradiated by light from a frequency-doubled diode laser at 397 nm and by light from a diode laser at 866 nm. We are able to cool a single ion and observe its fluorescence continuously with the laser diode locked to the external frequency-doubling cavity. Quantum jumps in the fluorescence light of a single ion and of a small cloud of five ions have been induced by driving the “clock” transition at 729 nm. We were able to resolve the influence of the micromotion on the excitation spectrum of the small ion cloud. Received: 10 July 1997/Revised version: 17 November 1997     

Coherent coupling of a single <Superscript>40</Superscript>Ca<Superscript>+</Superscript> ion to a high-finesse optical cavity

We demonstrate coherent coupling of the quadrupole S_1/2D_5/2 optical transition of a single trapped ⁴⁰Ca⁺ ion to the standing wave field of a high-finesse cavity. The dependence of the coupling on temporal dynamics and spatial variations of the intracavity field is investigated in detail. By precisely controlling the position of the ion in the cavity standing wave field and by selectively exciting vibrational state-changing transitions the ion’s quantized vibration in the trap is deterministically coupled to the cavity mode. We confirm coherent interaction of ion and cavity field by exciting Rabi oscillations with short resonant laser pulses injected into the cavity, which is frequency-stabilized to the atomic transition. Received: 23 August 2002 / Published online: 8 January 2003 RID="*" ID="*"Corresponding author. E-mail: christoph.becher@uibk.ac.at RID="**" ID="**"Present address: Time and Frequency Division, National Institute of Standards and Technology, Boulder, CO 80305, USA     

Selective loading and laser cooling of rare calcium isotope 43Ca+

We report a method for loading ⁴³Ca⁺ ions selectively in a linear Paul trap using ultraviolet light-emitting-diodes (LEDs) for the second excitation in a two-step photo-ionization process. The difficulty in working with ⁴³Ca⁺ is its low natural abundance (0.135%). In order to load ⁴³Ca⁺ selectively, we utilize the isotope shifts for the 4s^{2 1} S ₀–4s4p¹ P ₁ transition of neutral calcium atoms. We discuss the limitation of the selectivity of the employed photo-ionization scheme and observe spectra from unwanted isotopes as well as that from ⁴³Ca⁺. Purification of ⁴³Ca⁺ is performed by adjusting the detuning of the cooling laser frequency and trapping potential. The method of loading and purification can be used in the application of trapped ⁴³Ca⁺ for an optical frequency standard and for quantum information processing. PACS 32.80.Fb; 32.80.Pj     

Observation of motional sidebands in single 40Ca+ ions with improved detection efficiency

A method for effectively removing background photons and improving the signal-to-background ratio in detection of fluorescence from a single cooled ion is described. In the method, an additional spatial filter placed at an off-focal position is used to remove scattered photons from trap-electrode surfaces. A signal-to-background ratio of more than 200 is obtained. By using this setup, a resolved carrier and motional sidebands on the 4²S_1/2–3²D_5/2 electric quadrupole transition in ⁴⁰ Ca⁺ are observed.     

CW one-micron (4F3/2-4I11/2) laser oscillation of Nd3+ ions in the melilite-type crystal Ca2MgSi2O7:Nd3+(Na+) at its incommensurate–commensurate phase transition

The spectroscopic and stimulated-emission (⁴F_3/2→⁴I_11/2) properties of the novel melilite-type laser crystal Ca₂MgSi₂O₇:Nd³⁺(Na⁺) were studied in a temperature range that covers its incommensurate–commensurate (IC↔N) phase transition. The phase transition temperatures of both undoped Ca₂MgSi₂O₇ and the doped crystal were ascertained at 346.6 K (undoped) and 341.3 K (doped) by means of differential scanning calorimetry (DSC). The temperature-dependent spectroscopic and laser experiments showed a significant decrease in CW output power and a strong distortion of the generated lasing beam in the region of the phase transition. The observed crystal field disorder of Nd³⁺ lasants in Ca₂MgSi₂O₇:Nd³⁺(Na⁺) is dominantly due to occupation of the position of Ca²⁺ by cations of different valency, while the influence of incommensurability is of minor importance.     

Wave-particle duality of solitons and solitonic analog of the Ramsauer-Townsend effect

We study the interaction of light beams carrying angular momentum with a single, trapped and well localized ion. We provide a detailed calculation of selection rules and excitation probabilities for quadrupole transitions. The results show the dependencies on the angular momentum and polarization of the laser beam as well as the direction of the quantization magnetic field. In order to optimally observe the specific effects, focusing the angular momentum beam close to the diffraction limit is required. We discuss a protocol for examining experimentally the effects on the S_1/2 to D_5/2 transition using a ⁴⁰Ca⁺ ion. Various applications and advantages are expected when using light carrying angular momentum: in quantum information processing, where qubit states of ion crystals are controlled, parasitic light shifts could be avoided as the ion is excited in the dark zone of the beam at zero electric field amplitude. Such interactions also open the door to high dimensional entanglement between light and matter. In spectroscopy one might access transitions which have escaped excitation so far due to vanishing transition dipole moments.     

Ra+ ion trapping: toward an atomic parity violation measurement and an optical clock

A single Ra⁺ ion stored in a Paul radio frequency ion trap has excellent potential for a precision measurement of the electroweak mixing angle at low momentum transfer and as the most stable optical clock. The effective transport and cooling of singly charged ions of the isotopes ²⁰⁹Ra to ²¹⁴Ra in a gas filled radio frequency quadrupole device is reported. The absolute frequencies of the transition 7s²S_1/2–7d²D_3/2 at wavelength 828 nm have been determined in ^212–214Ra⁺ with ≤19 MHz uncertainty using laser spectroscopy on small samples of ions trapped in a linear Paul trap at the online facility Trapped Radioactive Isotopes: µicrolaboratories for fundamental Physics (TRIµP) of the Kernfysisch Versneller Instituut.     

Synthesis of two-species ion chains for a new optical frequency standard with an indium ion

Ion chains consisting of different species play an important role in new applications in quantum information processing as well as in optical frequency standards. We demonstrate generation and stabilization of ion chains consisting of Ca⁺ and In⁺. The Ca⁺ chains with In⁺ located at specified positions are synthesized using resonant photo-ionization, real-time imaging and trap field control techniques. A specific configuration of an ion chain is stabilized by destabilizing other configurations via selective excitation of vibrational modes using amplitude modulation on the cooling laser beam. New approaches to an indium ion optical clock are proposed using the ions chains.     

Toward an ion–photon quantum interface in an optical cavity

We demonstrate several building blocks for an ion–photon interface based on a trapped ⁴⁰Ca⁺ ion in an optical cavity. We identify a favorable experimental configuration and measure system parameters, including relative motion of the trapped ion and the resonator mode. A complete spectrum of cavity-assisted Raman transitions between the 4²S_1/2 and 3²D_5/2 manifolds is obtained. On two of these transitions, we generate orthogonally polarized cavity photons, and we demonstrate coherent manipulation of the corresponding pair of atomic states. Possible implementations of atom-photon entanglement and state mapping within the ion-cavity system are discussed.     

Precision spectroscopy with two correlated atoms

We discuss techniques that allow for long coherence times in laser spectroscopy experiments with two trapped ions. We show that for this purpose not only entangled ions prepared in decoherence-free subspaces can be used but also a pair of ions that are not entangled but subject to the same kind of phase noise. We apply this technique to a measurement of the electric quadrupole moment of the 3d²D_5/2 state of ⁴⁰Ca⁺ and to a measurement of the line width of an ultra-stable laser exciting a pair of ⁴⁰Ca⁺ ions. PACS 03.67.-a; 06.30.Ft; 37.10.Ty     

In situ 1H NMR Study of Nanoreactor Interaction NH3–H2O in Zeolite Nanopores

The interaction between ammonium NH₃ and H₂O molecules in zeolitic nanopores is studied by in situ ¹H nuclear magnetic resonance (NMR) method. The powder and single crystal samples of natural zeolites, heulandites Ca₄[Al₈Si₂₈O₇₂]·24H₂O and clinoptilolite (Na, K,Ca_1/2)₆[Al₆Si₃₀O₇₂], were used as the model system. It is shown that penetration of NH₃ into the zeolitic nanopores is accompanied by disordering of the hydrogen sublattice of zeolitic water and by the fast proton exchange NH₃ + H₂O ? [NH₄]⁺ + [OH]^? characterized by correlation frequency v _c = ~40 kHz. Another nanoreactor interactions are represented by interaction of [NH₄]⁺ ions with exchangeable Na⁺ and Ca²⁺ ions of the zeolitic structure. The slow ionic exchange [NH₄]⁺ → [Na,Ca_1/2]⁺ and binding of [NH₄]⁺ in cationic sites of the framework were visualized by NMR spectroscopy along with stepwise release of (Na,Ca_1/2)OH from zeolitic pores to the external surface of zeolite grains.     

Improved three-dimensional control of a single strontium ion in an endcap trap

An endcap ion trap is described for trapping and laser cooling of a single strontium-88 ion. The 422 nm cooling laser is offset locked to the Doppler-free 5s ²S_1/2(F^′′=2)–6p ²P_1/2(F^′=3) transition in ⁸⁵Rb using saturation spectroscopy. The peak fluorescence signal from a single ion is around 6.0×10⁴ counts/s with the cooling laser at saturation intensity. Optical pumping of the ion in zero magnetic field is eliminated by the use of two 1092 nm repumper laser beams incident on the ion to create a time-varying polarisation. The ion’s micromotion can be reduced in all three dimensions, and the motional sidebands on the weak 5s ²S_1/2–4d ²D_5/2 quadrupole transition in ⁸⁸Sr⁺ have been observed. These results show the ion to be confined to less than a wavelength in three dimensions.