Laser cooling of Cd<Superscript>+</Superscript> ions using a microwave transition as a repumping process

Cadmium ions trapped in a linear Paul trap have been laser cooled by use of a microwave transition as a repumping process. A 15.2-GHz microwave transition between a ground-state hyperfine splitting is used for repumping, while an all-solid-state laser with the wavelength of 214 nm drives the cooling transition between the ² S _1/2 and ² P _3/2 states. A phase transition from the cloud state to the crystal state of trapped ions has been observed both in fluorescence spectra and in images of an ion string. Cadmium ions have potential of application for quantum information processing where the ground-state microwave transition is used for both a repumping process and manipulation of quantum states of trapped ions. PACS 32.80.Pj     

Efficient Scheme for Greenberger-Horne-Zeilinger State and Cluster State with Trapped Ions

We propose a scheme to generate the Greenberger-Horne-Zeilinger （GHZ） states and the cluster states of many trapped ions. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. The scheme only requires resonant interactions. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed, which is important in view of decoherence.     

Laser cooling of molecules

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 some future applications.     

Collisional effects on the collective laser cooling . of trapped bosonic gases

We analyse the effects of atom–atom collisions on a collective laser cooling scheme. We derive a quantum master equation which describes the laser cooling in presence of atom–atom collisions in the weak-condensation regime. Using such equation, we perform Monte Carlo simulations of the population dynamics in one and three dimensions. We observe that the ground-state laser-induced condensation is maintained in the presence of collisions. Laser cooling causes a transition from a Bose–Einstein distribution describing collisionally induced equilibrium, to a distribution with an effective zero temperature. We analyse also the effects of atom–atom collisions on the cooling into an excited state of the trap. Received: 18 June 1999 / Revised version: 24 September 1999 / Published online: 10 November 1999     

Trapping State in a System of Single Three-level Trapped Ion Driven by External Fields

We investigate the interaction of a single three-level trapped ion with two laser beams. By applying a unitary transformation and a small rotating transformation, an exact solution to this quantum system is obtained without performing the Lamb-Dicke approximation, and the trapping state is observed.     

Photoionization cross-sections of the first excited states of sodium and lithium in a magneto-optical trap

A two element magneto-optical trap (MOT) for Na and ⁷Li or ⁶Li is used to cool and trap each of them separately. A fraction of the cold atoms is maintained in the first ²P_3/2 excited state by the cooling laser. These excited state atoms are ionized by laser light in the near-UV region, giving rise to a smaller number of trapped atoms and to different loading parameters. Photoionization cross-sections were derived out of these data. They are in reasonable agreement with data previously obtained using thermal samples and with theoretical predictions. Received 21 March 2001 and Received in final form 3 August 2001     

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     

Quantum control of 88Sr+ in a miniature linear Paul trap

We report on the construction and characterization of an apparatus for quantum information experiments using ⁸⁸Sr⁺ ions. A miniature linear radio-frequency (rf) Paul trap was designed and built. Trap frequencies above 1 MHz in all directions are obtained with 50 V on the trap end-caps and less than 1 W of rf power. We encode a quantum bit (qubit) in the two spin states of the S _1/2 electronic ground-state of the ion. We constructed all the necessary laser sources for laser cooling and full coherent manipulation of the ions’ external and internal states. Oscillating magnetic fields are used for coherent spin rotations. High-fidelity readout as well as a coherence time of 2.5 ms are demonstrated. Following resolved sideband cooling the average axial vibrational quanta of a single trapped ion is $\bar{n}=0.05$ and a heating rate of $\dot{\bar{n}}=0.016~\mathrm{ms}^{-1}$ is measured.     

Laser cooling force in noisy quadrature of squeezed light

The laser cooling of atoms is a result of the combined effect of Doppler shift, light shift and polarization gradient. These are the phenomena which generally introduce frequency shift and uncertainty. However, they combine gainfully in realizing laser cooling and trapping of the atoms. In this paper we discuss the laser cooling of atoms in the presence of the squeezed light with the decay of atomic dipole moment into noisy quadrature. We show that the higher decay rate of the atomic dipole moment into the noisy quadrature, which leads to decrease in the signal to noise ratio, may contribute in realizing larger cooling force vis-à-vis with coherent laser light.     

A single laser system for ground-state cooling of <Superscript>25</Superscript>Mg<Superscript>+</Superscript>

We present a single solid-state laser system to cool, coherently manipulate and detect ²⁵Mg⁺ ions. Coherent manipulation is accomplished by coupling two hyperfine ground state levels using a pair of far-detuned Raman laser beams. Resonant light for Doppler cooling and detection is derived from the same laser source by means of an electro-optic modulator, generating a sideband which is resonant with the atomic transition. We demonstrate ground-state cooling of one of the vibrational modes of the ion in the trap using resolved-sideband cooling. The cooling performance is studied and discussed by observing the temporal evolution of Raman-stimulated sideband transitions. The setup is a major simplification over existing state-of-the-art systems, typically involving up to three separate laser sources.     

Photoassociation of heteronuclear lithium

Photoassociation of ultracold heteronuclear ⁶Li⁷Li molecules is observed inside a combined magneto-optical trap for ⁶Li and ⁷Li. The trapped atomic cloud is illuminated by a tunable single-mode laser and the number of trapped ⁷Li atoms is monitored by absorption spectroscopy. Characteristic hyperfine resolved spectra have been recorded for singlet spin orientation. Interesting saturation effects have been observed. Received: 12 July 2001 / Revised version: 1 October 2001 / Published online: 23 November 2001     

Buffer-gas loaded magnetic traps for atoms and molecules: A primer

Over the past three years we have developed the technique of buffer-gas cooling and loading of atoms and molecules into magnetic traps. Buffer-gas cooling relies solely on elastic collisions (thermalization) of the species-to-be-trapped with a cryogenically cooled helium gas and so is independent of any particular energy level pattern. This makes the cooling technique general and potentially applicable to any species trappable at the temperature of the buffer gas (as low as 240 mK). Using buffer-gas loading, paramagnetic atoms (europium and chromium) as well as a molecule (calcium monohydride) were trapped at temperatures around 300 mK. The numbers of the trapped atoms and molecules were respectively about 10¹² and 10⁸. The atoms and molecules were produced by laser ablation of suitable solid precursors. In conjunction with evaporative cooling, buffer-gas loaded magnetic traps offer the means to further lower the temperature and increase the density of the trapped ensemble to study a large variety of both static (spectra) and dynamic (collisional cross-sections) properties of many atoms and molecules at ultra-low temperatures. In this article we survey our main results obtained on Cr, Eu, and CaH and outline prospects for future work. Received 2 November 1998 and Received in final form 19 February 1999     

Entanglement of three-level trapped ions with phonon trap modes

The entanglement between a single electron in the electronic states of a trapped three-level ion and the ionic vibrational modes of the trap is studied for an initially unentangled state of an electron level and a coherent phonon state. The effects of time-independent and time-dependent couplings are discussed.     

Lifetime of metastable fluorine atoms

For laser collimation of neutral F atoms, a resonance transition cycle between the metastable and the upper excited states (3s⁴ P _5/2?3p⁴ D ⁰ _7/2) can be used as a two-level closed system. We have determined the lifetime of the metastable state (3s⁴ P _5/2) in F atoms by measuring the decay curve of the fluorescence intensity as a function of distance from the plasma source. Combining the measured velocity of F radicals from the Doppler shift of the fluorescence peak, we have obtained the lifetime of the F metastable state as 3.7±0.5 μs. With this short metastable lifetime of F radicals, the simple Doppler cooling method using spontaneous light force is not practical for laser collimation of F radicals. Use of stimulated light force may be necessary to collimate F radical beams in a short distance. Received: 4 July 2000 / Published online: 13 September 2000     

Generation of a four-atom entangled cluster state in cavity QED

We propose a method of generating a four-atom entangled cluster state by considering two kinds of the atoms–cavity field interaction in cavity QED. During the preparation the cavity is only virtually excited no quantum information will be transferred from the atoms to the cavity and thus the scheme is insensitive to the cavity field states and cavity decay. The scheme can also be used to generate the cluster state for the trapped ions.     

Teleporting an Unknown Two-qubit Entangled State via Ion-Trap Systems

We propose a scheme for teleportation of an unknown two-qubit entangled state via trapped ions. In this scheme, we use the GHZ state as a quantum channel and the success probability can reach 1. The distinct advantage of our scheme is insensitive to the heating of the vibrational mode. In addition, Bell-state measurement is not required.     

A continuous cold atomic beam from a magneto-optical trap

We have developed and characterized a new method to produce a continuous beam of cold atoms from a standard vapour-cell magneto-optical trap (MOT). The experimental apparatus is very simple. Using a single laser beam it is possible to hollow out in the source MOT a direction of unbalanced radiation pressure along which cold atoms can be accelerated out of the trap. The transverse cooling process that takes place during the extraction reduces the beam divergence. The atomic beam is used to load a magneto-optical trap operating in an ultra-high vacuum environment. At a vapour pressure of 10^-8mbar in the loading cell, we have produced a continuous flux of 7×10⁷atoms/s at the recapture cell with a mean velocity of 14 m/s. A comparison of this method with a pulsed transfer scheme is presented. Received 19 February 2001     

Pulsed polarization gradient cooling in an optical dipole trap with a Laguerre-Gaussian laser beam

We utilized a blue-detuned Laguerre-Gaussian (doughnut) laser beam to trap cold rubidium atoms by optical dipole force. ”Pulsed” polarization gradient cooling was applied to the trapped atoms to suppress the trap loss due to heating caused by random photon scattering of the trapping light. In this trap about 10⁸ atoms were initially captured and the trap lifetime was 1.5 s, which was consistent with losses due to background gas collisions. This trap can readily be applied to atom guiding, compression, and evaporative cooling. Received: 10 July 1997 / Received in final form: 5 January 1998 / Accepted: 16 January 1998     

Five-beam magneto-optical trap and optical molasses

We have operated a magneto-optical trap and optical molasses for the laser cooling of cesium atoms on the basis of a five-beam laser configuration. For the magneto-optical trap two laser beams counterpropagate along the axis of a quadrupole trap and the remaining three beams propagate in the orthogonal plane at 120° to each other. The same optical configuration was used for the optical molasses. We have tested the efficiency in atom collection and the temperatures reached in both cooling processes. In comparison to previous results on a six-beam configuration, a lower number of atoms is collected, while comparable densities are realized. The atomic temperatures have been measured through a delayed shadow-image technique, where one of the running-wave cooling beams produces an absorptive image of the atoms on a camera. Received: 14 January 1999 / revised version: 23 June 1999 / Published online: 8 September 1999     

2D dark optical surface lattice with an efficient intensity-gradient cooling of atoms by evanescent wave interference

We propose a novel scheme to form a 2D dark optical surface lattice (DOSL) for cold atoms on the surface of the dense flint glass by using two sets of blue-detuned evanescent wave interference fields and a blue-detuned evanescent wave field. In the 2D DOSL, cold atoms will be trapped in the vicinity of minimum intensity and suffered the minimal light shift as well as the lowest coherence loss. The total potential and trap-depth of the individual optical micro-trap in the 2D DOSL are high enough to trap cold atoms (T = 120 μK) released from the standard magneto-optical trap (MOT), and atoms trapped in the 2D DOSL can be cooled to several μK with the efficient intensity-gradient Sisyphus cooling. The lattice constant of the DOSL can be controllable by changing the incident angles of lights.