The ion trap quantum information processor

Received: 16 October 1996/Revised version: 2 April 1997     

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     

Potential usage of the magnetron-motion-free mode of one ion confined in a combined trap

Received: 5 February 1998/Revised version: 18 March 1998     

Laser-induced hybrid trap for micro-bubbles

Micro-bubbles have been stably trapped in liquid ethanol by a focused argon laser beam. Two equilibrium points where bubbles can be trapped are observed to be at the center and the rim of the laser beam. The light force is also able to push a bubble into the liquid to a position well below the liquid surface. Both the light-pressure force and the fluid force induced by the convection of the liquid medium are calculated. The results clearly show that these two kinds of forces account for the formation of trapping potential. Received: 3 February 2000 / Revised version: 6 July 2000 / Published online: 8 November 2000     

Sympathetic cooling rate of gas-phase ions in a radio-frequency-quadrupole ion trap

We theoretically investigated the mass dependence of the sympathetic cooling rate of gas-phase ions trapped in a linear radio-frequency-quadrupole ion trap. Using an a priori molecular dynamical calculation, tracing numerically with Newtonian equations of motion, we found that ions with a mass greater than 0.54±0.04 times that of the laser-cooled ions are sympathetically cooled; otherwise, they are heated. To understand the mass dependence obtained using the molecular-dynamical calculation, we made a heat-exchange model of sympathetic cooling, which shows that the factor of 0.54±0.04 is a consequence of absence of micro-motion along the axis of the linear ion trap. Received: 10 December 2001 / Revised version: 28 January 2002 / Published online: 14 March 2002     

High-resolution atomic channeling using. velocity-selected atomic beam

High-resolution atomic channeling using velocity-controlled atoms may be able to overcome precision limitations of the conventional atom lithography. We have experimentally clarified the dependence of line width and contrast of atomic patterns in the channeling region on the velocity spread of the atomic source for the first time. Thermal or velocity-selected atomic beams prepared with a one-dimensional magneto-optical trap were employed as the atomic sources. We investigated the channeling characteristics by measuring the frequency shifts of the atomic absorption spectra in an intense standing wave light field. As a result, we can show that narrower line width and higher contrast atomic patterns are obtained as the velocity spread becomes narrower. An atomic pattern with an estimated line width of 57 nm was generated when the velocity spread of the atomic source was almost 50 m/s, that is, 1/6 that of the thermal beam. Received: 16 June 2001 / Published online: 7 November 2001     

Deterministic coupling of single ions to an optical cavity

By combining the technologies of ion trapping and cavity QED, we have achieved deterministic coupling of single ions to an optical field. By Doppler cooling, the spread of the ion’s wavepacket was reduced to 42 nm, corresponding to Lamb–Dicke localization. As an application, we have measured the three-dimensional structure of cavity eigenmodes with sub-wavelength precision. The setup presented is suited for the controlled coherent processing of atomic and photonic quantum information. Examples include the triggered generation of single photons and two-ion quantum gates. Received: 20 August 2002 / Revised version: 16 December 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-89/32905-200, E-mail: keller@mpq.mpg.de     

Observation of Doppler sidebands of a laser-cooled Ca+ ion by using a low-temperature-operated laser diode

1/2 -D_5/2 electric-quadrupole-allowed transitions of a laser-cooled Ca⁺ ion in a small rf trap. The electron shelving method was used to measure the absorption spectrum of the electric-quadrupole-allowed transitions, and the motional sidebands due to the secular motion of the ion in the harmonic potential well of the rf trap were completely resolved. The effective temperature of the ion, estimated by comparing the observed sideband intensities with the theoretical ones, was less than 4.4 mK. This result is in good agreement with that obtained from the analysis of the linewidth measurement. Received: 18 March 1998     

Endoscopy in the Paul trap: The influence of the micromotion

We show that three real-valued parameters govern the quantum motion of an ion stored in the Paul trap. These parameters are two angles of rotation in phase space and a squeezing parameter. The time dependence of these parameters simplifies considerably using Floquet solutions. This allows us to use the method of quantum state endoscopy to measure a pure state of the vibratory motion of an ion taking into account the full time dependence of the trapping potential. Received: 19 June 1996     

Atomic beam guide by a one-dimensional magneto-optical trap

An atomic beam has been collimated, compressed, and deflected simultaneously by an atomic beam guide based on an inclined one-dimensional magneto-optical trap (1D-MOT). Isotope-selected rubidium atoms were extracted from the naturally-mixed thermal atomic beam with this method. We could manipulate the transverse displacement of the deflected beam precisely by adjusting the current in the copper rods to generate the quadrupole magnetic field. We could extract more than 50% of the incident atoms as a deflection beam when we combined this deflection technique with the atomic deceleration using a broadband spectral light. Received: 10 December 1998 / Published online: 24 June 1999     

Investigation of ion dynamics in a Penning trap using a pulse-probe technique

We demonstrate a pulse-probe method for measuring the ion-cloud rotation frequency in a Penning trap. We show that it is useful over a range of parameters not accessible to the photon correlation method of Dholakia et al. [1]. In particular, the pulse-probe method works for larger clouds than the photon-correlation method. We show that the pulse-probe method measures the space-charge-shifted frequency and gives us the optical pumping times within clouds. Furthermore, we show that, for Mg⁺ ions, it is capable of measuring much higher degrees of space-charge shift than the photon-correlation method. Improvements to the method may enable its use in measuring diffusion rates for ions in clouds.     

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     

Ion strings for quantum gates

Received: 6 August 1997/Revised version: 21 October 1997     

Laser cooling of atoms in optical lattices including quantum statistics and dipole–dipole interactions

We develop a mean-field approach to include dipole-dipole interactions and quantum statistics in the atomic dynamics in bright and dark optical lattices including the proper spatial potentials instead of a simple δ-approximation. For classical distinguishable particles the results are even quantitatively similar to the properly scaled δ-function model. As the dominant effect bright and dark lattices exhibit opposite shifts in the lattice band energies and differ in their localisation properties as a function of density. The spatial-dependent potential allows strong modifications also in dark lattices, but the main conclusions obtained in the δ-approximation turn out to be still valid. Interestingly, important quantitative differences from the δ-model can occur as far as the effect of statistics in concerned, especially for fermions. We study the quantum statistical effects as a function of detuning and lattice well depths and identify the case of lattices with deep wells and large detunings as the preferred parameter region to observe them. Received 24 November 1999 / revised version: 24 June 1999 / Published online: 8 September 1999     

Writing a superlattice with light forces

In atom lithography the conventional roles played by light and matter are reversed. Instead of using a solid mask to pattern a light beam, a mask of light is used to pattern a beam of neutral atoms. In this paper we report the production of different chromium dot arrays with quadratic symmetry. The lattice period depends on the relative polarization and the phase of the two standing waves generating the light mask. A small angular misalignment of the laser beams breaks the high symmetry and a chromium superlattice is written, that is a continuous periodic change between two different quadratic lattices. The structures exhibit lines with a FWHM below 50 nm and clearly separated chromium dots with a FWHM below 70 nm. Received: 30 September 1999 / Revised version: 14 February 2000 / Published online: 5 April 2000     

Optimizing the production of metastable calcium atoms in a magneto-optical trap

We investigate the production of long-lived metastable (4³ P ₂ ) calcium atoms in a magneto-optical trap (MOT) operating on the 4¹ S ₀ ?4¹ P ₁ transition at 423 nm. For excited 4¹ P ₁ atoms a weak decay channel into the triplet states 4³ P ₂ and 4³ P ₁ exists via the 3¹ D ₂ state. The undesired 4³ P ₁ atoms decay back to the ground state within 0.4 ms and can be fully recaptured if the illuminated trap volume is sufficientlylarge. We obtain a flux of above 10¹⁰ atoms/s into the 4³ P ₂ state. We find that our MOT lifetime of 23 ms is mainly limited by this loss channel, and thus the 4³ P ₂ production is not hampered by inelastic collisions. If we close the loss channel by repumping the 3¹ D ₂ atoms with a 671 nm laser back into the MOT cycling transition, a non-exponential 72 ms trap decay is observed, indicating the presence of inelastic two-body collisions between 4¹ S ₀ and 4¹ P ₁ atoms. Received: 10 July 2001 / Revised version: 22 October 2001 / Published online: 23 November 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     

Decoding the dynamics of a single trapped atom from photon correlations

Received: 4 September 1998     

An optical conveyor belt for single neutral atoms

Using optical dipole forces we have realized controlled transport of a single or any desired small number of neutral atoms over a distance of a centimeter with sub-micrometer precision. A standing wave dipole trap is loaded with a prescribed number of cesium atoms from a magneto-optical trap. Mutual detuning of the counter-propagating laser beams moves the interference pattern, allowing us to accelerate and stop the atoms at preselected points along the standing wave. The transportation efficiency is close to 100%. This optical ‘single-atom conveyor belt’ represents a versatile tool for future experiments requiring deterministic delivery of a prescribed number of atoms on demand. Received: 6 July 2001 / Published online: 23 November 2001     

Coherent excitation of Rydberg atoms in an ultracold gas

We demonstrate two schemes for the coherent excitation of Rydberg atoms in an ultracold gas of rubidium atoms employing the three-level ladder system 5S_1/2-5P_3/2-n?_j. In the first approach rapid adiabatic passage with pulsed laser fields yields Rydberg excitation probabilities of 90% in the center of the laser focus. In a second experiment two-photon Rydberg excitation with continuous-wave fields is applied which results in Rabi oscillations between the ground and Rydberg state. The experiments represent a prerequisite for the control of interactions in ultracold Rydberg gases and the application of ultracold Rydberg gases for quantum information processing.