We study in detail the mechanisms causing dephasing of hyperfine coherences of cesium atoms confined by a far off-resonant standing wave optical dipole trap [S. Kuhr et al., Phys. Rev. Lett. 91, 213002 (2003)]. Using Ramsey spectroscopy and spin echo techniques, we measure the reversible and irreversible dephasing times of the ground state coherences. We present an analytical model to interpret the experimental data and identify the homogeneous and inhomogeneous dephasing mechanisms. Our scheme to prepare and detect the atomic hyperfine state is applied at the level of a single atom as well as for ensembles of up to 50 atoms.

We demonstrate the realization of a quantum register using a string of single neutral atoms which are trapped in an optical dipole trap. The atoms are selectively and coherently manipulated in a magnetic field gradient using microwave radiation. Our addressing scheme operates with a high spatial resolution and qubit rotations on individual atoms are performed with 99 % contrast. In a final read-out operation we analyze each individual atomic state. Finally, we have measured the coherence time and identified the predominant dephasing mechanism for our register.PACS numbers: 32.80.Pj, 39.25.+k, 42.50.Vk Information coded into the quantum states of physical systems (qubits) can be processed according to the laws of quantum mechanics. It has been shown that the quantum concepts of state superposition and entanglement can lead to a dramatic speed up in solving certain classes of computational problems [1,2]. Over the past decade various quantum computing schemes have been proposed. In a sequential network of quantum logic gates quantum information is processed using discrete one-and two-qubit operations [3]. Another approach is the oneway quantum computer which processes information by performing one-qubit rotations and measurements on an entangled cluster state [4]. All of these schemes rely on the availability of a quantum register, i. e. a well known number of qubits that can be individually addressed and coherently manipulated. There are several physical systems, such as trapped ions [5,6,7], nuclear spins in molecules [8], or magnetic flux qubits [9] that can serve as quantum registers.Neutral atoms exhibit favourable properties for storing and processing quantum information. Their hyperfine ground states are readily prepared in pure quantum states including state superpositions and can be well isolated from their environment. In addition, using laser cooling techniques, countable numbers of neutral atoms can be cooled, captured and transported [10,11]. The coherence properties of laser trapped atoms have been found to be adequate for storing quantum information [12,13]. Moreover, controlled cold collisions [14] or the exchange of microwave [15] or optical [16,17] photons in a resonator offer interesting schemes for mediating coherent atom-atom interaction, essential for the realization of quantum logic operations.In our experiment we use a string of an exactly known number of neutral caesium atoms. The atoms are trapped in the potential wells of a spatially modulated, light induced potential created by a far detuned standing wave dipole trap [10,18]. They can be optically resolved with an imaging system using an intensified CCD camera (ICCD) [19,20]. Our experimental setup is schematically depicted in Fig. 1. Two focussed counter-propagating Nd:YAG laser beams at a wavelength of λ = 1064 nm FIG. 1: Scheme of the experimental setup. Two focussed counter-propagating Nd:YAG laser beams form the dipole trap. We illuminate the trapped atoms by an optical molasses and split the fluorescence light with a beamsplit...

We present the design of a diffraction limited, long working distance monochromatic objective lens for efficient light collection. Consisting of four spherical lenses, it has a numerical aperture of 0.29, an effective focal length of 36 mm and a working distance of 36.5 mm. This inexpensive system allows us to detect 8 · 10 4 fluorescence photons per second from a single cesium atom stored in a magneto-optical trap.

Laser cooling and trapping techniques allow us to control and manipulate neutral atoms. Here we rearrange, with submicrometre precision, the positions and ordering of laser-trapped atoms within strings by manipulating individual atoms with optical tweezers. Strings of equidistant atoms created in this way could serve as a scalable memory for quantum information.

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 counterpropagating 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 "singleatom conveyor belt" represents a versatile tool for future experiments requiring deterministic delivery of a prescribed number of atoms on demand. PACS: 32.80.Lg, 32.80.Pj, 42.50.Vk Quantum engineering of microscopic systems requires manipulation of all degrees of freedom of isolated atomic particles. The most advanced experiments are implemented with trapped chains of ions [1,2,3]. Neutral atoms are more difficult to control because of the weaker interaction of induced electric or paramagnetic dipoles with inhomogeneous electromagnetic fields. Optical dipole traps [4] could provide a level of control similar to ion traps, since they store neutral atoms in a nearly conservative potential with long coherence times [5]. The variety of different dipole traps allows for an individual design, depending on the specific experimental demands [6].Here we use a time-varying standing wave optical dipole trap to displace atoms by macroscopic distances on the order of a centimeter with sub-micrometer precision [7]. A similar technique of moving optical lattices has been applied for the acceleration of large ensembles of atoms in [8,9]. Time-dependent magnetic fields can also be used for controlled transport of clouds of neutral atoms as has been demonstrated with a micro-fabricated device [10]. Recently, techniques have been developed to load a dipole trap with single atoms only [11,12]. In our case, we have combined controlled manipulation of the trapping potential with deterministic loading of a dipole trap with a prescribed small number of atoms [7]. These atoms are then transported with high efficiency over macroscopic distances and observed by positionsensitive fluorescence detection in the dipole trap. Here we describe the transportation technique in detail. We also analyze the dependency of the measured transportation efficiency on both the transportation distance and the acceleration. This is followed by a brief discussion of possible applications and alternative approaches. The standing-wave dipole trapOur dipole trap ( Fig.1) consists of two counter-propagating Gaussian laser beams with equal intensities and optical frequencies ν 1 and ν 2 producing a position-and time-dependent dipole potentialThe optical wavelength is λ = 2π/k, wis the beam radius with waist w 0 and the Rayleigh length z 0 = πw 2 0 /λ, and ∆ν = ν 1 −ν 2 ≪ ν 1 , ν 2 is the mutual detuning of the laser beams. The laser beams have parallel linear polarization and thus produce a standing wave interference pa...