Single Atoms: Controlling the Quantum World

Atoms and photons are the principal cases of microscopic particles, the hallmarks of quantum objects. For more than a century they have served as conceptual models to understand and investigate the microscopic structure of matter. More than 30 years ago it became possible to isolate and observe single ions in a trapping device. This experiment [1] may be taken as a turning point in the history of approaching the quantum world: experimenters left the role of pure observers and turned into quantum engineers striving to control the properties of matter down to the level of a single atom, molecule, or photon.

Ion storage relies on the interaction of its Coulomb charge with electromagnetic fields and has long since realized the "spectroscopist's dream of a single stored ion in free space" (H. Dehmelt [2]). Neutral atoms can only be trapped by means of their feeble electric or magnetic dipole moments which furthermore mix motional and internal degrees of freedom. However, in contrast to the long-range ionic Coulomb force, they offer short-range interactions which can be controlled by the experimenter, making them ideally suited for constructing many-body quantum systems atom by atom in the so-called bottom-up approach [3].

A light field induces an electric dipole moment in an atom, and a laser, red detuned from the atomic resonance frequency, exerts a force towards maximal intensity. Thus, in a standing wave with a transverse bell shape, atoms - after laser cooling - become trapped at the maxima of the standing wave which provide micro potentials with a trap depth energy U = _kB - 1 mK, 100 times or more above the typical kinetic energy of the trapped atoms. Illumination of the atoms with near resonant laser light allows to record, by means of a photon counting CCD camera real time movies of atoms travelling with a moving lattice (optical conveyor belt).

Adjacent micro-potentials are spaced by about 0.5 μm only, and hence below the Rayleigh resolution limit of about 2 μm of the microscope objective. It is thus an interesting question whether atoms (which are point-like radiation sources just like stars in space) in adjacent potentials can be detected. Neighboring atoms define one of the most interesting situations since they can be made to interact. It turns out that it is not necessary to obtain full Rayleigh resolution [4]: the point-spread function of an individual atom can be measured with very high precision, and hence the position quantum number can be inferred by deconvolution methods with high fidelity.

The atoms have two long-lived quantum states (hyperfine states) forming a pseudo spin _1⁄2 system. Pure spin quantum states ǀ↑〉 and ǀ↓〉 are prepared by optical hyperfine pumping. Microwave transitions at 9.2 GHz induce arbitrary spin (Rabi) rotations, e.g. an even superposition (ǀ↑〉+ǀ↓〉)/√2 is created in less than 10 μs by a so called π/2-pulse. The internal quantum states can be measured by e.g. the so called "push-out" technique with excellent fidelity, and we can observe rabi oscillations with excellent contrast.

For certain "magic wavelengths'" the conveyor belt can be made sensitive to the internal spin quantum number of the trapped atom, thus there is a right hand polarized (RHP) conveyor belt for the ǀ↑〉 and its left hand companion for the ǀ↓〉-state. RHP- and LHP-standing waves are created from a superposition of two counterpropagating linearly polarized waves. If one of the linear polarizations is rotated with respect to the other, the RHP- and LHP-waves walk in opposite directions. At present, the magic conveyor belt can only be shuttled back and forth for one lattice site, but changing the spin state after each transport step makes the atom continue its journey unidirectionally with a fidelity exceeding 99%/step and making transport distances of about 50 sites available.

Shifting spin-dependent potentials with respect to each other opens a highly efficient way to cool and manipulate the vibrational degree of freedom of trapped atoms: microwave transitions with _Δnvib ≠ 0 are now allowed with high and variable transition strengths enabling spectroscopy of all micro-potential levels, and moreover opening the route to cooling and coherent vibrational state engineering. [5]

An alternative approach to micro-wave cooling has been realized with a single Cs atom interacting with an ultracold gas of Rb atoms. In future experiments, single atoms can be used to probe quantum many-body systems like a dopant in conventional condensed matter. [6] We are thus able to control all degrees of freedom of the trapped atoms. Based on quantum states _{ǀn〉siteǀn〉vibǀ↑},↓〉 we have engineered a single atom interferometer. The single atom interferometer has achieved a sensitivity for measuring accelerations of ^10-4 g, it is of interest for nanometric applications, and extended versions may even rival the sensitivity promised by ballistic interferometers. [7]