Correlated motion of two atoms trapped in a single mode cavity field

We study the motion of two atoms trapped at distant positions in the field of a driven standing wave high-Q optical resonator. Even without any direct atom-atom interaction the atoms are coupled through their position dependent influence on the intracavity field. For sufficiently good trapping and low cavity losses the atomic motion becomes significantly correlated and the two particles oscillate in their wells preferentially with a 90 degrees relative phase shift. The onset of correlations seriously limits cavity cooling efficiency, raising the achievable temperature to the Doppler limit. The physical origin of the correlation can be traced back to a cavity mediated cross-friction, i.e. a friction force on one particle depending on the velocity of the second particle. Choosing appropriate operating conditions allows for engineering these long range correlations. In addition this cross-friction effect can provide a basis for sympathetic cooling of distant trapped clouds.Comment: 10 pages, 9 figures, accepted for publication in Phys. Rev. A. Minor grammatical changes to previous versio

Collective effects in the dynamics of driven atoms in a high-Q resonator

We study the quantum dynamics of N coherently driven two-level atoms coupled to an optical resonator. In the strong coupling regime the cavity field generated by atomic scattering interferes destructively with the pump on the atoms. This suppresses atomic excitation and even for strong driving fields prevents atomic saturation, while the stationary intracavity field amplitude is almost independent of the atom number. The magnitude of the interference effect depends on the detuning between laser and cavity field and on the relative atomic positions and is strongest for a wavelength spaced lattice of atoms placed at the antinodes of the cavity mode. In this case three dimensional intensity minima are created in the vicinity of each atom. In this regime spontaneous emission is suppressed and the dominant loss channel is cavity decay. Even for a cavity linewidth larger than the atomic natural width, one regains strong interference through the cooperative action of a sufficiently large number of atoms. These results give a new key to understand recent experiments on collective cavity cooling and may allow to implement fast tailored atom-atom interactions as well as nonperturbative particle detection with very small energy transfer.Comment: 12 pages, 13 figures, significantly extended version, slightly different from the published on

Resonance fluorescence of a trapped three-level atom

We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are $\Lambda$--shaped and driven at two-photon resonance by a pair of lasers, which cool the center--of--mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser--cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb--Dicke limit). We use the spectral decomposition of the Liouville operator of the master equation for the atomic density matrix and apply second order perturbation theory. We find that the spectrum of resonance fluorescence is composed by two narrow sidebands -- the Stokes and anti-Stokes components of the scattered light -- while all other signals are in general orders of magnitude smaller. For very low temperatures, however, the Mollow--type inelastic component of the spectrum becomes visible. This exhibits novel features which allow further insight into the quantum dynamics of the system. We provide a physical model that interprets our results and discuss how one can recover temperature and cooling rate of the atom from the spectrum. The behaviour of the considered system is compared with the resonance fluorescence of a trapped atom whose internal transition consists of two-levels.Comment: 11 pages, 4 Figure

Active laser frequency stabilization using neutral praseodymium (Pr)

We present a new possibility for the active frequency stabilization of a laser using transitions in neutral praseodymium. Because of its five outer electrons, this element shows a high density of energy levels leading to an extremely line-rich excitation spectrum with more than 25000 known spectral lines ranging from the UV to the infrared. We demonstrate the active frequency stabilization of a diode laser on several praseodymium lines between 1105 and 1123 nm. The excitation signals were recorded in a hollow cathode lamp and observed via laser-induced fluorescence. These signals are strong enough to lock the diode laser onto most of the lines by using standard laser locking techniques. In this way, the frequency drifts of the unlocked laser of more than 30 MHz/h were eliminated and the laser frequency stabilized to within 1.4(1) MHz for averaging times >0.2 s. Frequency quadrupling the stabilized diode laser can produce frequency-stable UV-light in the range from 276 to 281 nm. In particular, using a strong hyperfine component of the praseodymium excitation line E = 16 502.616_7/2 cm^-1 -> E' = 25 442.742_9/2 cm^-1 at lambda = 1118.5397(4) nm makes it possible - after frequency quadruplication - to produce laser radiation at lambda/4 = 279.6349(1) nm, which can be used to excite the D2 line in Mg^+.Comment: 10 pages, 14 figure

Trapping atoms in the vacuum field of a cavity

The aim of this work is to find ways to trap an atom in a cavity. In contrast to other approaches we propose a method where the cavity is basically in the vacuum state and the atom in the ground state. The idea is to induce a spatial dependent AC Stark shift by irradiating the atom with a weak laser field, so that the atom experiences a trapping force. The main feature of our setup is that dissipation can be strongly suppressed. We estimate the lifetime of the atom as well as the trapping potential parameters and compare our estimations with numerical simulations.Comment: 8 pages, 8 figure

Motion-light parametric amplifier and entanglement distributor

We propose a scheme for entangling the motional mode of a trapped atom with a propagating light field via a cavity-mediated parametric interaction. We then show that if this light field is subsequently coupled to a second distant atom via a cavity-mediated linear-mixing interaction, it is possible to transfer the entanglement from the light beam to the motional mode of the second atom to create an EPR-type entangled state of the positions and momenta of two distantly-separated atoms.Comment: 9 pages, 8 figures, REVTe

Architecture for a large-scale ion-trap quantum computer

Among the numerous types of architecture being explored for quantum computers are systems utilizing ion traps, in which quantum bits (qubits) are formed from the electronic states of trapped ions and coupled through the Coulomb interaction. Although the elementary requirements for quantum computation have been demonstrated in this system, there exist theoretical and technical obstacles to scaling up the approach to large numbers of qubits. Therefore, recent efforts have been concentrated on using quantum communication to link a number of small ion-trap quantum systems. Developing the array-based approach, we show how to achieve massively parallel gate operation in a large-scale quantum computer, based on techniques already demonstrated for manipulating small quantum registers. The use of decoherence-free subspaces significantly reduces decoherence during ion transport, and removes the requirement of clock synchronization between the interaction regions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62880/1/nature00784.pd