Complementarity and Young's interference fringes from two atoms

The interference pattern of the resonance fluorescence from a J=1/2 to J=1/2 transition of two identical atoms confined in a three-dimensional harmonic potential is calculated. Thermal motion of the atoms is included. Agreement is obtained with experiments [Eichmann et al., Phys. Rev. Lett. 70, 2359 (1993)]. Contrary to some theoretical predictions, but in agreement with the present calculations, a fringe visibility greater than 50% can be observed with polarization-selective detection. The dependence of the fringe visibility on polarization has a simple interpretation, based on whether or not it is possible in principle to determine which atom emitted the photon.Comment: 12 pages, including 7 EPS figures, RevTex. Submitted to Phys. Rev.

Testing the stability of fundamental constants with the 199Hg+ single-ion optical clock

Over a two-year duration, we have compared the frequency of the 199Hg+ 5d106s 2S 1/2 (F=0) 5d9 6s2 2D 5/2 (F=2) electric-quadrupole transition at 282 nm with the frequency of the ground-state hyperfine splitting in neutral 133Cs. These measurements show that any fractional time variation of the ratio nu(Cs)/nu(Hg) between the two frequencies is smaller than +/- 7 10^-15 / yr (1 sigma uncertainty). According to recent atomic structure calculations, this sets an upper limit to a possible fractional time variation of g(Cs) m_e / m_p alpha^6.0 at the same level.Comment: 4 pages with 3 figures. RevTeX 4, Submitted to Phys. Rev. Let

Terahertz frequency standard based on three-photon coherent population trapping

A scheme for a THz frequency standard based on three-photon coherent population trapping in stored ions is proposed. Assuming the propagation directions of the three lasers obey the phase matching condition, we show that stability of few 10$^{-14}$ at one second can be reached with a precision limited by power broadening to $10^{-11}$ in the less favorable case. The referenced THz signal can be propagated over long distances, the useful information being carried by the relative frequency of the three optical photons.Comment: article soumis a PRL le 21 mars 2007, accepte le 10 mai, version 2 (24/05/2007

'Designer atoms' for quantum metrology

Entanglement is recognized as a key resource for quantum computation and quantum cryptography. For quantum metrology, the use of entangled states has been discussed and demonstrated as a means of improving the signal-to-noise ratio. In addition, entangled states have been used in experiments for efficient quantum state detection and for the measurement of scattering lengths. In quantum information processing, manipulation of individual quantum bits allows for the tailored design of specific states that are insensitive to the detrimental influences of an environment. Such 'decoherence-free subspaces' protect quantum information and yield significantly enhanced coherence times. Here we use a decoherence-free subspace with specifically designed entangled states to demonstrate precision spectroscopy of a pair of trapped Ca+ ions; we obtain the electric quadrupole moment, which is of use for frequency standard applications. We find that entangled states are not only useful for enhancing the signal-to-noise ratio in frequency measurements - a suitably designed pair of atoms also allows clock measurements in the presence of strong technical noise. Our technique makes explicit use of non-locality as an entanglement property and provides an approach for 'designed' quantum metrology

Dynamics of Quantum Collapse in Energy Measurements

The influence of continuous measurements of energy with a finite accuracy is studied in various quantum systems through a restriction of the Feynman path-integrals around the measurement result. The method, which is equivalent to consider an effective Schr\"odinger equation with a non-Hermitian Hamiltonian, allows one to study the dynamics of the wavefunction collapse. A numerical algorithm for solving the effective Schr\"odinger equation is developed and checked in the case of a harmonic oscillator. The situations, of physical interest, of a two-level system and of a metastable quantum-well are then discussed. In the first case the Zeno inhibition observed in quantum optics experiments is recovered and extended to nonresonant transitions, in the second one we propose to observe inhibition of spontaneous decay in mesoscopic heterostructures. In all the considered examples the effect of the continuous measurement of energy is a freezing of the evolution of the system proportional to the accuracy of the measurement itself.Comment: 20 pages with figures, compressed and uuencoded ps fil

Doppler cooling of a Coulomb crystal

We study theoretically Doppler laser-cooling of a cluster of 2-level atoms confined in a linear ion trap. Using several consecutive steps of averaging we derive, from the full quantum mechanical master equation, an equation for the total mechanical energy of the one dimensional crystal, defined on a coarse-grained energy scale whose grid size is smaller than the linewidth of the electronic transition. This equation describes the cooling dynamics for an arbitrary number of ions and in the quantum regime. We discuss the validity of the ergodic assumption (i.e. that the phase space distribution is only a function of energy). From our equation we derive the semiclassical limit (i.e. when the mechanical motion can be treated classically) and the Lamb-Dicke limit (i.e. when the size of the mechanical wave function is much smaller than the laser wavelength). We find a Fokker-Planck equation for the total mechanical energy of the system, whose solution is in agreement with previous analytical calculations which were based on different assumptions and valid only in their specific regimes. Finally, in the classical limit we derive an analytic expression for the average coupling, by light scattering, between motional states at different energies.Comment: 19 pages, 3 figure