Atomic Molecular And Optical Physics

The energy spectrum for a system of atoms in a periodic potential can exhibit a gap in the band structure. We describe a system in which a laser is used to produce a mechanical potential for the atoms, and a standing wave light field is used to shift the atomic levels using the Autler-Townes effect, which produces a periodic potential. The band structure for atoms guided by a hollow optical fiber waveguide is calculated in three dimensions with quantised external motion. The size of the band gap is controlled by the light guided by the fiber. This variable band structure may allow the construction of devices which can cool atoms. The major limitation on this device would be the spontaneous emission losses.

The cyclic motion of particles in a periodic potential under the influence of a constant external force is analyzed in an atom optical approach based on Landau-Zener transitions between two resonant states. The resulting complex picture of population transfers can be interpreted in an intuitive diagrammatic way. The model is also applied to genuine atom optical systems and its applicability is discussed.

It is well known that at the thermodynamic limit there are no observable differences in the results obtained by grand canonical and canonical descriptions of a many-body system. In the present paper, we test the validity of this statement for finite systems using as an example an ensemble of bosons trapped in a 1D harmonic potential well. We have found an analytical formula for the canonical partition function and shown that, for 100 trapped atoms, the discrepancy between the grand canonical and canonical predictions for the condensate fraction reaches 10% in the vicinity of the Bose-Einstein threshold. This discrepancy decreases only logarithmically as the number of atoms increases. Furthermore we investigate numerically the case of a 3D "cigar-shape" trap in the range of parameters corresponding to current BEC experiments.

Single particle states in the atomic trap employing the rotating magnetic field are found using the full time-dependent instantaneous trapping potential. These states are compared with those of the effective time-averaged potential. We show that the trapping is possible when the frequency of the rotations exceeds some threshold. Slightly above this threshold the weakly interacting gas of the trapped atoms acquires the properties of a quasi-1D system in the frame rotating together with the field. The role of the atom-atom interaction in changing the ideal gas solution is discussed. We show that in the limit of large numbers of particles the rotating field whose angular frequency is appropriately modulated can be utilized as a driving force principally for the center of mass motion as well as for the angular momentum L=2 normal modes of the Bose condensate. A mechanism of quantum evaporation forced by the rotating field is analyzed.

For the time development of a single system in the quantum jump approach or for quantum trajectories one requires the conditional (reduced) Hamiltonian between jumps and the reset operator after a jump. Explicit expressions for them are derived for a general N-level system by employing the same assumptions as in the usual derivation of the Bloch equations. We discuss a possible minor problem with positivity for these expressions as well as for the corresponding Bloch equations.

We use continuous measurement theory to describe the evolution of two Bose condensates in an interference experiment. It is shown how the system evolves in a single run of the experiment into a state with a fixed relative phase, while the total gauge symmetry remains unbroken. Thus, an interference pattern is exhibited without violating atom number conservation.

We analyze the difference between the correlation energy as defined within the conventional quantum chemistry framework and its namesake in density-functional theory. Both quantities are rigorously defined concepts; one finds that E QC c ≥ E DFT c . We give numerical and analytical arguments suggesting that the numerical difference between the two rigorous quantities is small. Finally, approximate density functional correlation energies resulting from some popular correlation energy functionals are compared with the conventional quantum chemistry values.

A purely group-theoretical approach (for which the symmetric group plays a central rôle), based upon the use of properties of fractional-parentage coefficients and isoscalar factors, is developed for the derivation of the Coulomb energy averaged over the states, with a definite spin, arising from an atomic configuration n ℓ N .

The {\it intrinsic} decoherence from vibrational coupling of the ions in the Cirac-Zoller quantum computer [Phys. Rev. Lett. {\bf 74}, 4091 (1995)] is considered. Starting from a state in which the vibrational modes are at a temperature T , and each ion is in a superposition of an excited and a ground state, an adiabatic approximation is used to find the inclusive probability P(t) for the ions to evolve as they would without the vibrations, and for the vibrational modes to evolve into any final state. An analytic form is found for P(t) at T=0 , and the decoherence time is found for all T . The decoherence is found to be quite small, even for 1000 ions.

We report on a numerical study of the density matrix functional introduced by Lieb, Solovej and Yngvason for the investigation of heavy atoms in high magnetic fields. This functional describes {\em exactly} the quantum mechanical ground state of atoms and ions in the limit when the nuclear charge Z and the electron number N tend to infinity with N/Z fixed, and the magnetic field B tends to infinity in such a way that B/ Z 4/3 →∞ . We have calculated electronic density profiles and ground state energies for values of the parameters that prevail on neutron star surfaces and compared them with results obtained by other methods. For iron at B= 10 12 G the ground state energy differs by less than 2 \% from the Hartree-Fock value. We have also studied the maximal negative ionization of heavy atoms in this model at various field strengths. In contrast to Thomas-Fermi type theories atoms can bind excess negative charge in the density matrix model. For iron at B= 10 12 G the maximal excess charge in this model corresponds to about one electron.