Correlated motion in atomic and three-particle molecular systems

Daniele C E Bortolotti, А. V. Avdeenkov, Christopher Ticknor +1 more

We test a non equilibrium approach to study the behavior of a Bose-Fermi mixture of alkali atoms in the presence of a Feshbach resonance between bosons and fermions. To this end we derive the Hartree-Fock-Bogoliubov (HFB) equations of motion for, the interacting system. This approach has proven very successful in the study of resonant systems composed of Bose particles and Fermi particles. However, when applied to a Bose-Fermi mixture, the HFB theory fails to identify even the correct binding energy of molecules in the appropriate limit. Through a more rigorous analysis we are able to ascribe this difference to the peculiar role that bosonic depletion plays in the Bose-Fermi pair correlation, which is the mechanism through which molecules are formed. We therefore conclude that molecular formation in Bose-Fermi mixtures is driven by three point and higher order correlations in the gas, unlike any other resonant system studied in the context of ultra-cold atomic physics.

Harry J. Lipkin

Harry J. Lipkin

Xabier López, Jesús María Ugalde, Lorenzo Echevarría +1 more

A Hookean model of a three-body problem for particles with arbitrary masses and charges where two of them interact with each other through a Coulomb potential and with the third through a harmonic potential is presented. It is shown that a condition relating the masses to the harmonic coupling constants must be satisfied in order to render this problem separable. A general exact analytic solution written in terms of the relative interparticle coordinates is given as well as general expressions for the total and binding energies of this three-body system. We apply these results to examine electronic, muonic, antiprotonic, and pionic families of non-Born-Oppenheimer Hookean systems. The first contains the atoms or atomic ions: ${\mathrm{Ps}}^{\ensuremath{-}}({e}^{+}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}})$, ${\mathrm{H}}^{\ensuremath{-}}({p}^{+}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}})$, ${\mathrm{D}}^{\ensuremath{-}}({d}^{+}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}})$, ${\mathrm{T}}^{\ensuremath{-}}({p}^{+}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}})$, $^{4}\mathrm{He}(h{e}^{+2}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}})$, and the following molecular ions: ${\mathrm{Ps}}_{2}^{+}({e}^{\ensuremath{-}}{e}^{+}{e}^{+})$, ${\mathrm{H}}_{2}^{+}({e}^{\ensuremath{-}}{p}^{+}{p}^{+})$, $\mathrm{H}{\mathrm{D}}^{+}({e}^{\ensuremath{-}}{d}^{+}{p}^{+})$, ${\mathrm{HT}}^{+}({e}^{\ensuremath{-}}{t}^{+}{p}^{+})$, ${\mathrm{DT}}^{+}({e}^{\ensuremath{-}}{d}^{+}{t}^{+})$, ${\mathrm{D}}_{2}^{+}({e}^{\ensuremath{-}}{d}^{+}{d}^{+})$, ${\mathrm{T}}_{2}^{+}({e}^{\ensuremath{-}}{t}^{+}{t}^{+})$. The muonic and antiprotonic families are similar to the electronic ones except that the species are formed replacing ${e}^{\ensuremath{-}}$ by ${\ensuremath{\mu}}^{\ensuremath{-}}$ or ${p}^{\ensuremath{-}}$. The pionic family comprises exotic atoms containing at least one pion. We also apply these results to two-electron three-dimensional spherical quantum dots and for these systems we examine the effect of electronic correlation, particularly on the singlet-triplet transitions and on the collective motion of the electrons and center of mass leading to ``floppy''dynamics.

Geunsik Kim

Nikolay A. Veretenov, B. N. Levinsky, Leonid A. Nesterov +3 more

The paper deals with generalization of investigation materials performed by the authors in recent years and analysis of obtained results. The subject of the paper is accounting of many-particle interactions in molecular J-aggregates at their resonance excitation by laser radiation. In this case, not only twin interactions are taken into considerations, but also the interactions of a given particle with three and more particles simultaneously. Three basic directions can be denoted among carried out investigations. The first direction is connected with derivation (from the first principles) of motion equations for molecular of J-aggregates in view of many-particle interactions, and also twin correlations between particles. The derivation of equations from the first principles leads in general to the system of coupled equations for the means of products of n operators relating to n different molecules. Since n increases in every following equation, the problems arise, connected with uncoupling of this system and also factorization of the means with the highest n. The most difficult and complicated problem in this process is correct calculation of relaxed terms, arising due to exciton-exciton annihilation. The first direction is connected concretely with solution of all above mentioned problems. Within the second direction the study of bistability has been carried out on the basis of obtained equations, in view of three-particle interactions. Meanwhile primary attention has been concentrated on analysis of homogeneous regimes in J-aggregates. It has been shown, in particular, that accounting of many-particle contributions leads to the shift of bistability boundary into region of smaller constants of exciton-exciton annihilation. And, at last, the third direction of investigations is connected with analysis of modulation instability for stationary states of J-aggregates considered earlier at bistability study. The study of stability region boundaries and their correlation with boundaries of bistability regions has been carried out. Obtained results give the possibility to determine more rigorously the parameters region, where nonlinear effects can be observed. They can be used for development of optical logic devices and, in particular, molecular memory circuits.