Quantum Monte Carlo Wave-Function Method for Cold Atoms

Hao Shi, Peter Rosenberg, Ettore Vitali +2 more

Tohya Hiroshima, Y. Yamamoto

We develop an auxiliary field approximation scheme for the many-body quantum Monte Carlo wave-function method to analyze numerically the system of cold atoms undergoing laser cooling. Numerical simulations for the three-dimensional Doppler cooling of bosonic and fermionic atoms are performed, which clearly exhibit the effects of quantum statistics.

Kaoru Iguchi

Michal Bajdich, Jindřich Kolorenč, Luboš Mitáš +1 more

We discuss the importance of the fermion nodes for the quantum Monte Carlo (QMC) methods and find two cases of the exact nodes. We describe the structure of the generalized pairing wave functions in Pfaffian antisymmetric form and demonstrate their equivalency with certain class of configuration interaction wave functions. We present the QMC calculations of a model fermion system at unitary limit. We find the system to have the energy of E=0.425Efree and the condensate fraction of α=0.48. Further we also perform the QMC calculations of the potential energy surface and the electric dipole moment along that surface of the LiSr molecule. We estimate the vibrationally averaged dipole moment to be 〈D〉ν=0=−0.4(2).

Abhishek Mukherjee, Y. Alhassid

We develop a quantum Monte Carlo method to estimate the ground-state energy of a fermionic many-particle system in the configuration-interaction shell model approach. The fermionic sign problem is circumvented by using a guiding wave function in Fock space. The method provides an upper bound on the ground-state energy whose tightness depends on the choice of the guiding wave function. We argue that the antisymmetric geminal product class of wave functions is a good choice for guiding wave functions. We demonstrate our method for the trapped two-species fermionic cold atom system in the unitary regime of infinite scattering length using the particle-number projected Hartree-Fock-Bogoliubov wave function as the guiding wave function. We estimate the ground-state energy and energy-staggering pairing gap as a function of the number of particles. We compare our results with exact numerical diagonalization results and with previous fixed-node coordinate-space Monte Carlo calculations.

Dario Bressanini, Pietro Cremaschi, Massimo Mella +1 more