Quantum Many-body Simulation Research Articles

Number fluctuation dynamics of a spin-1 atomic condensate

We provide further details on atom number fluctuation during spin-mixing dynamics inside an $F=1$ spinor condensate, based on the effective quantization approach we reported earlier [L. Chang et al., Phys. Rev. Lett. 99, 080402 (2007)] for the semiclassical nonrigid pendulum model in terms of the relative phase and the atomic population in the magnetic $(B\text{\ensuremath{-}})$field insensitive hyperfine state $|{F}_{z}=0⟩$. Many features of the classical nonrigid pendulum model are reproduced. In addition, features typically associated with full quantum simulations specific to our model system, such as atom number fluctuations both in stationary states and during the dynamics of spin mixing, are faithfully revealed with our effective quantization approach. We check the validity of the effective quantization theory by performing extensive numerical comparisons with the results from full quantum many-body simulations. We study the effect of quantum coherence in our system and provide a solid theoretical basis to resolve the resolution limit in counting atoms that is needed to clearly detect quantum correlation effects in spin mixing.

Heavily Damped Motion of One-Dimensional Bose Gases in an Optical Lattice

We study the dynamics of strongly correlated one-dimensional Bose gases in a combined harmonic and optical lattice potential subjected to sudden displacement of the confining potential. Using the time-evolving block decimation method, we perform a first-principles quantum many-body simulation of the experiment of Fertig et al. [Phys. Rev. Lett. 94, 120403 (2005)] across different values of the lattice depth ranging from the superfluid to the Mott insulator regimes. We find good quantitative agreement with this experiment: the damping of the dipole oscillations is significant even for shallow lattices, and the motion becomes overdamped with increasing lattice depth as observed. We show that the transition to overdamping is attributed to the decay of superfluid flow accelerated by quantum fluctuations, which occurs well before the emergence of Mott insulator domains.

Finite-size errors in quantum many-body simulations of extended systems

Further developments are introduced in the theory of finite size errors in quantum many-body simulations of extended systems using periodic boundary conditions. We show that our recently introduced Model Periodic Coulomb interaction [A. J. Williamson et al., Phys. Rev. B 55, R4851 (1997)] can be applied consistently to all Coulomb interactions in the system. The Model Periodic Coulomb interaction greatly reduces the finite size errors in quantum many-body simulations. We illustrate the practical application of our techniques with Hartree-Fock and variational and diffusion quantum Monte Carlo calculations for ground and excited state calculations. We demonstrate that the finite size effects in electron promotion and electron addition/subtraction excitation energy calculations are very similar.

Elimination of Coulomb finite-size effects in quantum many-body simulations

A model interaction is introduced for quantum many-body simulations of Coulomb systems using periodic boundary conditions. The interaction gives much smaller finite size effects than the standard Ewald interaction and is also much faster to compute. Variational quantum Monte Carlo simulations of diamond-structure silicon with up to 1000 electrons demonstrate the effectiveness of our method.