Multispecies time-dependent restricted-active-space self-consistent-field theory for ultracold atomic and molecular gases

TL;DR

This paper introduces a versatile wavefunction-based theory for ultracold atomic and molecular mixtures, capable of capturing correlation effects at various approximation levels, demonstrated through ground state energy calculations of a Bose-Bose mixture.

Contribution

It develops a multispecies time-dependent restricted-active-space self-consistent-field theory, extending existing methods to better describe correlations in ultracold gas mixtures.

Findings

Accurately computes ground state energies of Bose-Bose mixtures.

Shows the importance of orbital restrictions for describing few-particle excitations.

Demonstrates the theory's ability to interpolate between mean-field and full configuration interaction.

Abstract

We discuss the multispecies time-dependent restricted-active-space self-consistent-field theory, an \textit{ab initio} wavefunction-based theory for mixtures of ultracold atomic and molecular gases. We present the general theory, based on the time-dependent variational principle, and derive the equations of motion. The theory captures in a time-dependent setting, via the specification of the restricted-active-space scheme, different levels of approximation from the mean-field to the full configuration interaction approach. To assess its accuracy and to illustrate its ability to identify correlation effects at successive approximation levels, we apply the theory to compute the ground state energy of a Bose-Bose mixture interacting through a harmonic potential, for which the exact ground state energy is known analytically. We focus on the case of an ideal Bose gas interacting with a few impurities. The intra-species interaction between the impurities is relatively strong compared to the inter-species interaction between the impurities and the ideal noninteracting Bose gas. For this system, we find that an accurate description of the ground state necessitates the possibility of the theory to account for few-particle excitations out of the condensed phase; a situation well accounted for by the present restricted-active-space theory for mixtures; and not within reach for approaches not incorporating orbital-restriction schemes.