A unified ab initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures

Abstract

We extent the recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons (ML-MCTDHB) for simulating the correlated quantum dynamics of bosonic mixtures to the fermionic sector and establish a unifying approach for the investigation of the correlated quantum dynamics of mixture of indistinguishable particles, be it fermions or bosons.Relying on a multi-layer wave-function expansion, the resulting Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX) can be adapted to efficiently resolve system-specific intra-and inter-species correlations. The versatility and efficiency of ML-MCTDHX is demonstrated by applying it to the problem of colliding few-atom mixtures of both Bose-Fermi and Fermi-Fermi type. Thereby, we elucidate the role of correlations in the transmission and reflection properties of the collisional events. In particular, we present examples where the reflection (transmission) at the other atomic species is a correlation-dominated effect, i.e. it is suppressed in the mean-field approximation.

Many-body quantum dynamics and induced correlations of Bose polarons

“…To calculate the stationary properties and to track the MB non-equilibrium quantum dynamics of the multicomponent bosonic system discussed above we employ the ML-MCTDHX method [70][71][72]. This is an ab initio variational method for solving the time-dependent MB Schrödinger equation of atomic mixtures and it is based on the expansion of the total MB wavefunction with respect to a time-dependent and variationally optimized basis tailored to capture both the intra-and the interspecies correlations of a multicomponent system [35,65,81,82].…”

“…The time-evolution of the (N B + N I )-body wavefunction | ( ) Y ñ t governed by the Hamiltonian of equation (1) is obtained via solving the so-called ML-MCTDHX equations of motion [70]. The latter are determined by utilizing e.g.the Dirac-Frenkel [85,86] variational principle for the generalized ansatz introduced in equations (3)-(5).…”

“…Below we consider either two non-interacting (g II =0) or two weakly interacting impurities (g II =0.2). To obtain the interacting ground state of the system as described by the Hamiltonian of equation (1) we employ either imaginary time propagation or improved relaxation [70,71] within ML-MCTDHX.…”

“…We have ensured that the position of the hard-walls does not affect the presented results by assuring that no appreciable density occurs beyond x ± =±20. The eigenstates of the composite MB system are obtained by means of the so-called improved relaxation method [70,71] implemented in ML-MCTDHX. In order to simulate the non-equilibrium dynamics we propagate in time the wavefunction (equation (3)) utilizing the appropriate Hamiltonian within the ML-MCTDHX equations of motion.…”

Repulsive Fermi polarons and their induced interactions in binary mixtures of ultracold atoms

“…To theoretically address the impurity problem, we use a variational method, namely the Multi-Layer Multi-Configuration Time-Dependent Hartree method for atomic mixtures (ML-MCTDHX), that takes into account all particle correlations [79,80]. Such a non-perturbative inclusion of correlations allows us to calculate the impurity spectrum and thus identify the emergent polaron states.…”