Induced pairing of fermionic impurities in a one-dimensional strongly correlated Bose gas

Abstract

We investigate numerically the problem of few (one, two) noninteracting spin−1/2 fermions in a shallow harmonic trap coupled via contact repulsive interactions to a uniform one-dimensional bath of lattice bosons, described by the Bose-Hubbard model. Through extensive density-matrix renormalization group calculations, we extract the binding energy and the effective mass of quasiparticles, including dressed impurities (polarons) and their two-body bound states (bipolarons), emerging from the effective non-local Casimir interaction between the impurities. We show that the mixture exhibits rather different pairing behaviors depending on the singlet vs. triplet spin state configurations of the two fermions. For opposite spin states, bipolarons are found for any finite value of the impurity-bath coupling. In particular, in the strong coupling regime their binding energy reduces to that of a single polaron, provided the boson-boson repulsion is not too weak. For equal spin states, we show that bipolarons emerge only beyond a critical strength of the Bose-Fermi interaction and their effective mass grows rapidly approaching the strong coupling regime.

Microscopic theory of the friction force exerted on a quantum impurity in one-dimensional quantum liquids

“…We point out that our results indicate that there is universal dependence of the low temperature T 4 friction force on the impurity velocity in one-dimensional systems as shown by Eqs. (9,26,32,45). This statement is in agreement with the findings of Ref.…”

Impurities in a one-dimensional Bose gas: the flow equation approach

“…One possible way to do this is to consider a Bose gas with two mobile impurities, see, e.g., Refs. [20,25,48,49]. We choose another approach.…”

“…This problem is of current theoretical interest, see Refs. [2,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], which provide us with data for benchmarking and interpreting some of our IM-SRG results.…”

Static Impurities in a Weakly Interacting Bose Gas

“…In 1D, the character of this interaction crucially depends on a sign of the boson-impurity coupling constant [35]; the effective attraction is found for positive couplings, while the induced repulsive potential is inherent for the negative interactions. While it increases, the induced attractive interaction between impurities leads to the formation of bipolarons [36] in the continuum and on the lattice [37] and even to the emergence of the two-polaron bound states [38]. In one-dimensional geometries with harmonic trapping, the induced interaction causes the clustering [39] of two initially non-interacting atoms and modifies their quench dynamics [40].…”