Mean-field construction for spectrum of one-dimensional Bose polaron

Abstract

The full momentum dependence of spectrum of a point-like impurity immersed in a dilute onedimensional Bose gas is calculated on the mean-field level. In particular we elaborate, to the finite-momentum Bose polaron, the path-integral approach whose semi-classical approximation leads to the conventional mean-field treatment of the problem while quantum corrections can be easily accounted by standard loop expansion techniques. The extracted low-energy parameters of impurity spectrum, namely, the binding energy and the effective mass of particle, are shown to be in qualitative agreement with the results of quantum Monte Carlo simulations.

Zero temperature momentum distribution of an impurity in a polaron state of one-dimensional Fermi and Tonks-Girardeau gases

“…That is, the impurity can be viewed as a free particle having the effective mass m * , and its momentum is P imp Q/m * . This is also seen from perturbative calculations, not limited to the exactly solvable case considered in our paper [48]. Figure 10: The reduced density matrix (y) is examined for a gas with N = 40 particles.…”

Strong-coupling Bose polarons in one dimension: Condensate deformation and modified Bogoliubov phonons

“…These expressions agree with previous findings in Refs. [43,45]. It is interesting to note that for η → ∞, Eq.…”

“…Thus the condensate must be stationary far away from the impurity up to 1/L corrections. Solutions of the mean-field equations exist in the literature where the phase is not periodic [42,47] and have been applied to the 1D polaron before [43][44][45]. The nonperiodic phase corresponds to unphysical sources at the boundary and leads to wrong predictions such as a negative kinematic polaron mass.…”

“…Another possible way to deal with the phase issue is to integrate the phaseout, as has been done in Ref. [45]. Upon considering quantum fluctuations on top of the mean-field solution, none of the above-mentioned methods allow a straightforward generalization.…”

“…Our treatment carries over naturally to higher dimensional systems with the only difference that the mean-field solutions have to be obtained numerically. Other treatments of the 1D polaron based on a factorization of the N-particle wave function in the LLP frame exist that take the deformation of the condensate into account [42][43][44][45]. The scope of extending them to incorporate quantum fluctuations is limited, however.…”