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

Abstract

A few years ago, flow equations were introduced as a technique for calculating the energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the energies, densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities.For a single mobile impurity, we show that the flow equation results agree well with the mean-field results obtained upon the Lee-Low-Pines transformation if the phase coherence length is larger than the healing length of the condensate. This agreement occurs for all values of the boson-impurity interaction strength as long as the boson-boson interaction is weak.For two static impurities, we calculate repulsive and attractive impurity-impurity correlations mediated by the Bose gas. We find that leading order perturbation theory fails when the boson-impurity interaction strength is larger than the boson-boson interaction strength. We note that the mean-field approximation reproduces the flow equation results for weak boson-boson interactions.

Entangling lattice-trapped bosons with a free impurity: impact on stationary and dynamical properties

“…In this latter context, an impurity species is embedded in an environment of the majority species called the medium. The presence of a finite impurity-medium coupling leads to an effective picture where the impurity properties deviate from the bare particle case exhibiting, for instance, an effective mass [15][16][17][18] and induced interactions [19][20][21][22] mediated by the medium. The resultant states are often called polarons [23,24] and have been experimentally realized mainly in higher-dimensions [25][26][27][28][29] and to a lesser extent in 1D [13,30] using spectroscopic schemes.…”

Mediated interaction between polarons in a one-dimensional Bose gas

“…In Bose gas environments various properties of a single polaron have been studied [30][31][32][33][34][35][36][37][38][39][40]. In cases when two (or more) impurities are present in the system, the induced interaction between them due to the interaction with particles of the medium is one of the most basic problems [41][42][43][44][45]. For identical impurities that are locally and weakly coupled to the Bose gas, an exponentially small attractive interaction proportional to e −2r/ξ was found in Ref.…”