Quantum Monte Carlo study of the Bose-polaron problem in a one-dimensional gas with contact interactions

Abstract

We present a theoretical study based upon quantum Monte Carlo methods of the Bose polaron in onedimensional systems with contact interactions. In this instance of the problem of a single impurity immersed in a quantum bath, the medium is a Lieb-Liniger gas of bosons ranging from the weakly interacting to the Tonks-Girardeau regime, whereas the impurity is coupled to the bath via a different contact potential, producing both repulsive and attractive interactions. Both the case of a mobile impurity, having the same mass as the particles in the medium, and the case of a static impurity with infinite mass are considered. We make use of numerical techniques that allow us to calculate the ground-state energy of the impurity, its effective mass, and the contact parameter between the impurity and the bath. These quantities are investigated as a function of the strength of interactions between the impurity and the bath and within the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. This heavy impurity hardly moves within the medium, thereby realizing the "self-localization" regime of the Landau-Pekar polaron. Furthermore, we compare our results with predictions of perturbation theory valid for weak interactions and with exact solutions available when the bosons in the medium behave as impenetrable particles.

Analytical approach to the Bose-polaron problem in one dimension

“…Our approach is well-suited for studying the energy and structural properties of the Bose polaron problem, and for investigating systems with finite number of particles. To illustrate this statement, we present analytical expressions for the ground state energy and contact parameter in the thermodynamic limit and show that they agree with the recent numerical results based upon the quantum Monte Carlo method [30]. Furthermore, we test our method for finite systems using results of a numerical similarity renormalization group method as a benchmark.…”

“…To this end, we show in Figs. 1 and 2 [30]. Note that here only the data points without error bars are included.…”

“…However, theoretical approaches face challenges in describing these parameter regimes if the boson-impurity interactions are strong [38]. In this case accurate results can be obtained only numerically using Monte-Carlo methods [30,38], and analytical calculations that can unravel underlying physics and correlations are highly desirable. In this Rapid Communication, we introduce a possible theoretical formalism for performing such calculations.…”

“…Fortunately, experiments with cold atomic gases, realizing the idea of a quantum simulator [7], open up the possibility to create and study the Bose polaron [8][9][10][11][12][13][14][15] in a laboratory. This intriguing possibility motivated a flurry of recent theoretical works on this problem [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Impurity states in the one-dimensional Bose gas

“…There is also an experimental realization of the one-dimensional Bose polaron [35], where a minority of 41 K atoms immersed in the 87 Rb medium was observed during expansion and the prediction for the impurity effective mass within Feynman's framework was given. Essentially exact recent Monte Carlo simulations [36] revealed the impact of the considerable strong phonon-mediated interaction on the properties of a one-dimensional Bose polaron and to describe the system properly one needs to go beyond [37] the Fröhlich model in this case.…”