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International Journal of Modern Physics B

Two-dimensional Bose polaron using diffusion Monte Carlo method

E. Akaturk, B. Tanatar

Published Aug 20, 2019• 4 citations
Publisher

Abstract

We investigate the properties of a mobile impurity immersed in a two-dimensional (2D) Bose gas at zero temperature using quantum Monte Carlo (QMC) methods. The repulsive boson–boson and impurity-boson interactions are modeled by hard-disk potentials with positive scattering lengths a and b, respectively, taken to be equal to the scattering lengths. We calculate the polaron energy and effective mass for the density parameter na2 [Formula: see text] 1 and the ratio a/b. We find that at low densities perturbation theory adequately describes the simulation results. As the impurity-boson interaction strength increases, the polaron mass is enhanced. Additionally, we calculate the structural properties of the Bose system, such as the impurity-boson pair-correlation function and the change of the density profile around the impurity.

DOI
10.1142/s0217979219502382

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We investigate the properties of a mobile impurity immersed in a two-dimensional (2D) Bose gas at zero temperature using quantum Monte Carlo (QMC) methods. The repulsive boson–boson and impurity-boson interactions are modeled by hard-disk potentials with positive scattering lengths a and b, respectively, taken to be equal to the scattering lengths. We calculate the polaron energy and effective mass for the density parameter na2 [Formula: see text] 1 and the ratio a/b. We find that at low densities perturbation theory adequately describes the simulation results. As the impurity-boson interaction strength increases, the polaron mass is enhanced. Additionally, we calculate the structural properties of the Bose system, such as the impurity-boson pair-correlation function and the change of the density profile around the impurity.
We investigate the properties of an impurity immersed in a dilute Bose gas at zero temperature using quantum Monte Carlo methods. The interactions between bosons are modeled by a hard-sphere potential with scattering length aaa, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length bbb can be varied by adjusting the well depth. We characterize the attractive and the repulsive polaron branch by calculating the binding energy and the effective mass of the impurity. Furthermore, we investigate the structural properties of the bath, such as the impurity-boson contact parameter and the change of the density profile around the impurity. At the unitary limit of the impurity-boson interaction, we find that the effective mass of the impurity remains smaller than twice its bare mass, while the binding energy scales with ${\ensuremath{\hbar}}^{2}{n}^{2/3}/m$, where nnn is the density of the bath and mmm is the common mass of the impurity and the bosons in the bath. The implications for the phase diagram of binary Bose-Bose mixtures at low concentrations are also discussed.
In this thesis we investigate the properties of impurities immersed in a dilute Bose gas at zero temperature using quantum Monte-Carlo methods. The interactions between bosons are modeled by a hard sphere potential with scattering length a, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length b can be varied by adjusting the well depth. We calculate the binding energy, the effective mass and the pair correlation functions of a impurity along the attractive and the repulsive polaron branch. In particular, at the unitary limit of the impurity-bosons interaction, we find that the binding energy is much larger than the chemical potential of the bath signaling that many bosons dress the impurity thereby lowering its energy and increasing its effective mass. We characterize this state by calculating the bosons-boson pair correlation function and by investigating the dependence of the binding energy on the gas parameter of the bosonic bath. We also investigate the ground-state properties of M impurities in a Bose gas at T=0. In particular, the energy and the phase diagram by using both quantum Monte-Carlo and mean field methods.
Abstract The detailed mean-field (MF) treatment of the Bose polaron problem in two and three dimensions is presented. Particularly, assuming that impurity is immersed in the dilute Bose gas and interacts with bosons via the hard-sphere two-body potential, we calculate the low-momentum parameters of its spectrum, namely, the binding energy and the effective mass. The limits of applicability of the MF approach to a problem of mobile impurity in Bose–Einstein condensates are discussed by comparing our results to the Monte Carlo simulations data.
We study the quasiparticle properties of a dipolar impurity immersed in a two-dimensional dipolar bath. We use the ab initio diffusion Monte Carlo technique to determine the polaron energy, effective mass, and quasiparticle residue. We find that both the polaron energy and quasiparticle residue follow a universal behavior with respect to the polarization angle when properly scaled in terms of the scattering length. This trend is maintained over a wide range of values of the gas parameter, even in the highly correlated regime. Instead, the effective mass shows growing anisotropy as the tilting angle is increased, which is induced, mainly, by the anisotropy of the impurity-boson dipole-dipole interaction. Surprisingly, the effective mass is larger in the direction of minimum interparticle repulsion. Finally, we use our Monte Carlo results to check the accuracy of perturbative approaches and determine their range of validity in terms of the gas parameter.
We present a theoretical study based upon quantum Monte Carlo methods of the Bose polaron in one-dimensional 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.
We study the repulsive polaron problem in a two-component two-dimensional system of fermionic atoms. We use two different interaction models: a short-range (hard-disk) potential and a dipolar potential. In our approach, all the atoms have the same mass and we consider the system to be composed of a uniform bath of a single species and a single atomic impurity. We use the diffusion Monte Carlo method to evaluate polaron properties such as its chemical potential and pair distribution functions, together with a discussion on the deficit of volume induced by the impurity. We also evaluate observables that allow us to determine the validity of the quasiparticle picture: the quasiparticle residue and the effective mass of the polaron. Employing two different potentials allows us to identify the universality regime, where the properties depend only on the gas parameter nas2n{a}_{s}^{2}nas2​ fixed by the bath density and the two-dimensional scattering length.