Response of the polaron system consisting of an impurity in a Bose-Einstein condensate to Bragg spectroscopy

Abstract

We expand the existing polaron response theory, expressed within the Mori-Zwanzig projection operator formalism applicable for the transfer of arbitrary energy and zero momentum, for the case of finite momentum exchange. A general formula is then derived that can be used to calculate the response of a system to a probe that transfers both momentum and energy to the system. The main extension of the existing polaron response theory is the finite momentum exchange, which was not needed until now, since it is negligible for optical absorption. However, this formalism is needed to calculate the response of the polaronic system consisting of an impurity in a Bose-Einstein condensate (BEC) to Bragg spectroscopy. We show that the well-known features that appear in the optical absorption of the solid-state Fröhlich polaron are also present in the Bragg response of the BEC-impurity polaron. The f-sum rule is written in a form suitable to provide an independent consistency test for our results. The effect of lifetime broadening on the BEC-impurity spectrum is examined. The results derived here are discussed in the framework of an experimental realization consisting of a lithium impurity in a sodium condensate.

Bloch oscillations of bosonic lattice polarons

“…However, from the case of unconfined impurities it is known that the MF ansatz (27) is unable to capture strong-coupling physics [83] corresponding to the regime of very large interaction strength g eff [20,25,29,30]. To obtain self-consistency equations for the polaron ground state, we minimize the MF variational energy H MF :…”

“…In this paper, we study theoretically a polaron system that consists of an impurity atom confined to a species-selective optical lattice and a homogeneous BEC. The rich toolbox available in the field of ultracold atoms has already made possible a detailed experimental study of Fermi polarons [9][10][11][12][13][14] and stimulated active theoretical study of both Fermi [14][15][16][17][18] and Bose polarons [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. First experiments have also started to explore physics connected to the Bose polaron [34][35][36][37][38].…”

“…1(a) consisting of a single-impurity atom, confined to the lowest Bloch band of an optical lattice (hopping J , lattice constant a), immersed in a weakly interacting Bose-Einstein condensate (BEC). The BEC hosts gapless Bogoliubov phonons which can scatter off the impurity, leading to polaron formation [19,[27][28][29][30]32,33]. We subject the impurity to a constant force and examine in detail how the dynamics of the impurity will be affected by its interaction with the surrounding phonons.…”

Radio-frequency spectroscopy of polarons in ultracold Bose gases

“…The model (3), (4), with parameters (5), in its regime of validity, constitutes a generalized Fröhlich model of polarons in ultracold BECs [29][30][31][32].…”

“…The authors of Refs. [29][30][31][32] took quantum impurities into account within a many-body treatment of the Bogoliubov excitations of the BEC, but considered equilibrium properties in the regime of weak impurity-boson interactions.…”