3Heimpurity excitation spectrum in liquid4He

Abstract

We microscopically evaluate the excitation spectrum of the 3 He impurity in liquid 4 He at Tϭ0 and compare it with the experimental curve at equilibrium density. The adopted correlated basis perturbative scheme includes up to two independent phonons, intermediate correlated states, and the correlation operator is built up with two-and three-body correlation functions. The experimental spectrum is well described by the theory along all the available momentum range. A marked deviation from the simple Landau-Pomeranchuck quadratic behavior is found and the momentum-dependent effective mass of the impurity increases by ϳ50% at q ϳ1.7 Å Ϫ1 with respect to its qϭ0 value. 6 There are also theoretical indications of a deviation of the spectrum from the LP form. 7,8 The presence of a possible rotonlike structure in e(q) near the crossing with the 4 He phonon-roton spectrum was supposed in Ref. 9 but not confirmed in Refs. 7, 8. However, in Ref. 8 an excitation spectrum quite higher than the experimental one was found.Here we will employ the CBF machinery of Ref. 5 ͑here-after denoted as I͒ to compute, in a microscopic way, the whole impurity spectrum. The CBF basis used in I consisted in correlated n-phonon states He correlation functionsand F 3 is given by the correspondent product of triplet correlations f (␣,␤,␥) (r ␣ ,r ␤ ,r ␥ ). The correlation functions are variationally obtained by minimizing the g.s. energy of the system E 0 . The procedure is outlined in I, where a parametrized form for the triplet correlations was used and the Jastrow factors were obtained by the Euler equations ␦E 0 /␦ f (␣␤) ϭ0. The equations were solved within the hypernetted chain ͑HNC͒ framework and the scaling approximation for the elementary diagrams. 11The Aziz interatomic potential 12 was used in the minimization process.The perturbative calculation of I included one independent phonon ͑OIP͒ and two independent phonon ͑TIP͒ states and all the diagrams corresponding to successive rescatterings of the one phonon ͑ROP͒ states. This contribution was obtained by solving a Dysonlike equation in the correlated basis. While the correlation factors are intended to care for the short-range modifications of the ground state wave function due to the strongly repulsive interatomic potential, the PHYSICAL REVIEW B 1 SEPTEMBER 1998-I VOLUME 58, NUMBER 9 PRB 58 0163-1829/98/58͑9͒/5209͑4͒/$15.00 5209

Quasiparticle nature of the Bose polaron at finite temperature

“…Also, our results do not show any signature of a second peak in S(q, ω) as initial perturbative estimations claimed [24]. Similar results to the ones obtained here appeared time ago for the problem of a single 3 He impurity in a 4 He bath [39,40].…”

Few particles with an impurity in a one-dimensional harmonic trap

“…The study of impurities interacting with a quantum bath is of relevance in many branches of physics. Examples range from the famous problems of electrons coupled to ionic crystals [1] and 3 He impurities in liquid Helium [2,3] to nucleon impurities in neutron matter [4]. More recently, ultracold atom experiments [5,6] have opened a new avenue for probing impurities in quantum baths, offering a unique setting to control impurity-bath systems.…”

Renormalization group study of Bose polarons

“…Such impurity is understood as a dressed quasiparticle referred to as a polaron. Impurities in bosonic baths have been studied in a variety of configurations and played a key role in elucidating the physics of helium liquids [2,3]. The polaron problem has been extensively studied also in fermionic mediums, particularly in condensed matter physics [4] and ultracold atoms [5][6][7][8][9][10][11][12][13][14][15][16].…”