Pattern formation in one-dimensional polaron systems and temporal orthogonality catastrophe

Abstract

Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity momentum and interactions. Following an interspecies interaction quench the temporal orthogonality catastrophe is identified, provided that bath-impurity interactions are sufficiently stronger than the intraspecies bath ones, thus generalizing the results of the confined case. This catastrophe originates from the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. For initially moving impurities, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated, resulting in a final polaronic state with reduced velocity. Our results clearly demonstrate the crucial role of non-linear excitations for determining the behavior of the onedimensional Bose polaron.

The effect of boson-boson interaction on the Bipolaron formation

“…We then discuss why the Yukawa potential is inadequate and also outline why some of the standard methods used to go beyond the Fröhlich model in the single impurity case do not generalize in a straightforward manner. We then show how those problems can be remedied in a conceptually simple and intuitive way by accounting for boson-boson interaction at the meanfield level, in line with previous treatments of bipolarons in 1D [40] and single polarons [34,[41][42][43][44][45][46][47]. This is done by applying the Lee-Low-Pines transformation [48] and transforming to the center of mass coordinates for the two impurities.…”

Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity

“…The heavy effective mass regime has potential experimental relevance, as it is relevant for realizing physical phenomena, such as Bloch oscillations [14,19]. Furthermore, a recent study demonstrates that the dynamical phenomenon of temporal orthogonality catastrophe is exhibited, given the impurity-boson couplings are sufficiently stronger than the intra-species background ones [28]. Another interesting feature shown in Figure 6b is that the impurity effective mass is approximately equal to the soliton mass for η = γ. the regime where η < γ (seen for γ = 0.2), the effective mass becomes very small in magnitude, trending towards zero.…”

“…While experimental studies have started, the quantitative understanding of impurity physics in a one-dimensional Bose gas is far from complete. The different theoretical approaches to the problem range from mean-field theory [25,26] and related variational theory [27][28][29] via the path-integral approach [30,31], the renormalization group [32][33][34] and flow equation [35] method to multiconfiguration time-dependent Hartree [36] and quantum Monte Carlo methods [37][38][39][40].…”

“…Many of the mentioned works focus on ground-state properties and effective mass of the one-dimensional Bose polaron with either zero or a very small total momentum. Although the dynamics of impurities have also been actively studied [28,29,36,41], limited understanding has been achieved on the full dispersion relation of a Bose gas coupled with a mobile impurity. There are analytical results on the dispersion relations restricted to specific models, such as the Yang-Gaudin model [42], and the Luttinger liquid [43].…”

Inducing spin-order with an impurity: phase diagram of the magnetic Bose polaron

“…We use the variational nonperturbative multi-layer multi-configuration time-dependent Hartree method for atomic mixtures (ML-MCTDHX) [42] to calculate the spin-order properties of an impurity immersed in a Bose gas. This method treats the impurity-gas system beyond the usual Bogoliubov treatment and thus the Fröhlich model [43], as well as to account for boson-boson correlations beyond the Lee-Low-Pines approach [44].…”