Abstract:We present a general variational principle for the dynamics of impurity particles immersed in a quantum-mechanical medium. By working within the Heisenberg picture and constructing approximate time-dependent impurity operators, we can take the medium to be in any mixed state, such as a thermal state. Our variational method is consistent with all conservation laws and, in certain cases, it is equivalent to a finite-temperature Green's function approach. As a demonstration of our method, we consider the dynamics… Show more
“…A intriguing aspect would be to examine whether thermalization of the impurities dynamics takes place for strong repulsions in the framework of the eigenstate thermalization hypothesis [101]. An imperative prospect is to study the robustness of the emergent quasiparticle picture in the current setting in the presence of temperature effects [102,103]. Moreover, the study of induced interactions of two bosonic impurities immersed in a Fermi sea would be an interesting prospect especially in order to expose their dependence on the different statistics of the medium.…”
We study the ground state properties and non-equilibrium dynamics of two spinor bosonic impurities immersed in a one-dimensional bosonic gas upon applying an interspecies interaction quench. For the ground state of two non-interacting impurities we reveal signatures of attractive induced interactions in both cases of attractive or repulsive interspecies interactions, while a weak impurityimpurity repulsion forces the impurities to stay apart. Turning to the quench dynamics we inspect the time-evolution of the contrast unveiling the existence, dynamical deformation and the orthogonality catastrophe of Bose polarons. We find that for an increasing postquench repulsion the impurities reside in a superposition of two distinct two-body configurations while at strong repulsions their corresponding two-body correlation patterns show a spatially delocalized behavior evincing the involvement of higher excited states. For attractive interspecies couplings, the impurities exhibit a tendency to localize at the origin and remarkably for strong attractions they experience a mutual attraction on the two-body level that is imprinted as a density hump on the bosonic bath.
“…A intriguing aspect would be to examine whether thermalization of the impurities dynamics takes place for strong repulsions in the framework of the eigenstate thermalization hypothesis [101]. An imperative prospect is to study the robustness of the emergent quasiparticle picture in the current setting in the presence of temperature effects [102,103]. Moreover, the study of induced interactions of two bosonic impurities immersed in a Fermi sea would be an interesting prospect especially in order to expose their dependence on the different statistics of the medium.…”
We study the ground state properties and non-equilibrium dynamics of two spinor bosonic impurities immersed in a one-dimensional bosonic gas upon applying an interspecies interaction quench. For the ground state of two non-interacting impurities we reveal signatures of attractive induced interactions in both cases of attractive or repulsive interspecies interactions, while a weak impurityimpurity repulsion forces the impurities to stay apart. Turning to the quench dynamics we inspect the time-evolution of the contrast unveiling the existence, dynamical deformation and the orthogonality catastrophe of Bose polarons. We find that for an increasing postquench repulsion the impurities reside in a superposition of two distinct two-body configurations while at strong repulsions their corresponding two-body correlation patterns show a spatially delocalized behavior evincing the involvement of higher excited states. For attractive interspecies couplings, the impurities exhibit a tendency to localize at the origin and remarkably for strong attractions they experience a mutual attraction on the two-body level that is imprinted as a density hump on the bosonic bath.
“…At finite temperature, we investigate the full spectral function of the Bose polaron within our variational approach [41]. Including all two-body correlations involving the impurity and a bosonic excitation, we recover the results of Ref.…”
Section: Introductionmentioning
confidence: 92%
“…The framework for our investigation of the Bose polaron at finite temperature is the variational approach for impurity dynamics first developed in Ref. [41] in the context of Fermi polarons. A variational method based on including only one excitation of the medium was first used to obtain the zero-temperature ground-state properties of the Fermi polaron [50] as well as the repulsive branch [51,52], and it has been demonstrated that such an approach is equivalent to a diagrammatic formulation [53].…”
Section: Variational Approachmentioning
confidence: 99%
“…For completeness, in the following we outline the variational approach of Ref. [41]. The key idea that distinguishes this method from the zero-temperature variational approach developed in Ref.…”
Section: Variational Approachmentioning
confidence: 99%
“…The time evolution governed by this equation conserves probability [41]; that is, ĉ 0 (t)ĉ † 0 (t) is constant. Specializing to the stationary variational impurity operators, these have coefficients of the form η j (t) = η j e −iEt .…”
We consider an impurity immersed in a Bose-Einstein condensate with tunable boson-impurity interactions. Such a Bose polaron has recently been predicted to exhibit an intriguing energy spectrum at finite temperature, where the ground-state quasiparticle evenly splits into two branches as the temperature is increased from zero [Guenther et al., Phys. Rev. Lett. 120, 050405 (2018)]. To investigate this theoretical prediction, we employ a recently developed variational approach that systematically includes multi-body correlations between the impurity and the finite-temperature medium, thus allowing us to go beyond previous finite-temperature methods. Crucially, we find that the number of quasiparticle branches is simply set by the number of hole excitations of the thermal cloud, such that including up to one hole yields one splitting, two holes yields two splittings, and so on. Moreover, this effect is independent of the impurity mass. We thus expect that the exact ground-state quasiparticle will evolve into a single broad peak for temperatures T > 0, with a broadening that scales as T 3/4 at low temperatures and sufficiently weak boson-boson interactions. In the zero-temperature limit, we show that our calculated ground-state polaron energy is in excellent agreement with recent quantum Monte Carlo results and with experiments. arXiv:1910.02620v1 [cond-mat.quant-gas]
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