Polaronic mass renormalization of impurities in BEC: correlated Gaussian wavefunction approach

Shchadilova, Yulia E.; Grusdt, Fabian; Rubtsov, Alexey N.; Demler, Eugene

doi:10.48550/arxiv.1410.5691

Cited by 10 publications

(22 citation statements)

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“…Results from Feynman path-integral calculations and diagrammatic Monte Carlo (MC) calculations -both taken from Ref. [105] -are compared to MF theory, the RG approach and to variational correlated Gaussian wavefunctions (CGWs) [57]. The results are sensitive to the value of the UV momentum cut-off Λ 0 , here Λ 0 = 2000/ξ.…”

Section: Renormalization Group Approachmentioning

confidence: 99%

“…We close this chapter by discussing an alternative approach [57,[122][123][124] to describing phonon correlations in the polaron cloud which is closely related to the RG method. This approach is variational and relies on the refinement of the mean-field wavefunction formulated in the polaron frame (i.e.…”

Section: Gaussian Variational Approachmentioning

confidence: 99%

“…Thus most of the progress in understanding of polarons came from numerical methods such as diagrammatic Monte Carlo analysis [53,54]. Two exceptions come from recently suggested semi-analytical methods that used non-perturbative techniques of renormalization group analysis [55,56] and Gaussian variational wavefunction [57] and demonstrated excellent agreement with Monte-Carlo calculations (for a review of earlier work on variational wavefunctions see Ref. [58]).…”

Section: Introductionmentioning

confidence: 99%

“…Recent revival of interest in the problem of mobile impurities interacting with a bath of phonons [55,57, comes from the rapid progress in the field of ultracold atoms. This new experimental platform not only allows to create a large variety of polaronic systems with different impurity masses and tunable interactions [44,56,[81][82][83][84][85], but also provides a new toolbox for studying equilibrium and dynamical properties of polarons [42,51,65,83,84,[86][87][88][89].…”

Section: Introductionmentioning

confidence: 99%

“…Traditional approaches such as mean-field, Feynman variational ansatz, and Landau-Pekar strong coupling expansion have a built-in suppression of the high energy modes, which precludes them from capturing the log-divergence. One needs more sophisticated techniques, such as renormalization group approach discussed in these lecture notes or Gaussian variational wavefunctions introduced in [57], to capture this physics.…”

Section: Introductionmentioning

confidence: 99%

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New theoretical approaches to Bose polarons

Grusdt¹,

Demler²

2015

Preprint

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The Fröhlich polaron model describes a ubiquitous class of problems concerned with understanding properties of a single mobile particle interacting with a bosonic reservoir. Originally introduced in the context of electrons interacting with phonons in crystals, this model found applications in such diverse areas as strongly correlated electron systems, quantum information, and high energy physics. In the last few years this model has been applied to describe impurity atoms immersed in Bose-Einstein condensates of ultracold atoms. The tunability of microscopic parameters in ensembles of ultracold atoms and the rich experimental toolbox of atomic physics should allow to test many theoretical predictions and give us new insights into equilibrium and dynamical properties of polarons. In these lecture notes we provide an overview of common theoretical approaches that have been used to study BEC polarons, including Rayleigh-Schrödinger and Green's function perturbation theories, self-consistent Born approximation, mean-field approach, Feynman's variational path integral approach, Monte Carlo simulations, renormalization group calculations, and Gaussian variational ansatz. We focus on the renormalization group approach and provide details of analysis that have not been presented in earlier publications. We show that this method helps to resolve striking discrepancy in polaron energies obtained using mean-field approximation and Monte Carlo simulations. We also discuss applications of this method to the calculation of the effective mass of BEC polarons. As one experimentally relevant example of a non-equililbrium problem we consider Bloch oscillations of Bose polarons and demonstrate that one should find considerable deviations from the commonly accepted phenomenological Esaki-Tsu model. We review which parameter regimes of Bose polarons can be achieved in various atomic mixtures.

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Section: Renormalization Group Approachmentioning

confidence: 99%

Section: Gaussian Variational Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New theoretical approaches to Bose polarons

Grusdt¹,

Demler²

2015

Preprint

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Real-time dynamics of an impurity in an ideal Bose gas in a trap

Volosniev¹,

Hammer²,

Zinner³

2015

Phys. Rev. A

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We investigate the behavior of a harmonically trapped system consisting of an impurity in a dilute ideal Bose gas after the boson-impurity interaction is suddenly switched on. As theoretical framework, we use a field theory approach in the space-time domain within the T-matrix approximation. We establish the form of the corresponding T-matrix and address the dynamical properties of the system. As a numerical application, we consider a simple system of a weakly interacting impurity in one dimension where the interaction leads to oscillations of the impurity density. Moreover, we show that the amplitude of the oscillations can be driven by periodically switching the interaction on and off.

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Quantum impurity in a one-dimensional trapped Bose gas

2015

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We present a new theoretical framework for describing an impurity in a trapped Bose system in one spatial dimension. The theory handles any external confinement, arbitrary mass ratios, and a weak interaction may be included between the Bose particles. To demonstrate our technique, we calculate the ground state energy and properties of a sample system with eight bosons and find an excellent agreement with numerically exact results. Our theory can thus provide definite predictions for experiments in cold atomic gases.PACS numbers: 03.75. Mn,67.85.Pq An impurity interacting with a reservoir of quantum particles is an essential problem of fundamental physics. Famous examples include a single charge in a polarizable environment, the Landau-Pekar polaron [1, 2], a neutral particle in superfluid 4 He [3], a magnetic impurity in a metal resulting in the Kondo effect [4], and a single scattering potential inside an ideal Fermi gas [5,6]. The latter system is famous for the Anderson's orthogonality catastrophe [7]. In these settings the impurity behavior can provide key insights into the many-body physics and guide our understanding of more general setups.A complicating feature of many impurity problems is the presence of interactions at a level that often precludes the use of perturbative analysis and self-consistent mean-field approximations. This implies that analytical approaches are highly desirable and exact solutions are, when available, coveted tools for benchmarking other techniques. This is particularly true for one-dimensional (1D) homogeneous systems where solutions can often be found based on the Bethe ansatz [8][9][10][11][12][13]. These solutions are the essential ingredients for our analytical understanding of highly controllable experiments with cold atoms [14][15][16][17][18][19]. For instance, the exactly solvable problem of the single impurity in a 1D Fermi sea [10] -the Fermi polaron -can be used to study the atom-by-atom formation of a 1D Fermi sea [20].While Fermi polarons have been studied intensively in recent times using cold atomic setups both experimentally and theoretically [21][22][23][24][25], the physics of impurities in a bosonic environment is only now becoming a frontier in cold atom experiments [26][27][28][29]. This pursuit requires theoretical models for describing the Bose polaron [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], where, in contrast to the Fermi polaron, an exact solution is not known even for a homogeneous 1D system. Here we provide a new theoretical framework that captures the properties of an impurity in a bosonic bath confined in one spatial dimension. Our (semi)-analytical theory thus provides a state-of-the-art tool for exploring the properties of Bose polarons in 1D.The proposed framework works with a zero-range potential of any strength and handles any number of ma- FIG. 1: (color online) a)A sketch of the doubly-degenerate ground state for the system of one A and eight B particles trapped in a one-dimensional harmonic potential ...

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Polaronic mass renormalization of impurities in BEC: correlated Gaussian wavefunction approach

Cited by 10 publications

References 0 publications

New theoretical approaches to Bose polarons

New theoretical approaches to Bose polarons

Real-time dynamics of an impurity in an ideal Bose gas in a trap

Quantum impurity in a one-dimensional trapped Bose gas

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