Yulia E. Shchadilova

Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem

When a mobile impurity interacts with a many-body system, such as a phonon bath, a polaron is formed. Despite the importance of the polaron problem for a wide range of physical systems, a unified theoretical description valid for arbitrary coupling strengths is still lacking. Here we develop a renormalization group approach for analyzing a paradigmatic model of polarons, the so-called Fröhlich model, and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. They are found to be logarithmically divergent with the ultra-violet cut-off, but physically meaningful regularized polaron energies are also presented. Moreover, we calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed.

Quantum Dynamics of Ultracold Bose Polarons

We analyze the dynamics of Bose polarons in the vicinity of a Feshbach resonance between the impurity and host atoms. We compute the radio-frequency absorption spectra for the case when the initial state of the impurity is noninteracting and the final state is strongly interacting with the host atoms. We compare results of different theoretical approaches including a single excitation expansion, a self-consistent T-matrix method, and a time-dependent coherent state approach. Our analysis reveals sharp spectral features arising from metastable states with several Bogoliubov excitations bound to the impurity atom. This surprising result of the interplay of many-body and few-body Efimov type bound state physics can only be obtained by going beyond the commonly used Fröhlich model and including quasiparticle scattering processes. Close to the resonance we find that strong fluctuations lead to a broad, incoherent absorption spectrum where no quasiparticle peak can be assigned.

Strong-coupling Bose polarons in a Bose-Einstein condensate

We use a non-perturbative renormalization group approach to develop a unified picture of the Bose polaron problem, where a mobile impurity is strongly interacting with a surrounding BoseEinstein condensate (BEC). A detailed theoretical analysis of the phase diagram is presented and the polaron-to-molecule transition is discussed. For attractive polarons we argue that a description in terms of an effective Fröhlich Hamiltonian with renormalized parameters is possible. Its strong coupling regime is realized close to a Feshbach resonance, where we predict a sharp increase of the effective mass. Already for weaker interactions, before the polaron mass diverges, we predict a transition to a regime where states exist below the polaron energy and the attractive polaron is no longer the ground state. On the repulsive side of the Feshbach resonance we recover the repulsive polaron, which has a finite lifetime because it can decay into low-lying molecular states. We show for the entire range of couplings that the polaron energy has logarithmic corrections in comparison with predictions by the mean-field approach. We demonstrate that they are a consequence of the polaronic mass renormalization which is due to quantum fluctuations of correlated phonons in the polaron cloud.

Rotation of a single acetylene molecule on Cu(001) by tunneling electrons in STM.

We study the elementary processes behind one of the pioneering works on scanning tunneling microscope controlled reactions of single molecules [Stipe et al., Phys. Rev. Lett. 81, 1263 (1998)]. Using the Keldysh-Green function approach for the vibrational generation rate in combination with density functional theory calculations to obtain realistic parameters we reproduce the experimental rotation rate of an acetylene molecule on a Cu(100) surface as a function of bias voltage and tunneling current. This combined approach allows us to identify the reaction coordinate mode of the acetylene rotation and its anharmonic coupling with the C-H stretch mode. We show that three different elementary processes, the excitation of C-H stretch, the overtone ladder climbing of the hindered rotational mode, and the combination band excitation together explain the rotation of the acetylene molecule on Cu(100).

Role of coherence in transport through engineered atomic spin devices

We give a further step in the quantum mechanical description of engineered atomic spin structures by deriving a master equation of the Redfield type that governs the dynamics of the atomic spin density matrix. By generalizing this approach to charge-specific density matrices, we are able to describe magnetic transport quantities, such as the average inelastic current and the shot noise, accessible by tunneling spectroscopy. Our method suitably describes moderate lead-atom coupling regimes where quantum coherence effects cannot be disregarded. We contrast our approach with the existing descriptions in terms of rate equations and show examples where coherence effects are crucial to understand the physics of spin-polarized tunnel current through spin structures.

Transient phases and dynamical transitions in the post-quench evolution of the generalized Bose-Anderson model

The exact description of the time evolution of open correlated quantum systems remains one of the major challenges of the condensed matter theory, specially for asymptotic long times where most numerical methods fail. Here, the post-quench dynamics of the

Modeling the metastable dynamics of correlated structures

N

Isotope effect in acetylene C2H2 and C2D2 rotations on Cu(001)

-component Bose-Anderson impurity model is studied in the

Two-dimensional Bose gas of tilted dipoles: Roton instability and condensate depletion

N\to\infty

Quantum statistical ensemble for emissive correlated systems

limit. The equilibrium phase diagram is similar to that of the Bose-Hubbard model in that it contains local versions of the Mott and Bose phases. Using a numerically exact procedure we are able to study the real time evolution including asymptotic long time regimes. The formation of long-lived transient phases is observed for quench paths crossing foreign phases. For quenches inside the local Bose condensed phase, a dynamical phase transition is reported, that separates the evolution towards a new equilibrium state and a regime characterized at large times by a persistent phase rotation of the order parameter. We explain how such non-decaying mode can exist in the presence of a dissipative bath. We discuss the extension of our results to the experimental relevant finite-