Anomalous screening of quantum impurities by a neutral environment

It is a common knowledge that an effective interaction of a quantum impurity with an electromagnetic field can be screened by surrounding charge carriers, whether mobile or static. Here we demonstrate that very strong, `anomalous' screening can take place in the presence of a neutral, weakly-polarizable environment, due to an exchange of orbital angular momentum between the impurity and the bath. Furthermore, we show that it is possible to generalize all phenomena related to isolated impurities in an external field to the case when a many-body environment is present, by casting the problem in terms of the angulon quasiparticle. As a result, the relevant observables such as the effective Rabi frequency, geometric phase, and impurity spatial alignment are straightforward to evaluate in terms of a single parameter: the angular-momentum-dependent screening factor.Comment: 6 pages, 2 figures including appendi

Anyonic statistics of quantum impurities in two dimensions

We demonstrate that identical impurities immersed in a two-dimensional many-particle bath can be viewed as flux-tube-charged-particle composites described by fractional statistics. In particular, we find that the bath manifests itself as an external magnetic flux tube with respect to the impurities, and hence the time-reversal symmetry is broken for the effective Hamiltonian describing the impurities. The emerging flux tube acts as a statistical gauge field after a certain critical coupling. This critical coupling corresponds to the intersection point between the quasiparticle state and the phonon wing, where the angular momentum is transferred from the impurity to the bath. This amounts to a novel configuration with emerging anyons. The proposed setup paves the way to realizing anyons using electrons interacting with superfluid helium or lattice phonons, as well as using atomic impurities in ultracold gases.Comment: 6 pages, 2 figur

Emergence of non-abelian magnetic monopoles in a quantum impurity problem

Recently it was shown that molecules rotating in superfluid helium can be described in terms of the angulon quasiparticles (Phys. Rev. Lett. 118, 095301 (2017)). Here we demonstrate that in the experimentally realized regime the angulon can be seen as a point charge on a 2-sphere interacting with a gauge field of a non-abelian magnetic monopole. Unlike in several other settings, the gauge fields of the angulon problem emerge in the real coordinate space, as opposed to the momentum space or some effective parameter space. Furthermore, we find a topological transition associated with making the monopole abelian, which takes place in the vicinity of the previously reported angulon instabilities. These results pave the way for studying topological phenomena in experiments on molecules trapped in superfluid helium nanodroplets, as well as on other realizations of orbital impurity problems.Comment: 6 pages, 2 figure

Above-threshold ionization with highly-charged ions in super-strong laser fields: I. Coulomb-corrected strong field approximation

Aiming at the investigation of above-threshold ionization in super-strong laser fields with highly charged ions, we develop a Coulomb-corrected strong field approximation (SFA). The influence of the Coulomb potential of the atomic core on the ionized electron dynamics in the continuum is taken into account via the eikonal approximation, treating the Coulomb potential perturbatively in the phase of the quasi-classical wave function of the continuum electron. In this paper the formalism of the Coulomb-corrected SFA for the nonrelativistic regime is discussed employing velocity and length gauge. Direct ionization of a hydrogen-like system in a strong linearly polarized laser field is considered. The relation of the results in the different gauges to the Perelomov-Popov-Terent'ev imaginary-time method is discussed.Comment: 8 pages, 3 figure

Above-threshold ionization with highly-charged ions in super-strong laser fields: II. Relativistic Coulomb-corrected strong field approximation

We develop a relativistic Coulomb-corrected strong field approximation (SFA) for the investigation of spin effects at above-threshold ionization in relativistically strong laser fields with highly charged hydrogen-like ions. The Coulomb-corrected SFA is based on the relativistic eikonal-Volkov wave function describing the ionized electron laser-driven continuum dynamics disturbed by the Coulomb field of the ionic core. The SFA in different partitions of the total Hamiltonian is considered. The formalism is applied for direct ionization of a hydrogen-like system in a strong linearly polarized laser field. The differential and total ionization rates are calculated analytically. The relativistic analogue of the Perelomov-Popov-Terent'ev ionization rate is retrieved within the SFA technique. The physical relevance of the SFA in different partitions is discussed.Comment: 11 pages, 4 figure

Analytical approach to the Bose polaron via a q-deformed Lie algebra

We present a novel approach to the polaron problem developed on the notion of quantum groups, also known as $q$-deformed Lie algebras. In this approach, the presence of an impurity in a bath can be depicted as a deformation of the Lie algebra of the bosonic creation and annihilation operators of the bath. In particular, we introduce a simple $q$-deformed bosonic \textit{parent} Hamiltonian whose truncation on the quartic level in the usual bosonic creation and annihilation operators corresponds to the Fr\"{o}hlich-Bogoliubov polaron Hamiltonian. By using the $q$-deformed Lie algebra, the introduced parent Hamiltonian allows us to derive the ground state energy of the Fr\"{o}hlich-Bogoliubov Hamiltonian analytically for the regime where the Bogoliubov dispersion law takes the phonon-like form.Comment: 5 pages, 1 figure with a Supplemental Materia

A Hamiltonian for the Hilbert-P\'olya Conjecture

We construct a similarity transformation of the Berry-Keating Hamiltonian, whose eigenfunctions vanish at the Dirichlet boundary as a consequence of the Riemann hypothesis (RH) so that the eigenvalues correspond to the imaginary parts of the nontrivial zeros of the Riemann zeta function. Conversely, if one is able to prove the reality of the eigenvalues, which corresponds to proving that the similarity transformation is bounded and boundedly invertible on the domain where the Berry-Keating Hamiltonian is self-adjoint, then the RH follows. In an attempt to show the latter heuristically, we first introduce an $su(1,1)$ algebra and then define an effective Hamiltonian in the Mellin space, where the Dirichlet boundary condition manifests itself as an integral boundary condition. The effective Hamiltonian can be transformed into the Berry-Keating Hamiltonian, $\hat{H}_\text{BK}$, without altering the domain on which $\hat{H}_\text{BK}$ is self-adjoint. In an essence, the nontrivial zeros of the Riemann zeta function follow from the eigenvalue equation, $\hat{H}_\text{BK} \, h_s (z) = \varepsilon_s \, h_s (z)$, with the integral boundary condition $\int_0^\infty dz \, (1+ e^z)^{-1} h_s(z) = 0$.Comment: 4 pages. arXiv admin note: substantial text overlap with arXiv:2211.0189