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

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

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

Relativistic features and time delay of laser-induced tunnel-ionization

Tunnel-ionization is investigated in the framework of relativistic quantum mechanics. For an arbitrary constant electromagnetic field a gauge invariant energy operator is introduced in order to identify the classically forbidden region for tunnel-ionization. Furthermore, relativistic features of tunnel-ionization are explored. A one-dimensional intuitive picture predicts that the ionized electron wave packet in the relativistic regime experiences a momentum shift along the laser’s propagation direction. This is shown to be consistent with the well-known strong field approximation. Furthermore, spin dynamics in tunnel-ionization process is discussed in the standard as well as in the dressed strong field approximation. Next, the tunneling time delay is investigated for tunnel-ionization by extending the definition of the Wigner time delay. Later, this concept is redefined in terms of the phase of the fixed energy propagator. The developed formalism is applied to the deep-tunneling and the near-threshold-tunneling regimes. It is shown that in the latter case signatures of the tunneling time delay can be measurable at remote distance. Finally, the path-dependent formulation of gauge theory is discussed. It is demonstrated that this equivalent formulation of gauge theory leads to a canonical gauge fixing, in which the Feynman path integral becomes more intuitive and the calculation of the quasiclassical propagator is considerably simplifie

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

The Wigner time delay for laser induced tunnel-ionization via the electron propagator

Recent attoclock experiments using the attsecond angular streaking technique enabled the measurement of the tunneling time delay during laser induced strong field ionization. Theoretically the tunneling time delay is commonly modelled by the Wigner time delay concept which is derived from the derivative of the electron wave function phase with respect to energy. Here, we present an alternative method for the calculation of the Wigner time delay by using the fixed energy propagator. The developed formalism is applied to the nonrelativistic as well as to the relativistic regime of the tunnel-ionization process from a zero-range potential, where in the latter regime the propagator can be given by means of the proper-time method.Comment: 5 pages, 4 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