The Seminars 2022: Term II

Stefan Rotter (Vienna University of Technology, Austria), 06/10/2022, 15:00 London time (=14:00 GMT)

Transforming space with non-Hermitian dielectrics

Abstract: Coordinate transformations are a versatile tool to mold the flow of light, enabling a host of astonishing phenomena such as optical cloaking with metamaterials. Moving away from the usual restriction that links isotropic materials with conformal transformations, we show how nonconformal distortions of optical space are intimately connected to the complex refractive index distribution of an isotropic non-Hermitian medium [1]. Remarkably, this insight is linked to the concept of “constant-intensity waves”, that were recently realized for the first time in optics using an optical mesh lattice [2]. We apply our approach to design a broadband unidirectional dielectric cloak, which relies on nonconformal coordinate transformations to tailor the non-Hermitian refractive index profile around a cloaked object. Our insights bridge the fields of two-dimensional transformation optics and non-Hermitian photonics. 

If time permits, I will also show a few slides on our recent realization of a massively degenerate coherent perfect absorber in which even very complex light fields are absorbed with close to perfect efficiency in a medium that would normally absorb light only very weakly [3]. 

[1] Krešić, Makris, Leonhardt, Rotter, Phys. Rev. Lett. 128, 183901 (2022)

[2] Steinfurth, Krešić, Weidemann, Kremer, Makris, Heinrich, Rotter, Szameit, Science Advances 8, eabl7412 (2022)

[3] Slobodkin, Weinberg, Hörner, Pichler, Rotter, Katz, Science 377, 995 (2022)

Marco Merkli (Memorial University of Newfoundland, Canada), 13/10/2022, 15:00 London time (=14:00 GMT)

Dynamics of entropy in bipartite quasi-Hermitian systems and their Hermitian counterparts

Abstract: A quasi-Hermitian quantum system can be mapped to a multitude of Hermitian systems by the Dyson map. All Hermitian systems thus obtained are globally unitarily equivalent but the unitary may entangle different parts of the whole system. The choice of the unitary in the Dyson map then leads to physically different Hermitian systems emerging from the same quasi-Hermitian system. We analyze the resulting dependence of the von Neumann entropy for an oscillator coupled to N other oscillators via a quasi-Hermitian Hamiltonian (a PT-symmetric Hamiltonian in the symmetry unbroken region). For this model, we explicitly find all Hermitian systems emerging by varying over all unitaries in the Dyson map. We show that the evolution of the entropy of the single oscillator in the Hermitian system depends on the choice of the unitary, but the period of the entropy is universally the same for all choices: it is exactly double that of the entropy of the quasi-Hermitian oscillator. We give a simple explanation of the origin of this phenomenon.

Fabio Bagarello (Università degli Studi di Palermo, Italy), 24/11/2022, 15:00 London time (=15:00 GMT)

A distributional approach to the inverted harmonic oscillator

Abstract: I show that the inverted harmonic oscillator (IHO) can be seen as a particular weak
limit of a Swanson-like model. In particular, the eigenvectors of the Hamiltonian of the IHO, and of its adjoint, are tempered distributions, weak limits of sequences of square-integrable functions. The bi-coherent states for the IHO are also constructed, and some of their properties
are deduced.

Ali Mostfazadeh (Koç University, Turkey), 01/12/2022, 15:00 London time (=15:00 GMT)

Propagating-wave approximation

Abstract: TBA

Abstract: We introduce an approximation scheme for performing scattering calculations in two dimensions that involves neglecting the contribution of the evanescent waves to the scattering amplitude. This corresponds to replacing the interaction potential with an associated energy-dependent nonlocal potential which does not couple to the evanescent waves.  We construct a transfer matrix for this class of nonlocal potentials and explore its representation in terms of the evolution operator for an effective non-unitary quantum system. The above approximation turns out to agree with first Born approximation for weak potentials, and similarly to the semiclassical approximation, becomes valid at high energies. We identify an infinite class of complex potentials for which this approximation scheme is exact and discuss its appealing practical and mathematical aspects. The latter allow for a rigorous proof of the existence of the associated transfer matrix.


– F. Loran and A. M., Phys. Rev. A 106, 032207 (2022)arXiv: 2204.05153 

 – F. Loran and A. M., J. Phys. A 55, 435202 (2022); arXiv: 2207.10054 

Marta Reboiro (University of La Plata, Argentina), 15/12/2022, 15:00 London time (=15:00 GMT)

PT-symmetry Hamiltonians at finite temperature

Abstract: The Double Green Function Formalism has been extensively used in dealing with the thermodynamics of quantum systems which evolved in time under the action of a given self-adjoined hamiltonian. In this work, we extend the formalism to include PT-symmetry hamiltonains. We apply the formalism to study the PT-symmetry Swanson hamiltonian at finite temperature, both in the PT and in the non-PT symmetry phase. We analyze the behaviour of the system, which is initially at equilibrium, when it is perturbed by a periodic time dependent interaction.