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.

Andrei Smilga (University of Nantes, France), 20/10/2022, 15:00 London time (=14:00 GMT)

Non-commutative quantum mechanics as an ordinary QM in disguise

Abstract: We start with the simplest non-commutative quantum systems including only two coordinates x,y with a nontrivial commutator [x,y] = iθ. We show that a naturally defined Hamiltonian of this treated in momentum space describes the plane motion in a constant magnetic field B = θ.
   Then we consider quantum mechanics on the more complicated noncommutative spaces characterized by the commutation relations [xa, xb] =iθ fabcxc where fabc are the structure constants of a Lie algebra. We note that this problem can be reformulated as an ordinary quantum problem in a commuting momentum space. The coordinates are then represented as linear differential operators x̂a = -i D̂a = -iRab (p) ∂/∂pb. Generically, the matrix Rab (p) represents a certain infinite series over the deformation parameter θ: Rab (p) = δab + ⋯. The deformed Hamiltonian, Ĥ = – ½ D̂a2 describes the motion along the corresponding group manifolds with the characteristic size of order θ-1. Their metrics are also expressed into certain infinite series in θ.
   For the algebras su(2) and u(2), it has been possible to represent the operators x̂a in a simple finite form. A byproduct of our study are new nonstandard formulas for the metrics on SU(2) ≈ S3 and on SO(3).
   For the algebra u(N>2), the corresponding Hamiltonian in momentum space turns out to be non-Hermitian and describes a motion along some manifold with complex metric. It is an open question whether one can still attribute a meaning to this problem is a pseudo-quasi-crypto spirit.

Emil Bergholtz (Stockholm University, Sweden), 27/10/2022, 15:00 London time (=14:00 GMT)

Topology of Non-Hermitian Systems

Abstract: Non-Hermitian “Hamiltonians” occur in the effective description of various physical settings ranging from classical photonics to quantum materials. Using simple examples, I will discuss topological aspects of such systems related to the non-Hermitian concept of exceptional degeneracies at which both eigenvalues and eigenvectors coalesce. I will also discuss how the bulk-boundary correspondence is modified in non-Hermitian systems and how this might be harnessed in novel sensor devices.

Cancelled: Jacob Muldoon (Indiana University Purdue University, US), 10/11/2022, 15:00 London time (=15:00 GMT)

Exploring Super-Quantum Temporal Correlations of Non-Hermitian Systems

Abstract: During the twentieth century, the probabilistic nature of quantum mechanics was demonstrated through an extensive list of multiple-measurement schemes.  The most well-known of these are Bell’s Inequalities, where entangled but spacially separated systems can yield correlations higher than possible in deterministic models.  A second set of measurement schemes, referred to as Leggett-Garg Inequalities (LGI), similarly demonstrate this quantum reality through the temporal correlations of a single system.  However, expanding Leggett-Garg Inequalities to open quantum systems requires that the coherences of the system be maintained.  Here we develop an expansion of the Leggett-Garg parameter K3 to open quantum systems through the framework of PT-symmetry, which predicts non-unitary but coherent evolution.  We show that open systems allow K3 ≥ 1.5, which marks the upper bound possible with unitary evolution.  We found that K3 approaches the algebraic bound as exceptional points are approached from the PT-symmetric regime, and that the algebraic bound is always achievable in the PT-broken regime.  Our findings can be recreated through the postselection of systems governed by the Lindblad master equation, allowing verification through existing experimental platforms.  Furthermore, our approach provides a framework for the expansion of multiple-measurement schemes such as other Leggett-Garg Inequalities, Bell Inequalities, or the Jarzynski Equality to non-Hermitian systems, while keeping the PT-symmetric, PT-broken, and trivially-broken regimes accessible.*

*In collaboration with Sourin Das Group and Kater Murch Lab

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)

TBA

Abstract: TBA

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.

Özlem Yeşiltaş (Gazi University, Turkey), 12/01/2023, 15:00 London time (=15:00 GMT)

Revisited Pseudosupersymmetric Approach To The Dirac Fields In Different Geometries

Abstract: In the previous work, pseudo-supersymmetry of the Dirac Hamiltonian in three -dimensional curved space-time was studied with a metric for an expanding de Sitter space-time which is two spheres [1]. This study includes pseudo-supersymmetric approach to the fermion motion in different geometries which are represented by static conformally flat, Schwarzchild and Friedmann–Robertson–Walker metrics.

[1] Ö. Yeşiltaş, Non-Hermitian Dirac Hamiltonian in Three-Dimensional Gravity and Pseudosupersymmetry, Adv. High En. Phys. Article ID 484151 2015.