08:45  09:00

Holger Kantz (MPIPKS) & scientific coordinators
opening


Chair: Kohei Kawabata

09:00  09:40

Cristiane de Morais Smith
(Utrecht University)
Quantum Geometry and Monomodes in NonHermitian Topological Systems
In the first part of this talk, I will discuss a quantum geometric approach to various Hermitian and nonHermitian versions of the SuSchriefferHeeger (SSH) model. We find that this method allows one to correctly identify different topological phases and topological phase transitions for all SSH models. Whereas the quantum geometry of Hermitian systems is Riemannian, introducing nonHermiticity leads to pseudoRiemannian and complex geometries, thus significantly generalizing from the quantum geometries studied thus far. We find a “dark” direction in some cases, such that within linear response, one can perturb the system by a particular change of parameters while maintaining a zero excitation rate [1].
In the second part of the talk, I will present a remarkably simple model and the experimental observation of topological monomodes generated dynamically. By focusing on nonHermitian onedimensional (1D) and 2D SuSchriefferHeeger (SSH) models, we theoretically unveil the minimal configuration to realize a topological monomode upon engineering losses and breaking of lattice symmetries. Furthermore, we classify the systems in terms of the (nonHermitian) symmetries that are present and calculate the corresponding topological invariants. To corroborate the theory, we present experiments in photonic lattices, in which a monomode is observed in the nonHermitian 1D and 2D SSH models, thus breaking the paradigm that topological corner states should appear in pairs [2].
[1] Chen Chao Ye, W. L. Vleeshouwers, S. Heatley, V. Gritsev, and C. Morais Smith,
arXiv: 2305.17675
[2] E. Slootman, W. Cherifi, L. Eek, R. Arouca, E. J. Bergholtz, M. Bourennane, and C. Morais Smith, arXiv:2304.05748

09:40  10:20

Pavel Cejnar
(Charles University of Prague)
Complex time in quantum mechanics
Although time is naturally a real variable, it is sometimes useful to consider it extended to the complex domain. After a general introduction, we will discuss two specific applications of such an extension within the framework of nonHermitian quantum mechanics.
The first application [1,2] concerns quantum tunneling. We will show that specific complextime classical trajectories through multibarrier potentials yield correct semiclassical approximations of the smoothed transmission amplitudes. It turns out that the corresponding complexextended continuum level density exhibits singularities analogous to excitedstate quantum phase transitions in bound (discreteenergy) quantum systems. Potential wider consequences of complextime tunneling and its link to the concept of weak measurements will be mentioned.
The second application [3] is related to quantum quench dynamics. We will demonstrate that zeros of the afterquench survival amplitude of the initial state in complexextended time represent computationally detectable precursors of dynamical quantum phase transitions in finite systems. The behavior of zeros with increasing system size makes it possible to distinguish true precursors of criticality from the false ones. This approach hints at similar descriptions of equilibrium phase transitions, particularly those in the thermodynamic domain.
References:
[1] P. Stránský, M. Sindelka, M. Kloc, P. Cejnar, Complex density of continuum states in resonant quantum tunneling, Phys. Rev. Lett. 125 (2020) 020401.
[2] P. Stránský, M. Sindelka, P. Cejnar, Continuum analogs of excitedstate quantum phase transitions, Phys. Rev. A 103 (2021) 062207.
[3] Á.L. Corps, P. Stránský, P. Cejnar, Mechanism of dynamical phase transitions: The complextime survival amplitude, Phys. Rev. B 107 (2023) 094307.

10:20  10:50

coffee break

10:50  11:30

Jack Harris
(Yale University)
What we do when we go around EPs: Measuring the knots and braids of nonHermitian oscillators
Many properties of a linear system are determined by the manner in which its eigenvalue spectrum can be tuned. NonHermitian systems offer unique features in this regard. Among the most striking is that tuning control parameters around a closed loop can cause the system's spectrum to return to itself in a topologically nontrivial manner. It is wellknown that this behavior is related to the manner in which the control loop encircles points of degeneracy.
The general relationship between control loops, eigenvalue spectra, and points of degeneracy (for any number of modes and for any degree of degeneracy!) maps exactly on to an elegant and easily visualizable piece of mathematics. The results of this are that: 1) degeneracies lie on knots in the space of control parameters; 2) a control loop causes the eigenvalue spectrum to trace out a braid; and 3) the specific braid is determined by the manner in which the control loop encircles the knot of degeneracies.
I will give a pedagogical introduction to these results (with lots of images and animations). I will also present measurements that illustrate these structures, including the knot of degeneracies and the nonAbelian character of the resulting braids.

11:30  11:50

Rodrigo Arouca
Exceptionally enhanced topological superconductivity
Majorana zero modes (MZMs) emerge as edge states in topological superconductors and are promising for topological quantum computation, but their detection has so far been elusive. Here we show that nonHermiticity can be used to obtain dramatically more robust MZMs. The enhanced properties appear as a result of an extreme instability of exceptional points to superconductivity, such that even a vanishingly small superconducting order parameter already opens a large energy gap, produces welllocalized MZMs, and leads to strong superconducting pair correlations. Our work thus illustrates the large potential of enhancing topological superconductivity using nonHermitian exceptional points.

11:50  12:10

Viktoriia Kornich
(Wuerzburg University)
Currentvoltage characteristics of the NIPTsymmetric nonHermitian superconductor junction as a probe of nonHermitian formalisms
We study theoretically a junction consisting of a normal metal, PTsymmetric
nonHermitian superconductor, and an insulating thin layer between them. We
calculate currentvoltage characteristics for this junction using leftright
and rightright bases and compare the results. We find that leftright basis
gives the opposite current of Andreevscattered particles compared to the
rightright basis and conventional Andreev scattering. This leads to profound
differences in currentvoltage characteristics. Based on this and other
signatures, we argue that leftright basis is not applicable in this case.
Remarkably, we find that the quasiparticle current is conserved across the
junction in both bases, and the growth and decay with time of the states with
imaginary energies in rightright basis is equilibrated.

12:10  12:30

YowMing Hu
(Australian National University)
Selfacceleration and emergent topological defects in nonHermitian exciton polaritons
Open dissipative systems described by nonHermitian Hamiltonians have recently attracted a lot of interests as they lead to a wide range of effects such as coherentperfect absorption and lasing [1], directional emission [1], novel topological invariants [2] and edge states [3]. One of such systems is the exciton polaritons in an optical microcavity which arise from the strong coupling of excitons in a semiconductor and cavity photon modes. The inherent loss and gain in this system have already enabled measurements of nonHermitian degeneracies [4] and topological invariants [2]. Inspired by recent studies [3, 5] showing the selfacceleration of wave packets in nonHermitian systems, we theoretically investigate the timeevolution of wave packets in a nonHermitian excitonpolariton system.
In particular, we numerically study wavepacket dynamics in momentum space and observe selfacceleration. The wave packets tend to evolve into the eigenstate with the smaller decay rate (or the larger imaginary part of the eigenenergy), then propagate towards the momenta corresponding to the minima of the decay rate (or the maxima of the imaginary part of the eigenenergies). We also observe the generation of pseudospin defects (half skyrmions) along the imaginary Fermi arc in momentum space, where the decay rates of the two eigenstates coincide. All of these effects do not require an external potential and can be measured in an excitonpolariton system with optical anisotropy, e.g., perovskite [2], organics [6], or ZnObased microcavities [7]. Our results highlight the excellent potential of exciton polaritons as a platform to study nonHermitian dynamics.
[1] Ş. K. Özdemir, et al., Natural Materials 18, 783798 (2019).
[2] R. Su, et al., Science Advances 7, eabi8905 (2021).
[3] S. Longhi, Phys. Rev. B 105, 245143 (2022).
[4] T. Gao, et al., Nature 526, 554–558 (2015).
[5] D. D. Solnyshkov, et al., Phys. Rev. B 103, 125302 (2021).
[6] Q. Liao, et al., Phys. Rev. Lett. 127, 107402 (2021).
[7] S. Richter, et al., Phys. Rev. Lett. 123, 227401 (2019).

12:30  14:00

lunch break


Chair: Masahito Ueda

14:00  14:40

Kohei Kawabata
(University of Tokyo)
Entanglement Phase Transition Induced by the NonHermitian Skin Effect
Recent years have seen remarkable development in open quantum systems effectively described by nonHermitian Hamiltonians. A unique feature of nonHermitian topological systems is the skin effect, anomalous localization of an extensive number of eigenstates driven by nonreciprocal dissipation. Despite its significance for nonHermitian topological phases, the relevance of the skin effect to quantum entanglement and critical phenomena has remained unclear. Here, we find that the skin effect induces a nonequilibrium quantum phase transition in the entanglement dynamics. We show that the skin effect gives rise to a macroscopic flow of particles and suppresses the entanglement propagation and thermalization, leading to the area law of the entanglement entropy in the nonequilibrium steady state. Moreover, we reveal an entanglement phase transition induced by the competition between the unitary dynamics and the skin effect even without disorder or interactions. This entanglement phase transition accompanies nonequilibrium quantum criticality characterized by a nonunitary conformal field theory whose effective central charge is extremely sensitive to the boundary conditions. We also demonstrate that it originates from an exceptional point of the nonHermitian Hamiltonian and the concomitant scale invariance of the skin modes localized according to the power law. Furthermore, we show that the skin effect leads to the purification and the reduction of von Neumann entropy even in Markovian open quantum systems described by the Lindblad master equation. Our work opens a way to control the entanglement growth and establishes a fundamental understanding of phase transitions and critical phenomena in open quantum systems far from thermal equilibrium.
Reference: K. Kawabata, T. Numasawa, and S. Ryu, Phys. Rev. X 13, 021007 (2023).

14:40  15:20

Henning Schomerus
(Lancaster University)
Physical response of nonHermitian topological systems
In photonic systems, gain and loss can be used to induce intriguing effects that are linked to nonHermitian and topological physics. Prominent examples are exceptional points and the nonHermitian skin effect, which can be used for enhanced sensing and directed amplification, as well as symmetryprotected states, which can be addressed by topological mode selection. Many of these applications make explicit use of mode nonorthogonality, which becomes especially intriguing when the system is nonreciprocal. I describe how these effects can be probed in response theory, transport, and scattering, and highlight fundamental practical limits of the observability of some effects.
[1] H. Schomerus, "Fundamental constraints on the observability of nonHermitian effects in passive systems," Phys. Rev. A 106, 063509 (2022).
[2] H. Schomerus, "Quantum Noise and SelfSustained Radiation of PTSymmetric Systems, " Phys. Rev. Lett. 104, 233601 (2010).
[3] G. Yoo, H.S. Sim, and H. Schomerus, "Quantum noise and mode nonorthogonality in nonHermitian PTsymmetric optical resonators, " Phys. Rev. A 84, 063833 (2011).
[4] H. Schomerus, "Nonreciprocal response theory of nonHermitian mechanical metamaterials: Response phase transition from the skin effect of zero modes", Phys. Rev. Research 2, 013058 (2020).

15:30  15:45

group photo (to be published on the website under the 'Access tab')

16:00  16:30

coffee break


Chair: Matt Eiles

16:30  17:30

Flore Kunst
(MPI für die Physik des Lichts)
NHTOP23 Colloquium  Exceptional nonHermitian topology
While topological phases of matter have predominantly been studied for isolated
Hermitian systems, a recent shift has been made towards considering these
phases in the context of nonHermitian Hamiltonians. NonHermitian topological
phenomena reveal an enrichment of the phenomenology of topological phases,
and forms a rapidly growing new crossdisciplinary field. In particular, non
Hermiticity plays a central role in both classical and quantum systems. In the
classical realm, this comes about due to, e.g., gain and loss processes in
optics, while in the quantum realm, nonHermiticity describes the dynamics of
open quantum systems as well as scattering, decay, broadening and
resonances due to, e.g., interactions and disorder. NonHermitian Hamiltonians
may feature many exotic properties, which are radically different from their
Hermitian counterparts, such as the generic appearance of exotic exceptional
structures, a break down of the famed bulkboundary correspondence, and the
piling up of bulk states at the boundaries known as the nonHermitian skin
effect. In this talk, I will provide an overview of the field focussing on
fundamental aspects, experimental realizations and I will briefly touch upon
applications.

18:00

dinner

19:00

discussions
