08:45 - 09:00
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Holger Kantz (MPI-PKS) & scientific coordinators
opening
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Chair: Kohei Kawabata
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09:00 - 09:40
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Cristiane de Morais Smith
(Utrecht University)
Quantum Geometry and Monomodes in Non-Hermitian Topological Systems
In the first part of this talk, I will discuss a quantum geometric approach to various Hermitian and non-Hermitian versions of the Su-Schrieffer-Heeger (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 non-Hermiticity leads to pseudo-Riemannian 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 non-Hermitian one-dimensional (1D) and 2D Su-Schrieffer-Heeger (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 (non-Hermitian) 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 non-Hermitian 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
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09:40 - 10:20
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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 non-Hermitian quantum mechanics.
The first application [1,2] concerns quantum tunneling. We will show that specific complex-time classical trajectories through multibarrier potentials yield correct semiclassical approximations of the smoothed transmission amplitudes. It turns out that the corresponding complex-extended continuum level density exhibits singularities analogous to excited-state quantum phase transitions in bound (discrete-energy) quantum systems. Potential wider consequences of complex-time 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 after-quench survival amplitude of the initial state in complex-extended 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 excited-state quantum phase transitions, Phys. Rev. A 103 (2021) 062207.
[3] Á.L. Corps, P. Stránský, P. Cejnar, Mechanism of dynamical phase transitions: The complex-time survival amplitude, Phys. Rev. B 107 (2023) 094307.
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10:20 - 10:50
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coffee break
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10:50 - 11:30
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Jack Harris
(Yale University)
What we do when we go around EPs: Measuring the knots and braids of non-Hermitian oscillators
Many properties of a linear system are determined by the manner in which its eigenvalue spectrum can be tuned. Non-Hermitian 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 non-trivial manner. It is well-known 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 non-Abelian character of the resulting braids.
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11:30 - 11:50
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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 non-Hermiticity 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 well-localized MZMs, and leads to strong superconducting pair correlations. Our work thus illustrates the large potential of enhancing topological superconductivity using non-Hermitian exceptional points.
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11:50 - 12:10
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Viktoriia Kornich
(Wuerzburg University)
Current-voltage characteristics of the N-I-PT-symmetric non-Hermitian superconductor junction as a probe of non-Hermitian formalisms
We study theoretically a junction consisting of a normal metal, PT-symmetric
non-Hermitian superconductor, and an insulating thin layer between them. We
calculate current-voltage characteristics for this junction using left-right
and right-right bases and compare the results. We find that left-right basis
gives the opposite current of Andreev-scattered particles compared to the
right-right basis and conventional Andreev scattering. This leads to profound
differences in current-voltage characteristics. Based on this and other
signatures, we argue that left-right 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 right-right basis is equilibrated.
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12:10 - 12:30
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Yow-Ming Hu
(Australian National University)
Self-acceleration and emergent topological defects in non-Hermitian exciton polaritons
Open dissipative systems described by non-Hermitian Hamiltonians have recently attracted a lot of interests as they lead to a wide range of effects such as coherent-perfect 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 non-Hermitian degeneracies [4] and topological invariants [2]. Inspired by recent studies [3, 5] showing the self-acceleration of wave packets in non-Hermitian systems, we theoretically investigate the time-evolution of wave packets in a non-Hermitian exciton-polariton system.
In particular, we numerically study wavepacket dynamics in momentum space and observe self-acceleration. 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 exciton-polariton system with optical anisotropy, e.g., perovskite [2], organics [6], or ZnO-based microcavities [7]. Our results highlight the excellent potential of exciton polaritons as a platform to study non-Hermitian dynamics.
[1] Ş. K. Özdemir, et al., Natural Materials 18, 783-798 (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).
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12:30 - 14:00
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lunch break
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Chair: Masahito Ueda
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14:00 - 14:40
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Kohei Kawabata
(University of Tokyo)
Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
Recent years have seen remarkable development in open quantum systems effectively described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological systems is the skin effect, anomalous localization of an extensive number of eigenstates driven by nonreciprocal dissipation. Despite its significance for non-Hermitian 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 non-Hermitian 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).
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14:40 - 15:20
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Henning Schomerus
(Lancaster University)
Physical response of non-Hermitian topological systems
In photonic systems, gain and loss can be used to induce intriguing effects that are linked to non-Hermitian and topological physics. Prominent examples are exceptional points and the non-Hermitian skin effect, which can be used for enhanced sensing and directed amplification, as well as symmetry-protected 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 non-Hermitian effects in passive systems," Phys. Rev. A 106, 063509 (2022).
[2] H. Schomerus, "Quantum Noise and Self-Sustained Radiation of PT-Symmetric Systems, " Phys. Rev. Lett. 104, 233601 (2010).
[3] G. Yoo, H.-S. Sim, and H. Schomerus, "Quantum noise and mode nonorthogonality in non-Hermitian PT-symmetric optical resonators, " Phys. Rev. A 84, 063833 (2011).
[4] H. Schomerus, "Nonreciprocal response theory of non-Hermitian mechanical metamaterials: Response phase transition from the skin effect of zero modes", Phys. Rev. Research 2, 013058 (2020).
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15:30 - 15:45
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group photo (to be published on the website under the 'Access tab')
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16:00 - 16:30
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coffee break
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Chair: Matt Eiles
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16:30 - 17:30
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Flore Kunst
(MPI für die Physik des Lichts)
NHTOP23 Colloquium - Exceptional non-Hermitian 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 non-Hermitian Hamiltonians. Non-Hermitian topological
phenomena reveal an enrichment of the phenomenology of topological phases,
and forms a rapidly growing new cross-disciplinary 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, non-Hermiticity describes the dynamics of
open quantum systems as well as scattering, decay, broadening and
resonances due to, e.g., interactions and disorder. Non-Hermitian 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 bulk-boundary correspondence, and the
piling up of bulk states at the boundaries known as the non-Hermitian 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.
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18:00
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dinner
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19:00
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discussions
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