Observation of supersymmetric pseudo-Landau levels in strained microwave graphene.

Using an array of coupled microwave resonators arranged in a deformed honeycomb lattice, we experimentally observe the formation of pseudo-Landau levels in the whole crossover from vanishing to large pseudomagnetic field strengths. This result is achieved by utilising an adaptable setup in a geometry that is compatible with the pseudo-Landau levels at all field strengths. The adopted approach enables us to observe the fully formed flat-band pseudo-Landau levels spectrally as sharp peaks in the photonic density of states and image the associated wavefunctions spatially, where we provide clear evidence for a characteristic nodal structure reflecting the previously elusive supersymmetry in the underlying low-energy theory.

Universal hypotrochoidic law for random matrices with cyclic correlations.

The celebrated elliptic law describes the distribution of eigenvalues of random matrices with correlations between off-diagonal pairs of elements, having applications to a wide range of physical and biological systems. Here, we investigate the generalization of this law to random matrices exhibiting higher-order cyclic correlations between k tuples of matrix entries. We show that the eigenvalue spectrum in this ensemble is bounded by a hypotrochoid curve with k-fold rotational symmetry.

Supersymmetric Polarization Anomaly in Photonic Discrete-Time Quantum Walks.

Quantum anomalies lead to finite expectation values that defy the apparent symmetries of a system. These anomalies are at the heart of topological effects in electronic, photonic, and atomic systems, where they result in a unique response to external fields but generally escape a more direct observation. Here, we implement an optical-network realization of a discrete-time quantum walk, where such an anomaly can be observed directly in the unique circular polarization of a topological midgap state.

Topological dynamics and excitations in lasers and condensates with saturable gain or loss.

We classify symmetry-protected and symmetry-breaking dynamical solutions for nonlinear saturable bosonic systems that display a non-hermitian charge-conjugation symmetry, as realized in a series of recent groundbreaking experiments with lasers and exciton polaritons. In particular, we show that these systems support stable symmetry-protected modes that mirror the concept of zero-modes in topological quantum systems, as well as symmetry-protected power-oscillations with no counterpart in the linear case. In analogy to topological phases in linear systems, the number and nature of symmetry-protected solutions can change.

Topological hybrid silicon microlasers.

Topological physics provides a robust framework for strategically controlling wave confinement and propagation dynamics. However, current implementations have been restricted to the limited design parameter space defined by passive topological structures. Active systems provide a more general framework where different fundamental symmetry paradigms, such as those arising from non-Hermiticity and nonlinear interaction, can generate a new landscape for topological physics and its applications.

Sonic Landau Levels and Synthetic Gauge Fields in Mechanical Metamaterials.

Mechanical strain can lead to a synthetic gauge field that controls the dynamics of electrons in graphene sheets as well as light in photonic crystals. Here, we show how to engineer an analogous synthetic gauge field for lattice vibrations. Our approach relies on one of two strategies: shearing a honeycomb lattice of masses and springs or patterning its local material stiffness.

Universal Sign Control of Coupling in Tight-Binding Lattices.

We present a method of locally inverting the sign of the coupling term in tight-binding systems, by means of inserting a judiciously designed ancillary site and eigenmode matching of the resulting vertex triplet. Our technique can be universally applied to all lattice configurations, as long as the individual sites can be detuned. We experimentally verify this method in laser-written photonic lattices and confirm both the magnitude and the sign of the coupling by interferometric measurements.

Nonequilibrium steady states of ideal bosonic and fermionic quantum gases.

We investigate nonequilibrium steady states of driven-dissipative ideal quantum gases of both bosons and fermions. We focus on systems of sharp particle number that are driven out of equilibrium either by the coupling to several heat baths of different temperature or by time-periodic driving in combination with the coupling to a heat bath. Within the framework of (Floquet-)Born-Markov theory, several analytical and numerical methods are described in detail.

Topologically Protected Defect States in Open Photonic Systems with Non-Hermitian Charge-Conjugation and Parity-Time Symmetry.

We show that topologically protected defect states can exist in open (leaky or lossy) systems even when these systems are topologically trivial in the closed limit. The states appear from within the continuum, thus in the absence of a band gap, and are generated via exceptional points (a spectral transition that occurs in open wave and quantum systems with a generalized time-reversal symmetry), or via a degeneracy induced by charge-conjugation symmetry (which is related to the pole transition of Majorana zero modes). We demonstrate these findings for a leaking passive coupled-resonator optical waveguide with asymmmetric internal scattering, where the required symmetries (non-Hermitian versions of time-reversal symmetry, chirality, and charge conjugation) emerge dynamically.

Many-Body Localization Characterized from a One-Particle Perspective.

We show that the one-particle density matrix ρ can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of ρ) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of ρ) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a steplike discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition.

Selective enhancement of topologically induced interface states in a dielectric resonator chain.

The recent realization of topological phases in insulators and superconductors has advanced the search for robust quantum technologies. The prospect to implement the underlying topological features controllably has given incentive to explore optical platforms for analogous realizations. Here we realize a topologically induced defect state in a chain of dielectric microwave resonators and show that the functionality of the system can be enhanced by supplementing topological protection with non-hermitian symmetries that do not have an electronic counterpart.

Transport signatures of pseudomagnetic Landau levels in strained graphene ribbons.

In inhomogeneously strained graphene, low-energy electrons experience a valley-antisymmetric pseudomagnetic field which leads to the formation of localized states at the edge between the valence and conduction bands, understood in terms of peculiar n=0 pseudomagnetic Landau levels. Here we show that such states can manifest themselves as an isolated quadruplet of low-energy conductance resonances in a suspended stretched graphene ribbon, where clamping by the metallic contacts results in a strong inhomogeneity of strain near the ribbon ends.

Topologically protected midgap states in complex photonic lattices.

One of the principal goals in the design of photonic crystals is the engineering of band gaps and defect states. Here I describe the formation of topologically protected localized midgap states in systems with spatially distributed gain and loss. These states can be selectively amplified, which finds applications in the beam dynamics along a photonic lattice and in the lasing of quasi-one-dimensional photonic crystals.

From scattering theory to complex wave dynamics in non-Hermitian PT-symmetric resonators.

I review how methods from mesoscopic physics can be applied to describe the multiple wave scattering and complex wave dynamics in non-Hermitian PT-symmetric resonators, where an absorbing region is coupled symmetrically to an amplifying region. Scattering theory serves as a convenient tool to classify the symmetries beyond the single-channel case and leads to effective descriptions that can be formulated in the energy domain (via Hamiltonians) and in the time domain (via time evolution operators). These models can then be used to identify the mesoscopic time and energy scales that govern the spectral transition from real to complex eigenvalues.

Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices.

We describe the formation of highly degenerate, Landau-level-like amplified states in a strained photonic honeycomb lattice in which amplification breaks the sublattice symmetry. As a consequence of the parity anomaly, the zeroth Landau level is localized on a single sublattice and possesses an enhanced or reduced amplification rate. The selection of the sublattice depends on the strain orientation but is independent of the valley.

Weyl law for open systems with sharply divided mixed phase space.

A generalization of the Weyl law to systems with a sharply divided mixed phase space is proposed. The ansatz is composed of the usual Weyl term which counts the number of states in regular islands and a term associated with sticky regions in phase space. For a piecewise linear map, we numerically check the validity of our hypothesis, and find good agreement not only for the case with a sharply divided phase space but also for the case where tiny island chains surround the main regular island.

Counting statistics for mesoscopic conductors with internal degrees of freedom.

We consider the transport of electrons passing through a mesoscopic device possessing internal dynamical quantum degrees of freedom. The mutual interaction between the system and the conduction electrons contributes to the current fluctuations, which we describe in terms of full counting statistics. We identify conditions where this discriminates coherent from incoherent internal dynamics and also identify and illustrate conditions under which the device acts to dynamically bunch transmitted or reflected electrons, thereby generating super-Poissonian noise.

Quantum noise and self-sustained radiation of PT-symmetric systems.

The observation that PT-symmetric Hamiltonians can have real-valued energy levels even if they are non-Hermitian has triggered intense activities, with experiments, in particular, focusing on optical systems, where Hermiticity can be broken by absorption and amplification. For classical waves, absorption and amplification are related by time-reversal symmetry. This work shows that microreversibility-breaking quantum noise turns PT-symmetric systems into self-sustained sources of radiation, which distinguishes them from ordinary, Hermitian quantum systems.

Fractal Weyl laws for quantum decay in dynamical systems with a mixed phase space.

Weyl's law approximates the number of states in a quantum system by partitioning the energetically accessible phase-space volume into Planck cells. Here, we show that resonances in open quantum systems can follow a modified fractal Weyl law, even when their classical dynamics is not globally chaotic but also contains domains of regular motion. Using an appropriate phase-space representation for open quantum systems, we connect this behavior to emerging quantum-to-classical correspondence.

Semiclassical transport in nearly symmetric quantum dots. II. Symmetry breaking due to asymmetric leads.

In this work-the second of a pair of articles-we consider transport through spatially symmetric quantum dots with leads whose widths or positions do not obey the spatial symmetry. We use the semiclassical theory of transport to find the symmetry-induced contributions to weak localization corrections and universal conductance fluctuations for dots with left-right, up-down, inversion, and fourfold symmetries. We show that all these contributions are suppressed by asymmetric leads; however, they remain finite whenever leads intersect with their images under the symmetry operation.

Semiclassical transport in nearly symmetric quantum dots. I. Symmetry breaking in the dot.

We apply the semiclassical theory of transport to quantum dots with exact and approximate spatial symmetries; left-right mirror symmetry, up-down mirror symmetry, inversion symmetry, or fourfold symmetry. In this work-the first of a pair of articles-we consider (a) perfectly symmetric dots and (b) nearly symmetric dots in which the symmetry is broken by the dot's internal dynamics. The second article addresses symmetry-breaking by displacement of the leads.

Adsorbate-limited conductivity of graphene.

We present a theory of electronic transport in graphene in the presence of randomly placed adsorbates. Our analysis predicts a marked asymmetry of the conductivity about the Dirac point, as well as a negative weak-localization magnetoresistivity. In the region of strong scattering, renormalization group corrections drive the system further towards insulating behavior.

Nonexponential decoherence and momentum subdiffusion in a quantum lévy kicked rotator.

We investigate decoherence in the quantum kicked rotator (modeling cold atoms in a pulsed optical field) subjected to noise with power-law tail waiting-time distributions of variable exponent (Lévy noise). We demonstrate the existence of a regime of nonexponential decoherence where the notion of a decoherence rate is ill defined. In this regime, dynamical localization is never fully destroyed, indicating that the dynamics of the quantum system never reaches the classical limit.

Superconducting terminals as sensitive probes for scarred states.

When a quantum-chaotic normal conductor is coupled to a superconductor, the random-matrix theory (RMT) predicts that a gap opens up in the excitation spectrum which is of universal size E(g)(RMT) approximately 0.3 Planck/t(D), where t(D) is the mean scattering time between Andreev reflections. We show that a scarred state of long lifetime t(S)>>t(D) suppresses the excitation gap over a window DeltaE approximately 2E(g)(RMT) which can be much larger than the narrow resonance width GammaS= Planck/t(S) of the scar in the normal system.

Correcting ray optics at curved dielectric microresonator interfaces: phase-space unification of Fresnel filtering and the Goos-Hänchen shift.

We develop an amended ray-optics description for reflection at the curved dielectric interfaces of optical microresonators which improves the agreement with wave optics by about one order of magnitude. The corrections are separated into two contributions of similar magnitude, corresponding to ray displacement in independent quantum-phase-space directions, which can be identified with Fresnel filtering and the Goos-Hänchen shift, respectively. Hence we unify two effects which only have been studied separately in the past.