arXiv subjects

Tomoki Ozawa

Publications and source records attributed to Tomoki Ozawa.

At least 19 recordsLinked to original sources

arXiv2026

Non-Abelian Gauge Field Mechanics

Non-Abelian gauge fields play a key role in describing the behavior of particles whose motion is coupled to internal degrees of freedom, such as their spin. Here, we experimentally realize a tuneable non-Abelian gauge field in an active mechanical lattice by using pairs of oscillators to encode a local pseudo-spin for each site, with inter-site spin-dependent couplings engineered via real-time measurement and feedback. We experimentally extract Wilson-loop observables in our set-up and hence demonstrate that we can create a genuinely non-Abelian gauge field. We then exploit the controllability of our mechanical lattice to engineer non-reciprocal hoppings to explore non-Hermitian non-Abelian gauge potentials. For a two-dimensional (2D) lattice, we demonstrate that the non-Hermiticity can manifest in direction-dependent Wilson loops for a single plaquette, while for a one-dimensional (1D) system, we show that a non-Abelian gauge potential can switch the localization of non-Hermitian skin modes between opposite ends of a chain. Our work establishes active mechanical lattices as a flexible and programmable platform for probing non-Abelian gauge fields and exploring their interplay with non-Hermitian dynamics.

cond-mat.mes-hall↗

arXiv2026

Hall viscosity from metric-sensitive dichroic probes

Hall viscosity characterizes the geometric response of a quantum Hall droplet to deformations of the underlying metric, yet it has remained difficult to measure directly. We propose a spectroscopic probe based on circular dichroism, using chiral metric-sensitive drives -- implemented as rotating quadrupolar ("saddle") perturbations -- that effectively modulate the metric and couple to the generators of area-preserving deformations. The resulting dichroic signal directly measures the Hall viscosity, while frequency-resolved spectroscopy disentangles it from other excitations. A local formulation further enables spatially resolved markers of Hall viscosity applicable to both continuum and lattice systems. Our results open a direct route to measuring Hall viscosity in quantum-engineered platforms such as cold atoms in optical lattices.

cond-mat.mes-hall↗

arXiv2026

Perfect elliptic dichroism: Probing the metric of anisotropic quantum Hall droplets

Understanding the geometry of quantum Hall systems is a central challenge in modern condensed matter physics. We introduce a framework for probing the geometric structure of quantum Hall droplets by engineering the geometry of a dichroic probe and identifying the onset of "perfect elliptic dichroism", a regime in which the system responds exclusively to an elliptically polarized drive of a given chirality. This phenomenon provides a direct diagnostic of the droplet's intrinsic metric, and we show that it extends naturally to ideal Chern bands, where holomorphicity of the occupied states guarantees the vanishing of one chiral absorption rate with a quantized response for the other. In lattice realizations, such as the Harper-Hofstadter model, finite lattice-spacing corrections break the exact continuum metric description and give rise to a renormalized, emergent Landau-orbit metric; the probe ellipticity at which perfect dichroism is achieved then shifts accordingly, offering a direct spectroscopic window onto this lattice-induced geometric renormalization. Our results illuminate the rich geometric structure of quantum Hall phases and offer concrete pathways for observing these effects in quantum-engineered platforms.

cond-mat.mes-hall↗

arXiv2026

Non-Hermitian Bloch Oscillations

We establish a general framework for non-Hermitian Bloch oscillations by investigating the wave-packet dynamics in one-dimensional non-Hermitian lattices driven by a dc force. The equations of motion for the momentum, center of mass, and group velocity of a wave packet are derived, where an anomalous group velocity due to the non-Hermiticity is identified. We show that nonreciprocal non-smooth Bloch oscillations, characterized by periodic jumps in group velocity, can emerge, and we analyze the role of finite-size effects. In non-Hermitian lattices with unidirectional hopping under open boundary conditions, we further uncover the emergence of periodic temporal Goos--H\"anchen shifts together with an anomalous wave propagation along the direction of vanishing hopping.

quant-ph↗

arXiv2026

Non-Hermitian Landau Levels

We formulate non-Hermitian Landau levels in two-dimensional systems under a complex perpendicular magnetic field. In the symmetric gauge, we derive their discretely spaced, highly degenerate complex spectra and biorthogonal eigenstates, and clarify the role of non-unitary gauge transformations. A non-Hermitian Harper-Hofstadter lattice model confirms the continuum theory and reveals Gaussian wave packet dynamics governed by semiclassical equations with a complex Lorentz force, pointing to possible experimental realizations of complex magnetic fields.

quant-ph↗

arXiv2025

Harmonic band theory: rigidity of non-zero degree harmonic maps from 2-torus to complex projective space

We prove the rigidity of isotropic harmonic maps from a 2-torus to a complex projective space, when they are constructed from holomorphic embeddings associated to complete linear systems. We also prove that this rigidity holds for any holomorphic embeddings without special hyperosculation points, with an extra assumption on the pullbacks of Fubini--Study symplectic forms. These results ensure the rigidity of towers of harmonic bands in condensed matter physics.

math-ph↗

arXiv2025

Emergent topological properties in spatially modulated sub-wavelength barrier lattices

We investigate topological phenomena in a spatially modulated Dirac-$\delta$ lattice, where the scattering potential varies periodically in space. Changing the potential modulation frequency leads to Hofstadter's butterfly-like energy spectrum and enables the emergence of topological transport regimes characterized by non-trivial Chern numbers. We show how the considered modulated system is connected to the Hofstadter model via the Harper equation. By adiabatically varying spatial modulation parameters, we demonstrate controllable quantum transport and verify the topological nature of these effects through Wannier center displacement and bulk invariant calculations. We also propose an experimentally feasible realization of such a system using optically controlled three-level atoms. Our findings showcase spatially engineered Kronig-Penney-type systems as versatile platforms for investigating and exploiting different topological quantum transport regimes.

cond-mat.quant-gas↗

arXiv2025

Anomalous Wave-Packet Dynamics in One-Dimensional Non-Hermitian Lattices

Non-Hermitian (NH) systems have attracted great attention due to their exotic phenomena beyond Hermitian domains. Here we study the wave-packet dynamics in general one-dimensional NH lattices and uncover several unexpected phenomena. The group velocity of a wave packet during the time evolution in such NH lattices is not only governed by the real part of the band structure but also by its imaginary part. The momentum also evolves due to the imaginary part of the band structure, which can lead to a self-induced Bloch oscillation in the absence of external fields. Furthermore, we discover the wave-packet dynamics can exhibit disorder-free NH jumps even when the energy spectra are entirely real. Finally, we show that the NH jumps can lead to both positive and negative temporal Goos--H\"{a}nchen shifts at the edge.

physics.optics↗

arXiv2025

Quantum geometrical effects in non-Hermitian systems

We explore the relation between quantum geometry in non-Hermitian systems and physically measurable phenomena. We highlight various situations in which the behavior of a non-Hermitian system is best understood in terms of quantum geometry, namely the notion of adiabatic potentials in non-Hermitian systems and the localization of Wannier states in periodic non-Hermitian systems. Further, we show that the non-Hermitian quantum metric appears in the response of the system upon time-periodic modulation, which one can use to experimentally measure the non-Hermitian quantum metric. We validate our results by providing numerical simulations of concrete exemplary systems.

quant-ph↗

arXiv2025

Relaxation toward an Ideal Chern Band through Coupling to a Markovian Bath

We propose a microscopic, weak-coupling mechanism by which generic Chern bands asymptotically relax toward ideal bands. We consider coupling interacting electrons to a Caldeira-Leggett-like Ohmic bosonic bath. Using the Born-Markov approximation, we analytically show that, upon taking the leading order contribution in momentum of the form factor, Slater determinant states of a Chern band under Hartree-Fock approximation evolve toward Slater determinant states corresponding to an ideal Chern band. We also numerically validate our proposal by performing simulation of a massive Dirac model with the extended Hubbard interaction, showing that the Berry curvature and quantum metric co-evolve toward saturation of the trace condition. Our proposal provides a concrete dissipative mechanism for driving Chern bands toward ideal quantum geometry, a fundamental building block for the stabilization of fractional Chern insulators.

cond-mat.mes-hall↗

arXiv2025

Density Matrix Geometry and Sum Rules

Geometry plays a fundamental role in a wide range of physical responses, from anomalous transport coefficients to their related sum rules. Notable examples include the quantization of the Hall conductivity and the Souza-Wilkens-Martin (SWM) sum rule -- both valid at zero temperature, independent of interactions and disorder. The finite-temperature generalization of the SWM sum rule has been explored in the literature, revealing deep connections to the geometry of density matrices. Building on recent advances in time-dependent geometric frameworks, we propose a time-dependent quantum geometric tensor for thermal density matrices. This formalism provides a unified interpretation of known sum rules within the framework of the fluctuation-dissipation theorem, further elucidating their fundamental geometric origin. In addition, it provides experimentally accessible methods to probe quantum geometry beyond the zero-temperature regime.

cond-mat.mes-hall↗

arXiv2025

Geometric contribution to adiabatic amplification in non-Hermitian systems

Concepts from non-Hermitian quantum mechanics have proven useful in understanding and manipulating a variety of classical systems, such as those encountered in optics, classical mechanics, and metamaterial design. Recently, the non-Hermitian analog of the Berry phase for adiabatic processes was experimentally measured. In non-Hermitian systems, the Berry phase can have an imaginary part, which contributes to the amplification or decay of the total wave intensity. When the imaginary part of the Berry curvature is zero, this geometric amplification factor is determined solely by the initial and final points of the adiabatic path in parameter space, and it does not depend on how these points are connected by the path. We list classes of non-Hermitian Hamiltonians where this path independence is guaranteed by suitable symmetries, and we find that, for some of these classes, the amplification factor can be written only in terms of the Petermann factors of the initial and final points. Our result can, in turn, be used to experimentally obtain the Petermann factor by observing how the norm of the wave function changes under adiabatic processes. We validate our theory using a couple of concrete examples of physical relevance.

quant-ph↗

arXiv2025

Non-equilibirum physics of density-difference dependent Hamiltonian: Quantum Scarring from Emergent Chiral Symmetry

Quantum many-body scars represent a form of weak ergodicity breaking that highlights the unusual physics of thermalization in quantum systems. Understanding scar formation promises insight into the connection between classical statistical mechanics and the quantum world. The existence of quantum many-body scars calls into question how the macroscopic world can arise from the Schrodinger equation. In this work, we demonstrate the existence of quantum many-body scars in the density-difference-dependent Hamiltonian. This Hamiltonian has a particular manifestation of chiral symmetry due to its interaction being neither attractive nor repulsive a prior, but depending on the configuration. As a result of this symmetry and peculiar interaction, we find that this system hosts two different classes of quantum scars; a charge density wave ordered scar and an edge-mode scar. We establish the existence of these scars by examining the entanglement entropy of the system as well as demonstrating robust thermalization breaking time dynamics. For each, we propose simple mechanisms that give rise to these scars which may be applicable to other systems.

cond-mat.quant-gas↗

arXiv2025

Geometrical Responses of Generalized Landau Levels: Structure Factor and the Quantized Hall Viscosity

We present a new geometric characterization of generalized Landau levels (GLLs). The GLLs are a generalization of Landau levels to non-uniform Berry curvature, and are mathematically defined in terms of a holomorphic curve -- an ideal Kähler band -- and its associated unitary Frenet-Serret moving frame. Here, we find that GLLs are harmonic maps from the Brillouin zone to the complex projective space and they are critical points of the Dirichlet energy functional, as well as the static structure factor up to fourth order. We also find that filled GLLs exhibit quantized Hall viscosity, similar to the ordinary Landau levels. These results establish GLLs as a versatile generalization of Landau levels.

cond-mat.mes-hall↗

arXiv2025

Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice

Realizing topological flat bands with tailored single-particle Hilbert spaces is a critical step toward exploring many-body phases, such as those featuring anyonic excitations. One prominent example is the Kapit-Mueller model, a variant of the Harper-Hofstadter model that stabilizes lattice analogs of the lowest Landau level states. The Kapit-Mueller model is constructed based on the Poisson summation rule, an exact lattice sum rule for coherent states. In this work, we consider higher Landau-level generalizations of the Poisson summation rule, from which we derive families of parent Hamiltonians on a half-flux lattice which have exact flat bands whose flatband wavefunctions are lattice version of higher Landau level states. Focusing on generic Bravais lattices with only translation and inversion symmetries, we discuss how these symmetries enforced gaplessness and singular points for odd Landau level series, and how to achieve fully gapped parent Hamiltonians by mixing even and odd series. Our model points to a large class of tight-binding models with suitable energetic and quantum geometries that are potentially useful for realizing non-Abelian fractionalized states when interactions are included. The model exhibits fast decay hopping amplitudes, making it potentially realizable with neutral atoms in optical lattices.

cond-mat.mes-hall↗

arXiv2024

Quantized Hall drift in a frequency-encoded photonic Chern insulator

The quantization of transport and its resilience to backscattering are key features for leveraging topological matter in applications that demand stringent noise mitigation, such as metrology and quantum information processing. Due to the bosonic nature of light, engineering such robust, ``one-way'' channels in synthetic photonic systems imposes the implementation of topological models with broken time-reversal symmetry; this is challenging since photons possess neither an electric charge nor a magnetic moment. Here, we propose and demonstrate a novel approach to realizing photonic Chern insulators - topological insulators with broken time-reversal symmetry - by encoding a Haldane-like model in the synthetic frequency dimension of an optical fiber loop platform. The bands' topology is assessed by reconstructing the Bloch states geometry across the Brillouin zone. We further highlight its consequences by measuring a driven-dissipative analogue of the quantized transverse Hall conductivity. Our results open new avenues for harnessing topologically protected light propagation in frequency-multiplexed photonic systems, with applications ranging from precision metrology to photonic quantum processors.

physics.optics↗

arXiv2024

Uniqueness of Landau levels and their analogs with higher Chern numbers

Landau levels are the eigenstates of a charged particle in two dimensions under a magnetic field, and are at the heart of the integer and fractional quantum Hall effects, which are two prototypical phenomena showing topological features. Following recent discoveries of fractional quantum Hall phases in van der Waals materials, there is a rapid progress in understanding of the precise condition under which the fractional quantum Hall phases can be stabilized. It is now understood that the key to obtaining the fractional quantum Hall phases is the energy band whose eigenstates are holomorphic functions in both real and momentum space coordinates. Landau levels are indeed examples of such energy bands with an additional special property of having flat geometrical features. In this paper, we prove that, in fact, the only energy eigenstates having holomorphic wave functions with a flat geometry are the Landau levels and their higher Chern number analogs. Since it has been known that any holomorphic eigenstates can be constructed from the ones with a flat geometry such as the Landau levels, our uniqueness proof of the Landau levels allows one to construct any possible holomorphic eigenstate with which the fractional quantum Hall phases can be stabilized.

cond-mat.mes-hall↗

arXiv2024

Mean-chiral displacement in coherently driven photonic lattices and its application to synthetic frequency dimensions

Characterizing topologically nontrivial photonic lattices by measuring their topological invariants is crucial in topological photonics. In conservative one-dimensional systems, a widely used observable to extract the winding number is the mean-chiral displacement. In many realistic photonic systems, however, losses can hardly be avoided, and little is known on how one can extend the mean-chiral displacement to a driven-dissipative context. Here we theoretically propose an experimentally viable method to directly detect the topological winding number of one-dimensional chiral photonic lattices. The method we propose is a generalization of the mean-chiral displacement to a driven-dissipative context with coherent illumination. By integrating the mean-chiral displacement of the steady state over the pump light frequency, one can obtain the winding number with a correction of the order of the loss rate squared. We demonstrate that this method can be successfully applied to lattices along synthetic frequency dimensions.

physics.optics↗