Related papers: Detection of quantum geometric tensor by nonlinear…
Recent studies have revealed that the quantum geometry of electronic bands determines the electromagnetic properties of non-interacting insulators and semimetals. However, the role of quantum geometry in the optical responses of interacting…
An isolated classical chaotic system, when driven by the slow change of several parameters, responds with two reaction forces: geometric friction and geometric magnetism. By using the theory of quantum fluctuation relations we show that…
Quantum materials are characterized by electromagnetic responses intrinsically linked to the geometry and topology of electronic wavefunctions, encoded in the quantum metric and Berry curvature. Whereas Berry curvature-mediated transport…
Second-order nonlinear optical response allows to detect different properties of the system associated with the inversion symmetry breaking. Here, we use a second harmonic generation effect to investigate the alignment of a…
The size of Cooper pairs defines a fundamental length scale of superconductivity, conventionally set by band dispersion and the superconducting gap. This picture breaks down in flat bands, where quenched dispersion makes quantum geometry…
Berry phases and gauge structures in parameter spaces of quantum systems are the foundation of a broad range of quantum effects such as quantum Hall effects and topological insulators. The gauge structures of interacting many-body systems,…
The effect of the transversality condition on the quantization of the photon orbital angular momentum is studied. The quantum gauge that is deduced from the transversality condition is shown to be a Berry gauge. It determines a…
The experimental realisation of the basic constituents of quantum information processing devices, namely fault-tolerant quantum logic gates, requires conditional quantum dynamics, in which one subsystem undergoes a coherent evolution that…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative…
We describe a method for measuring the Berry curvature from the wave-packet dynamics in perturbed arrays of evanescently coupled optical waveguides with honeycomb lattice structure. To disentangle the effects of the Berry curvature and the…
The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but…
The Berry curvature and quantum metric are the imaginary part and real part, respectively, of the quantum geometric tensor which characterizes the topology of quantum states. The former is known to generate a zoo of important discoveries…
The quantum geometric tensor is composed of the Berry curvature and the quantum metric, which is observable by means of optical absorption of elliptically polarized light. Especially, the quantum geometric tensor at the zero-momentum is…
The quantum geometric tensor and quantum Fisher information have recently been shown to provide a unified geometric description of the linear response of many-body systems. However, a similar geometric description of higher-order…
In this paper, we consider a method for implementing a quantum logic gate with photons whose wave function propagates in a one-dimensional Kerr-nonlinear photonic crystal. The photonic crystal causes the incident photons to undergo Bragg…
We develop a unified framework to compute band-geometric quantities in multiband systems whose low-energy Hamiltonians realize arbitrary $SU(2)$ representations. Exploiting the presence of a quantization axis, we use the Wigner--Eckart…
The appearance of a Hall conductance necessarily requires breaking of time-reversal symmetry, either by an external magnetic field or by the internal magnetization of a material. However, as a second response, Hall dissipationless…
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate…
The Berry curvature is a fundamental concept describing topological order of quantum systems. While it can be analytically tractable in non-interacting systems, numerical simulations are necessary in interacting systems. We present a…
The quantum regression theorem (QRT) is the most-widely used tool for calculating multitime correlation functions for the assessment of quantum emitters. It is an approximate method based on a Markov assumption for the environmental…