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Simultaneous optimization of multiple quantum objectives is often considered a demanding task. However, a special circumstance arises when a primary objective is pitted against a set of secondary objectives, which we show leads to invariant…
The existence of surface electromagnetic waves in the dielectric-metal interface is due to the sign change of real parts of permittivity across the interface. In this work, we demonstrate that the interface constructed by two semi-infinite…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
We show that customized optical patterns can be generated by employing feedback-based wavefront shaping without prior knowledge of the transmission matrix of optical systems. To control the spatial distribution of intensity within the…
Controlling light-matter based quantum systems in the strong coupling regime allows for exploring quantum simulation of many-body physics in nowadays architectures. For instance, the atom-field interaction in a cavity QED network provides…
We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is…
A number of physical processes show some form of bifurcation or periodic splintering of a single distribution into two new ones. Recently, it has been noted that cavity searches for interactions between photons and exotic fields may also…
We show that microwave-driven NV centers can function as topological mode switches by utilizing a special degeneracy called an exceptional point (EP). By tuning the intensities and frequencies of the driving fields, we find an EP---where…
Nascent quantum computers motivate the exploration of quantum many-body systems in nontraditional scenarios. For example, it has become natural to explore the dynamics of systems evolving under both unitary evolution and measurement. Such…
We study optomechanically induced transparency in a microresonator coupled with nanoparticles. By tuning the relative angle of the nanoparticles, exceptional points (EPs) emerge periodically in this system and thus strongly modify both the…
Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. In this work, we consider a well investigated phase field model including contact line…
When sources of energy gain and loss are introduced to a wave-scattering system, the underlying mathematical formulation will be non-Hermitian. This paves the way for the existence of exceptional points, where eigenmodes are linearly…
Statistical fluctuations in the eigenvalues of the scattering, impedance and admittance matrices of 2-Port wave-chaotic systems are studied experimentally using a chaotic microwave cavity. These fluctuations are universal in that their…
The scattering of a flying photon by a two-level system ultrastrongly coupled to a one-dimensional photonic waveguide is studied numerically. The photonic medium is modeled as an array of coupled cavities and the whole system is analyzed…
We investigate the conditions yielding plasmon-exciton strong coupling at the single emitter level in the gap between two metal nanoparticles. A quasi-analytical transformation optics approach is developed that makes possible a thorough…
We use supersymmetry transformations to design transparent and one-way reflectionless (thus unidirectionally invisible) complex crystals with balanced gain and loss profiles. The scattering coefficients are investigated using the transfer…
We present a transmission line theory of exceptional points of degeneracy (EPD) in coupled-mode guiding structures, i.e., a theory that illustrates the characteristics of coupled electromagnetic modes under a special dispersion degeneracy…
We study one- and two-dimensional models which undergo a transition between active and absorbing phases. The transition point in these models is of novel type: jump of the order parameter coincides with its power-law singularity. Some…
This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to…
Recent technological advancements have enabled strong light-matter interaction in highly dissipative cavity-emitter systems. However, in these systems, which are well described by the Tavis-Cummings model, the considerable loss rates render…