Plasmon Injection to Compensate and Control Losses in Negative Index Metamaterials

Metamaterials have introduced a whole new world of unusual materials with functionalities that cannot be attained in naturally occurring material systems by mimicking and controlling the natural phenomena at subwavelength scales. However, the inherent absorption losses pose fundamental challenge to the most fascinating applications of metamaterials. Based on a novel plasmon injection (PI or \Pi) scheme, we propose a coherent optical amplification technique to compensate losses in metamaterials. Although the proof of concept device here operates under normal incidence only, our proposed scheme can be generalized to arbitrary form of incident waves. The \Pi-scheme is fundamentally different than major optical amplification schemes. It does not require gain medium, interaction with phonons, or any nonlinear medium. The \Pi-scheme allows for loss-free metamaterials. It is ideally suited for mitigating losses in metamaterials operating in the visible spectrum and is scalable to other optical frequencies. These findings open the possibility of reviving the early dreams of making 'magical' metamaterials from scratch.Comment: Main text, 8 pages with 4 figures; supplemental material, 21 pages with 21 figure

Liouvillian Exceptional Points of Non-Hermitian Systems via Quantum Process Tomography

Hamiltonian exceptional points (HEPs) are spectral degeneracies of non-Hermitian Hamiltonians describing classical and semiclassical open systems with gain and/or loss. However, this definition overlooks the occurrence of quantum jumps in the evolution of open quantum systems. These quantum effects are properly accounted for by considering Liouvillians and their exceptional points (LEPs) [Minganti et al., Phys. Rev. A {\bf 100}, 062131 (2019)]. Here, we explicitly describe how standard quantum process tomography, which reveals the dynamics of a quantum system, can be readily applied to reveal and characterize LEPs of non-Hermitian systems. We conducted experiments on an IBM quantum processor to implement a prototype model simulating the decay of a single qubit through three competing channels. Subsequently, we performed tomographic reconstruction of the corresponding experimental Liouvillians and their LEPs using both single- and two-qubit operations. This example underscores the efficacy of process tomography in tuning and observing LEPs, despite the absence of HEPs in the model.Comment: 9+17 pages, 2+4 figure

Geometry of the Field-Moment Spaces for Quadratic Bosonic Systems: Diabolically Degenerated Exceptional Points on Complex kk-Polytopes

$k$-Polytopes are a generalization of polyhedra in $k$ dimensions. Here, we show that complex $k$-polytopes naturally emerge in the higher-order field moments spaces of quadratic bosonic systems, thus revealing their geometric character. In particular, a complex-valued evolution matrix, governing the dynamics of $k$th-order field moments of a bosonic dimer, can describe a complex $k$-dimensional hypercube. The existence of such $k$-polytopes is accompanied by the presence of high-order diabolic points (DPs). Interestingly, when the field-moment space additionally exhibits exceptional points (EPs), the formation of $k$-polytopes may lead to the emergence of diabolically degenerated EPs, due to the interplay between DPs and EPs. Such intriguing spectral properties of complex polytopes may enable constructing photonic lattice systems with similar spectral features in real space. Our results can be exploited in various quantum protocols based on EPs, paving a new direction of research in this field.Comment: 9 page

Restoring Adiabatic State Transfer in Time-Modulated Non-Hermitian Systems

Non-Hermitian systems have attracted much interest in recent decades, driven partly by the existence of exotic spectral singularities, known as exceptional points (EPs), where the dimensionality of the system evolution operator is reduced. Among various intriguing applications, the discovery of EPs has suggested the potential for implementing a symmetric mode switch, when encircling them in a system parameter space. However, subsequent theoretical and experimental works have revealed that {\it dynamical} encirclement of EPs invariably results in asymmetric mode conversion; namely, the mode switching depends only on the winding direction but not on the initial state. This chirality arises from the failure of adiabaticity due to the complex spectrum of non-Hermitian systems. Although the chirality revealed has undoubtedly made a significant impact in the field, a realization of the originally sought symmetric adiabatic passage in non-Hermitian systems with EPs has since been elusive. In this work, we bridge this gap and theoretically demonstrate that adiabaticity, and therefore a symmetric state transfer, is achievable when dynamically winding around an EP. This becomes feasible by specifically choosing a trajectory in the system parameter space along which the corresponding evolution operator attains a real spectrum. Our findings, thus, offer a promise for advancing various wave manipulation protocols in both quantum and classical domains.Comment: 6 pages, 4 figure

Kraus representation of damped harmonic oscillator and its application

By definition, the Kraus representation of a harmonic oscillator suffering from the environment effect, modeled as the amplitude damping or the phase damping, is directly given by a simple operator algebra solution. As examples and applications, we first give a Kraus representation of a single qubit whose computational basis states are defined as bosonic vacuum and single particle number states. We further discuss the environment effect on qubits whose computational basis states are defined as the bosonic odd and even coherent states. The environment effects on entangled qubits defined by two different kinds of computational basis are compared with the use of fidelity.Comment: 9 pages, 3 figure

Dynamics of entanglement for coherent excitonic states in a system of two coupled quantum dots and cavity QED

The dynamics of the entanglement for coherent excitonic states in the system of two coupled large semiconductor quantum dots ($R/a_{B}\gg 1$) mediated by a single-mode cavity field is investigated. Maximally entangled coherent excitonic states can be generated by cavity field initially prepared in odd coherent state. The entanglement of the excitonic coherent states between two dots reaches maximum when no photon is detected in the cavity. The effects of the zero-temperature environment on the entanglement of excitonic coherent state are also studied using the concurrence for two subsystems of the excitonsComment: 7 pages, 6 figure

Size-dependent decoherence of excitonic states in semiconductor microcrystallites

The size-dependent decoherence of the exciton states resulting from the spontaneous emission is investigated in a semiconductor spherical microcrystallite under condition $a_{B}\ll R_{0}\leq\lambda$. In general, the larger size of the microcrystallite corresponds to the shorter coherence time. If the initial state is a superposition of two different excitonic coherent states, the coherence time depends on both the overlap of two excitonic coherent states and the size of the microcrystallite. When the system with fixed size is initially in the even or odd coherent states, the larger average number of the excitons corresponds to the faster decoherence. When the average number of the excitons is given, the bigger size of the microcrystallite corresponds to the faster decoherence. The decoherence of the exciton states for the materials GaAs and CdS is numerically studied by our theoretical analysis.Comment: 4 pages, two figure

Quantum Statistics of Surface Plasmon Polaritons in Metallic Stripe Waveguides

Single surface plasmon polaritons are excited using photons generated via spontaneous parametric down-conversion. The mean excitation rates, intensity correlations and Fock state populations are studied. The observed dependence of the second order coherence in our experiment is consistent with a linear uncorrelated Markovian environment in the quantum regime. Our results provide important information about the effect of loss for assessing the potential of plasmonic waveguides for future nanophotonic circuitry in the quantum regime.Comment: 21 pages, 6 figures, published in Nano Letters, publication date (web): March 27 (2012