Simple representation of the quantum entanglement of coupled harmonic oscillators in terms of the reflection coefficient

Quantum entanglement of coupled harmonic oscillators is frequently applied in quantum and non-linear physics, molecular chemistry and biophysics, which is why its study is of a great interest for modern physics. In this work a quantum entanglement of a coupled harmonic oscillator in a simple form was found. This simple form is presented as a single parameter – reflection coefficient R. All parameters of the studied system are included in the R coefficient. It is shown that the derivation of the expression can have applications in quantum optics, in particular in quantum metrology.

Strong Dipole–Quadrupole–Exciton Coupling Realized in a Gold Nanorod Dimer Placed on a Two-Dimensional Material

Simple systems in which strong coupling of different excitations can be easily realized are highly important, not only for fundamental research but also for practical applications. Here, we proposed a T-shaped gold nanorod (GNR) dimer composed of a long GNR and a short GNR perpendicular to each other and revealed that the dark quadrupole mode of the long GNR can be activated by utilizing the dipole mode excited in the short GNR. It was found that the strong coupling between the dipole and quadrupole modes can be achieved by exciting the T-shaped GNR dimer with a plane wave. Then, we demonstrated the realization of strong dipole–quadrupole–exciton coupling by placing a T-shaped GNR on a tungsten disulfide (WS2) monolayer, which leads to a Rabi splitting as large as ~299 meV. It was confirmed that the simulation results can be well fitted by using a Hamiltonian based on the coupled harmonic oscillator model and the coupling strengths for dipole–quadrupole, dipole–exciton and quadrupole–exciton can be extracted from the fitting results. Our findings open new horizons for realizing strong plasmon–exciton coupling in simple systems and pave the way for constructing novel plasmonic devices for practical applications.

Nonlinear Dynamics of Wave Packets in Tunnel-Coupled Harmonic-Oscillator Traps

We consider a two-component linearly coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap acting in both components, we consider Josephson oscillations (JO) initiated by an input in the form of the HO’s ground state (GS) or dipole mode (DM), placed in one component. With the increase of the strength of the self-focusing nonlinearity, spontaneous symmetry breaking (SSB) between the components takes place in the dynamical JO state. Under still stronger nonlinearity, the regular JO initiated by the GS input carries over into a chaotic dynamical state. For the DM input, the chaotization happens at smaller powers than for the GS, which is followed by SSB at a slightly stronger nonlinearity. In the system with the defocusing nonlinearity, SSB does not take place, and dynamical chaos occurs in a small area of the parameter space. In the asymmetric half-trapped system, with the HO potential applied to a single component, we first focus on the spectrum of confined binary modes in the linearized system. The spectrum is found analytically in the limits of weak and strong inter-component coupling, and numerically in the general case. Under the action of the coupling, the existence region of the confined modes shrinks for GSs and expands for DMs. In the full nonlinear system, the existence region for confined modes is identified in the numerical form. They are constructed too by means of the Thomas–Fermi approximation, in the case of the defocusing nonlinearity. Lastly, particular (non-generic) exact analytical solutions for confined modes, including vortices, in one- and two-dimensional asymmetric linearized systems are found. They represent bound states in the continuum.

Outgrowth of quasi pure states in isolated coupled-harmonic-oscillator

Isolated coupled-harmonic-oscillator here is the system of two distinguishable particles coupled with a harmonic oscillator interaction potential. Each particle stays in a mixed state due to entanglement. However, in center-of-mass reference frame, we obtain quasi wavefunction of the first particle expressing quasi pure state by replacing the second coordinate in the total wavefunction. We discuss the similar systems with the first particle and the potential being same and the second mass changing from micro to macro one. Measured by fidelity and coherence, the quasi pure state approaches to the pure state of a usual harmonic oscillator with same mass and similar potential. It conversely shows that the latter purely superposed state in position representation and its coherence originate from those of the first particle, which are related with some neglected macro object and the interaction between them. The current results provide a possible clue to new insights into quantum states.

Quantum Description of a Damped Coupled Harmonic Oscillator via White-Noise Analysis

Propagator, White-Noise Analysis, Coupled Oscillators, Quantum Mechanics

Independently tunable electromagnetically induced transparency effect and dispersion in a multi-band terahertz metamaterial

In this article, we experimentally and numerically investigate a planar terahertz metamaterial (MM) geometry capable of exhibiting independently tunable multi-band electromagnetically induced transparency effect (EIT). The MM structure exhibits multi-band EIT effect due to the strong near field coupling between the bright mode of the cut-wire (CW) and dark modes of pair of asymmetric double C resonators (DCRs). The configuration allows us to independently tune the transparency windows which is challenging task in multiband EIT effect. The independent modulation is achieved by displacing one DCR with respect to the CW, while keeping the other asymmetric DCR fixed. We further examine steep dispersive behavior of the transmission spectra within the transparency windows and analyze slow light properties. A coupled harmonic oscillator based theoretical model is employed to elucidate as well as understand the experimental and numerical observations. The study can be highly significant in the development of multi-band slow light devices, buffers and modulators.