non-Hermitian Hamiltonian Model Research Articles

Application of non-Hermitian Hamiltonian model in open quantum optical systems* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61925503, 11874038, and 11654002), the Key Project of the National Key R&D Program of China (Grant Nos. 2016YFA0301402 and 2020YFA0309400), the Program for the Innovative Talents of Higher Education Institutions of Shanxi, the Program for Sanjin Scholars of

Non-Hermitian systems have observed numerous novel phenomena and might lead to various applications. Unlike standard quantum physics, the conservation of energy guaranteed by the closed system is broken in the non-Hermitian system, and the energy can be exchanged between the system and the environment. Here we present a scheme for simulating the dissipative phase transition with an open quantum optical system. The competition between the coherent interaction and dissipation leads to the second-order phase transition. Furthermore, the quantum correlation in terms of squeezing is studied around the critical point. Our work may provide a new route to explore the non-Hermitian quantum physics with feasible techniques in experiments.

Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla.

In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system–environment dynamics, which are trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an ancillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arising from the procedure. In this paper, we demonstrate the effectiveness of such a protocol by applying it to physically relevant multi-spin models, showing that the effective non-Hermitian Hamiltonian drives the system to a maximally entangled stationary state. In addition, we report a new recipe to construct a physical scenario where the quantum dynamics of a physical system represented by a given non-Hermitian Hamiltonian model may be simulated. The physical implications and the broad scope potential applications of such a scheme are highlighted.

Dissipative dynamics of an entangled three-qubit system via non-Hermitian Hamiltonian: Its correspondence with Markovian and non-Markovian regimes

We investigate an entangled three-qubit system in which only one of the qubits experiences the decoherence effect by considering a non-Hermitian Hamiltonian, while the other two qubits are isolated, i.e., do not interact with environment, directly. Then, the time evolution of the density matrix (for the pure as well as mixed initial density matrix) and the corresponding reduced density matrices are obtained, by which we are able to utilize the dissipative non-Hermitian Hamiltonian model with Markovian and non-Markovian regimes via adjusting the strange of the non-Hermitian term of the total Hamiltonian of the under-considered system.

Realization of complex conjugate media using non-PT-symmetric photonic crystals

Abstract Although parity-time (PT)-symmetric systems can exhibit real spectra in the exact PT-symmetry regime, PT-symmetry is actually not a necessary condition for the real spectra. Here, we show that non-PT-symmetric photonic crystals (PCs) carrying Dirac-like cone dispersions can always exhibit real spectra as long as the average non-Hermiticity strength within the unit cell for the eigenstates is zero. By building a non-Hermitian Hamiltonian model, we find that the real spectra of the non-PT-symmetric system can be explained using the concept of pseudo-Hermiticity. We demonstrate using effective medium theories that, in the long-wavelength limit, such non-PT-symmetric PCs behave like the so-called complex conjugate medium (CCM) whose refractive index is real but whose permittivity and permeability are complex numbers. The real refractive index for this effective CCM is guaranteed by the real spectrum of the PCs, and the complex permittivity and permeability come from non-PT-symmetric loss-gain distributions. We show some interesting phenomena associated with CCM, such as the lasing effect.

Exceptional points and their coalescence ofPT-symmetric interface states in photonic crystals

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 photonic crystals with different signs of the imaginary parts of permittivity also supports surface electromagnetic eigenmodes with real eigenfrequencies, protected by $ PT $ symmetry of such loss-gain interface. Using a multiple scattering method and full wave numerical methods, we show that the dispersion of such interface states exhibit unusual features such as zig-zag trajectories or closed-loops. To quantify the dispersion, we establish a non-Hermitian Hamiltonian model that can account for the zig-zag and closed-loop behaviour for arbitrary Bloch momentums. The properties of the interface states near the Brillouin zone center can also be explained within the framework of effective medium theory. It is shown that turning points of the dispersion are exceptional points (EPs), which are characteristic features of non-Hermitian systems. When the permittivity of photonic crystal changes, these EPs can coalesce into higher order EPs or anisotropic EPs. These interface modes hence exhibit and exemplify many complex phenomena related to exceptional point physics.

CPT symmetry in honeycomb lattices and quantum brachistochrone problem

Abstract In this paper, we have provided a matrix Hamiltonian model for honeycomb lattices and subsequently obtained the dispersion relation. Furthermore, we have constructed the C operator for the given non-Hermitian Hamiltonian model. The quadratic surfaces are sketched and the quantum Brachistochrone problem is discussed for the given honeycomb lattice model.

Metric operator for the non-Hermitian Hamiltonian model and pseudo-super-symmetry

We have obtained the metric operator for the non-Hermitian Hamiltonian model . We also found the intertwining operator that connects the Hamiltonian to the adjoint of its pseudo-super-symmetric partner Hamiltonian for the model of the hyperbolic Rosen–Morse II potential.

\U0001d4ab\U0001d4af Symmetric Hamiltonian Model and Exactly Solvable Potentials

Searching for non-Hermitian, \U0001d4ab\U0001d4af-symmetric Hamiltonians [1] with real spectra has been acquiring much interest for fourteen years. In this article, we have introduced a \U0001d4ab\U0001d4af symmetric non-Hermitian Hamiltonian model which is given as where ω and α are real constants, and are first order differential operators. Because the Hamiltonian ℋ is pseudo-Hermitian, we have obtained the Hermitian equivalent of ℋ which is in Sturm- Liouville form leads to exactly solvable potential models which are effective screened and hyperbolic Rosen-Morse II potentials. Using convenient sinilarity transformations, we have obtained a physical Hamiltonian h for each case. Then, the Schrödinger equation is solved exactly using Shape Invariance method of Supersymmetric Quantum Mechanics [2].

Symmetric Hamiltonian model and Dirac equation in 1+1 dimensions

In this paper, we have introduced a symmetric non-Hermitian Hamiltonian model which is given as where ω and α are real constants, and are first-order differential operators. The Hermitian form of the Hamiltonian is obtained by suitable mappings and it is interrelated to the time-independent one-dimensional Dirac equation in the presence of position-dependent mass. Then, Dirac equation is reduced to a Schrödinger-like equation and two new complex non- symmetric vector potentials are generated. We have obtained a real spectrum for these new complex vector potentials using the shape invariance method. We have searched the real energy values using numerical methods for the specific values of the parameters.

Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism

Using an energy-independent non-Hermitian Hamiltonian approach to open systems, we fully describe transport through a sequence of potential barriers as external barriers are varied. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian model, a transition to a superradiant regime is shown to occur. Transport properties undergo a strong change at the superradiance transition, where the transmission is maximized and a drastic change in the structure of resonances is demonstrated. Finally, we analyze the effect of the superradiance transition in the Anderson localized regime.