Effect of PT-Symmetric Operator on Coherence Under the Non-Markovian Environments

In this work, we mainly investigate effect of PT-symmetric operation on the dynamic behavior of the relative entropy of coherence for a two-level system within non-Markovian environments and put forward a feasible physical scheme to recover coherence by utilizing optimal PT-symmetric operation. The results show that the damaged quantum coherence can be effectively restored under influence of the non-Markovian regimes. Furthermore, the freezing phenomenon of the coherence can be detected by using the optimal PT-symmetric operation strength within the non-Markovian environments.

     

Reduction of entropic uncertainty in entangled qubits system by local PT-symmetric operation

We investigate the quantum-memory-assisted entropic uncertainty for an entangled two-qubit system in a local quantum noise channel with PT-symmetric operation performing on one of the two particles. Our results show that the quantum-memory-assisted entropic uncertainty in the qubits system can be reduced effectively by the local PT-symmetric operation. Physical explanations for the behavior of the quantum-memory-assisted entropic uncertainty are given based on the property of entanglement of the qubits system and the non-locality induced by the re-normalization procedure for the non-Hermitian PT-symmetric operation.     

Entropic uncertainty relation of a qubit-qutrit Heisenberg spin model and its steering

We investigate the quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in a Heisenberg XYZ mixed-spin (1/2, 1) model. Coupling strength, Dzyaloshinskii-Moriya (DM) interaction and inhomogeneous magnetic field, respectively, contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail. Furthermore, we compare the uncertainty of the bipartite hybrid model with those of qubit-qubit and qutrit-qutrit systems. Meanwhile, the effects of local PT-symmetric operation and weak measurement on the steering of entropic uncertainty are analyzed. We find that the local PT-symmetric operation can reduce the entropic uncertainty, and the entropic uncertainty can also be decreased by weak measurement reversal.     

Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass

We present a new method to construct the exactly solvable PT-symmetric potentials within the framework of the position-dependent effective mass Dirac equation with the vector potential coupling scheme in 1 + 1 dimensions. In order to illustrate the procedure, we produce three PT-symmetric potentials as examples, which are PT-symmetric harmonic oscillator-like potential, PT-symmetric potential with the form of a linear potential plus an inversely linear potential, and PT-symmetric kink-like potential, respectively. The real relativistic energy levels and corresponding spinor components for the bound states are obtained by using the basic concepts of the supersymmetric quantum mechanics formalism and function analysis method.     

Investigation of PT-symmetric Hamiltonian Systems from an Alternative Point of View

Two non-Hermitian PT-symmetric Hamiltonian systems are reconsidered by means of the algebraic method which was originally proposed for the pseudo-Hermitian Hamiltonian systems rather than for the PT-symmetric ones.Compared with the way converting a non-Hermitian Hamiltonian to its Hermitian counterpart,this method has the merit that keeps the Hilbert space of the non-Hermitian PT-symmetric Hamiltonian unchanged.In order to give the positive definite inner product for the PT-symmetric systems,a new operator V,instead of C,can be introduced.The operator V has the similar function to the operator C adopted normally in the PT-symmetric quantum mechanics,however,it can be constructed,as an advantage,directly in terms of Hamiltonians.The spectra of the two non-Hermitian PT-symmetric systems are obtained,which coincide with that given in literature,and in particular,the Hilbert spaces associated with positive definite inner products are worked out.     

Relativistic Confinement of Neutral Fermions with Partially Exactly Solvable and Exactly Solvable PT-Symmetric Potentials in the Presence of Position-Dependent Mass

The relativistic problems of neutral fermions subject to a new partially exactly solvable PT-symmetric potential and an exactly solvable PT-symmetric hyperbolic cosecant potential in 1+1 dimensions are investigated. The Dirac equation with the double-well-like mass distribution in the background of the PT-symmetric vector potential coupling can be mapped into the Schrödinger-like equation with the partially exactly solvable double-well potential. The position-dependent effective mass Dirac equation with the PT-symmetric hyperbolic cosecant potential can be mapped into the Schrödinger-like equation with the exactly solvable modified Pöschl-Teller potential. The real relativistic energy levels and corresponding spinor wavefunctions for the bound states have been given in a closed form.     

Visualization of branch points in PT-symmetric waveguides

The visualization of an exceptional point in a PT-symmetric directional coupler (DC) is demonstrated. In such a system the exceptional point can be probed by varying only a single parameter. Using the Rayleigh-Schr?dinger perturbation theory we prove that the spectrum of a PT-symmetric Hamiltonian is real as long as the radius of convergence has not been reached. We also show how one can use a PT-symmetric directional coupler to measure the radius of convergence for non-PT-symmetric structures. For such systems the physical meaning of the rather mathematical term radius of convergence is exemplified.     

Optimally weighted maximum a posteriori probabilities based on minimum classification error for dual-microphone voice activity detection

The dual-microphone voice activity detection (VAD) technique is proposed by applying discriminative weight training to achieve optimal weighting of spatial features available within the dual-microphone VAD. Since the motivation behind our method is to use the relevant spatial information available from the two microphones, we employ the phase difference, coherence, and power level difference ratio (PLDR) as a feature vector, and then use this feature vector to derive the maximum a posteriori (MAP) probabilities. Then, we combine each MAP probability based on a discriminative weight training, i.e., the minimum classification error (MCE) method to offer an optimal VAD decision in a spectral domain, which successfully represents the dynamic evolution of speech over time even in the non-stationary noise environments. The proposed dual-microphone VAD algorithm outperforms conventional dual-microphone VAD methods based on only single feature among the PLDR, phase difference, and spectral coherence.     

Geometry of time-dependent PT-symmetric quantum mechanics

A new type of quantum theory known as time-dependent PT-symmetric quantum mechanics has received much attention recently. It has a conceptually intriguing feature of equipping the Hilbert space of a PT-symmetric system with a time-varying inner product. In this work, we explore the geometry of time-dependent PT-symmetric quantum mechanics. We find that a geometric phase can emerge naturally from the cyclic evolution of a PT-symmetric system,and further formulate a series of related differential-geometry concepts, including connection, curvature, parallel transport,metric tensor, and quantum geometric tensor. These findings constitute a useful, perhaps indispensible, tool to investigate geometric properties of PT-symmetric systems with time-varying system's parameters. To exemplify the application of our findings, we show that the unconventional geometric phase [Phys. Rev. Lett. 91 187902(2003)], which is the sum of a geometric phase and a dynamical phase proportional to the geometric phase, can be expressed as a single geometric phase unveiled in this work.     

Finding Short-Range Parity-Time Phase-Transition Points with a Neural Network

The non-Hermitian PT-symmetric system can live in either unbroken or broken PT-symmetric phase. The separation point of the unbroken and broken PT-symmetric phases is called the PT-phase-transition point.Conventionally, given an arbitrary non-Hermitian PT-symmetric Hamiltonian, one has to solve the corresponding Schrodinger equation explicitly in order to determine which phase it is actually in. Here, we propose to use artificial neural network(ANN) to determine the PT-phase-transition points for non-Hermitian PT-symmetric systems with short-range potentials. The numerical results given by ANN agree well with the literature, which shows the reliability of our new method.     

Dynamics and Protection of the Relative Entropy of Coherence via Additional Non-interacting Qubits

We analytically study the dynamical behavior of the quantum coherence of a single-qubit coupled to a bosonic reservoir at zero temperature via plugging additional non-interacting qubits into the reservoir in both Markovian and non-Markovian regimes. The influences of detuning, memory effects and number of additional qubits on the dynamics of the quantum coherence are considered. It is found that, via increasing the number of the additional qubits in the reservoir, the quantum coherence can be preserved. Moreover, the method based on the combination of larger effective detuning, the stronger non-Markovian effects and the more number of additional qubits, can more effectively prevent the loss of the quantum coherence.

     

On “Comment on Supersymmetry, PT-symmetry and spectral bifurcation”

In “Comment on Supersymmetry, PT-symmetry and spectral bifurcation” [1], Bagchi and Quesne correctly show the presence of a class of states for the complex Scarf-II potential in the unbroken PT-symmetry regime, which were absent in [2]. However, in the spontaneously broken PT-symmetry case, their argument is incorrect since it fails to implement the condition for the potential to be PT-symmetric: C^PT[2(A − B) + α] = 0. It needs to be emphasized that in the models considered in [2], PT is spontaneously broken, implying that the potential is PT-symmetric, whereas the ground state is not. Furthermore, our supersymmetry (SUSY)-based ‘spectral bifurcation’ holds independent of the sl(2) symmetry consideration for a large class of PT-symmetric potentials.     

Analytical Study on Propagation Dynamics of Optical Beam in Parity-Time Symmetric Optical Couplers

We present exact analytical solutions to parity-time(P T) symmetric optical system describing light transport in P T-symmetric optical couplers. We show that light intensity oscillates periodically between two waveguides for unbroken P T-symmetric phase, whereas light always leaves the system from the waveguide experiencing gain when light is initially input at either waveguide experiencing gain or waveguide experiencing loss for broken P T-symmetric phase. These analytical results agree with the recent experimental observation reported by Ru¨ter et al. [Nat. Phys.6(2010) 192]. Besides, we present a scheme for manipulating P T symmetry by applying a periodic modulation. Our results provide an efficient way to control light propagation in periodically modulated P T-symmetric system by tuning the modulation amplitude and frequency.     

Nonlocality in PT-symmetric waveguide arrays with gain and loss

We demonstrate that light propagation in waveguide arrays that include PT-symmetric structures can exhibit strongly nonlocal sensitivity to topology of the array at fixed other parameters. We consider an array composed of lossless waveguides, that includes a pair of PT-symmetric waveguides with balanced gain and loss, and reveal that PT-symmetry breaking thresholds are different for planar and circular array configurations. These results demonstrate that PT-symmetric structures can offer new regimes for optical beam shaping compared to conservative structures.     

Oscillatory stability of quantum droplets in PT-symmetric optical lattice

We study stability and collisions of quantum droplets(QDs) forming in a binary bosonic condensate trapped in parity-time (PT)-symmetric optical lattices. It is found that the stability of QDs in the PT-symmetric system depends strongly on the values of the imaginary part W_0 of the PT-symmetric optical lattices, self-repulsion strength g, and the condensate norm N. As expected,the PT-symmetric QDs are entirely unstable in the broken PT-symmetric phase. However, the PT-symmetric QDs exhibit oscillatory stability with the increase of N and g in the unbroken PT-symmetric phase. Finally, collisions between PT-symmetric QDs are considered. The collisions of droplets with unequal norms are completely different from that in free space. Besides, a stable PT-symmetric QDs collides with an unstable ones tend to merge into breathers after the collision.     

Variance Measure of Coherence of Quantum Pure States

We provide an expression for the measure of coherence of quantum pure states, which is obtained by quantifying the deviation or distance between the measured state and the maximally coherent states in the same Hilbert space. We classify quantum pure states in a Hilbert space according to their coherence and prove that the variance measure of coherence is proper for all quantum pure states. We demonstrate that the variance measure of coherence is simpler and easier to obtain than the l₁-norm of coherence and the relative entropy of coherence.

     

Negative refraction based on purely imaginary metamaterials

By introducing a new mechanism based on purely imaginary metamaterials (PIMs), we reveal that bidirectional negative refraction and planar focusing can be obtained using a pair of PIM slabs, overcoming the unidirectional limit in parity-time (PT)-symmetric systems. Compared with PT-symmetric systems, which require two different types of materials, the proposed negative refraction can be realized using two identical media. In addition, asymmetric excitation with bidirectional total transmission is observed in our PIM system. Therefore, a new way to realize negative refraction with properties that are unavailable in PT-symmetric systems is presented.     

Stabilization of optical solitons in chirped PT-symmetric lattices

We investigate the stability properties of optical solitons in a chirped PT-symmetric lattice whose frequency changes in the transverse direction. Linear-stability analysis together with the direct propagation simulations demonstrates that the chirped lattice can improve the stability of optical solitons dramatically. The instability of fundamental solitons can be completely suppressed if the chirp rate exceeds a critical value. A broad stability area of dipole solitons appears if the lattice is appropriately chirped. Thus, we propose an effective way to suppress the instability of solitons in PT-symmetric potentials.     

Full Bandwidth Measurement of Supercontinuum Spectral Phase Coherence in Long Pulse Regime

Abstract

This article reports that spectral phase coherence in the supercontinuum in long pulse regime can be measured simply and effectively by using an interference technique with the help of a Mach–Zehnder interferometer. It is also demonstrated that chromatic dispersion on the fringe visibility of interference spectral patterns is overcome in the setup. The technique is applied to characterize supercontinuum spectral phase coherence in a highly non-linear optical fiber with different input conditions: unseeded, coherent seeded, and incoherent seeded picosecond pumps. The results confirm the phase coherence characteristic predicted theoretically in previous studies.     

Solitons in PT-symmetric potential with competing nonlinearity

We investigate the effect of competing nonlinearities on beam dynamics in PT-symmetric potentials. In particular, we consider the stationary nonlinear Schrödinger equation (NLSE) in one dimension with competing cubic and generalized nonlinearity in the presence of a PT-symmetric potential. Closed form solutions for localized states are obtained. These solitons are shown to be stable over a wide range of potential parameters. The transverse power flow associated with these complex solitons is also examined.