High resolution time-delay estimation of underwater target geometric scattering

The geometric scatterings carry the information of the shape of an underwater target. While the time-delay of the weak geometric scattering exists in the received signal cannot be obtained accurately by the conventional time-delay estimation methods because of the limit of the main-lobe width and the interferences from the side-lobe. In this paper, we propose a high resolution time-delay estimation (HRTDE) scheme consisting of two steps. Firstly, when a linear-frequency-modulated (LFM) pulse is transmitted by sonar, the dechirping method transforms the geometric scatterings with different time-delays into multiple single-frequency components respectively, in which the frequency of the dechirped signal shows a linear relationship with the time-delay of the geometric scattering. Then the multiple signal classification (MUSIC) algorithm is adopted to increase the spectrum resolution when multiple single-frequency signals exist in the dechirped signal and the frequency interval is smaller than the frequency resolution limit of the Fourier transform. Simulation results show that the main lobe of the proposed scheme is sharper and with less interference from the side-lobe, compared with the conventional time-delay estimation methods. The results from the anechoic pool experiment demonstrate that the proposed scheme achieves a better time-delay estimation performance for the weak geometric scattering generated by the bottom edge of the underwater target model than match filter based methods.     

Curvature-induced bound states and coherent electron transport on the surface of a truncated cone

We study the curvature-induced bound states and the coherent transport properties for a particle constrained to move on a truncated cone-like surface. With longitudinal hard wall boundary condition, the probability densities and spectra energy shifts are calculated, and are found to be obviously affected by the surface curvature. The bound-state energy levels and energy differences decrease as increasing the vertex angle or the ratio of axial length to bottom radius of the truncated cone. In a two-dimensional (2D) GaAs substrate with this geometric structure, an estimation of the ground-state energy shift of ballistic transport electrons induced by the geometric potential (GP) is addressed, which shows that the fraction of the ground-state energy shift resulting from the surface curvature is unnegligible under some region of geometric parameters. Furthermore, we model a truncated cone-like junction joining two cylinders with different radii, and investigate the effect of the GP on the transmission properties by numerically solving the open-boundary 2D Schrödinger equation with GP on the junction surface. It is shown that the oscillatory behavior of the transmission coefficient as a function of the injection energy is more pronounced when steeper GP wells appear at the two ends of the junction. Moreover, at specific injection energy, the transmission coefficient is oscillating with the ratio of the cylinder radii at incoming and outgoing sides.     

Geometric Phase in a Two Energy Level Jaynes-Cummings Model with Imaginary Photon Process

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a two energy level Jaynes-Cummings model with imaginary photon process. We find that the geometric phases in a cycle case have nothing to do with the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. If we use the more accuracy device, the geometric phases in the imaginary photon process may be observed, and the geometric phases in this process have the observable physical effect.     

Geometric Phase in a Λ-type <Emphasis Type="Italic">k</Emphasis>-photon Jaynes-Cummings Model with Imaginary Photon Process

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent Λ-type k-photon Jaynes-Cummings model with imaginary photon process. We find that the geometric phases in a cycle case are independent of the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. If we use the more accuracy device, the geometric phases in this process may be observed, and the geometric phases in this process have the observable physical effect.     

Enhanced and confined light transmission through a funnel-type aperture with a sub-wavelength outlet

Enhanced transmission through sub-wavelength hole arrays and a single sub-wavelength aperture with periodic corrugations surrounded have been investigated extensively. We report the similar phenomenon through a funnel-type aperture with a sub-wavelength outlet in a thick silver film, which was obtained numerically by using finite-difference time-domain method. Properties of the transmission spectrum can be modulated by geometric parameters of the funnel-type aperture. With periodic grooves or dielectric gratings on the output surface of the structure, beaming light emission can be obtained.     

Geometric Phase in a Two Energy Level <Emphasis Type="Italic">k</Emphasis>-Photon Jaynes-Cummings Model with Imaginary Photon Process

By using the Lewis-Riesenfeld invariant theory, we have studied the dynamical phase and the geometric phase in a two energy level k-photon Jaynes-Cummings model with imaginary photon process. We find that the geometric phase in a cycle case is independent of the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. We predict the physical effect of the geometric phase in the imaginary photon process may be measured.     

Geometric phase in Bohmian mechanics

Using the quantum kinematic approach of Mukunda and Simon, we propose a geometric phase in Bohmian mechanics. A reparametrization and gauge invariant geometric phase is derived along an arbitrary path in configuration space. The single valuedness of the wave function implies that the geometric phase along a path must be equal to an integer multiple of 2π. The nonzero geometric phase indicates that we go through the branch cut of the action function from one Riemann sheet to another when we locally travel along the path. For stationary states, quantum vortices exhibiting the quantized circulation integral can be regarded as a manifestation of the geometric phase. The bound-state Aharonov-Bohm effect demonstrates that the geometric phase along a closed path contains not only the circulation integral term but also an additional term associated with the magnetic flux. In addition, it is shown that the geometric phase proposed previously from the ensemble theory is not gauge invariant.     

The geometric phase of a two-level atom in a narrow-bandwidth squeezed vacuum

In this paper, we derive the time dependent solution of the effective master equation for the reduced density matrix operator of a two level atom driven by a coherent laser field and damped by a finite bandwidth squeezed vacuum. The results show that the initial state setting, detuning parameter and Rabi frequency play important roles in the evolution of the system dynamics and geometric phase. We present a useful way for controlling the geometric phase variation for the system under consideration.     

Geometric Phase in a Generalized Time-Dependent Jaynes-Cummings Model

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent Jaynes-Cummings model. It is found that the geometric phases in a cycle case have nothing to do with the frequency of the electromagnetic wave, the energy difference between two levels of the atom, and the coupling strength between the atom and the light field.     

Light transmission by a three-level emitter embedded in a waveguide-coupled two-mode photonic crystal nanocavity

We investigate light transmission obtained from a three-level V-type emitter embedded in a waveguide-coupled two-mode photonic crystal nanocavity operating in the weak-coupling regime. It is shown that the composite system exhibits double electromagnetically-induced-transparency-like characteristics and a π phase shift while not suffering from absorption in the experimentally available parameter range. The double-frequency transparency of the input light expands the frequency range of EIT and may improve the controllability of EIT. The proposed scheme also provides a way to achieve integrated photonic devices on a chip for applications requiring multiple EIT effect.     

抗JPEG压缩和几何攻击的鲁棒零水印算法

针对数字图像传输时经常面临JPEG压缩和几何攻击,提出一种抗JPEG压缩和几何攻击的鲁棒零水印算法.将原始图像分割成互不重叠的子块,对每个子块进行奇异值分解,对奇异值矩阵进行harr小波变换,通过比较相邻两个子块奇异值矩阵小波低频逼近子带对角线元素的均值大小关系产生零水印序列.数学理论分析表明:通过比较相邻两个子块奇异值矩阵所有奇异值的均值大小关系产生零水印序列,算法实质上没有对原始图像做任何改动,具有非常好的不可见性.实验结果表明,该算法在抵抗JPEG压缩和旋转、尺寸缩放、随机删除行列、偏移行列、打印-扫描几种几何攻击表现出比较强的鲁棒性.     

Geometric curvature and phase of the Rabi model

We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to measure in the qubit–cavity system. We also calculate the geometric phase beyond the RWA and find an anomalous sudden change, which implies the breakdown of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution are ill-defined near the anti-crossing point in the spectrum.     

An angular frequency dependence on the Aharonov–Casher geometric phase

A quantum effect characterized by a dependence of the angular frequency associated with the confinement of a neutral particle to a quantum ring on the quantum numbers of the system and the Aharonov–Casher geometric phase is discussed. Then, it is shown that persistent spin currents can arise in a two-dimensional quantum ring in the presence of a Coulomb-type potential. A particular contribution to the persistent spin currents arises from the dependence of the angular frequency on the geometric quantum phase.     

Geometric Phase in a Time-Dependent <Emphasis Type="Italic">k</Emphasis>-Photon Λ-Type Jaynes–Cummings Model

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent k-photon Λ-type Jaynes–Cummings model. It is found that, different from the dynamical phases, the geometric phases in a cycle case are independent of the photon numbers, the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency.     

Quantum motion of a point particle in the presence of the Aharonov–Bohm potential in curved space

The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov–Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The geometry of this line element establishes that the motion of the particle can occur on the surface of a cone or an anti-cone. As a consequence of the nontrivial topology of the cone and also because of two-dimensional confinement, the geometric potential should be taken into account. At first, we establish the conditions for the particle describing a circular path in such a context. Because of the presence of the geometric potential, which contains a singular term, we use the self-adjoint extension method in order to describe the dynamics in all space including the singularity. Expressions are obtained for the bound state energies and wave functions.     

Enhanced transmission through nano-aperture on a tapered metallic substrate

The optical transmission and distribution through a subwavelength slit on a tapered metallic substrate was investigated. By using a 45° tapered structure rather than a traditional metallic plate, a 6-fold transmission enhancement could be achieved. This is due to the asymmetrical excitation of surface waves and the matching of propagation constants between the surface waves and slit waveguide. In addition, by patterning surface corrugations in the exit plane, the beam could be focused. By tuning the period of the surface corrugations, we were able to adjust the focal length. For an input wavelength of 0.5 μm, the focal point could be kept within 0.6 μm with a focal length extending from 0.5 μm to 2.5 μm and a grating period ranging from 0.5 μm to 0.6 μm.     

Geometric phase within the complex quantum Hamilton-Jacobi formalism

We derive a geometric phase using the quantum kinematic approach within the complex quantum Hamilton-Jacobi formalism. The single valuedness of the wave function implies that the geometric phase along an arbitrary path in the complex plane must be equal to an integer multiple of 2π. The nonzero geometric phase indicates that we travel along the path through the branch cut of the phase function from one Riemann sheet to another.     

Enhanced optical reflection and multiple-peak transmission from a subwavelength slit with surface corrugations

We have observed a new phenomenon of the enhanced optical reflection and transmission from a subwavelength metallic slit with surface corrugations. The reflected energy is focused by the periodic structure and our experiment shows that it is more effective than a planar metal surface in real situations. The transmission spectrum performs the feature of a multipeak narrow-band transmission with a wavelength spacing of 1.4 nm resulting from the FP cavity resonance in the substrate film. Such optical response properties of our sample will be very useful for applications in many fields including wavelength-division-multiplexing (WDM) optical communications systems.     

Quantum phases for a generalized harmonic oscillator

An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.      

Use of non-adiabatic geometric phase for quantum computing by NMR

Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.