Fluxons interactions in a Josephson junction with a phase-shift

We consider a long Josephson junction with a discontinuity point characterized by a gauge phase-shift. The system is described by a modified sine-Gordon equation. We study, in particular, the interactions between a fluxon and a fractional fluxon. A perturbation theory is developed in the small phase-shift limit to understand the characteristics of the interaction. Finally, numerical computations of the threshold bias current and the threshold velocity for a fluxon running over a fractional fluxon are presented.     

New Eigenmodes of Propagation in Quadratic Graded Index Media and Complex Fractional Fourier Transform

By introducing a convenient complex form of the α-th 2-dimensional fractional Fourier transform (CFFT) operation we find that it possesses new eigenmodes which are two-mode Hermite polynomials. We prove the eigenvalues of propagation in quadratic graded-index medium over a definite distance are the same as the eigenvalues of the α-th CFFT, which means that our definition of the α-th CFFT is physically meaningful.     

Fractional ac Josephson effect in p- and d-wave superconductors

For certain orientations of Josephson junctions between two p_x-wave or two d-wave superconductors, the subgap Andreev bound states produce a -periodic relation between the Josephson current I and the phase difference : . Consequently, the ac Josephson current has the fractional frequency , where V is the dc voltage. In the tunneling limit, the Josephson current is proportional to the first power (not square) of the electron tunneling amplitude. Thus, the Josephson current between unconventional superconductors is carried by single electrons, rather than by Cooper pairs. The fractional ac Josephson effect can be observed experimentally by measuring frequency spectrum of microwave radiation from the junction. We also study junctions between singlet s-wave and triplet p_x-wave, as well as between chiral -wave superconductors.Received: 24 September 2003, Published online: 2 April 2004PACS: 74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects - 74.70.Kn Organic superconductors - 74.72.-h Cuprate superconductors (high-T_c and insulating parent compounds) - 74.70.Pq Ruthenates     

Fractional Josephson vortices: oscillating macroscopic spins

Photon-induced band bending changes and subsequent relaxation at the buried insulator/semiconductor interface of BaF₂/Si(001) have been investigated. This is achieved by creating free charge carriers through absorption of a visible pump laser pulse (λ=532 nm, E=2.33 eV) in the silicon, followed by time resolved photoelectron spectroscopy using vacuum-ultraviolet synchrotron radiation (E=18 eV) as a probe of the BaF₂ valence band (VB). Since the excitation takes place in the semiconductor and the probe photoemission signal originates from the BaF₂, the relaxation at the interface has been probed. PACS 41.60.Ap; 33.60.Cv; 79.60.Jv; 73.40.Qv     

Fractional Josephson current through a Luttinger liquid with topological excitations

Recently, the Majorana fermion has received great attentions due to its promising application in the fault-tolerant quantum computation. This application requires more accessible methods to detect the motion and braiding of the Majorana fermions. We use a Luttinger liquid ring to achieve this goal, where the ring geometry is nontrivial in the sense that it leads to fermion-parity-dependent topological excitations. First, we briefly review the essential physics of the Luttinger liquid and the Majorana fermion, in order to give an introduction of the general framework used in the following main work. Then, we theoretically investigated the DC Josephson effect between two topological superconductors via a Luttinger liquid ring. A low-energy effective Hamiltonian is derived to show the existence of the fractional Josephson current. Also, we find that the amplitude of the Josephson current, which is determined by the correlation function of Luttinger liquid, exhibits different behaviors in terms of the parity of Luttinger liquid due to the topological excitations. Our results suggest a possible method to detect the Majorana fermions and their tunneling process.     

On Sound Propagation in Dispersive Media

Sound propagation in monodisperse emulsions with arbitrary volume concentrations is studied theoretically using a cell model. It is assumed that emulsion cells are bounded by thin and imponderable rigid shells allowing realization of the minimum energy dissipation principle with viscous acoustic losses. Solutions covering many particular cases and wide parameter and variable ranges have been obtained. These solutions are suitable for studying acoustic properties of emulsions and suspensions, marine sediments, fogs, and smoke, as well as elastoviscous materials with solid or liquid inclusions, etc. Sound propagation and absorption in emulsions and suspensions are considered in more detail. The experimental data in the literature is compared.     

Fermi-Dirac Kink Propagation in High-Order Nonlinear Media

We show analytically that addition of a quintic term to the positive Kerr-type nonlinearity offers a unique type of kink soliton-like solution with Fermi-Dirac profile. This type of optical kink allows, in contrast to other optical kinks discovered so far, stationary kink formation not only in the time domain but in the spatial domain. The latter could admit of a route for the first time to our knowledge to spatial kink solitons of intensified laser beams. The underlying principle of the optical kink propagation is described.     

梯度折射率介质中高斯光束的非线性传输特性

 利用无像差自聚焦理论研究了梯度折射率非线性Kerr介质中高斯光束的传输特性,得到了高斯光束光斑半径和波面曲率半径的表达式。解析结果清楚地表明了衍射、自聚焦以及梯度折射率效应之间的竞争对高斯光束传输行为的影响。梯度折射率效应使光束自聚焦的距离缩短。     

Propagation of Smooth Pulses in Anomalously Dispersive Media

In the present letters we study the propagation of smooth pulses in anomalously dispersive media. We prove that non-analytical but smooth points in a pulse still propagate with the vacuum speed of light, c. It gives an upper limit for signal velocity as well as the non-continuous points of the envelop of a pulse or its derivatives of arbitrary order do.     

Propagation of Smooth Pulses in Anomalously Dispersive Media

In the present letter, we study the propagation of smooth pulses in anomalously dispersive media. We prove that non-analytical but smooth points in a pulse still propagate with the vacuum speed of light, c. It gives an upper limit for signal velocity as well as the non-continuous points of the envelop of a pulse or its derivatives of arbitrary order do.     

Generation of macroscopic entangled coherent states with large Josephson junctions

We propose a simple and experimental architecture to generate macroscopic entanglement in a solid system which consists of two large Josephson junctions and a flux qubit. Through quantum measuring of flux qubit, entangled coherent states of two large Josephson junctions are obtained. The concurrence of entangled coherent states can be accommodated by adjusted systematic parameters. We also give a brief discussion on the experimental feasibility of this proposal.     

Beam Propagation Factor and Generation of Cosh-squared-Gaussian Beams

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Beam Propagation Factor and Generation of Cosh-squared-Gaussian Beams

A new light beam termed as a cosh-squared-Gaussian beam (ChSGB) which may be one of solutions of the paraxial wave equation for propagation in complex optical systems has been introduced. Their beam propagation factor (M2-factor) is derived and schemes to generate this light beams are proposed.     

Generation and Propagation of Optical Superoscillatory Vortex Arrays

Superoscillation is an intriguing wave phenomenon which enables subwavelength features propagating into far field and hence has potential applications in super‐resolution microscopy as well as particle trapping and manipulation. While previous demonstrations mostly concentrate on designing complicated nanostructures for generating uncontrollable superoscillatory functions, here a new technique which allows for creating polynomially shaped superoscillatory functions that contain phase singularity arrays is demonstrated both theoretically and experimentally. Such a technique is implemented in optical experiments for the first time and controllable superoscillatory lobes with feature much below the diffraction limit is achieved. More importantly, a general theoretical framework, which, to our knowledge, has not been reported before, is developed to show how the created superoscillations propagate to a distance of many Rayleigh ranges and eventually disappear when the distance is sufficiently larger. The validity of the model is confirmed by the experiments. The results may trigger further studies in light field shaping and manipulations in subwavelength scale.     

部分相干平顶光束在梯度折射率介质中的传输特性

利用广义惠更斯-菲涅尔衍射积分方法,推导出部分相干平顶光束在梯度折射率介质中传输的交叉谱密度函数解析表达式,对部分相干平顶光束在梯度折射率介质中的传输特性进行了分析,并进一步讨论了介质梯度折射率系数、光束阶数以及光束相干性对传输特性的影响.结果表明,部分相干平顶光束在梯度折射率介质中传输时的轴上光强分布呈现周期性变化了,且周期由梯度折射率系数决定,而与光束相干性无关.光束阶数越高、相干性越好、介质梯度折射率系数越大,则在介质中的轴上峰值光强越大.并且,在光强峰值位置附近的光强分布随传输距离的变化非常剧烈.     

脉冲在时域二次折射率介质中的传播

从空域与时域的相似性出发，把克尔介质近似为时域二次折射率介质，从而得到了脉冲在该介质中的解析形式，并给出了相应的时域传输矩阵。     

正色散克尔介质中光脉冲的传输

综合考虑了在２＋１维正色散介质中克尔效应衍射、色散对光脉冲传输的影响，得到了脉宽、束宽传输的一般规律，并以高斯光束为例用数值法近似讨论了耦合强度、初始脉宽、初始啁啾对自聚焦及自相位调制自脉宽压缩的影响。