Generation of sub‐terahertz repetition rates from a monolithic self‐mode‐locked laser coupled with an external Fabry‐Perot cavity

A novel scheme to multiply the repetition rate of a monolithic self‐mode‐locked laser for generating sub‐terahertz pulse sources is successfully demonstrated. A coated Yb:KGW crystal is designed to achieve a self‐mode‐locked operation at a repetition rate of 24 GHz with an average output power exceeding 1.0 W at a pump power of 4.8 W. A partially reflective mirror is utilized to combine with the output surface of the gain medium to constitute an external Fabry‐Perot cavity. It is theoretically and experimentally verified that adjusting the external cavity length to satisfy the commensurate condition can lead to the frequency spacing to be various order harmonics of the mode spacing of the monolithic cavity. The maximum pulse repetition rate of the laser output can be up to 216 GHz and the pulse duration is as short as 330 fs. More importantly, the overall characteristics of the first‐order temporal autocorrelation traces obtained by sequentially scanning the external cavity.length display an intriguing phenomenon of temporally fractional revivals, similar to the feature of spatial Talbot revivals.

     

Conductance distribution at criticality: one‐dimensional Anderson model with random long‐range hopping

We study numerically the conductance distribution function w(T) for the one‐dimensional Anderson model with random long‐range hopping described by the Power‐law Banded Random Matrix model at criticality. We concentrate on the case of two single‐channel leads attached to the system. We observe a smooth transition from localized to delocalized behavior in the conductance distribution by increasing b, the effective bandwidth of the model. Also, for b < 1 we show that w(ln T/T_typ) is scale invariant, where T_typ = exp 〈 ln T 〉 is the typical value of T. Moreover, we find that for T < T_typ, w(ln T/T_typ) shows a universal behavior proportional to (T/T_typ)^‐1/2.     

Evolution of electric‐field‐induced quasibound states and resonances in one‐dimensional open quantum systems

A comparative analysis of three different time‐independent approaches to studying open quantum structures in a uniform electric field was performed using the example of a one‐dimensional attractive or repulsive δ‐potential and the surface that supports the Robin boundary condition. The three considered methods exploit different properties of the scattering matrix as a function of energy E: its poles, real values, and zeros of the second derivative of its phase. The essential feature of the method of zeroing the resolvent, which produces complex energies, is the unlimited growth of the wave function at infinity, which is, however, eliminated by the time‐dependent interpretation. The real energies at which the unitary scattering matrix becomes real correspond to the largest possible distortion, , or its absence at which in either case leads to the formation of quasibound states. Depending on their response to the increasing electric intensity, two types of field‐induced positive energy quasibound levels are identified: electron‐ and hole‐like states. Their evolution and interaction in the enlarging field lead ultimately to the coalescence of pairs of opposite states, with concomitant divergence of the associated dipole moments in what is construed as an electric breakdown of the structure. The characteristic features of the coalescence fields and energies are calculated and the behavior of the levels in their vicinity is analyzed. Similarities between the different approaches and their peculiarities are highlighted; in particular, for the zero‐field bound state in the limit of the vanishing , all three methods produce the same results, with their outcomes deviating from each other according to growing electric intensity. The significance of the zero‐field spatial symmetry for the formation, number, and evolution of the electron‐ and hole‐like states, and the interaction between them, is underlined by comparing outcomes for the symmetric δ geometry and asymmetric Robin wall.

     

Magnetic quantum criticality in quasi‐one‐dimensional Heisenberg antiferromagnet

We analyze exciting recent measurements [Phys. Rev. Lett. 114 (2015) 037202] of the magnetization, differential susceptibility and specific heat on one dimensional Heisenberg antiferromagnet Cu(C₄H₄N₂)(NO₃)₂ (CuPzN) subjected to strong magnetic fields. Using the mapping between magnons (bosons) in CuPzN and fermions, we demonstrate that magnetic field tunes the insulator towards quantum critical point related to so‐called fermion condensation quantum phase transition (FCQPT) at which the resulting fermion effective mass diverges kinematically. We show that the FCQPT concept permits to reveal the scaling behavior of thermodynamic characteristics, describe the experimental results quantitatively, and derive for the first time the (temperature—magnetic field) phase diagram, that contains Landau‐Fermi‐liquid, crossover and non‐Fermi liquid parts, thus resembling that of heavy‐fermion compounds.     

Ultra‐short and ultra‐intense X‐ray free‐electron laser single pulse in one‐dimensional photonic crystals

The propagation within a one‐dimensional photonic crystal of a single ultra‐short and ultra‐intense pulse delivered by an X‐ray free‐electron laser is analysed with the framework of the time‐dependent coupled‐wave theory in non‐linear media. It is shown that the reflection and the transmission of an ultra‐short pulse present a transient period conditioned by the extinction length and also the thickness of the structure for transmission. For ultra‐intense pulses, non‐linear effects are expected: they could give rise to numerous phenomena, bi‐stability, self‐induced transparency, gap solitons, switching, etc., which have been previously shown in the optical domain.     

Relaxation of ideal classical particles in a one‐dimensional box

We study the deterministic dynamics of non‐interacting classical gas particles confined to a one‐dimensional box as a pedagogical toy model for the relaxation of the Boltzmann distribution towards equilibrium. Hard container walls alone induce a uniform distribution of the gas particles at large times. For the relaxation of the velocity distribution we model the dynamical walls by independent scatterers. The Markov property guarantees a stationary but not necessarily thermal velocity distribution for the gas particles at large times. We identify the conditions for physical walls where the stationary velocity distribution is the Maxwell distribution. For our numerical simulation we represent the wall particles by independent harmonic oscillators. The corresponding dynamical map for oscillators with a fixed phase (Fermi–Ulam accelerator) is chaotic for mesoscopic box dimensions.     

Fabrication of three‐dimensional photonic crystals in quantum‐dot‐based materials

Controlling spontaneous emission (SE) is of fundamental importance to a diverse range of photonic applications including but not limited to quantum optics, low power displays, solar energy harvesting and optical communications. Characterized by photonic bandgap (PBG) property, three‐dimensional (3D) photonic crystals (PCs) have emerged as a promising synthetic material, which can manipulate photons in much the same way as a semiconductor does to electrons. Emission tunable nanocrystal quantum dots (QDs) are ideal point sources to be embedded into 3D PCs towards active devices. The challenge however lies in the combination of QDs with 3D PCs without degradation of their emission properties. Polymer materials stand out for this purpose due to their flexibility of incorporating active materials. Combining the versatile multi‐photon 3D micro‐fabrication techniques, active 3D PCs have been fabricated in polymer‐QD composites with demonstrated control of SE from QDs. With this milestone novel miniaturized photonic devices can thus be envisaged.     

Infrared and Raman spectroscopic studies of the charge localization in one‐dimensional organic metals (DMtTTF)2X (X = ReO4, ClO4) with regular organic stacks

A novel selective synthesis of the unsymmetrically substituted tetrathiafulvalene dimethyltrimethylene‐tetrathiafulvalene (DMtTTF) is described together with its electrocrystallization to the known conducting mixed‐valence ClO₄^– and ReO₄^– salts. Infrared (IR) and Raman spectra of the two isostructural quasi‐one‐dimensional cation radical salts (DMtTTF)₂X (X = ReO₄^–, ClO₄^–) are investigated as a function of temperature (T = 5–300 K). At ambient temperature, these salts show metallic‐like properties and below T_ρ = 100–150 K, they undergo a smeared transition to semiconducting state. To study this charge localization, we measured temperature dependence of polarized IR reflectance spectra (700–16 000 cm^–1) and Raman spectra (150–3500 cm^–1, excitation λ = 632.8 nm) of single crystals. For both compounds, the Raman data and especially the bands related to the C=C stretching vibration of the DMtTTF molecule show that the charge distribution on molecules is uniform down to the lowest temperatures. Similarly, IR data confirm that down to the lowest temperatures, there is neither charge ordering nor important modification of the electronic structure. However, the temperature dependence of Raman spectra of both salts reveals a regime change at about 150 K. Additionally, using Density Functional Theory (DFT) methods, the normal vibrational modes of the neutral DMtTTF⁰ and cationic DMtTTF⁺ species and also their theoretical IR and Raman spectra were calculated. The theoretical data were compared with the experimental IR and Raman spectra of neutral DMtTTF⁰ molecule. Copyright © 2013 John Wiley & Sons, Ltd.     

Radiation coupling with two‐dimensional electron systems in the low limit of the microwave band: magnetoresistance response

We report on a theoretical study of radiation‐induced resistance oscillations and zero‐resistance states in two‐dimensional electron systems when the irradiation frequency is very low. In this situation the photon energy is much smaller than the spacing between the Landau levels and therefore interlevel transitions are excluded. Experiments show that when these frequencies are used, resistance oscillations disappear and, instead, a strong suppression of magnetoresistance response is obtained. We apply the radiation‐driven electron orbit model concluding that the resistance suppression is a manifestation of an oscillation of very large wavelength. Under this regime we study the connection with larger frequencies and the dependence on radiation power and temperature. For high enough radiation intensity, we predict that a regime of zero‐resistance states can be reached at these low frequencies, too. The calculated results are in good agreement with experiments. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Methodology for the solutions of some reduced Fokker‐Planck equations in high dimensions

In this paper, a new methodology is formulated for solving the reduced Fokker‐Planck (FP) equations in high dimensions based on the idea that the state space of large‐scale nonlinear stochastic dynamic system is split into two subspaces. The FP equation relevant to the nonlinear stochastic dynamic system is then integrated over one of the subspaces. The FP equation for the joint probability density function of the state variables in another subspace is formulated with some techniques. Therefore, the FP equation in high‐dimensional state space is reduced to some FP equations in low‐dimensional state spaces, which are solvable with exponential polynomial closure method. Numerical results are presented and compared with the results from Monte Carlo simulation and those from equivalent linearization to show the effectiveness of the presented solution procedure. It attempts to provide an analytical tool for the probabilistic solutions of the nonlinear stochastic dynamics systems arising from statistical mechanics and other areas of science and engineering.