Harmonic Oscillator in a 1D or 2D Cavity with General Perfectly Reflecting Walls

We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the self-adjoint extension parameter. For sufficiently negative values of the self-adjoint extension parameter, there are bound states localized at the wall of the box or the cavity that resonate with the standard bound states of the simple harmonic oscillator or the isotropic oscillator. A free particle in a circular cavity has been studied for the sake of comparison. This work represents an application of the recent generalization of the Heisenberg uncertainty relation related to the theory of self-adjoint extensions in a finite volume.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

Yellow laser light generation by frequency doubling of the output from a master oscillator fiber power amplifier system

We present a power-scalable approach for yellow laser-light generation based on standard Ytterbium (Yb) doped fibers. To force the cavity to lase at 1154 nm, far above the gain-maximum, measures must be taken to fulfill lasing condition and to suppress competing amplified spontaneous emission (ASE) in the high-gain region. To prove the principle we built a fiber-laser cavity and a fiber-amplifier both at 1154 nm. In between cavity and amplifier we suppressed the ASE by 70 dB using a fiber Bragg grating (FBG) based filter. Finally we demonstrated efficient single pass frequency doubling to 577 nm with a periodically poled lithium niobate crystal (PPLN). With our linearly polarized 1154 nm master oscillator power fiber amplifier (MOFA) system we achieved slope efficiencies of more than 15 % inside the cavity and 24 % with the fiber-amplifier. The frequency doubling followed the predicted optimal efficiency achievable with a PPLN crystal. So far we generated 1.5 W at 1154nm and 90 mW at 577 nm. Our MOFA approach for generation of 1154 nm laser radiation is power-scalable by using multi-stage amplifiers and large mode-area fibers and is therefore very promising for building a high power yellow laser-light source of several tens of Watt.

Cellular and network mechanisms of rhythm generation in spinal cord circuits

The generation of rhythmic electrical activity is a prominent feature of spinal cord circuits that is used for locomotion and also for circuit refinement during development. The mechanisms involved in rhythm generation in spinal cord networks are not fully understood. It is for example not known whether spinal cord rhythms are driven by pacemaker neurons and if yes, which neurons are involved in this function. We studied the mechanisms involved in rhythm generation in slice cultures from fetal rats that were grown on multielectrode arrays (MEAs). We combined multisite extracellular recordings from the MEA electrodes with intracellular patch clamp recordings from single neurons. We found that spatially restricted oscillations of activity appeared in most of the cultures spontaneously. Such activity was based on intrinsic activity in a percentage of the neurons that could activate the spinal networks through recurrent excitation. The local oscillator networks critically involved NMDA, AMPA and GABA / glycine receptors at subsequent phases of the oscillation cycle. Intrinsic spiking in individual neurons (in the absence of functional synaptic coupling) was based on persistent sodium currents. Intrinsic firing as well as persistent sodium currents were increased by 5-HT through 5-HT2 receptors. Comparing neuronal activity to muscle activity in co-cultures of spinal cord slices with muscle fibers we found that a percentage of the intrinsically spiking neurons were motoneurons. These motoneurons were electrically coupled among each other and they could drive the spinal networks through cholinergic recurrent excitation. These findings open the possibility that during development rhythmic activity in motoneurons is not only involved in circuit refinement downstream at the neuromuscular endplates but also upstream at the level of spinal cord circuits.

Low-lying excited states and nonradiative processes of 9-methyl-2-aminopurine

he UV spectrum of the adenine analogue 9-methyl-2-aminopurine (9M-2AP) is investigated with one- and two-color resonant two-photon ionization spectroscopy at 0.3 and 0.05 cm−1 resolution in a supersonic jet. The electronic origin at 32 252 cm−1 exhibits methyl torsional subbands that originate from the 0A′′1 (l = 0) and 1E ″ (l = ±1) torsional levels. These and further torsional bands that appear up to 000+230 cm−1 allow to fit the threefold (V 3) barriers of the torsional potentials as ∣∣V′′3∣∣=50 cm−1 in the S 0 and ∣∣V′3∣∣=126 cm−1 in the S 1 state. Using the B3LYP density functional and correlated approximate second-order coupled cluster CC2 methods, the methyl orientation is calculated to be symmetric relative to the 2AP plane in both states, with barriers of V′′3=20 cm−1 and V′3=115 cm−1. The 000 rotational band contour is 75% in-plane (a/b) polarized, characteristic for a dominantly long-axis 1ππ* excitation. The residual 25% c-axis polarization may indicate coupling of the 1ππ* to the close-lying 1 nπ* state, calculated at 4.00 and 4.01 eV with the CC2 method. However, the CC2 calculated 1 nπ oscillator strength is only 6% of that of the 1ππ* transition. The 1ππ* vibronic spectrum is very complex, showing about 40 bands within the lowest 500 cm−1. The methyl torsion and the low-frequency out-of-plane ν′1 and ν′2 vibrations are strongly coupled in the 1ππ* state. This gives rise to many torsion-vibration combination bands built on out-of-plane fundamentals, which are without precedence in the 1ππ* spectrum of 9H-2-aminopurine [S. Lobsiger, R. K. Sinha, M. Trachsel, and S. Leutwyler, J. Chem. Phys.134, 114307 (2011)]. From the Lorentzian broadening needed to fit the 000 contour of 9M-2AP, the 1ππ* lifetime is τ ⩾ 120 ps, reflecting a rapid nonradiative transition.

Subharmonic Mixer Based on EBG Technology

We present the design of a submillimeter-wave mixer based on electromagnetic band gap (EBG) technology and using subharmonic local oscillator (LO) injection. The indicated device converts an incoming submilimeter wavelength signal into a 1-5 GHz intermediate frequency (IF) signal by mixing it with a subharmonic LO signal. The mixer consists of a dual-band receiver and two coplanar stripline (CPS) filters, collocated on top of a three-dimensional (3-D) EBG structure. A four-element array of the proposed receivers was designed, fabricated and tested. The configuration demonstrated reasonable performance: conversion loss below 8 dB and noise temperature below 3000 K. The presented concept can be used for higher frequencies, provided the availability of sufficiently powerful LO sources.

Sideband characterization and atmospheric observations with various 340 GHz heterodyne receivers

This paper describes sideband response measurements and atmospheric observations with a double sideband and two Single Sideband (SSB) receiver prototypes developed for the multi-beam limb sounder instrument stratosphere-troposphere exchange and climate monitor radiometer. We first show an advanced Fourier-Transform Spectroscopy (FTS) method for sideband response and spurious signal characterization. We then present sideband response measurements of the different prototype receivers and we compare the results of the SSB receivers with sideband measurements by injecting a continuous wave signal into the upper and lower sidebands. The receivers were integrated into a total-power radiometer and atmospheric observations were carried out. The observed spectra were compared to forward model spectra to conclude on the sideband characteristics of the different receivers. The two sideband characterization methods show a high degree of agreement for both SSB receivers with various local oscillator settings. The measured sideband response was used to correct the forward model simulations. This improves the agreement with the atmospheric observations and explains spectral features caused by an unbalanced sideband response. The FTS method also allows to quantify the influence of spurious harmonic responses of the receiver.

The elusive S2 state, the S1/S2 splitting, and the excimer states of the benzene dimer

We observe the weak S 0 → S 2 transitions of the T-shaped benzene dimers (Bz)2 and (Bz-d 6)2 about 250 cm−1 and 220 cm−1 above their respective S 0 → S 1 electronic origins using two-color resonant two-photon ionization spectroscopy. Spin-component scaled (SCS) second-order approximate coupled-cluster (CC2) calculations predict that for the tipped T-shaped geometry, the S 0 → S 2 electronic oscillator strength f el (S 2) is ∼10 times smaller than f el (S 1) and the S 2 state lies ∼240 cm−1 above S 1, in excellent agreement with experiment. The S 0 → S 1 (ππ ∗) transition is mainly localized on the “stem” benzene, with a minor stem → cap charge-transfer contribution; the S 0 → S 2 transition is mainly localized on the “cap” benzene. The orbitals, electronic oscillator strengths f el (S 1) and f el (S 2), and transition frequencies depend strongly on the tipping angle ω between the two Bz moieties. The SCS-CC2 calculated S 1 and S 2 excitation energies at different T-shaped, stacked-parallel and parallel-displaced stationary points of the (Bz)2 ground-state surface allow to construct approximate S 1 and S 2 potential energy surfaces and reveal their relation to the “excimer” states at the stacked-parallel geometry. The f el (S 1) and f el (S 2) transition dipole moments at the C 2v -symmetric T-shape, parallel-displaced and stacked-parallel geometries are either zero or ∼10 times smaller than at the tipped T-shaped geometry. This unusual property of the S 0 → S 1 and S 0 → S 2 transition-dipole moment surfaces of (Bz)2 restricts its observation by electronic spectroscopy to the tipped and tilted T-shaped geometries; the other ground-state geometries are impossible or extremely difficult to observe. The S 0 → S 1/S 2 spectra of (Bz)2 are compared to those of imidazole ⋅ (Bz)2, which has a rigid triangular structure with a tilted (Bz)2 subunit. The S 0 → S 1/ S 2 transitions of imidazole-(benzene)2 lie at similar energies as those of (Bz)2, confirming our assignment of the (Bz)2 S 0 → S 2 transition.