Sigma models with AkA_k singularities in Euclidean spacetime of dimension 0<=D<4 and in the limit N->infinity

For the case of the single-O($N$)-vector linear sigma models the critical behaviour following from any $A_k$ singularity in the action is worked out in the double scaling limit $N \rightarrow \infty$, $f_r \rightarrow f_r^c$, $2 \leq r \leq k$. After an exact elimination of Gaussian degrees of freedom, the critical objects such as coupling constants, indices and susceptibility matrix are derived for all $A_k$ and spacetime dimensions $0 \leq D < 4$. There appear exceptional spacetime dimensions where the degree $k$ of the singularity $A_k$ is more strongly constrained than by the renormalizability requirement.Comment: LaTeX, 25 pages, no figure

Double Scaling Limits, Airy Functions and Multicritical Behaviour in O(N) Vektor Sigma Models

O(N) vector sigma models possessing catastrophes in their action are studied. Coupling the limit N --> infinity with an appropriate scaling behaviour of the coupling constants, the partition function develops a singular factor. This is a generalized Airy function in the case of spacetime dimension zero and the partition function of a scalar field theory for positive spacetime dimension.Comment: 14 pages, LaTe

On the critical behaviour of hermitean f-matrix models in the double scaling limit with f >= 3

An algorithm for the isolation of any singularity of f-matrix models in the double scaling limit is presented. In particular it is proved by construction that only those universality classes exist that are known from 2-matrix models.Comment: 24 pages, LaTex, correction of some notation errors and addition of four reference

The Continuous Series of Critical Points of the Two-Matrix Model at N -> infinity in the Double Scaling Limit

The critical points of the continuous series are characterized by two complex numbers l_1,l_2 (Re(l_1,l_2)=3) which enters the string susceptibility constant through gamma = -2/(n-1). The critical potentials are analytic functions with a convergence radius depending on l_1 or l_2. We use the orthogonal polynomial method and solve the Schwinger-Dyson equations with a technique borrowed from conformal field theory.Comment: 24 pages, LaTe

Full phase stabilization of a Yb:fiber femtosecond frequency comb via high-bandwidth transducers

We present full phase stabilization of an amplified Yb:fiber femtosecond frequency comb using an intra-cavity electro-optic modulator and an acousto-optic modulator. These transducers provide high servo bandwidths of 580 kHz and 250 kHz for frep and fceo, producing a robust and low phase noise fiber frequency comb. The comb was self-referenced with an f - 2f interferometer and phase locked to an ultra-stable optical reference used for the JILA Sr optical clock at 698 nm, exhibiting 0.21 rad and 0.47 rad of integrated phase errors (over 1 mHz - 1 MHz) respectively. Alternatively, the comb was locked to two optical references at 698 nm and 1064 nm, obtaining 0.43 rad and 0.14 rad of integrated phase errors respectively

Transverse and longitudinal characterization of electron beams using interaction with optical near-fields

We demonstrate an experimental technique for both transverse and longitudinal characterization of bunched femtosecond free electron beams. The operation principle is based on monitoring of the current of electrons that obtained an energy gain during the interaction with the synchronized optical near-field wave excited by femtosecond laser pulses. The synchronous accelerating/decelerating fields confined to the surface of a silicon nanostructure are characterized using a highly focused sub-relativistic electron beam. Here the transverse spatial resolution of 450 nm and femtosecond temporal resolution achievable by this technique are demonstrated

Broadband Phase-Noise Suppression in a Yb-Fiber Frequency Comb

We report a simple technique to suppress high frequency phase noise of a Yb-based fiber optical frequency comb using an active intensity noise servo. Out-of-loop measurements of the phase noise using an optical heterodyne beat with a continuous wave (cw) laser show suppression of phase noise by \geq7 dB out to Fourier frequencies of 100 kHz with a unity-gain crossing of -700 kHz. These results are enabled by the strong correlation between the intensity and phase noise of the laser. Detailed measurements of intensity and phase noise spectra, as well as transfer functions, reveal that the dominant phase and intensity noise contribution above -100 kHz is due to amplified spontaneous emission (ASE) or other quantum noise sources.Comment: 4 pages, 3 figure