A single laser system for ground-state cooling of <Superscript>25</Superscript>Mg<Superscript>+</Superscript>

We present a single solid-state laser system to cool, coherently manipulate and detect ²⁵Mg⁺ ions. Coherent manipulation is accomplished by coupling two hyperfine ground state levels using a pair of far-detuned Raman laser beams. Resonant light for Doppler cooling and detection is derived from the same laser source by means of an electro-optic modulator, generating a sideband which is resonant with the atomic transition. We demonstrate ground-state cooling of one of the vibrational modes of the ion in the trap using resolved-sideband cooling. The cooling performance is studied and discussed by observing the temporal evolution of Raman-stimulated sideband transitions. The setup is a major simplification over existing state-of-the-art systems, typically involving up to three separate laser sources.     

A small decrease in the degree of a polynomial with a given sign function can exponentially increase its weight and length

A Boolean function f: {?1, +1} ⁿ → {?1, +1} is called the sign function of an integer-valued polynomial p(x) if f(x) = sgn(p(x)) for all x ∈ {?1, +1} ⁿ . In this case, the polynomial p(x) is called a perceptron for the Boolean function f. The weight of a perceptron is the sum of absolute values of the coefficients of p. We prove that, for a given function, a small change in the degree of a perceptron can strongly affect the value of the required weight. More precisely, for each d = 1, 2, ..., n ? 1, we explicitly construct a function f: {?1, +1} ⁿ → {?1, +1} that requires a weight of the form exp{Θ(n)} when it is represented by a degree d perceptron, and that can be represented by a degree d + 1 perceptron with weight equal to only O(n ²). The lower bound exp{Θ(n)} for the degree d also holds for the size of the depth 2 Boolean circuit with a majority function at the top and arbitrary gates of input degree d at the bottom. This gap in the weight values is exponentially larger than those that have been previously found. A similar result is proved for the perceptron length, i.e., for the number of monomials contained in it.     

The unbounded-error communication complexity of symmetric functions

We prove an essentially tight lower bound on the unbounded-error communication complexity of every symmetric function, i.e., f(x,y)=D(|x∧y|), where D: {0,1,…,n}→{0,1} is a given predicate and x,y range over {0,1} ⁿ . Specifically, we show that the communication complexity of f is between Θ(k/log⁵ n) and Θ(k logn), where k is the number of value changes of D in {0,1,…, n}. Prior to this work, the problem was solved only for the parity predicate D (Forster 2001).     

Mid-IR Range Quantum-Cascade Lasers in Compact Optoacoustic Gas Analyzers

Journal of Applied Spectroscopy - The generation regimes of quantum-cascade lasers for optoacoustic sensors of methane and ammonia are examined, and the tuning and output characteristics of these...     

Frequency measurements in the b <Superscript>3</Superscript>Π(0<Subscript>u</Subscript><Superscript>+</Superscript>) - X <Superscript>1</Superscript>Σ<Subscript>g</Subscript><Superscript>+</Superscript> system of K<Subscript>2</Subscript>

Absolute transition frequencies of the b ³Π(0_u ⁺) - X ¹Σ_g ⁺ system of K₂ were measured in a molecular beam with Lamb dip absorption spectroscopy applying a frequency comb from a femtosecond pulsed laser. Both, K atoms and K₂ molecules are present in the beam and are expected to interact by collisions. The atoms can be deflected optically out of the beam, and thus the collision rate between K atoms and K₂ molecules is changed by about an order of magnitude. The molecular transition frequencies for low collisional rate are compared with those for high one. Limits for the collisional frequency shift within the beam are determined.     

LaserBreeze gas analyzer for noninvasive diagnostics of air exhaled by patients

A laser gas analyzer has been designed for determining the composition of exhaled air by means of photoacoustic spectroscopy. The analyzer, based on a broadband optical parametric oscillator and photoacoustic detector, provides high-precision rapid analysis of the multicomponent composition of human exhaled air for dynamic estimation of the efficiency of treating bronchus and lung diseases.     

Optimal bounds for sign-representing the intersection of two halfspaces by polynomials

The threshold degree of a function f: {0,1} ⁿ → {?1,+1} is the least degree of a real polynomial p with f(x) ≡ sgnp(x). We prove that the intersection of two halfspaces on {0,1} ⁿ has threshold degree Ω(n), which matches the trivial upper bound and solves an open problem due to Klivans (2002). The best previous lower bound was Ω({ie73-1}). Our result shows that the intersection of two halfspaces on {0,1} ⁿ only admits a trivial {ie73-2}-time learning algorithm based on sign-representation by polynomials, unlike the advances achieved in PAC learning DNF formulas and read-once Boolean formulas.     

The A 1Sigmau+ state of K2 up to the dissociation limit

We report an experimental study of the K(2) A (1)Sigma(u) (+) state. Long-range levels up to the dissociation limit were observed in a two laser spectroscopic experiment using a highly collimated molecular beam. We derive an analytical potential energy curve for the complete A state including long-range dispersion terms. From these, we obtain radiative atomic lifetimes of 26.74(3) ns for the 4p(1/2) state and 26.39(3) ns for the 4p(3/2) state of (39)K. The dissociation energy of the X (1)Sigma(g) (+) ground state with respect to v=0, J=0 is found to be D(0)=4404.808(4) cm(-1).     

Ramsey-Bordé interferometer and embedded Ramsey interferometer with molecular matter waves of 39K2

A matter wave interferometer based on a molecular beam of K₂ has been designed for observation of both exits: with molecules in the electronically excited state and in the ground state. In addition to the excited state fluorescence the molecular ground state population is detected with a further laser. Two transitions to different electronic states were employed for this purpose and their usefulness is compared. Under the present experimental conditions both interferometer exits show a superposition of different interference patterns due to the influence of transverse and longitudinal overlaps of the interfering matter waves. The interference patterns have been analyzed to be composed of a contribution caused by a two beam splitter Ramsey interference and Ramsey-Bordé pattern with four beam splitters. This overlap of interference signals influences the suitability of the matter wave interferometer for phase measurements of the interferences.