Spontaneous macroscopic spin polarization in independent spinor Bose-Einstein condensates

We present experimental evidence for the spontaneous formation of a macroscopic spin polarization in overlapping regions of two independent Bose-Einstein condensates produced in different hyperfine states of 87Rb. The condensates are independent in the sense that we do not explicitly introduce a relative phase between them. A single "spin-tip" pulse maps the transverse spin polarization into longitudinal spin polarization, and the atomic density distributions are measured with a Stern-Gerlach imaging method. The resulting matter-wave interference patterns are anticorrelated.     

Nanofocusing of optical energy in tapered plasmonic waveguides

We predict theoretically that surface plasmon polaritons propagating toward the tip of a tapered plasmonic waveguide are slowed down and asymptotically stopped when they tend to the tip, never actually reaching it (the travel time to the tip is logarithmically divergent). This phenomenon causes accumulation of energy and giant local fields at the tip. There are various prospective applications in nano-optics and nanotechnology.     

One-dimensional Tiling Semigroups

We investigate the structure of Kellendonks tiling semigroup in the case of 1-dimensional tilings.     

Class numbers of imaginary quadratic fields

The classical class number problem of Gauss asks for a classification of all imaginary quadratic fields with a given class number . The first complete results were for by Heegner, Baker, and Stark. After the work of Goldfeld and Gross-Zagier, the task was a finite decision problem for any . Indeed, after Oesterlé handled , in 1985 Serre wrote, ``No doubt the same method will work for other small class numbers, up to 100, say.' However, more than ten years later, after doing , Wagner remarked that the case seemed impregnable. We complete the classification for all , an improvement of four powers of 2 (arguably the most difficult case) over the previous best results. The main theoretical technique is a modification of the Goldfeld-Oesterlé work, which used an elliptic curve -function with an order 3 zero at the central critical point, to instead consider Dirichlet -functions with low-height zeros near the real line (though the former is still required in our proof). This is numerically much superior to the previous method, which relied on work of Montgomery-Weinberger. Our method is still quite computer-intensive, but we are able to keep the time needed for the computation down to about seven months. In all cases, we find that there is no abnormally large ``exceptional modulus' of small class number, which agrees with the prediction of the Generalised Riemann Hypothesis.

     

Random Euclidean embeddings in spaces of bounded volume ratio

Let $\text{(}\text{R}{}^{\mathrm{N}}\text{,6·6)}$ be the space $\text{R}{}^{\mathrm{N}}$ equipped with a norm 6·6 whose unit ball has a bounded volume ratio with respect to the Euclidean unit ball. Let Γ be any random N×n matrix with N>n, whose entries are independent random variables satisfying some moment assumptions. We show that with high probability Γ is a good isomorphism from the n-dimensional Euclidean space $\text{(}\text{R}{}^{\mathrm{n}}\text{,|·|)}$ onto its image in $\text{(}\text{R}{}^{\mathrm{N}}\text{,6·6)}$: there exist α,β>0 such that for all $\text{x∈}\text{R}{}^{\mathrm{n}}$, $\text{α}\text{N}\text{|x|?6Γx6?β}\text{N}\text{|x|}$. This solves a conjecture of Schechtman on random embeddings of ?₂ⁿ into ?₁^N. To cite this article: A. Litvak et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Measurement of an individual silver perch Bairdiella chrysoura sound pressure level in a field recording

Simultaneous audio and video were recorded of a silver perch Bairdiella chrysoura producing its characteristic drumming sound in the field. The background noise contribution to the total sound pressure level is estimated using sounds that occurred between the pulses of the silver perch sound. This background contribution is subtracted from the total sound to give an estimate of the sound pressure level of the individual fish. A silver perch source level in the range 128-135 dB (re: 1 microPa) is obtained using an estimate of the distance between the fish and the hydrophone. The maximum distance at which an individual silver perch could be detected depends on the background sound level as well as the propagation losses. Under the conditions recorded in this study, the maximum detection distance would be 1-7 m from the hydrophone.     

Exploiting independent filter bandwidth of human factor cepstral coefficients in automatic speech recognition

Mel frequency cepstral coefficients (MFCC) are the most widely used speech features in automatic speech recognition systems, primarily because the coefficients fit well with the assumptions used in hidden Markov models and because of the superior noise robustness of MFCC over alternative feature sets such as linear prediction-based coefficients. The authors have recently introduced human factor cepstral coefficients (HFCC), a modification of MFCC that uses the known relationship between center frequency and critical bandwidth from human psychoacoustics to decouple filter bandwidth from filter spacing. In this work, the authors introduce a variation of HFCC called HFCC-E in which filter bandwidth is linearly scaled in order to investigate the effects of wider filter bandwidth on noise robustness. Experimental results show an increase in signal-to-noise ratio of 7 dB over traditional MFCC algorithms when filter bandwidth increases in HFCC-E. An important attribute of both HFCC and HFCC-E is that the algorithms only differ from MFCC in the filter bank coefficients: increased noise robustness using wider filters is achieved with no additional computational cost.     

Hydrogenic Rydberg states of molecular van der Waals complexes: resolved Rydberg spectroscopy of DABCO-N2

The complementary threshold ionization techniques of MATI and ZEKE spectroscopy have been used to reveal well-resolved, long-lived (>10 micros) hydrogenic Rydberg series (50< or =n< or =98) in a van der Waals complex formed between a polyatomic molecule and a diatomic molecule for the first time. The series are observed within 50 cm(-1) of the adiabatic ionization threshold as well as two core-excited thresholds corresponding to excitation of up to two quanta in the van der Waals vibrational mode.     

Spin readout and initialization in a semiconductor quantum dot

Electron spin qubits in semiconductors are attractive from the viewpoint of long coherence times. However, single spin measurement is challenging. Several promising schemes incorporate ancillary tunnel couplings that may provide unwanted channels for decoherence. Here, we propose a novel spin-charge transduction scheme, converting spin information to orbital information within a single quantum dot by microwave excitation. The same quantum dot can be used for rapid initialization, gating, and readout. We present detailed modeling of such a device in silicon to confirm its feasibility.     

Addressing atoms in optical lattices with Bessel beams

A method of synthesizing localized optical fields with zeros on a periodic lattice is analyzed. The applicability to addressing atoms trapped in optical lattices with low cross talk is discussed.