Optical scattering angles and Bose-stimulated motion in cold atomic gas

Bose statistics imply a substantial enhancement at small angles for light scattering off a cold, Bose gas. The enhancement increases dramatically at the Bose-Einstein temperature. This phenomenon could be utilized to eliminate almost entirely the heating of the gas by a weak probe light beam.Comment: 9 pages (REVTeX) and 1 figure (ps); revisions: some new comments relevant to current experiments and one math typo; to appear in Physics Letters

Collisional effects on the collective laser cooling of trapped bosonic gases

We analyse the effects of atom-atom collisions on collective laser cooling scheme. We derive a quantum Master equation which describes the laser cooling in presence of atom-atom collisions in the weak-condensation regime. Using such equation, we perform Monte Carlo simulations of the population dynamics in one and three dimensions. We observe that the ground-state laser-induced condensation is maintained in the presence of collisions. Laser cooling causes a transition from a Bose-Einstein distribution describing collisionally induced equilibrium,to a distribution with an effective zero temperature. We analyse also the effects of atom-atom collisions on the cooling into an excited state of the trap.Comment: 9 pages, 5 figure

Managing Unbounded-Length Keys in Comparison-Driven Data Structures with Applications to On-Line Indexing

This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose comparison cost is not a constant. Examples of these keys are strings, multi-dimensional points, multiple-precision numbers, multi-key data (e.g.~records), XML paths, URL addresses, etc. The technique is more general than what has been done in previous work as no particular exploitation of the underlying structure of is required. The only requirement is that the insertion of a key must identify its predecessor or its successor. Using the proposed technique, online suffix tree can be constructed in worst case time $O(\log n)$ per input symbol (as opposed to amortized $O(\log n)$ time per symbol, achieved by previously known algorithms). To our knowledge, our algorithm is the first that achieves $O(\log n)$ worst case time per input symbol. Searching for a pattern of length $m$ in the resulting suffix tree takes $O(\min(m\log |\Sigma|, m + \log n) + tocc)$ time, where $tocc$ is the number of occurrences of the pattern. The paper also describes more applications and show how to obtain alternative methods for dealing with suffix sorting, dynamic lowest common ancestors and order maintenance

Separability Criteria from Uncertainty Relations

We explain several separability criteria which rely on uncertainty relations. For the derivation of these criteria uncertainty relations in terms of variances or entropies can be used. We investigate the strength of the separability conditions for the case of two qubits and show how they can improve entanglement witnesses.Comment: 4 pages, 2 figures, contribution for the proceedings of QCMC 2004 in Glasgo

Clustered Integer 3SUM via Additive Combinatorics

We present a collection of new results on problems related to 3SUM, including: 1. The first truly subquadratic algorithm for $\ \ \ \ \$ 1a. computing the (min,+) convolution for monotone increasing sequences with integer values bounded by $O(n)$, $\ \ \ \ \$1b. solving 3SUM for monotone sets in 2D with integer coordinates bounded by $O(n)$, and $\ \ \ \ \$1c. preprocessing a binary string for histogram indexing (also called jumbled indexing). The running time is: $O(n^{(9+\sqrt{177})/12}\,\textrm{polylog}\,n)=O(n^{1.859})$ with randomization, or $O(n^{1.864})$ deterministically. This greatly improves the previous $n^2/2^{\Omega(\sqrt{\log n})}$ time bound obtained from Williams' recent result on all-pairs shortest paths [STOC'14], and answers an open question raised by several researchers studying the histogram indexing problem. 2. The first algorithm for histogram indexing for any constant alphabet size that achieves truly subquadratic preprocessing time and truly sublinear query time. 3. A truly subquadratic algorithm for integer 3SUM in the case when the given set can be partitioned into $n^{1-\delta}$ clusters each covered by an interval of length $n$, for any constant $\delta>0$. 4. An algorithm to preprocess any set of $n$ integers so that subsequently 3SUM on any given subset can be solved in $O(n^{13/7}\,\textrm{polylog}\,n)$ time. All these results are obtained by a surprising new technique, based on the Balog--Szemer\'edi--Gowers Theorem from additive combinatorics

Quantum control of spin-correlations in ultracold lattice gases

We demonstrate that it is possible to prepare a lattice gas of ultracold atoms with a desired non-classical spin-correlation function using atom-light interaction of the kind routinely employed in quantum spin polarization spectroscopy. Our method is based on quantum non-demolition (QND) measurement and feedback, and allows in particular to create on demand exponentially or algebraically decaying correlations, as well as a certain degree of multi-partite entanglement.Comment: 2 figure