Related papers: Gauss sum factorization with cold atoms
We present a fast Gauss transform in one dimension using nearly optimal sum-of-exponentials approximations of the Gaussian kernel. For up to about ten-digit accuracy, the approximations are obtained via best rational approximations of the…
This paper presents the concept of digit polynomials, which leads to a deterministic and unconditional integer factorization algorithm with the runtime complexity $\mathcal{O}(N^{1/4+\epsilon})$. Strassen's well known factoring approach is…
Estimating multiple parameters simultaneously is of great importance to measurement science and application. For a single parameter, atomic Ramsey interferometry (or equivalently optical Mach-Zehnder interferometry) is capable of providing…
We address precision of optical interferometers fed by Gaussian states and involving passive and/or active elements, such as beam splitters, photodetectors and optical parametric amplifiers. We first address the ultimate bounds to precision…
In many signal processing applications it is required to estimate the unobservable state of a dynamic system from its noisy measurements. For linear dynamic systems with Gaussian Mixture (GM) noise distributions, Gaussian Sum Filters (GSF)…
Coherent superpositions of the 49s and 48s Rydberg states of cold Rb atoms were studied near the surface of an atom chip. The superpositions were created and manipulated using microwaves resonant with the two-photon 49s-48s transition.…
We propose an algorithm that combines the inchworm method and the frozen Gaussian approximation to simulate the Caldeira-Leggett model in which a quantum particle is coupled with thermal harmonic baths. In particular, we are interested in…
Exact calculation of the condensate fraction in multi-dimensional inhomogeneous interacting Bose systems which do not possess continuous symmetries is a difficult computational problem. We have developed an iterative procedure which allows…
We present results on a free-space atom interferometer operating on the first order magnetically insensitive |F=1,mF=0> -> |F=2,mF=0> transition of Bose-condensed 87Rb atoms. A pulsed atom laser is output-coupled from a Bose-Einstein…
Prime factorization is an outstanding problem in arithmetic, with important consequences in a variety of fields, most notably cryptography. Here we employ the intriguing analogy between prime factorization and optical interferometry in…
Shor's algorithm can find prime factors of a large number more efficiently than any known classical algorithm. Understanding the properties that gives the speedup is essential for a general and scalable construction. Here we present a…
We investigate experimentally the number statistics of a mesoscopic ensemble of cold atoms in a microscopic dipole trap loaded from a magneto-optical trap, and find that the atom number fluctuations are reduced with respect to a Poisson…
The optimal estimation of a quantum mechanical 2-state system (qubit) - with N identically prepared qubits available - is obtained by measuring all qubits simultaneously in an entangled basis. We report the experimental estimation of qubits…
Finding a minimal factorization for a generic semigroup can be done by using the Froidure-Pin Algorithm, which is not feasible for semigroups of large sizes. On the other hand, if we restrict our attention to just a particular semigroup, we…
Incoherent harmonic summing is a technique which is used to improve the sensitivity of Fourier domain search methods. A one dimensional harmonic sum is used in time-domain radio astronomy as part of the Fourier domain periodicity search, a…
An interferometric method is proposed to controllably split an atomic condensate in two spatial components with strongly reduced population fluctuations. All steps in our proposal are in current use in cold atom laboratories, and we show…
In this paper, we have proposed a new method for solving the Gaussian integral. Introducing a parameter that depends on a $n$ index, we have found a general solution for this type of integral inspired by Taylor series of a simple function.…
We develop an analytic approach that draws on tools from Fourier analysis and ergodic theory to study Ramsey-type problems involving sums and products in the integers. Suppose $Q$ denotes a polynomial with integer coefficients. We establish…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
We propose here a model and a numerical scheme to compute the motion of rigid particles interacting through the lubrication force. In the case of a particle approaching a plane, we propose an algorithm and prove its convergence towards the…