Versatile Digital GHz Phase Lock for External Cavity Diode Lasers

We present a versatile, inexpensive and simple optical phase lock for applications in atomic physics experiments. Thanks to all-digital phase detection and implementation of beat frequency pre-scaling, the apparatus requires no microwave-range reference input, and permits phase locking at frequency differences ranging from sub-MHz to 7 GHz (and with minor extension, to 12 GHz). The locking range thus covers ground state hyperfine splittings of all alkali metals, which makes this system a universal tool for many experiments on coherent interaction between light and atoms.Comment: 4.5 pages, 5 figures v3: fixed error in schematic: R10 connects to other end of C

Exact Maps in Density Functional Theory for Lattice Models

In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and for the first time the exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in density functional theory. Having the explicit wavefunction-to- density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening. We show that for fully decoupled subsystems the intra-system steepening transforms into the well-known inter-system derivative discontinuity. An important conclusion is that for e.g. charge transfer processes between localized fragments within the same system it is not the usual inter-system derivative discontinuity that is missing in common ground-state functionals, but rather the differentiable intra-system steepening that we illustrate in the present work

Photons as quasi-charged particles

The Schrodinger motion of a charged quantum particle in an electromagnetic potential can be simulated by the paraxial dynamics of photons propagating through a spatially inhomogeneous medium. The inhomogeneity induces geometric effects that generate an artificial vector potential to which signal photons are coupled. This phenomenon can be implemented with slow light propagating through an a gas of double-Lambda atoms in an electromagnetically-induced transparency setting with spatially varied control fields. It can lead to a reduced dispersion of signal photons and a topological phase shift of Aharonov-Bohm type

The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect

We address and quantify the role of non-adiabaticity ("memory effects") in the exchange-correlation (xc) functional of time-dependent density functional theory (TDDFT) for describing non-linear dynamics of many-body systems. Time-dependent resonant processes are particularly challenging for available TDDFT approximations, due to their strong non-linear and non-adiabatic character. None of the known approximate density functionals are able to cope with this class of problems in a satisfactory manner. In this work we look at the prototypical example of the resonant processes by considering Rabi oscillations within the exactly soluble 2-site Hubbard model. We construct the exact adiabatic xc functional and show that (i) it does not reproduce correctly resonant Rabi dynamics, (ii) there is a sizable non-adiabatic contribution to the exact xc potential, which turns out to be small only at the beginning and at the end of the Rabi cycle when the ground state population is dominant. We then propose a "two-level" approximation for the time-dependent xc potential which can capture Rabi dynamics in the 2-site problem. It works well both for resonant and for detuned Rabi oscillations and becomes essentially exact in the linear response regime. This new, fully non-adiabatic and explicit density functional constitutes one of the main results of the present work.Comment: 8 pages, 5 figure

Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker

Since the proof of the four color theorem in 1976, computer-generated proofs have become a reality in mathematics and computer science. During the last decade, we have seen formal proofs using verified proof assistants being used to verify the validity of such proofs. In this paper, we describe a formalized theory of size-optimal sorting networks. From this formalization we extract a certified checker that successfully verifies computer-generated proofs of optimality on up to 8 inputs. The checker relies on an untrusted oracle to shortcut the search for witnesses on more than 1.6 million NP-complete subproblems.Comment: IMADA-preprint-c

Quantum memory for squeezed light

We produce a 600-ns pulse of 1.86-dB squeezed vacuum at 795 nm in an optical parametric amplifier and store it in a rubidium vapor cell for 1 us using electromagnetically induced transparency. The recovered pulse, analyzed using time-domain homodyne tomography, exhibits up to 0.21+-0.04 dB of squeezing. We identify the factors leading to the degradation of squeezing and investigate the phase evolution of the atomic coherence during the storage interval.Comment: To appear in PRL. Changes to version 3: we present a larger data set featuring somewhat less squeezing, but also better statistics and a lower margin of error. Some additional revisions are made in response to the referees' comment

A new proof that alternating links are non-trivial

We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are non-trivial. This proof uses only classic results in topology and combinatorial group theory.Comment: Minor changes. To appear in Fundamenta Mathematica

Coloring random graphs

We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on $q$, we find the precise value of the critical average connectivity $c_q$. Moreover, we show that below $c_q$ there exist a clustering phase $c\in [c_d,c_q]$ in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms.Comment: 4 pages, 1 figure, version to app. in PR