Atom Chips: Fabrication and Thermal Properties

Neutral atoms can be trapped and manipulated with surface mounted microscopic current carrying and charged structures. We present a lithographic fabrication process for such atom chips based on evaporated metal films. The size limit of this process is below 1$\mu$m. At room temperature, thin wires can carry more than 10$^7$A/cm$^2$ current density and voltages of more than 500V. Extensive test measurements for different substrates and metal thicknesses (up to 5 $\mu$m) are compared to models for the heating characteristics of the microscopic wires. Among the materials tested, we find that Si is the best suited substrate for atom chips

Warm dark matter at small scales: peculiar velocities and phase space density

We study the scale and redshift dependence of the power spectra for density perturbations and peculiar velocities, and the evolution of a coarse grained phase space density for (WDM) particles that decoupled during the radiation dominated stage. The (WDM) corrections are obtained in a perturbative expansion valid in the range of redshifts at which N-body simulations set up initial conditions, and for a wide range of scales. The redshift dependence is determined by the kurtosis $\beta_2$ of the distribution function at decoupling. At large redshift there is an enhancement of peculiar velocities for $\beta_2 > 1$ that contributes to free streaming and leads to further suppression of the matter power spectrum and an enhancement of the peculiar velocity autocorrelation function at scales smaller than the free streaming scale. Statistical fluctuations of peculiar velocities are also suppressed on these scales by the same effect. In the linearized approximation, the coarse grained phase space density features redshift dependent (WDM) corrections from gravitational perturbations determined by the power spectrum of density perturbations and $\beta_2$. For $\beta_2 > 25/21$ it \emph{grows logarithmically} with the scale factor as a consequence of the suppression of statistical fluctuations. Two specific models for WDM are studied in detail. The (WDM) corrections relax the bounds on the mass.Comment: 22 pages, 9 figs, more explanations. Published versio

Power Spectra for Cold Dark Matter and its Variants

The bulk of recent cosmological research has focused on the adiabatic cold dark matter model and its simple extensions. Here we present an accurate fitting formula that describes the matter transfer functions of all common variants, including mixed dark matter models. The result is a function of wavenumber, time, and six cosmological parameters: the massive neutrino density, number of neutrino species degenerate in mass, baryon density, Hubble constant, cosmological constant, and spatial curvature. We show how observational constraints---e.g. the shape of the power spectrum, the abundance of clusters and damped Lyman-alpha systems, and the properties of the Lyman-alpha forest--- can be extended to a wide range of cosmologies, including variations in the neutrino and baryon fractions in both high-density and low-density universes.Comment: 20 pages, LaTeX, 4 figures. Submitted to ApJ. Electronic versions of the fitting formula, as well as simple codes to output cosmological quantities (e.g. sigma_8) as a function of parameters and illustrative animations of parameter dependence, are available at http://www.sns.ias.edu/~whu/transfer/transfer.htm

An optical lattice on an atom chip

Optical dipole traps and atom chips are two very powerful tools for the quantum manipulation of neutral atoms. We demonstrate that both methods can be combined by creating an optical lattice potential on an atom chip. A red-detuned laser beam is retro-reflected using the atom chip surface as a high-quality mirror, generating a vertical array of purely optical oblate traps. We load thermal atoms from the chip into the lattice and observe cooling into the two-dimensional regime where the thermal energy is smaller than a quantum of transverse excitation. Using a chip-generated Bose-Einstein condensate, we demonstrate coherent Bloch oscillations in the lattice.Comment: 3 pages, 2 figure

Snarky Signatures: Minimal Signatures of Knowledge from Simulation-Extractable SNARKs

We construct a pairing based simulation-extractable SNARK (SE-SNARK) that consists of only 3 group elements and has highly efficient verification. By formally linking SE-SNARKs to signatures of knowledge, we then obtain a succinct signature of knowledge consisting of only 3 group elements. SE-SNARKs enable a prover to give a proof that they know a witness to an instance in a manner which is: (1) succinct - proofs are short and verifier computation is small; (2) zero-knowledge - proofs do not reveal the witness; (3) simulation-extractable - it is only possible to prove instances to which you know a witness, even when you have already seen a number of simulated proofs. We also prove that any pairing based signature of knowledge or SE-NIZK argument must have at least 3 group elements and 2 verification equations. Since our constructions match these lower bounds, we have the smallest size signature of knowledge and the smallest size SE-SNARK possible

Matter-wave interferometry in a double well on an atom chip

Matter-wave interference experiments enable us to study matter at its most basic, quantum level and form the basis of high-precision sensors for applications such as inertial and gravitational field sensing. Success in both of these pursuits requires the development of atom-optical elements that can manipulate matter waves at the same time as preserving their coherence and phase. Here, we present an integrated interferometer based on a simple, coherent matter-wave beam splitter constructed on an atom chip. Through the use of radio-frequency-induced adiabatic double-well potentials, we demonstrate the splitting of Bose-Einstein condensates into two clouds separated by distances ranging from 3 to 80 microns, enabling access to both tunnelling and isolated regimes. Moreover, by analysing the interference patterns formed by combining two clouds of ultracold atoms originating from a single condensate, we measure the deterministic phase evolution throughout the splitting process. We show that we can control the relative phase between the two fully separated samples and that our beam splitter is phase-preserving