A Bose-Einstein Condensate in a Uniform Light-induced Vector Potential

We use a two-photon dressing field to create an effective vector gauge potential for Bose-condensed Rb atoms in the F=1 hyperfine ground state. The dressed states in this Raman field are spin and momentum superpositions, and we adiabatically load the atoms into the lowest energy dressed state. The effective Hamiltonian of these neutral atoms is like that of charged particles in a uniform magnetic vector potential, whose magnitude is set by the strength and detuning of Raman coupling. The spin and momentum decomposition of the dressed states reveals the strength of the effective vector potential, and our measurements agree quantitatively with a simple single-particle model. While the uniform effective vector potential described here corresponds to zero magnetic field, our technique can be extended to non-uniform vector potentials, giving non-zero effective magnetic fields.Comment: 5 pages, submitted to Physical Review Letter

Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition

We realize a single-band 2D Bose-Hubbard system with Rb atoms in an optical lattice and measure the condensate fraction as a function of lattice depth, crossing from the superfluid to the Mott-insulating phase. We quantitatively identify the location of the superfluid to normal transition by observing when the condensed fraction vanishes. Our measurement agrees with recent quantum Monte Carlo calculations for a finite-sized 2D system to within experimental uncertainty.Comment: 4 pages, 3 figure

Smooth analysis of the condition number and the least singular value

Let \a be a complex random variable with mean zero and bounded variance. Let $N_{n}$ be the random matrix of size $n$ whose entries are iid copies of \a and $M$ be a fixed matrix of the same size. The goal of this paper is to give a general estimate for the condition number and least singular value of the matrix $M + N_{n}$, generalizing an earlier result of Spielman and Teng for the case when \a is gaussian. Our investigation reveals an interesting fact that the "core" matrix $M$ does play a role on tail bounds for the least singular value of $M+N_{n}$. This does not occur in Spielman-Teng studies when \a is gaussian. Consequently, our general estimate involves the norm $\|M\|$. In the special case when $\|M\|$ is relatively small, this estimate is nearly optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde

Stability of the Excitonic Phase in Bilayer Quantum Hall Systems at Total Filling One -- Effects of Finite Well Width and Pseudopotentials --

The ground state of a bilayer quantum Hall system at $\nu_{\rm T}=1$ with model pseudopotential is investigated by the DMRG method. Firstly, pseudopotential parameters appropriate for the system with finite layer thickness are derived, and it is found that the finite thickness makes the excitonic phase more stable. Secondly, a model, where only a few pseudopotentials with small relative angular momentum have finite values, is studied, and it is clarified how the excitonic phase is destroyed as intra-layer pseudopotential becomes larger. The importance of the intra-layer repulsive interaction at distance twice of the magnetic length for the destruction of the excitonic phase is found.Comment: 7 pages, 7 figure

A synthetic electric force acting on neutral atoms

Electromagnetism is a simple example of a gauge theory where the underlying potentials -- the vector and scalar potentials -- are defined only up to a gauge choice. The vector potential generates magnetic fields through its spatial variation and electric fields through its time-dependence. We experimentally produce a synthetic gauge field that emerges only at low energy in a rubidium Bose-Einstein condensate: the neutral atoms behave as charged particles do in the presence of a homogeneous effective vector potential. We have generated a synthetic electric field through the time dependence of an effective vector potential, a physical consequence even though the vector potential is spatially uniform