Carl J. Williams

Precise determination of 6Li cold collision parameters by radio-frequency spectroscopy on weakly bound molecules

We employ radio-frequency spectroscopy on weakly bound (6)Li(2) molecules to precisely determine the molecular binding energies and the energy splittings between molecular states for different magnetic fields. These measurements allow us to extract the interaction parameters of ultracold (6)Li atoms based on a multichannel quantum scattering model. We determine the singlet and triplet scattering lengths to be a(s) = 45.167(8)a(0) and a(t) = -2140(18)a(0) (1a(0) = 0.052 917 7 nm), and the positions of the broad Feshbach resonances in the energetically lowest three s-wave scattering channels to be 83.41(15), 69.04(5), and 81.12(10) mT.

Creation of a molecular condensate by dynamically melting a Mott insulator

We propose the creation of a molecular Bose-Einstein condensate by loading an atomic condensate into an optical lattice and driving it into a Mott insulator with exactly two atoms per site. Molecules in a Mott insulator state are then created under well defined conditions by photoassociation with essentially unit efficiency. Finally, the Mott insulator is melted and a superfluid state of the molecules is created. We study the dynamics of this process and photoassociation of tightly trapped atoms.

Quantum key distribution with 1.25 Gbps clock synchronization

Clock recovery techniques at 1.25 Gbps enable continuous quantum key distribution at demonstrated sifted-key rates up to 1.0 Mbps. This rate is two orders of magnitude faster than has been reported previously

Dynamics of triatomic photodissociation in the interaction representation. I. Methodology

This paper presents a new, quantum mechanical, time dependent approach to the photodissociation of triatomic molecules in Jacobi coordinates. The algorithm is based on a nested interaction representation, designed to make the representation of the time evolving wave packet as compact as possible. The new equations of motion are solved numerically using a synthesis of grid techniques: the fast Fourier transform (FFT) method is used in Cartesian‐like coordinates, and the discrete variable representation (DVR) method in the angular or bending coordinate. A variant on the short iterative Lanczos (SIL) procedure is used for the temporal propagation of the wave packet. Rotational state distributions obtained from this new algorithm are presented for the single surface photodissociation of ClCN and for the two surface photodissociation of ICN. The ClCN results are in good agreement with the semiclassical results of Barts and Halpern [J. Phys. Chem. 93, 7346 (1989)] and in excellent agreement with the time indepe...

Measurement of the Zero Crossing in a Feshbach Resonance of Fermionic 6Li

We measure a zero crossing in the scattering length of a mixture of the two lowest hyperfine states of 6 Li. To locate the zero crossing, we monitor the decrease in temperature and atom number arising from evaporation in a CO 2 laser trap as a function of magnetic field B. The temperature decrease and atom loss are minimized for B=52.8′0.4 mT, consistent with no evaporation. We also present preliminary calculations using potentials that have been constrained by the measured zero crossing and locate a broad Feshbach resonance at 86 mT, in agreement with previous theoretical predictions. In addition, our theoretical model predicts a second and much narrower Feshbach resonance near 55 mT.

Estimating Bounds on Collisional Relaxation Rates of Spin-Polarized 87Rb Atoms at Ultracold Temperatures

We present quantum scattering calculations for the collisional relaxation rate coefficient of spin-polarized 87Rb(f = 2,m = 2) atoms, which determines the loss rate of cold Rb atoms from a magnetic trap. Unlike the lighter alkali atoms, spin-polarized 87Rb atoms can undergo dipolar relaxation due to both the normal spin-spin dipole interaction and a second-order spin-orbit interaction with distant electronic states of the dimer. We present ab initio calculations for the second-order spin-orbit terms for both Rb2 and Cs2. The corrections lead to a reduction in the relaxation rate for 87Rb. Our primary concern is to analyze the sensitivity of the 87Rb trap loss to the uncertainties in the ground state molecular potentials. Since the scattering length for the a3Σ+u state is already known, the major uncertainties are associated with the X1Σ+g potential. After testing the effect of systematically modifying the short-range form of the molecular potentials over a reasonable range, and introducing our best estimate of the second-order spin-orbit interaction, we estimate that in the low temperature limit the rate coefficient for loss of Rb atoms from the f = 2,m = 2 state is between 0.4 × 10−15 cm3/s and 2.4 × 10−15 cm3/s (where this number counts two atoms lost per collision). In a pure condensate the rate coefficient would be reduced by 1/2.

Feshbach resonances in fermionic 6Li

Feshbach resonances in lithium-6 were experimentally studied and theoretically analyzed. In addition to two previously known s-wave resonances, we found three p-wave resonances. Four of these resonances are narrow and yield a precise value of the singlet scattering length, but do not allow us to accurately predict the location of the broad resonance near 83 mT. Its position was previously measured in a molecule-dissociation experiment for which we, here, discuss systematic shifts.

Effective three-body interactions of neutral bosons in optical lattices

We show that there are effective three- and higher-body interactions generated by the two-body collisions of atoms confined in the lowest vibrational states of a three-dimensional (3D) optical lattice. The collapse and revival dynamics of approximate coherent states loaded into a lattice are a particularly sensitive probe of these higher-body interactions; the visibility of interference fringes depend on both two-, three- and higher-body energy scales, and these produce an initial dephasing that can help explain the surprisingly rapid decay of revivals seen in experiments. If inhomogeneities in the lattice system are sufficiently reduced, longer timescale partial and nearly full revivals will be visible. Using Feshbach resonances or control of the lattice potential it is possible to tune the effective higher-body interactions and simulate effective field theories in optical lattices.

Experimental study of high speed polarization-coding quantum key distribution with sifted-key rates over Mbit/s

We present a quantitative study of various limitations on quantum cryptographic systems operating with sifted-key rates over Mbit/s. The dead time of silicon APDs not only limits the sifted-key rate but also causes correlation between the neighboring key bits. In addition to the well-known count-rate dependent timing jitter in avalanche photo-diode (APD), the faint laser sources, the vertical cavity surface emission lasers (VCSELs) in our system, also induce a significant amount of data-dependent timing jitter. Both the dead time and the data-dependent timing jitter are major limiting factors in designing QKD systems with sifted-key rates beyond Mbit/s.

Nested interaction representations in time dependent quantum mechanics

Two significant developments in the formulation of the equations of motion in the interaction representation (IR) are introduced in this paper. These developments have direct bearing on the efficient propagation in the interaction representation. The first of these developments involves the concept of sequential, or ‘‘nested’’ interaction transformations on the Hamiltonian and the wave function. Two such nested IRs are described. The first is a momentum‐ or ‘‘P‐adapted’’ IR which, in addition to removing wave packet spreading, systematically maintains the average momentum 〈P〉 at zero. This facilitates a grid which not only has a minimal range, but whose points are maximally sparse. Evaluating the Hamiltonian operator in the P‐adapted interaction representation involves only one simple algorithmic modification to the ordinary IR: replacing eiH0t/ℏV(R)e−iH0t /ℏ→eiH0t/ℏV(R+〈P〉t/m) eiH0t/ℏ, i.e., using the potential energy function which is downstream from the wave function by the classical propagation distan...