Observing the Profile of an Atom Laser Beam

We report on an investigation of the beam profile of an atom laser extracted from a magnetically trapped $^{87}$Rb Bose-Einstein condensate. The transverse momentum distribution is magnified by a curved mirror for matter waves and a momentum resolution of 1/60 of a photon recoil is obtained. We find the transverse momentum distribution to be determined by the mean-field potential of the residing condensate, which leads to a non-smooth transverse density distribution. Our experimental data are compared with a full 3D simulation of the output coupling process and we find good agreement.Comment: 4 pages, 4 figure

On the atomic structure of cocaine in solution

Cocaine is an amphiphilic drug which has the ability to cross the blood–brain barrier (BBB). Here, a combination of neutron diffraction and computation has been used to investigate the atomic scale structure of cocaine in aqueous solutions. Both the observed conformation and hydration of cocaine appear to contribute to its ability to cross hydrophobic layers afforded by the BBB, as the average conformation yields a structure which might allow cocaine to shield its hydrophilic regions from a lipophilic environment. Specifically, the carbonyl oxygens and amine group on cocaine, on average, form ~5 bonds with the water molecules in the surrounding solvent, and the top 30% of water molecules within 4 Å of cocaine are localized in the cavity formed by an internal hydrogen bond within the cocaine molecule. This water mediated internal hydrogen bonding suggests a mechanism of interaction between cocaine and the BBB that negates the need for deprotonation prior to interaction with the lipophilic portions of this barrier. This finding also has important implications for understanding how neurologically active molecules are able to interact with both the blood stream and BBB and emphasizes the use of structural measurements in solution in order to understand important biological function.Peer ReviewedPostprint (author's final draft

Low-density, one-dimensional quantum gases in a split trap

We investigate degenerate quantum gases in one dimension trapped in a harmonic potential that is split in the centre by a pointlike potential. Since the single particle eigenfunctions of such a system are known for all strengths of the central potential, the dynamics for non-interacting fermionic gases and low-density, strongly interacting bosonic gases can be investigated exactly using the Fermi-Bose mapping theorem. We calculate the exact many-particle ground-state wave-functions for both particle species, investigate soliton-like solutions, and compare the bosonic system to the well-known physics of Bose gases described by the Gross-Pitaevskii equation. We also address the experimentally important questions of creation and detection of such states.Comment: 7 pages, 5 figure

Radiating dipoles in photonic crystals

The radiation dynamics of a dipole antenna embedded in a Photonic Crystal are modeled by an initially excited harmonic oscillator coupled to a non--Markovian bath of harmonic oscillators representing the colored electromagnetic vacuum within the crystal. Realistic coupling constants based on the natural modes of the Photonic Crystal, i.e., Bloch waves and their associated dispersion relation, are derived. For simple model systems, well-known results such as decay times and emission spectra are reproduced. This approach enables direct incorporation of realistic band structure computations into studies of radiative emission from atoms and molecules within photonic crystals. We therefore provide a predictive and interpretative tool for experiments in both the microwave and optical regimes.Comment: Phys. Rev. E, accepte

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Measurement uncertainty relations

Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by Heisenberg. Here we prove such relations for the case of two canonically conjugate observables like position and momentum, and establish a close connection with the more familiar preparation uncertainty relations constraining the sharpness of the distributions of the two observables in the same state. Both sets of relations are generalized to means of order $\alpha$ rather than the usual quadratic means, and we show that the optimal constants are the same for preparation and for measurement uncertainty. The constants are determined numerically and compared with some bounds in the literature. In both cases the near-saturation of the inequalities entails that the state (resp. observable) is uniformly close to a minimizing one.Comment: This version 2 contains minor corrections and reformulation

Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process

The accuracy of the Arthurs-Kelly model of a simultaneous measurement of position and momentum is analysed using concepts developed by Braginsky and Khalili in the context of measurements of a single quantum observable. A distinction is made between the errors of retrodiction and prediction. It is shown that the distribution of measured values coincides with the initial state Husimi function when the retrodictive accuracy is maximised, and that it is related to the final state anti-Husimi function (the P representation of quantum optics) when the predictive accuracy is maximised. The disturbance of the system by the measurement is also discussed. A class of minimally disturbing measurements is characterised. It is shown that the distribution of measured values then coincides with one of the smoothed Wigner functions described by Cartwright.Comment: 12 pages, 0 figures. AMS-Latex. Earlier version replaced with final published versio

Dark-Bright Solitons in Inhomogeneous Bose-Einstein Condensates

We investigate dark-bright vector solitary wave solutions to the coupled non-linear Schr\"odinger equations which describe an inhomogeneous two-species Bose-Einstein condensate. While these structures are well known in non-linear fiber optics, we show that spatial inhomogeneity strongly affects their motion, stability, and interaction, and that current technology suffices for their creation and control in ultracold trapped gases. The effects of controllably different interparticle scattering lengths, and stability against three-dimensional deformations, are also examined.Comment: 5 pages, 5 figure

Curie-Weiss model of the quantum measurement process

A hamiltonian model is solved, which satisfies all requirements for a realistic ideal quantum measurement. The system S is a spin-\half, whose $z$-component is measured through coupling with an apparatus A=M+B, consisting of a magnet \RM formed by a set of $N\gg 1$ spins with quartic infinite-range Ising interactions, and a phonon bath \RB at temperature $T$. Initially A is in a metastable paramagnetic phase. The process involves several time-scales. Without being much affected, A first acts on S, whose state collapses in a very brief time. The mechanism differs from the usual decoherence. Soon after its irreversibility is achieved. Finally the field induced by S on M, which may take two opposite values with probabilities given by Born's rule, drives A into its up or down ferromagnetic phase. The overall final state involves the expected correlations between the result registered in M and the state of S. The measurement is thus accounted for by standard quantum statistical mechanics and its specific features arise from the macroscopic size of the apparatus.Comment: 5 pages Revte