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Physical Review A

Measuring the quantum state of cold atoms using momentum-shearing interferometry

Ian A. Walmsley, N. P. Bigelow

Published Feb 1, 1998• 10 citations
Publisher

Abstract

We describe a method for measuring the density matrix of the transverse component of an atomic beam using a two-color, double-grating lateral shearing interferometer. From a set of measurements made in the far field of the atom interferometer, it is possible to reconstruct the one-particle density matrix with a very simple algorithm that involves no integral transforms.

DOI
10.1103/physreva.57.r713

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We describe a method for measuring the density matrix of the transverse component of an atomic beam using a two-color, double-grating lateral shearing interferometer. From a set of measurements made in the far field of the atom interferometer, it is possible to reconstruct the one-particle density matrix with a very simple algorithm that involves no integral transforms.
This thesis describes the construction of an atomic matter-wave interferometer, combined with a spin-state interferometer, used to weakly measure the average transverse momentum of the atoms. A velocity-tuneable cold atomic beam was constructed and characterised. By applying radiation pressure to a magneto-optical trap, the beam's velocity was selected between 1-52 ms-1. The beam was used to produce interference fringes in a matter-wave interferometer which consisted of a mutli-slit Si3Ni4 grating and a planar atom detector placed below the grating. The interference pattern was used to measure the average beam velocity and the Van der Waals coefficient between the atoms and the grating. This was the first instance of such a measurement. Below the grating a longitudinal Stern-Gerlach interferometer was constructed. The phase shift of the atom's spin, due to the Zeeman effect from the interferometer's magnetic field, was measured. The phase shift provided a measurement of the interferometer's magnetic field in the μT range. An experiment combining the two interferometers to weakly measure the atom's transverse momentum is described and modelled.
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wave function, but the entire density matrix, whose phases carry information about momentum and how pure the state is. An experimental setup is presented that can measure the density matrix (or equivalently, the Wigner function) of a beam of identically prepared charged particles to an arbitrary accuracy, limited only by count statistics and detector resolution. The particles enter into an electric field, causing simple harmonic oscillation in the transverse direction. This corresponds to rotating the Wigner function in phase space. With a slidable detector, the marginal distribution of the Wigner function can be measured from all angles. Thus the phase-space tomography formalism can be used to recover the Wigner function by the standard inversion of the radon transform. By applying this technique to, for instance, double-slit experiments with various degrees of environment-induced decoherence, it should be possible to make our understanding of decoherence and apparent wave-function collapse less qualitative and more quantitative. \textcopyright{} 1996 The American Physical Society.