Overcoming loss of contrast in atom interferometry due to gravity gradients

Long-time atom interferometry is instrumental to various high-precision measurements of fundamental physical properties, including tests of the equivalence principle. Due to rotations and gravity gradients, the classical trajectories characterizing the motion of the wave packets for the two branches of the interferometer do not close in phase space, an effect which increases significantly with the interferometer time. The relative displacement between the interfering wave packets in such open interferometers leads to a fringe pattern in the density profile at each exit port and a loss of contrast in the oscillations of the integrated particle number as a function of the phase shift. Paying particular attention to gravity gradients, we present a simple mitigation strategy involving small changes in the timing of the laser pulses which is very easy to implement. A useful representation-free description of the state evolution in an atom interferometer is introduced and employed to analyze the loss of contrast and mitigation strategy in the general case. (As a by-product, a remarkably compact derivation of the phase-shift in a general light-pulse atom interferometer is provided.) Furthermore, exact results are obtained for (pure and mixed) Gaussian states which allow a simple interpretation in terms of the alignment of Wigner functions in phase-space. Analytical results are also obtained for expanding Bose-Einstein condensates within the time-dependent Thomas-Fermi approximation. Finally, a combined strategy for rotations and nonaligned gravity gradients is considered as well.Comment: 14+7 pages including appendices, 9 figures; v2 minor changes, matches published versio

Conformal Mapping and Bound States in Bent Waveguides

Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending. The problem can be reduced to a one dimensional matrix Schroedinger equation using two descriptions: oblique modes and conformal coordinates. We use a corner-corrected WKB formalism to find the energies of the one dimensional problem. It is shown that the presence of bound states is an effect due to the boundary alone, with no classical counterpart for this geometry. The conformal description proves to be simpler, as the coupling of transversal modes is not essential in this case.Comment: 16 pages, 10 figures. To appear in the Proceedings of the Symposium "Symmetries in Nature, in memoriam Marcos Moshinsky

Fractional Talbot effect in phase space: A compact summation formula

A phase space description of the fractional Talbot effect, occurring in a one-dimensional Fresnel diffraction from a periodic grating, is presented. Using the phase space formalism a compact summation formula for the Wigner function at rational multiples of the Talbot distance is derived. The summation formula shows that the fractional Talbot image in the phase space is generated by a finite sum of spatially displaced Wigner functions of the source field.Comment: 4 pages, LaTeX. Submitted to Optics Expres

Endoscopic Tomography and Quantum-Non-Demolition

We propose to measure the quantum state of a single mode of the radiation field in a cavity---the signal field---by coupling it via a quantum-non-demolition Hamiltonian to a meter field in a highly squeezed state. We show that quantum state tomography on the meter field using balanced homodyne detection provides full information about the signal state. We discuss the influence of measurement of the meter on the signal field.Comment: RevTeX, 10 pages, 1 eps figure with psfig. To appear In Physical Review A 59 (January 1999

Trapping state restoration in the randomly-driven Jaynes-Cummings model by conditional measurements

We propose a scheme which can effectively restore fixed points in the quantum dynamics of repeated Jaynes-Cummings interactions followed by atomic state measurements, when the interaction times fluctuate randomly. It is based on selection of superposed atomic states whose phase correlations tend to suppress the phase fluctuations of each separate state. One suggested realization involves the convergence of the cavity field distribution to a single Fock state by conditional measurements performed on two-level atoms with fluctuating velocities after they cross the cavity. Another realization involves a trapped ion whose internal-motional state coupling fluctuates randomly. Its motional state is made to converge to a Fock state by conditional measurements of the internal state of the ion.Comment: RevTeX, 5 pages, four (EPS) figures automatically included through epsfig. Physical Review A 1998 (accepted for publication) Two references added to Ref. [8]. No other change. Final version which will appear in Physical Review