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  • BEC Interferometry and Applications Robert Horne, Bob Leonard, and Cass Sackett

    Atom Interferometry Manipulate atomic wave functions

    Measure phase

    Measurement of gravity, inertial effects, atomic properties

    Advantages of Condensates

    Easier to control permit guided wave interferometers

    Hope for more flexible trajectories, longer interaction times

    Support atoms against gravity - shorter apparatus

    Coherent waves means high contrast

    ~Eti

    e

    x y

    z

    Waveguide

    Supports atoms against gravity and provide spatial confinement

    Harmonic confinement:

    Weak Longitudinal Confinement Reduces Noise Lower density weaker atomic interactions

    Energy differential across wave packet

    x

    y

    z

    / 2 5.7 Hz

    / 2 0.21 Hz

    / 2 3.3 Hz

    =

    =

    =

    y

    Symmetric Trajectory Phase = (y), varies across packet

    Symmetric interferometer cancels the effect of these gradients

    Recombination & Phase Extraction Overlapping atoms have inference fringes too small to resolve

    The split pulse acting on & gives:

    For a phase shifted wave function, , we find

    the number of atoms coming to rest by:

    ( ) Split

    Split

    1U 0 2 2 Split

    2

    U Split 0

    = + + =

    =

    2 , 2 , 0+

    2 20N Split cosN 2

    = =

    kp

    kp

    2moving2

    2moving2

    restat0

    =

    +=+

    2 2+0

    Split & Reflect Beam The atoms achieve spatial separation via

    pulses of off-resonant light

    This light forms a standing wave which acts

    similar to an optical diffraction gating

    Split operation is a two photon process

    involving an absorption and stimulated emission

    The same beam reverses the motion of the atoms

    by driving them from .

    ts = 24 s t

    s = 24 s

    tw

    = 33 s

    3.03 r

    Split Pulse:

    0 T/4 3T/4 T

    Position (y)

    Time

    Measurements

    AC Polarizability (AC Stark Shift) Shine laser on one packet Measure induced phase

    0 2 4 60.0

    0.2

    0.4

    0.6

    0.8

    1.0

    N0/N

    It [mW ms cm-2]

    Itc 02

    =

    = polarizability I = intensity t = pulse time

    Measure at = 6.6 GHz, 13 THz 6% accuracy

    DC Polarizability Sagnac

    m4 A =

    tEDC

    2

    2

    1 =

    V

    y

    x

    Current & Future Work

    0 T/4 3T/4 T

    Position (y)

    Time

    Dual Interferometer

    Noise from vibrations currently limit visibility

    Vibrations will couple to both interferometers in a dual setup

    2 2+

    Imaging

    is determined by

    absorption imaging

    Atoms absorb resonant light, casting a

    shadow which we image on a CCD camera

    0N

    N

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