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Photon Recoil in Dispersive
Media
The momentum of a photon in a dispersive medium is
of conceptual and practical importance. When a photon
enters a medium with index of refraction n,
the electromagnetic momentum changes from h/l
to nh/l where, l
is the vacuum wavelength of the photon, and h is Plank's
constant. Momentum conservation requires that the medium
now has a mechanical momentum corresponding to the change
in the photon’s electromagnetic momentum. Recently,
there have been discussions about what happens to an
atom when it absorbs a photon within the medium. Is
the recoil momentum nh/l,
the electromagnetic momentum? Or, if one assumes no
momentum is left in the medium is the recoil momentum
h/l. We have measured a systematic
shift of the photon recoil momentum due the index of
refraction of a Bose Einstein condensate. The essential
idea of our experiment is to measure the recoil frequency
interferometrically using a two-pulse Ramsey interferometer.
The two pulses are optical standing waves separated
by a delay time t (Fig 1). The first pulse diffracts
the atoms in an 87Rb BEC into discrete momentum states.
During the delay time t the phase of each momentum state
evolves at a different rate according to its recoil
energy. The second pulse recombines the atoms with the
initial condensate. The recombined components have differing
phases leading to interference fringes that oscillate
at the two-photon recoil frequency. By measuring the
resulting frequency as a function of the standing wave
detuning from the atomic resonance, we found a distinctive
dispersive shape for the recoil frequency that fit the
recoil momentum as nh/l (Fig
2). This has important consequences for atom interferometers
using optical waves to manipulate atoms by the transfer
of recoil momentum, and in particular for high precision
measurements of the photon recoil which are used to
determine the fine structure constant aa.
Fig. 1.
Two-pulse Interferometer. The first pulse outcoupled
a small fraction of atoms into discrete momentum states.
The outcoupled atoms moved within the initial condensate.
After a variable delay a second pulse was applied and
the outcoupled atoms interfered with those outcoupled
by the first pulse. The laser beam was applied perpendicular
to the long axis of the condensate; the polarization,
E, was parallel to it and to the applied magnetic field
bias, B. 600 ms after the
first pulse was applied the atoms were released from
the magnetic trap and imaged after 38 ms of ballistic
expansion. The field of view is 0.5 mm x 1.5 mm
Fig. 2.
Recoil frequency as a function of detuning, D/2p,
showing the dispersive effect of the index of refraction.
The shaded area gives the expected recoil frequency
including the uncertainty in the density. The dashed
line is at the expected value without index of refraction
effects.
- Gretchen K. Campbell, Aaron E. Leanhardt, Jonchul
Mun, Micah Boyd, Erik W. Streed, Wolfgang Ketterle
and David E. Pritchard: Photon Recoil Momentum in
Dispersive Media.
Phys. Rev. Lett. 94 170403 (2005)
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