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note
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In writing this Hamiltonian we drop terms which depend on the total number of atoms and photons and are unimportant for the dynamics.
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18
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18444416117
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note
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Strictly speaking the operators contain the retarded Fourier transforms of the (cross) spectral densities of the electric field components. For a more rigorous treatment of the propagating field modes we refer to Ref. [3].
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19
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18444383460
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note
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Spatial correlations due to the indistinguishability of the particles are neglected here.
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20
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18444415235
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note
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This procedure is valid for Gaussian input states like coherent or squeezed states.
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18444396682
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note
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Here we reintroduce implicitly the noise due to quantum fluctuations.
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0003972070
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18444409103
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note
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2 line the recoil time is 0.3 ms.
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31
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18444408461
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note
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Since we treat the scattered wave as a scalar the phase of the scattering amplitude has to be chosen with care.
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18444365347
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note
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Here we neglect other potentials, like gravity, for simplicity.
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-
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35
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18444393162
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-
note
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Our simple analytical estimate at this length is already wrong by about a factor of 2.
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-
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38
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18444410022
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note
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2 appears linearly here.
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39
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18444382125
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note
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This value corresponds to the variance in the population difference for a sample of Nat independent atoms residing with equal probability in two internal states.
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-
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41
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18444363419
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note
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3 has to be smaller than 1 for the model to be valid, otherwise the neglect of multiple scattering is not possible.
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45
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18444399042
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note
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To lowest order in a multiple-scattering expansion the dynamics of the density correlation function can be just described by recoil heating.
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47
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