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, For each positive q value, one has 2 Fourier components: ? nq,c = 2/L dzn(z) cos(qz) and?nqand? and?nq,s = 2/L dzn(z) sin(qz), with similar expressions for ?. We omit the subscript c or s in the text for simplicity
, For quasi-1D gases the hydrodynamic condition is replaced by ?q ? ?
, The phase space area is preserved, one quadrature being squeezed, while the other is anti-squeezed
, For the q values considered, ?q kBT and the Raighley-Jeans approximation holds
, the evolution of density fluctuations has however been investigated for a 2D gas
, Isolating the contribution of individual modes to the function g1(z) requires looking at the Fourier transform of ln(g1(z)), which requires large detection dynamics
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, For consistency we rederive this expression (first established in [21]) see
q = (? 2 q,c + ? 2 q,s )/2 where ?q,c and ?q,s are the cosine and sine Fourier components, which fulfill ? 2 q,c = ? 2 q,s for translationally invariant systems ,
, Validity of LDA is established in Appendix E
, The experiment is described in more detail in, vol.43
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, We thus expect slightly different optical resolutions, ?i and ? f for data taken before and after the quench respectively, The transverse size of the cloud after the time-of-flight is comparable to the depth of focus of the imaging system and depends on the transverse confinement
, The values of resolution obtained by such fits are close to the expected values if one takes into account the depth of field of our imaging system and the fact that
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, We corrected the formula published in, vol.21
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, This term is due to the approximation made when going from Eq. (A1) to Eq. (A2), which is valid only for q values larger than the inverse of the cloud size
, Since the Hamiltonian of interest is quadratic in ?, the distribution of ? is Gaussian at thermal equilibrium. The squeezing of each collective mode produced by the interaction quench preserves the Gaussian nature of ?
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DOI : 10.1103/physreva.86.043626