A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys, vol.83, issue.3, pp.863-883, 2011.

S. Trotzky, Y. Chen, A. Flesch, I. P. Mcculloch, U. Schollwck et al., Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas, Nature Physics, vol.8, issue.4, p.2232, 2012.

M. Cheneau, P. Barmettler, D. Poletti, M. Endres, P. Schau et al.,

, Light-cone-like spreading of correlations in a quantum many-body system, Nature, vol.481, issue.7382, pp.484-487, 2012.

C. Hung, V. Gurarie, and C. Chin, From Cosmology to Cold Atoms: Observation of Sakharov Oscillations in a Quenched Atomic Superfluid, Science, vol.341, issue.6151, pp.1213-1215, 2013.

T. Langen, T. Schweigler, E. Demler, and J. Schmiedmayer, Double light-cone dynamics establish thermal states in integrable 1d Bose gases, September 2017

J. Jaskula, G. B. Partridge, M. Bonneau, R. Lopes, J. Ruaudel et al., Acoustic Analog to the Dynamical Casimir Effect in a BoseEinstein Condensate, Phys. Rev. Lett, vol.109, issue.22, p.220401, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00817102

J. De-nardis, B. Wouters, M. Brockmann, and J. Caux, Solution for an interaction quench in the Lieb-Liniger Bose gas, Phys. Rev. A, vol.89, issue.3, p.33601, 2014.

P. Calabrese and P. L. Doussal, Interaction quench in a LiebLiniger model and the KPZ equation with flat initial conditions, J. Stat. Mech, issue.5, p.5004, 2014.

M. A. Cazalilla and M. Chung, Quantum quenches in the Luttinger model and its close relatives, J. Stat. Mech, issue.6, p.64004, 2016.

T. Wisocki and P. Deuar, Quantum fluctuation effects on the quench dynamics of thermal quasicondensates, J. Phys. B: At. Mol. Opt. Phys, vol.49, issue.14, p.145303, 2016.

B. Rauer, S. Erne, T. Schweigler, and F. Cataldini, Mohammadamin Tajik, and Jrg Schmiedmayer. Recurrences in an isolated quantum many-body system, 2017.

C. Mora and Y. Castin, Extension of Bogoliubov theory to quasicondensates, Phys. Rev. A, vol.67, issue.5, p.53615, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00157445

M. Schemmer, A. Johnson, R. Photopoulos, and I. Bouchoule, Monte Carlo wave-function description of losses in a one-dimensional Bose gas and cooling to the ground state by quantum feedback, Phys. Rev. A, vol.95, issue.4, p.43641, 2017.

, 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

A. Imambekov, I. E. Mazets, D. S. Petrov, V. Gritsev, S. Manz et al., Density ripples in expanding lowdimensional gases as a probe of correlations, Phys. Rev. A, vol.80, issue.3, p.33604, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00423924

S. Dettmer, D. Hellweg, P. Ryytty, J. J. Arlt, W. Ertmer et al., Observation of Phase Fluctuations in Elongated Bose-Einstein Condensates, Phys. Rev. Lett, vol.87, issue.16, p.160406, 2001.

S. Manz, R. Bcker, T. Betz, . Ch, S. Koller et al., Two-point density correlations of quasicondensates in free expansion, Phys. Rev. A, vol.81, issue.3, p.31610, 2010.

B. Rauer, P. Griins, I. E. Mazets, T. Schweigler, W. Rohringer et al., Cooling of a One-Dimensional Bose Gas, Phys. Rev. Lett, vol.116, issue.3, p.30402, 2016.

, For consistency we rederive this expression (first established in [21]) see

I. Eq, 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

K. V. Kheruntsyan, D. M. Gangardt, P. D. Drummond, and G. V. Shlyapnikov, Pair Correlations in a Finite-Temperature 1d Bose Gas, Phys. Rev. Lett, vol.91, issue.4, p.40403, 2003.

J. N. Fuchs, X. Leyronas, and R. Combescot, Hydrodynamic modes of a one-dimensional trapped Bose gas, Phys. Rev. A, vol.68, issue.4, p.43610, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00002736

, 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

T. Jacqmin, J. Armijo, T. Berrada, K. V. Kheruntsyan, and I. Bouchoule, SubPoissonian Fluctuations in a 1d Bose Gas: From the Quantum Quasicondensate to the Strongly Interacting Regime, Phys. Rev. Lett, vol.106, issue.23, p.230405, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00576883

A. Johnson, S. S. Szigeti, M. Schemmer, and I. Bouchoule, Long-lived nonthermal states realized by atom losses in one-dimensional quasicondensates, Phys. Rev. A, vol.96, issue.1, p.13623, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01479415

, We corrected the formula published in, vol.21

D. Hellweg, S. Dettmer, P. Ryytty, J. J. Arlt, W. Ertmer et al., Phase fluctuations in BoseEinstein condensates, Appl Phys B, vol.73, issue.8, pp.781-789, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00002131

, 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 ?

M. Olshanii, Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons, Phys. Rev. Lett, vol.81, issue.5, pp.938-941, 1998.

A. Mitra, Quantum quench dynamics, 2017.

T. Jacqmin, B. Fang, T. Berrada, T. Roscilde, and I. Bouchoule, Momentum distribution of one-dimensional Bose gases at the quasicondensation crossover: Theoretical and experimental investigation, Phys. Rev. A, vol.86, issue.4, p.43626, 2012.
DOI : 10.1103/physreva.86.043626