Experimental Investigation of a Bipartite Quench in a 1D Bose gas

TL;DR

This work probes the out-of-equilibrium dynamics of a 1D Bose gas under a bipartite quench using Generalized Hydrodynamics (GHD). The boundary density evolves ballistically at the Euler scale, and the boundary profile encodes the initial rapidity distribution, which the authors extract via parametric fits to a GHD model. While zero-temperature GHD captures the main features, nonzero entropy and experimental imperfections introduce deviations, particularly in the tail regions. Beyond boundary dynamics, a slice-expansion protocol reveals a pronounced asymmetry in the local rapidity distribution within the boundary, offering a window into zero-entropy-like features predicted by GHD, though tails remain to be explained. Overall, the study validates Euler-scale GHD for confined 1D Bose gases while highlighting the need for non-thermal stationary-state modeling and further exploration of diffusion, transverse excitations, and edge effects.

Abstract

Long wavelength dynamics of 1D Bose gases with repulsive contact interactions can be captured by Generalized HydroDynamics (GHD) which predicts the evolution of the local rapidity distribution. The latter corresponds to the momentum distribution of quasiparticles, which have infinite lifetime owing to the integrability of the system. Here we experimentally investigate the dynamics for an initial situation that is the junction of two semi-infinite systems in different stationary states, a protocol referred to as `bipartite quench' protocol. More precisely we realise the particular case where one half of the system is the vacuum state. We show that the evolution of the boundary density profile exhibits ballistic dynamics obeying the Euler hydrodynamic scaling. The boundary profiles are similar to the ones predicted with zero-temperature GHD in the quasi-BEC regime, with deviations due to non-zero entropy effects. We show that this protocol, provided the boundary profile is measured with infinite precision, permits to reconstruct the rapidity distribution of the initial state. For our data, we extract the initial rapidity distribution by fitting the boundary profile and we use a 3-parameter ansatz that goes beyond the thermal assumption. Finally, we investigate the local rapidity distribution inside the boundary profile, which, according to GHD, presents, on one side, features of zero-entropy states. The measured distribution shows the asymmetry predicted by GHD, although unelucidated deviations remain.

Figures (9)

• Figure 1: (a) Schematic drawing of the atom chip. The $3$ blue wires produce the transverse trapping, the $4$ other wires produce the longitudinal trapping. The red oval ball represents the atomic cloud, trapped 12 microns above the wires $-$ (b) Linear density profiles extracted from absorption images. The gray curve is the linear density profile of gas confined within a quartic potential. The atomic cloud is then illuminated during $30 \mu$s by a near resonant light beam, shaped using a DMD. The resulting density profile after a time of flight of $1$ms is depicted in yellow.
• Figure 2: Test of the ballistic scaling. Boundary density profiles obtained for different evolution times $t$ and represented as a function of $x / t$. The profiles overlap remarkably well, showing that the Euler scale is reached within this time interval. The longitudinal dynamics after $t = 18$ms cannot be probed due to the fact that our initial semi-homogeneous gas has a finite size. For shorter deformation times, experimental boundary profiles are smoother than the Euler-scale GHD predictions, which might be due to the failure of Euler scale, and/or to the fact that the cut at $t=0$ is not infinitely sharp.
• Figure 3: Occupation ratio $\nu^* (\zeta,\theta)$ solving the equation (\ref{['eq:nuetoile']}) for an initial occupation ratio $\nu_0 (\theta)$ in the right half-system corresponding to thermal equilibrium at temperature $T$. The dashed green line is the curve $\theta^*(\zeta)$, i.e. it is the set of points $(\zeta,\theta)$ such that $v^{\rm eff}_{[\nu^* (\zeta,.)]} (\theta) = \zeta$. [Parameters: $\gamma_0=mg/(n_0\hbar^2)=0.005$, $k_B T \hbar^2/(mg^2) = 365$, close to the experimental parameters of the data set of Fig. \ref{['fig:fitted_border']}.] The two vertical red dashed lines show a typical 'slice' of the boundary profile, which we study in detail in Section \ref{['sec:local']}. In that slice, the occupation factor is highly asymmetric: it varies smoothly with $\theta$ for negative values of $\theta$, while it behaves as a step function for $\theta$ close to $\theta^*$.
• Figure 4: (a) Boundary profile predictions from GHD for system initially in the ground state as a function of $\gamma$. The velocity is normalized to the radius of the intial Fermi sea $\Delta \theta_0$. On the negative side the point where $n$ reaches 0 is at $\Delta \theta_0$ whatever $\gamma$. On the positive side, the point where $n$ reaches $n_0$ is at the speed of sound $c$. The black, resp. grey, dashed line corresponds to the hydrodynamic prediction in the quasi-BEC regime (Eq. \ref{['eq:GPE']}), resp. in the hard-core regime (Eq.\ref{['eq:HS']}). (b) Comparison between experimental data and zero temperature prediction. The latter is given by eq. \ref{['eq:GPE']} with very good precision since the interaction parameter of the data is as low as $\gamma = 4.6\times 10^{-3}$. [The experimental curve, recorded for an evolution time $t=10$ ms, belongs to a different data-set than that used in Fig. \ref{['fig:euler']}.]
• Figure 5: (a) The experimental boundary profile plotted in yellow is compared to fitted profiles using for $\nu_0(\theta)$ either a thermal ansatz, i.e. the solution of Eqs. \ref{['eq:fonctions']} and \ref{['eq:stherm']}, (black dashed line) or the three-parameters ansatz defined by Eqs.\ref{['eq:fonctions']} and \ref{['eq:s']} (red line). The dark grey zones mark regions where the kinetic energy $m(x/t)^2/2$ is greater than the transverse energy gap $\hbar \omega_\perp$. Atoms with such kinetic energies might populate transversely excited states. Since almost all the boundary profile lies between these grey zones, one expects that the physics is well captured by the one-dimensional model. (b) Comparison of the occupation factors obtained for both fitted occupation factor distributions.