Generalized HydroDynamics on an Atom Chip (1810.07170v2)

Abstract: The emergence of a special type of fluid-like behavior at large scales in one-dimensional (1d) quantum integrable systems, theoretically predicted in 2016, is established experimentally, by monitoring the time evolution of the in situ density profile of a single 1d cloud of $^{87}{\rm Rb}$ atoms trapped on an atom chip after a quench of the longitudinal trapping potential. The theory can be viewed as a dynamical extension of the thermodynamics of Yang and Yang, and applies to the whole range of repulsion strength and temperature of the gas. The measurements, performed on weakly interacting atomic clouds that lie at the crossover between the quasicondensate and the ideal Bose gas regimes, are in very good agreement with the 2016 theory. This contrasts with the previously existing 'conventional' hydrodynamic approach---that relies on the assumption of local thermal equilibrium---, which is unable to reproduce the experimental data.

Generalized Hydrodynamics on an Atom Chip

The paper "Generalized Hydrodynamics on an Atom Chip" presents experimental verification of the emergent hydrodynamic behavior in one-dimensional (1d) quantum integrable systems, specifically within the context of generalized hydrodynamics (GHD). This work monitors the time evolution of a 1d cloud of $^{87}$Rb atoms after a quench of the longitudinal trapping potential, a challenging experimental setup that confirms theoretical predictions made in 2016 regarding fluid-like behavior in 1d Bose gases.

Theoretical Framework and Experimental Setup

GHD is positioned as a dynamic extension of the thermodynamics of Yang and Yang, applying across different repulsive interaction strengths and temperatures of the gas. The paper contrasts GHD with conventional hydrodynamics (CHD), which assumes local thermal equilibrium but fails to reproduce experimental data under certain conditions. The innovative aspect of GHD is its treatment of local distributions of rapidities, which allows for more accurate predictions of the atom cloud's behavior under a variety of quenches in potential.

The authors fabricate a unique experimental setup using an atom chip, which allows precise manipulation of the atomic cloud using both AC and DC currents to create transverse and longitudinal potentials. By tuning these potentials, the experiment can simulate different quench scenarios, such as expansion from harmonic and double-well potentials.

Results and Discussion

The strong agreement between GHD predictions and experimental measurements of the in situ density profiles confirms the validity of GHD over CHD. The expansion from a double-well potential, in particular, exemplifies where CHD diverges from experimental results due to its inability to account for non-equilibrium rapidity distributions at given positions and times. Conversely, GHD captures such distributions and describes the time-evolution of the cloud accurately.

In these experiments, various regimes of the Lieb-Liniger model were explored, ranging from quasicondensate to ideal Bose gas. The comparisons between experimental data and results from both GHD and CHD highlight the limitations of CHD, which predicts non-physical shock formations due to restricted conservation laws.

Implications and Future Work

This experimental verification establishes GHD as crucial for understanding hydrodynamic behavior in 1d Bose gases and potentially other quantum integrable systems. The approach offers insights into the variations in hydrodynamic behavior, from quasicondensation to non-degenerate Bose gasses. The research holds significance for further exploration in strongly interacting regimes and multicomponent mixtures, which may yield novel applications in quantum computing and precision measurement technologies.

Future directions include extending GHD methodologies to other quantum systems where integrability provides predictive power. Investigating more complex systems, such as multicomponent fermionic or bosonic gases, could provide further understanding of non-equilibrium dynamics and contribute to the development of new theoretical models that address even broader classes of many-body quantum mechanics. The experimental techniques demonstrated establish a foundation for such explorations, emphasizing the versatility and robustness of the atom chip setup in quantum physics research.