Measuring correlation functions in interacting systems of cold atoms

Lia Izabella Lovas

Michael Streif, Andreas Buchleitner, Dieter Jaksch +1 more

We present a nondestructive method to probe a complex quantum system using multiple-impurity atoms as quantum probes. Our protocol provides access to different equilibrium properties of the system by changing its coupling to the probes. In particular, we show that measurements with two probes reveal the system's nonlocal two-point density correlations, for probe-system contact interactions. We illustrate our findings with analytic and numerical calculations for the Bose-Hubbard model in the weakly and strongly interacting regimes, under conditions relevant to ongoing experiments in cold-atom systems.

Daniel Manzano

C. Lobo, S. D. Gensemer

We propose an experimental method that allows for scaling of all the diagonal correlation functions (such as the density and pair correlation function) during the expansion of harmonically trapped cold atomic gases with arbitrary interactions even if the trapping is anisotropic. To do this we require that the interaction be tunable by the use of a Feshbach resonance and that the trapping potential can be manipulated independently along the axial and radial directions. This permits a much greater accuracy and resolution in measurements of correlation functions. We explain the explicit control procedure, outline the scaling ansatz that we use, and briefly discuss the systems where it could be applied as well as possible experimental obstacles to its implementation.

Lexter Savio Rodriguez

Brian G. Swingle, Gregory S. Bentsen, Monika Schleier-Smith +1 more

We provide a general protocol to measure out-of-time-order correlation functions. These correlation functions are of broad theoretical interest for diagnosing the scrambling of quantum information in interacting quantum systems and have recently received particular attention in the study of chaos and black holes within holographic duality. Measuring them requires an echo-type sequence in which the sign of a many-body Hamiltonian is reversed. We illustrate our protocol by detailing an implementation employing cold atoms and cavity quantum electrodynamics to probe spin models with nonlocal interactions. To verify the feasibility of the scheme with current technology, we analyze the effects of dissipation in a chaotic kicked-top model. Finally, we propose a number of other experimental platforms where similar out-of-time-order correlation functions can be measured.