Abstract
The dynamic structure factor is a central quantity describing the physics of quantum many-body systems, capturing structure and collective excitations of a material. In condensed matter, it can be measured via inelastic neutron scattering, which is an energy-resolving probe for the density fluctuations. In ultracold atoms, a similar approach could so far not be applied because of the diluteness of the system. Here we report on a direct, real-time and nondestructive measurement of the dynamic structure factor of a quantum gas exhibiting cavity-mediated long-range interactions. The technique relies on inelastic scattering of photons, stimulated by the enhanced vacuum field inside a high finesse optical cavity. We extract the density fluctuations, their energy and lifetime while the system undergoes a structural phase transition. We observe an occupation of the relevant quasi-particle mode on the level of a few excitations, and provide a theoretical description of this dissipative quantum many-body system.
Highlights
The dynamic structure factor is a central quantity describing the physics of quantum manybody systems, capturing structure and collective excitations of a material
Knowledge of the dynamic structure factor provides a complete picture of the emerging quasi-particle modes[3], their excitation energy, lifetime and mean occupation number
In a long-range interacting system, a structural phase transition can be driven by a roton-like mode softening[5,6,7,8], which is expected to show up as a thermally enhanced peak in the dynamic structure factor[9]
Summary
The dynamic structure factor is a central quantity describing the physics of quantum manybody systems, capturing structure and collective excitations of a material In condensed matter, it can be measured via inelastic neutron scattering, which is an energy-resolving probe for the density fluctuations. A technique measuring the spectral response function of a quantum gas, that is, the dynamic structure factor at zero temperature[18], is Bragg spectroscopy[19,20] It is based on stimulated rather than spontaneous inelastic scattering of photons between two laser beams. Bragg beams[21] and could in principle be extended with the help of cavities to be only weakly perturbative[22] All these methods measure the linear response of the gas on a perturbation and are insensitive to thermally excited quasi-particles. Similar to the analysis of noise correlations from images of ballistically expanded ultracold gases[24], this approach gives no access to the quasi-particle spectrum, that is, the temporal dynamics
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