Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a ${}^{87}\mathrm{Rb}$ condensate in a two-dimensional lattice potential. The dynamical structure factor of the system is probed by energy deposition through low-momentum Bragg excitations. The experimental signals are compared to recent theoretical predictions for the dynamical structure factor of the Lieb-Liniger model at $T>0$. Our results demonstrate that the main contribution to the spectral widths stems from the dynamics of the interaction-induced excitations in the gas, which cannot be described by the Luttinger liquid theory.

We report the Bragg spectroscopy of interacting one-dimensional Bose gases loaded in an optical lattice across the superfluid to the Mott-insulator phase transition. Elementary excitations are created with a nonzero momentum and the response of the correlated 1D gases is in the linear regime. The complexity of the strongly correlated quantum phases is directly displayed in the spectra which exhibit novel features. This work paves the way for a precise characterization of the state of correlated gases in optical lattices.

Quantum systems can be exquisite sensors thanks to their sensitivity to external perturbations. This same characteristic also makes them fragile to external noise. Quantum control can tackle the challenge of protecting a quantum sensor from environmental noise, while strongly coupling the sensor with the field to be measured. As the compromise between these two conflicting requirements does not always have an intuitive solution, optimal control based on a numerical search could prove very effective. Here, we adapt optimal control theory to the quantum-sensing scenario by introducing a cost function that, unlike the usual fidelity of operation, correctly takes into account both the field to be measured and the environmental noise. We experimentally implement this novel control paradigm using a nitrogen vacancy center in diamond, finding improved sensitivity to a broad set of time-varying fields. The demonstrated robustness and efficiency of the numerical optimization, as well as the sensitivity advantage it bestows, will prove beneficial to many quantum-sensing applications.

We investigate the coherence properties of an array of one-dimensional Bose gases with short-scale phase fluctuations. The momentum distribution is measured using Bragg spectroscopy, and an effective coherence length of the whole ensemble is defined. In addition, we propose and demonstrate that time-of-flight absorption imaging can be used as a simple probe to directly measure the coherence length of one-dimensional gases in the regime where phase fluctuations are strong. This method is suitable for future studies such as investigating the effect of disorder on the phase coherence.

We present experimental evidence of the successful closed-loop optimization of the dynamics of cold atoms in an optical lattice. We optimize the loading of an ultracold atomic gas minimizing the excitations in an array of one-dimensional (1D) tubes (3D-1D crossover) and we perform an optimal crossing of the quantum phase-transition from a superfluid to a Mott insulator in a 3D lattice. In both cases we enhance the experiment performances with respect to those obtained via adiabatic dynamics, effectively speeding up the process by more than a factor three while improving the quality of the desired transformation.