Quantum metrology aims to describe the potentially enhanced usefulness of quantum systems over classical systems to carry out precise measurements of important physical quantities. To this end, the quantum Cramér-Rao theorem along with the Quantum Fisher Information contained in it gives an ultimate bound on the precision of the estimation of any classical parameter. In a quantum estimation framework, many-body physics can play a very valuable role. Indeed, many-body correlations are a useful resource for quantum metrology. Using our expertise on many-body physics, and on dilute ultracold gases in particular, we aim to better understand the role of interactions in metrology. On the other hand, we also study relativistic quantum metrology. By combining general relativity and quantum parameter estimation, we can find the estimation precision of parameters like the speed of light, curvature, Schwarzschild radius, etc.

A variety of cosmologically motivated effective quasiparticle space-times can be produced in harmonically trapped superfluid Bose and Fermi gases. We have studied the analog of cosmological particle production in these effective space-times, induced by trapping potentials and coupling constants possessing an arbitrary time dependence. The WKB probabilities for phonon creation from the superfluid vacuum have been calculated, and an experimental procedure to detect quasiparticle production by measuring density-density correlation functions was proposed.

We investigate whether the many-body ground states of bosons in a generalized two-mode model with localized inhomogeneous single-particle orbitals and anisotropic long-range interactions (e.g., dipole-dipole interactions) are coherent or fragmented. It is demonstrated that fragmentation can take place in a single trap for positive values of the interaction couplings, implying that the system is potentially stable. Furthermore, the degree of fragmentation is shown to be insensitive to small perturbations on the single-particle level.

We have established a long-lived and rapidly accessible quantum memory unit (quantum RAM) in a hybrid system. The operational Hilbert space is spanned by states involving the two macroscopically occupied hyperfine levels of a miscible binary atomic Bose-Einstein condensate and the Rydberg state of a single atom therein, which interacts magnetically with the flux qubit of a SQUID. An arbitrary qubit state, initially prepared using the flux qubit, can be rapidly transferred to and from the trapped atomic ensemble in approximately 10 ns and with a large fidelity of 97%, via an effective two-photon process using an external laser for the transition to the Rydberg level. The achievable ultrafast transfer of quantum information enables a large number of storage and retrieval cycles from the highly controllable quantum optics setup of a dilute ultracold gas, even within the typically very short flux qubit lifetimes of the order of microseconds.