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A fundamental description of time can be consistent not only with the usual monotonic behavior but also with a periodic physical clock variable, coupled to the degrees of freedom of a system evolving in time. Generically, one would in fact…

Quantum entanglement offers powerful opportunities for enhancing measurement sensitivity beyond classical limits, with optical atomic clocks serving as a leading platform for such advances. This chapter introduces the principles of…

An ensemble density matrix model that includes one- and two-body losses is derived for a trapped-atom clock. A trapped-atom clock is mainly affected by one- and two-body losses, generally giving nonexponential decays of populations;…

The sensitivity of an atomic interferometer increases when the phase evolution of its quantum superposition state is measured over a longer interrogation interval. In practice, a limit is set by the measurement process, which returns not…

Advanced quantum technologies, such as quantum simulation, computation, and metrology are thriving for the implementation of large-scale configurations of identical quantum systems. Sets of atoms and molecules have the advantage of having…

We experimentally demonstrate the coherent manipulation of atomic states in far-detuned dipole traps and registers of dipole traps based on two-dimensional arrays of microlenses. By applying Rabi, Ramsey, and spin-echo techniques, we…

Spin squeezing is a form of entanglement that can improve the stability of quantum sensors operating with multiple particles, by inducing inter-particle correlations that redistribute the quantum projection noise. Previous analyses of…

Quantum coherences are paramount resources for applications, such as quantum-enhanced light-harvesting or quantum computing, which are fragile against environmental noise. We here derive generalized quantum master equations using…

Optical atomic clocks have been rapidly developing in recent decades, resulting in major improvements in both precision and accuracy. As a result, they have become instrumental in multiple areas of applied and fundamental research. Despite…

The exquisite control exhibited over quantum states of individual particles has revolutionized the field of precision measurement, as exemplified by the most accurate atomic clock realized in single trapped ions. Whereas many-atom lattice…

Precise understanding of the dynamics of trapped particles is crucial for nascent quantum technologies, including atomic clocks and quantum simulators. Here we present a framework to systematically include quantum effects arising from the…

All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks…

Optically trapped ensembles are of crucial importance for frequency measurements and quantum memories, but generally suffer from strong dephasing due to inhomogeneous density and light shifts. We demonstrate a drastic increase of the…

Frequency metrology is a cornerstone of modern precision measurements and optical atomic clocks have emerged as the most precise measurement devices. In this progress report, we explore various Ramsey interrogation schemes tailored to…

An exact generalization of the Ramsey transition probability is derived to improve ultra-high precision measurement and quantum state engineering when a particle is subjected to independently-tailored separated oscillating fields. The…

Coherence time is an important resource to generate enhancement in quantum metrology. In this work, based on continuous-variable models, we propose a new design of the signal-probe Hamiltonian which generates an exponential enhancement of…

Rapid progress in the precision and accuracy of optical atomic clocks over the last decade has advanced the frontiers of timekeeping, metrology, and quantum science. However, the stabilities of most optical clocks remain limited by the…

Ultra-cold atoms trapped in an optical dipole trap and prepared in a coherent superposition of their hyperfine ground states, decohere as they interact with their environment. We demonstrate than the loss in coherence in an "echo"…

Optical atomic clocks are poised to redefine the SI second, thanks to stability and accuracy more than one hundred times better than the current microwave atomic clock standard. However, the best optical clocks have not seen their…

Atomic clocks are crucial for science and technology, but their sensitivity is often restricted by the standard quantum limit. To surpass this limit, correlations between particles or interrogation times must be leveraged. Although the…