Quantum Metrology with Cold Atoms

Quantum metrology is the science that aims to achieve precision measurements by making use of quantum principles. Attribute to the well-developed techniques of manipulating and detecting cold atoms, cold atomic systems provide an excellent platform for implementing precision quantum metrology. In this chapter, we review the general procedures of quantum metrology and some experimental progresses in quantum metrology with cold atoms. Firstly, we give the general framework of quantum metrology and the calculation of quantum Fisher information, which is the core of quantum parameter estimation. Then, we introduce the quantum interferometry with single and multiparticle states. In particular, for some typical multiparticle states, we analyze their ultimate precision limits and show how quantum entanglement could enhance the measurement precision beyond the standard quantum limit. Further, we review some experimental progresses in quantum metrology with cold atomic systems.Comment: 53 pages, 9 figures, revised versio

Asymmetric sequential Landau-Zener dynamics of Bose condensed atoms in a cavity

We explore the asymmetric sequential Landau-Zener (LZ) dynamics in an ensemble of interacting Bose condensed two-level atoms coupled with a cavity field. Assuming the couplings between all atoms and the cavity field are identical, the interplay between atom-atom interaction and detuning may lead to a series of LZ transitions. Unlike the conventional sequential LZ transitions, which are symmetric to the zero detuning, the LZ transitions of Bose condensed atoms in a cavity field are asymmetric and sensitively depend on the photon number distribution of the cavity. In LZ processes involving single excitation numbers, both the variance of the relative atom number and the step slope of the sequential population ladder are asymmetric, and the asymmetry become more significant for smaller excitation numbers. Furthermore, in LZ processes involving multiple excitation numbers, there may appear asymmetric population ladders with decreasing step heights. During a dynamical LZ process, due to the atom-cavity coupling, the cavity field shows dynamical collapse and revivals. In comparison with the symmetric LZ transitions in a classical field, the asymmetric LZ transitions in a cavity field originate from the photon-number-dependent Rabi frequency. The asymmetric sequential LZ dynamics of Bose condensed atoms in a cavity field may open up a new way to explore the fundamental many-body physics in coupled atom-photon systems.Comment: 14 pages, 6 figure

Kibble-Zurek dynamics in an array of coupled binary Bose condensates

Universal dynamics of spontaneous symmetry breaking is central to understanding the universal behavior of spontaneous defect formation in various system from the early universe, condensed-matter systems to ultracold atomic systems. We explore the universal real-time dynamics in an array of coupled binary atomic Bose-Einstein condensates in optical lattices, which undergo a spontaneous symmetry breaking from the symmetric Rabi oscillation to the broken-symmetry self-trapping. In addition to Goldstone modes, there exist gapped Higgs mode whose excitation gap vanishes at the critical point. In the slow passage through the critical point, we analytically find that the symmetry-breaking dynamics obeys the Kibble-Zurek mechanism. From the scalings of bifurcation delay and domain formation, we numerically extract two Kibble-Zurek exponents $b_{1}=\nu/(1+\nu z)$ and $b_{2}=1/(1+\nu z)$, which give the static correlation-length critical exponent $\nu$ and the dynamic critical exponent $z$. Our approach provides an efficient way to simultaneous determination of the critical exponents $\nu$ and $z$ for a continuous phase transition.Comment: 6 pages, 4 figures, accepted for publication in EPL (Europhysics Letters