Real-world quantum sensors: evaluating resources for precision measurement.

Quantum phenomena present in many experiments signify nonclassical behavior, but do not always imply superior performance. Quantifying the enhancement achieved from quantum behavior needs careful analysis of the resources involved. We analyze the case of parameter estimation using an optical interferometer, where increased precision can in principle be achieved using quantum probe states. Common performance measures are examined and some are shown to overestimate the improvement. For the simplest experimental case we compare the different measures and exhibit this overestimation explicitly. We give the preferred analysis of these experiments and calculate benchmark values for experimental parameters necessary to realize a precision enhancement. Our analysis shows that unambiguous real-world enhancements in optical quantum metrology with fixed photon number are yet to be attained.

Phase transition in space: how far does a symmetry bend before it breaks?

We extend the theory of symmetry-breaking dynamics in non-equilibrium second-order phase transitions known as the Kibble-Zurek mechanism (KZM) to transitions where the change of phase occurs not in time but in space. This can be due to a time-independent spatial variation of a field that imposes a phase with one symmetry to the left of where it attains critical value, while allowing spontaneous symmetry breaking to the right of that critical borderline. Topological defects need not form in such a situation. We show, however, that the size, in space, of the 'scar' over which the order parameter adjusts as it 'bends' interpolating between the phases with different symmetries follows from a KZM-like approach. As we illustrate on the example of a transverse quantum Ising model, in quantum phase transitions this spatial scale--the size of the scar--is directly reflected in the energy spectrum of the system: in particular, it determines the size of the energy gap.

Dynamics of a quantum phase transition.

We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatment of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses Landau-Zener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.