All Abstracts | Poster Abstracts | Talk Abstracts | Tutorial Abstracts

Quantum limited metrology with (β0〉 + 0β〉)/√2 states

Vaibhav Madhok, University Of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. We show how to achieve Heisenberg-limited sensitivity using states of the form (β0〉 + 0β〉)/√2 where | β〉 is a coherent state, in a two-arm interferometer. We describe appropriate measurements to achieve the above limit and discuss a scheme for making such states and measurements. We compare these states with "NOON" states and with other methods for achieving the Heisenberg-limited sensitivity.

Entanglement, bifurcations and the generation of random states in the quantum chaotic dynamics of kicked coupled tops

Vaibhav Madhok, University Of New Mexico

(Session 5 : Friday from 5:00-7:00)

Abstract. We study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time averaged entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section – it is nearly uniform in the chaotic sea, and reproduces detailed structure of the regular islands. The uniform value in the chaotic sea in explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions quantized version take localized coherent states to pseudo-random states in Hilbert space. Such random states are highly entangled, with an average value near that of maximally entangled state. For a map with global chaos, we derive that value based on new analytic results for the entropy of random states. For a mixed phase space, we use the Percival conjecture to identify a “chaotic subspace” of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long time averaged entanglement for initial states in the chaotic sea. We also study the entanglement and the Husimi entropy of eigenstates of the system as a function of the coupling parameter. In addition, we examine behavior in the entanglement of eigenstates when the classical region supporting them undergoes a bifurcation. We study the Husimi entropy of the eigenstates as they make a transition from the “regular subspace” to the “chaotic subspace” in Hilbert space as the system becomes more chaotic.