States for phase estimation in quantum interferometry
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Ramsey interferometry allows the estimation of the phase f of rotation of the pseudospin vector of an ensemble of two-state quantum systems. For f small, the noise-to-signal ratio scales as the spin-squeezing parameter ?, with ? < 1 possible for an entangled ensemble. However states with minimum ? are not optimal for single-shot measurements of an arbitrary phase. We define a phase-squeezing parameter, ?, which is an appropriate figure of merit for this case. We show that (unlike the states that minimize ?) the states that minimize can be created by evolving an unentangled state (coherent spin state) by the well known two-axis counter-twisting Hamiltonian. We analyse these and other states (for example the maximally entangled state, analogous to the optical 'NOON' state |?) = (|N, 0) + |0, N))/v2) using several different properties, including ?, <, the coefficients in the pseudo-angular momentum basis (in the three primary directions) and the angular Wigner function W(?,F). Finally, we discuss the experimental options for creating phase-squeezed states and doing single-shot phase estimation.
Journal of Optics B: Quantum and semiclassical optics
© 2005 Institute of Physics Publishing. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher.Please refer to the journal's website for access to the definitive, published version.