dorsal/arxiv
View SchemaStates for phase estimation in quantum interferometry
| Authors | Joshua Combes, H. M. Wiseman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412037 |
| URL | https://arxiv.org/abs/quant-ph/0412037 |
| DOI | 10.1088/1464-4266/7/1/004 |
| Journal | J. Opt. B: Quantum Semiclass. Opt. 7 (2005) 14-21 |
Abstract
Ramsey interferometry allows the estimation of the phase $\phi$ of rotation of the pseudospin vector of an ensemble of two-state quantum systems. For $\phi$ small, the noise-to-signal ratio scales as the spin-squeezing parameter $\xi$, with $\xi<1$ possible for an entangled ensemble. However states with minimum $\xi$ are not optimal for single-shot measurements of an arbitrary phase. We define a phase-squeezing parameter, $\zeta$, which is an appropriate figure-of-merit for this case. We show that (unlike the states that minimize $\xi$), the states that minimize $\zeta$ can be created by evolving an unentangled state (coherent spin state) by the well-known 2-axis counter-twisting Hamiltonian. We analyse these and other states (for example the maximally entangled state, analogous to the optical "NOON" state $|\psi> = (|N,0>+|0,N>)/\sqrt{2}$) using several different properties, including $\xi$, $\zeta$, the coefficients in the pseudo angular momentum basis (in the three primary directions) and the angular Wigner function $W(\theta,\phi)$. Finally we discuss the experimental options for creating phase squeezed states and doing single-shot phase estimation.
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"abstract": "Ramsey interferometry allows the estimation of the phase $\\phi$ of rotation\nof the pseudospin vector of an ensemble of two-state quantum systems. For\n$\\phi$ small, the noise-to-signal ratio scales as the spin-squeezing parameter\n$\\xi$, with $\\xi\u003c1$ possible for an entangled ensemble. However states with\nminimum $\\xi$ are not optimal for single-shot measurements of an arbitrary\nphase. We define a phase-squeezing parameter, $\\zeta$, which is an appropriate\nfigure-of-merit for this case. We show that (unlike the states that minimize\n$\\xi$), the states that minimize $\\zeta$ can be created by evolving an\nunentangled state (coherent spin state) by the well-known 2-axis\ncounter-twisting Hamiltonian. We analyse these and other states (for example\nthe maximally entangled state, analogous to the optical \"NOON\" state $|\\psi\u003e =\n(|N,0\u003e+|0,N\u003e)/\\sqrt{2}$) using several different properties, including $\\xi$,\n$\\zeta$, the coefficients in the pseudo angular momentum basis (in the three\nprimary directions) and the angular Wigner function $W(\\theta,\\phi)$. Finally\nwe discuss the experimental options for creating phase squeezed states and\ndoing single-shot phase estimation.",
"arxiv_id": "quant-ph/0412037",
"authors": [
"Joshua Combes",
"H. M. Wiseman"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1464-4266/7/1/004",
"journal_ref": "J. Opt. B: Quantum Semiclass. Opt. 7 (2005) 14-21",
"title": "States for phase estimation in quantum interferometry",
"url": "https://arxiv.org/abs/quant-ph/0412037"
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