### Abstract

When measuring a time-varying phase, the standard quantum limit and Heisenberg limit as usually defined, for a constant phase, do not apply. If the phase has Gaussian statistics and a power-law spectrum 1/|ω|^{p} with *p*>1, then the generalized standard quantum limit and Heisenberg limit have recently been found to have scalings of 1/*N*^{(p-1)/p} and 1/*N*^{2(p-1)/(p+1)}, respectively, where *N* is the mean photon flux. We show that this Heisenberg scaling can be achieved via adaptive measurements on squeezed states. We predict the experimental parameters analytically, and test them with numerical simulations. Previous work had considered the special case of *p*=2.

Language | English |
---|---|

Article number | 063821 |

Pages | 1-10 |

Number of pages | 10 |

Journal | Physical Review A |

Volume | 95 |

Issue number | 6 |

DOIs | |

Publication status | Published - 15 Jun 2017 |

### Fingerprint

### Cite this

*Physical Review A*,

*95*(6), 1-10. [063821]. https://doi.org/10.1103/PhysRevA.95.063821

}

*Physical Review A*, vol. 95, no. 6, 063821, pp. 1-10. https://doi.org/10.1103/PhysRevA.95.063821

**Adaptive estimation of a time-varying phase with a power-law spectrum via continuous squeezed states.** / Dinani, Hossein T.; Berry, Dominic W.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Adaptive estimation of a time-varying phase with a power-law spectrum via continuous squeezed states

AU - Dinani, Hossein T.

AU - Berry, Dominic W.

PY - 2017/6/15

Y1 - 2017/6/15

N2 - When measuring a time-varying phase, the standard quantum limit and Heisenberg limit as usually defined, for a constant phase, do not apply. If the phase has Gaussian statistics and a power-law spectrum 1/|ω|p with p>1, then the generalized standard quantum limit and Heisenberg limit have recently been found to have scalings of 1/N(p-1)/p and 1/N2(p-1)/(p+1), respectively, where N is the mean photon flux. We show that this Heisenberg scaling can be achieved via adaptive measurements on squeezed states. We predict the experimental parameters analytically, and test them with numerical simulations. Previous work had considered the special case of p=2.

AB - When measuring a time-varying phase, the standard quantum limit and Heisenberg limit as usually defined, for a constant phase, do not apply. If the phase has Gaussian statistics and a power-law spectrum 1/|ω|p with p>1, then the generalized standard quantum limit and Heisenberg limit have recently been found to have scalings of 1/N(p-1)/p and 1/N2(p-1)/(p+1), respectively, where N is the mean photon flux. We show that this Heisenberg scaling can be achieved via adaptive measurements on squeezed states. We predict the experimental parameters analytically, and test them with numerical simulations. Previous work had considered the special case of p=2.

UR - http://www.scopus.com/inward/record.url?scp=85026809726&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.95.063821

DO - 10.1103/PhysRevA.95.063821

M3 - Article

VL - 95

SP - 1

EP - 10

JO - Physical Review A: covering atomic, molecular, and optical physics and quantum information

T2 - Physical Review A: covering atomic, molecular, and optical physics and quantum information

JF - Physical Review A: covering atomic, molecular, and optical physics and quantum information

SN - 2469-9926

IS - 6

M1 - 063821

ER -