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arXiv:quant-ph/0605002 · Physical Review A

Towards the Heisenberg limit in magnetometry with parametric down-converted photons

Aziz Kolkıran, G. S. Agarwal

Published Nov 16, 2006• 4 citations
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Abstract

Recent theoretical and experimental papers have shown how one can achieve Heisenberg-limited measurements by using entangled photons. Here we show how the photons in a noncollinear down-conversion process can be used for improving the sensitivity of magneto-optical rotation by a factor of 4 which takes us towards the Heisenberg limit. Our results apply to sources with arbitrary pumping. We also present several generalizations of earlier results for the collinear geometry. The sensitivity depends on whether the two-photon or four-photon coincidence detection is used.

DOI
10.1103/physreva.74.053810

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Recent theoretical and experimental papers have shown how one can achieve Heisenberg-limited measurements by using entangled photons. Here we show how the photons in a noncollinear down-conversion process can be used for improving the sensitivity of magneto-optical rotation by a factor of 4 which takes us towards the Heisenberg limit. Our results apply to sources with arbitrary pumping. We also present several generalizations of earlier results for the collinear geometry. The sensitivity depends on whether the two-photon or four-photon coincidence detection is used.
This dissertation contains new theoretical work on how to utilize the entangled photons produced in a parametric down conversion to improve resolution and sensitivity in quantum interferometry, magnetometry and lithography. Chapter 1 introduces some basics of quantum imaging and sensing systems and gives an outline of the thesis. Chapter 2 deals with the use of entangled photons in Sagnac interferometry. We introduce the Sagnac ring interferometer and analyze the Sagnac phase shift with classical and quantum inputs of light. We compare the results obtained from entangled photon pairs input with classical and single-photon inputs. We show how the photon-photon correlation measurements increase the resolution and the sensitivity in the phase shift. In chapter three, we present an analysis of how parametric down-converted photons could be utilized in getting better spectroscopic information about a medium which has magnetic field induced anisotropy. We demonstrate how the improvement in magneto-optical rotation (MOR) of light could be realized by employing two different schemes with collinear and noncollinear down-conversion geometries compared to the use of coherent light. We calculate the resolution that can be achieved in the MOR's both by the use of coherent light and down-converted light. We discuss the possibility that the Heisenberg limit could be reached in magnetometry by the use of down-converted light. In chapter 4, we propose a new idea of using coherent beam stimulated parametric processes along with spontaneous ones to produce resolution improvement in two-photon interferometry. The stimulated processes enhance the count rate by several orders of magnitude while at the same time maintaining high visibility at large gains of the parametric process. We further find that the phases of coherent fields can also be used as tuning knobs to control the visibility of the pattern. We use coherent beams at the signal and idler frequencies as the seed light for the down-conversion process. In chapter 5, we analyze the minimum phase uncertainty of the phase measurement in a Mach-Zehnder interferometer using stimulated parametric down-conversion. We calculate the phase sensitivities for different measurement schemes. We conclude the thesis in chapter 6 and give an outlook for future work.
The feasibility of a Heisenberg-limited phase measurement using a Mach-Zehnder interferometer fed with twin photon correlated light is investigated theoretically. To take advantage of the Heisenberg limit, 1/N1/N1/N, for the phase sensitivity, one wants the number of correlated photons, NNN, to be high. This favors the use of parametric oscillation rather than the weaker but better correlated source given by parametric down-conversion. In real systems, decorrelation arising from photon absorption, mode mismatch, and nonideal detectors must be considered. In this paper we address the problem of detection when correlated photons are used as the input. We study the influence of photon statistics and of imperfect quantum correlation of the input light, and show that it is still possible to break the classical 1/N1/\sqrt{N}1/N​ phase sensitivity limit in nonideal experimental conditions. All the results are valid in the general case of quantum correlated bosons.