Phase estimation with squeezed single photons

Stefano Olivares 1 , Maria Popovic 2 ,  and Matteo G. A. Paris 3
  • 1 Quantum Technology Lab, Dipartimento di Fisica, Università degli Studi di Milano
  • 2 Dipartimento di Fisica dell’Università degli Studi di Milano, I-20133 Milano, Italy
  • 3 Quantum Technology Lab, Dipartimento di Fisica, Università degli Studi di Milano, Italy

Abstract

We address the performance of an interferometric setup in which a squeezed single photon interferes at a beam splitter with a coherent state. Our analysis in based on both the quantum Fisher information and the sensitivity when a Mach-Zehnder setup is considered and the difference photocurrent is detected at the output. We compare our results with those obtained feeding the interferometer with a squeezed vacuum (with the same squeezing parameter of the squeezed single photon) and a coherent state in order to have the same total number of photons circulating in the interferometer. We find that for fixed squeezing parameter and total number of photons there is a threshold of the coherent amplitude interfering with the squeezed single photon above which the squeezed single photons outperform the performance of squeezed vacuum (showing the highest quantum Fisher information). When the difference photocurrent measurement is considered, we can always find a threshold of the squeezing parameter (given the total number of photons and the coherent amplitude) above which squeezed single photons can be exploited to reach a better sensitivity with respect to the use of squeezed vacuum states also in the presence of non unit quantum efficiency.

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  • [1] M. Kacprowicz, R. Demkowicz-Dobrzanski, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift”, Nature Phot. 4, 357 (2010).

  • [2] J. Abadie, et al. (the LIGO Scientific Collaboration), A gravitational wave observatory operating beyond the quantum shot-noise limit, Nat. Phys. 7, 962 (2011).

  • [3] R. Demkowicz-Dobrzanski, K. Banaszek, and R. Schnabel, “Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational wave detector GEO 600”, Phys. Rev. A 88, 041802(R) (2013).

  • [4] I. Ruo Berchera, I. P. Degiovanni, S. Olivares, and M. Genovese, “Quantum light in coupled interferometers for quantum gravity tests”, Phys. Rev. Lett. 110, 213601 (2013).

  • [5] I. Ruo-Berchera, I. P. Degiovanni, S. Olivares, N. Samantaray, P. Traina, and M. Genovese, “One- and two-mode squeezed light in correlated interferometry”, Phys. Rev. A 92, 053821 (2015).

  • [6] M. G. A. Paris, “Small amount of squeezing in high-sensitive realistic interferometry”, Phys. Lett A 201, 132 (1995)

  • [7] L. Pezzé, and A. Smerzi, “Mach-Zehnder Interferometry at the Heisenberg Limit with Coherent and Squeezed-Vacuum Light”, Phys. Rev. Lett. 100, 073601 (2008).

  • [8] S. Olivares, and M. G. A. Paris, “Optimized Interferometry with Gaussian States”, Optics Spectr. 103, 231 (2007).

  • [9] M. D. Lang, and C. M. Caves, “Optimal Quantum-Enhanced Interferometry Using a Laser Power Source”, Phys. Rev. Lett. 111, 173601 (2013).

  • [10] M. D. Lang, and C. M. Caves, “Optimal quantum-enhanced interferometry”, Phys. Rev. A 90, 025802 (2014).

  • [11] C. Sparaciari, S. Olivares, and M. G. A. Paris, “Bounds to precision for quantum interferometry with Gaussian states and operations”, J. Opt. Soc. Am. B 32, 1354 (2015).

  • [12] R. Demkowicz-Dobrzański, M. Jarzyna, and J. Kołodynski, “Quantum Limits in Optical Interferometry”, Progress in Optics 60, 345 (2015).

  • [13] C. Sparaciari, S. Olivares, and M. G. A. Paris, “Gaussian-state interferometry with passive and active elements”, Phys. Rev. A 93, 023810 (2016).

  • [14] P. Sekatski, N. Sangouard, M. Stobinska, F. Bussières, M. Afzelius, and N. Gisin, “Proposal for exploring macroscopic entanglement with a single photon and coherent states”, Phys. Rev. A 86, 060301(R) (2012).

  • [15] C. Vitelli, N. Spagnolo, L. Toffoli, F. Sciarrino, and F. De Martini, “Enhanced resolution of lossy interferometry by coherent amplification of single photons”, Phys. Rev. Lett. 105, 113602 (2010)

  • [16] J. Wenger, R. Tualle-Bouri, and P. Grangier, “Non-Gaussian Statistics from Individual Pulses of Squeezed Light”, Phys. Rev. Lett. 92 153601 (2004).

  • [17] S. Olivares, and M. G. A. Paris, “Squeezed Fock state by inconclusive photon subtraction”, J. Opt. B: Quantum Semiclass. Opt. 7, S616 (2005).

  • [18] M. G. A. Paris, “Quantum estimation for quantum technology”, Int. J. Quant. Inf. 7, 125 (2009).

  • [19] C.W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976).

  • [20] D. C. Brody, and L. P. Hughston, “Statistical geometry in quantum mechanics”, Proc. Roy. Soc. Lond. A 454, 2445 (1998); “Geometrization of statistical mechanics”, Proc. Roy. Soc. Lond. A 455, 1683 (1999).

  • [21] S. L. Braunstein, and C. M. Caves, “Statistical distance and the geometry of quantum states”, Phys. Rev. Lett. 72, 3439 (1994).

  • [22] S. L. Braunstein, C. M. Caves, and G. J. Milburn, “Generalized uncertainty relations: Theory, examples, and Lorentz invariance”, Ann. Phys. 247, 135 (1996).

  • [23] A. Ferraro, S. Olivares, and M. G. A. Paris, Gaussian States in Quantum Information (Bibliopolis, Napoli, 2005).

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Quantum Measurements and Quantum Metrology (QMTR) is an international, peer-reviewed journal publishing original research in the field of quantum-enhanced measurements and technologies. QMTR welcomes theoretical and experimental papers on all aspects of quantum measurements ranging from purely abstract matter to commercial applications.

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