Source: https://www.osapublishing.org/oe/abstract.cfm?uri=oe-27-3-2589
Timestamp: 2019-04-18 18:41:32+00:00

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We study polarization effects in the nonlinear interference of photons generated via frequency nondegenerate spontaneous parametric-down conversion. Signal and idler photons, which are generated in the visible and infrared (IR) range, respectively, are split into different arms of a nonlinear Michelson interferometer, and the interference pattern for signal photons is detected. Due to the effect of induced coherence, the interference pattern for the signal photons depends on the polarization rotation of idler photons, which are introduced by a birefringent sample. Based on this concept, we realize two new methods of measuring sample retardation in the IR range by using well-developed and inexpensive components for visible light. The methods’ accuracy reaches specifications that are reported for industrial-grade optical elements. The developed IR polarimetry technique is relevant to material research, optical inspection, and quality control.
D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
S. Gasparoni, J.-W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93(2), 020504 (2004).
V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306(5700), 1330–1336 (2004).
C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
D. A. Kalashnikov, E. V. Melik-Gaykazyan, A. A. Kalachev, Y. F. Yu, A. I. Kuznetsov, and L. A. Krivitsky, “Quantum interference in the presence of a resonant medium,” Sci. Rep. 7(1), 11444 (2017).
D. Branning, A. L. Migdall, and A. V. Sergienko, “Simultaneous measurement of group and phase delay between two photons,” Phys. Rev. A 62(6), 063808 (2000).
T. Ono, R. Okamoto, and S. Takeuchi, “An entanglement-enhanced microscope,” Nat. Commun. 4(1), 2426 (2013).
X. Y. Zou, L. J. Wang, and L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. 67(3), 318–321 (1991).
L. J. Wang, X. Y. Zou, and L. Mandel, “Induced coherence without induced emission,” Phys. Rev. A 44(7), 4614–4622 (1991).
H. M. Wiseman and K. Molmer, “Induced coherence with and without induced emission,” Phys. Lett. A 270(5), 245–248 (2000).
M. V. Chekhova and Z. Y. Ou, “Nonlinear interferometers in quantum optics,” Adv. Opt. Photonics 8(1), 104–155 (2016).
G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature 512(7515), 409–412 (2014).
A. V. Burlakov, S. P. Kulik, A. N. Penin, and M. V. Chekhova, “Three-photon interference: spectroscopy of linear and nonlinear media,” Sov. Phys. JETP 86(6), 1090–1097 (1998).
S. P. Kulik, G. A. Maslennikov, S. P. Merkulova, A. N. Penin, L. K. Radchenko, and V. N. Krasheninnikov, “Two-photon interference in the presence of absorption,” Sov. Phys. JETP 98(1), 31–38 (2004).
D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, “Infrared spectroscopy with visible light,” Nat. Photonics 10(2), 98–101 (2016).
A. Paterova, S. Lung, D. A. Kalashnikov, and L. A. Krivitsky, “Nonlinear infrared spectroscopy free from spectral selection,” Sci. Rep. 7(1), 42608 (2017).
A. Paterova, H. Yang, Ch. An, D. Kalashnikov, and L. Krivitsky, “Measurement of infrared optical constants with visible photons,” New J. Phys. 20(4), 043015 (2018).
A. V. Paterova, H. Yang, Ch. An, D. A. Kalashnikov, and L. A. Krivitsky, “Tunable optical coherence tomography in the infrared range using visible photon,” Quantum Science and Technology 3(2), 025008 (2018).
T. P. Grayson and G. A. Barbosa, “Spatial properties of spontaneous parametric down-conversion and their effect on induced coherence without induced emission,” Phys. Rev. A 49(4), 2948–2961 (1994).
M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Twin-photon correlations in single-photon interference,” Phys. Rev. A (Coll. Park) 96(1), 013822 (2017).
X. Y. Zou, T. Grayson, G. A. Barbosa, and L. Mandel, “Control of visibility in the interference of signal photons by delays imposed on the idler photons,” Phys. Rev. A 47(3), 2293–2295 (1993).
M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Theory of quantum imaging with undetected photons,” Phys. Rev. A 92(1), 013832 (2015).
L. C. Ryff, “Interference, distinguishability, and apparent contradiction in an experiment on induced coherence,” Phys. Rev. A 52(4), 2591–2596 (1995).
T. P. Grayson, J. R. Torgerson, and G. A. Barbosa, “Observation of a nonlocal Pancharatnam phase shift in the process of induced coherence without induced emission,” Phys. Rev. A 49(1), 626–628 (1994).
M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, “Partial polarization by quantum distinguishability,” Phys. Rev. A (Coll. Park) 95(3), 033816 (2017).
S. P. Walborn, C. H. Monken, S. Padua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495(4–5), 87–139 (2010).
S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-mandel interference,” Phys. Rev. Lett. 90(14), 143601 (2003).
J.-Ch. Lee and Y.-H. Kim, “Spatial and spectral properties of entangled photons from spontaneous parametric down conversion with a focused pump,” Opt. Commun. 366, 442–450 (2016).
T. J. Herzog, J. G. Rarity, H. Weinfurter, and A. Zeilinger, “Frustrated two-photon creation via interference,” Phys. Rev. Lett. 72(5), 629–632 (1994).
A. Heuer, S. Raabe, and R. Menzel, “Phase memory across two single photon interferometers including wavelength conversion,” Phys. Rev. A 90(4), 045803 (2014).
S.-Y. Baek and Y.-H. Kim, “Spectral properties of entangled photons generated via type-I frequency-nondegenerate spontaneous parametric down-conversion,” Phys. Rev. A 80(3), 033814 (2009).
D. H. Goldstein, Polarized Light (CRC, 2011).
P. A. Williams, A. H. Rose, and C. M. Wang, “Rotating-polarizer polarimeter for accurate retardance measurement,” Appl. Opt. 36(25), 6466–6472 (1997).
J. F. de Boer, C. K. Hitzenberger, and Y. Yasuno, “Polarization sensitive optical coherence tomography - a review [Invited],” Biomed. Opt. Express 8(3), 1838–1873 (2017).
M. C. Booth, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Polarization-sensitive quantum-optical coherence tomography,” Phys. Rev. A 69(4), 043815 (2004).
Fig. 1 (a) The nonlinear Michelson interferometer. The pump beam (green) generates SPDC photons (yellow and red), which are separated into different arms by the dichroic mirror DM1. The dichroic mirror DM2 separates signal and pump photons. Mirrors Ms, Mp and Mi reflect all the photons into the crystal, where the pump generates another pair of photons. Then, the interference of signal photons is detected. (b) The beam splitter model which accounts for the double pass through the sample and reflection from the mirror Mi; τi is the amplitude transmission of the beam splitter. A mode ai1 transforms into a mode ai2 by injecting vacuum modes a0 and a0” from open ports of the beam splitter. The mirror Mi inverts the Cartesian coordinate system from the right-handed to the left-handed (x-y).
Fig. 2 The experimental setup. The cw-laser pumps the PPLN crystal, where SPDC occurs. The PPLN is set to generate signal and idler photons in the visible and IR range, respectively. The photons are split by the dichroic mirror DM2 into different arms. Pump and signal photons are separated by the dichroic mirror DM3. All the photons are reflected by the mirrors Ms, Mp, and Mi. Filters DM1, NF, and BP filter the detected signal photons. The interference is detected either by the avalanche photodiode (APD) or by the CCD camera. Mirror Ms is mounted on the translation stage for adjustment of the optical path Δzs. The sample is inserted into the path of idler/ signal photons. Mirrors Mi and Mp are placed on piezo-translators for fine scans of interference fringes.
Fig. 3 The count rate of signal photons at λs = 809.2 nm versus translation of the mirror Mi in the idler channel for (a) QWP at 1550 nm and (b) HWP at 1550 nm. The orientation of the optical axis at 0° (black squares), 45° (red dots) and 90° (blue triangles). Points are experimental data, and solid lines are fits by Eq. (8) (R2>0.99). The relative phase shift between interference patterns at θ = 0° and 90° is equal to retardation δ. (c) The dependence of the visibility on the sample orientation θ for QWP (blue triangles) and HWP (red circles) at 1550 nm. Points are experimental data, and solid lines are fits by Eq. (10) (R2>0.99). The inset shows zoomed results for QWP at 1550 nm at visibility values close to zero.
Fig. 4 The count rate of signal photons at λs = 809.2 nm versus translation of the mirror Mi in the idler channel for (a) QWP and (b) HWP at 532 nm inserted in the path of idler photons. The orientation of the optical axis of the sample is at 0° (black squares), 45° (red dots) and 90° (blue triangles). Points are experimental data, and solid lines are fits by Eq. (8) (R2>0.99). The relative phase shift between interference patterns at θ = 0° and 90° is equal to δ. (c) The dependence of the visibility on the orientation of the sample θ for QWP (blue triangles) and HWP (red circles) designed for 532 nm. The solid curves show fits by Eq. (10) (R2 = 0.98).
Fig. 5 The count rate measured by translating pump mirror Mp for (a) QWP at 1550 nm, (b) HWP at 1550 nm, (c) QWP at 532 nm, (d) HWP at 532 nm inserted in the idler arm with orientations of the optical axis at 0° (black), 45° (red) and 90° (blue). Points are experimental data, and solid lines are fits by Eq. (8) (R2>0.99).
Fig. 6 (a) The count rate measured by translating the mirror Mi in the idler channel when the QWP at 800 nm is inserted in the signal channel. Orientations of the optical axis are at 0° (black squares), 45° (red dots) and 90° (blue triangles). (b) The dependence of the visibility of the interference on the orientation of the sample. Points are experimental data, and solid lines are fits with Eq. (8) in (a) and Eq. (11) in (b) (both R2 > 0.99). The inset shows zoomed visibility values near zero for QWP at 800 nm (yellow rhombuses and line), and for QWP at 1550 nm (blue line) for reference.
Fig. 7 The shift of the interference pattern after the introduction of the sample in the path of idler photons. Data for HWP at 1550 nm, QWP at 1550 nm, HWP at 532 nm and QWP at 532 nm with the orientation of the optical axis at θ = 0°.
Fig. 8 The shift of the interference pattern due to the change of the optical path for the signal and idler photons after insertion of the HWP at 800 nm with the orientation of the optical axis at θ = 0°.
Fig. 9 Measurement of the phase drift in the interferometer.
Fig. 10 The experimental procedure of the “phase shift” measurements with the QWP designed for 532 nm wavelength. Region “1” corresponds to the reference point, where each scan starts from the θ = 0° orientation of the waveplate; “2” corresponds to the region, where the orientation of the waveplate is changed; “3” is the region where the retardation of the waveplate is measured.
Table 1 Results of retardation measurements at 1553 nm by the two methods (idler mirror scan).
Table 2 Results of retardation measurements at 1553 nm by the two methods (pump mirror scan).
Table 3 Results of retardation measurements at 800 nm by the two methods (idler mirror scan).
Table 4 Transmission coefficient |τm|2 for different samples.
(18) δ=arccos( V min V min ).
Results of retardation measurements at 1553 nm by the two methods (idler mirror scan).
Results of retardation measurements at 1553 nm by the two methods (pump mirror scan).
Results of retardation measurements at 800 nm by the two methods (idler mirror scan).
Transmission coefficient |τm|2 for different samples.

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