Engineering Schrödinger cat states with a photonic even-parity detector

G. S. Thekkadath; B. A. Bell; I. A. Walmsley; A. I. Lvovsky

doi:10.22331/q-2020-03-02-239

Engineering Schrödinger cat states with a photonic even-parity detector

G. S. Thekkadath¹, B. A. Bell¹, I. A. Walmsley¹, and A. I. Lvovsky^1,2

¹Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
²Russian Quantum Center, 100 Novaya St., Skolkovo, Moscow 143025, Russia

Published:	2020-03-02, volume 4, page 239
Eprint:	arXiv:1908.10314v3
Doi:	https://doi.org/10.22331/q-2020-03-02-239
Citation:	Quantum 4, 239 (2020).

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Abstract

When two equal photon-number states are combined on a balanced beam splitter, both output ports of the beam splitter contain only even numbers of photons. Consider the time-reversal of this interference phenomenon: the probability that a pair of photon-number-resolving detectors at the output ports of a beam splitter both detect the same number of photons depends on the overlap between the input state of the beam splitter and a state containing only even photon numbers. Here, we propose using this even-parity detection to engineer quantum states containing only even photon-number terms. As an example, we demonstrate the ability to prepare superpositions of two coherent states with opposite amplitudes, i.e. two-component Schrödinger cat states. Our scheme can prepare cat states of arbitrary size with nearly perfect fidelity. Moreover, we investigate engineering more complex even-parity states such as four-component cat states by iteratively applying our even-parity detector.

► BibTeX data

@article{Thekkadath2020engineering,
  doi = {10.22331/q-2020-03-02-239},
  url = {https://doi.org/10.22331/q-2020-03-02-239},
  title = {Engineering {S}chr{\"{o}}dinger cat states with a photonic even-parity detector},
  author = {Thekkadath, G. S. and Bell, B. A. and Walmsley, I. A. and Lvovsky, A. I.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {239},
  month = mar,
  year = {2020}
}

► References

[1] A. I. Lvovsky, Photonics: Scientific Foundations, Technology and Applications 1, 121 (2015).
https://doi.org/10.1002/9781119009719.ch5

[2] C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).
https://doi.org/10.1103/RevModPhys.84.621

[3] S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
https://doi.org/10.1103/RevModPhys.77.513

[4] C. M. Caves, Phys. Rev. D 23, 1693 (1981).
https://doi.org/10.1103/PhysRevD.23.1693

[5] E. Schrödinger, Naturwissenschaften 23, 823 (1935).
https://doi.org/10.1007/BF01491891

[6] M. J. Holland and K. Burnett, Phys. Rev. Lett. 71, 1355 (1993).
https://doi.org/10.1103/PhysRevLett.71.1355

[7] D. Gottesman, A. Kitaev, and J. Preskill, Phys. Rev. A 64, 012310 (2001).
https://doi.org/10.1103/PhysRevA.64.012310

[8] B. Yurke and D. Stoler, Phys. Rev. Lett. 57, 13 (1986).
https://doi.org/10.1103/PhysRevLett.57.13

[9] C. K. Law and J. H. Eberly, Phys. Rev. Lett. 76, 1055 (1996).
https://doi.org/10.1103/PhysRevLett.76.1055

[10] C. C. Gerry, A. Benmoussa, and R. A. Campos, Phys. Rev. A 72, 053818 (2005).
https://doi.org/10.1103/PhysRevA.72.053818

[11] B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
https://doi.org/10.1038/s41566-018-0339-5

[12] A. I. Lvovsky and J. Mlynek, Phys. Rev. Lett. 88, 250401 (2002).
https://doi.org/10.1103/PhysRevLett.88.250401

[13] A. Zavatta, S. Viciani, and M. Bellini, Science 306, 660 (2004).
https://doi.org/10.1126/science.1103190

[14] J. Fiurášek, R. García-Patrón, and N. J. Cerf, Phys. Rev. A 72, 033822 (2005).
https://doi.org/10.1103/PhysRevA.72.033822

[15] E. Bimbard, N. Jain, A. MacRae, and A. Lvovsky, Nat. Photonics 4, 243 (2010).
https://doi.org/10.1038/nphoton.2010.6

[16] J. Sperling, W. Vogel, and G. S. Agarwal, Phys. Rev. A 89, 043829 (2014).
https://doi.org/10.1103/PhysRevA.89.043829

[17] S. Glancy and H. M. de Vasconcelos, J. Opt. Soc. Am. B 25, 712 (2008).
https://doi.org/10.1364/JOSAB.25.000712

[18] M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D.-G. Welsch, Phys. Rev. A 55, 3184 (1997).
https://doi.org/10.1103/PhysRevA.55.3184

[19] J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, Phys. Rev. Lett. 97, 083604 (2006).
https://doi.org/10.1103/PhysRevLett.97.083604

[20] A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, Science 312, 83 (2006).
https://doi.org/10.1126/science.1122858

[21] A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, Nature 448, 784 (2007).
https://doi.org/10.1038/nature06054

[22] K. Wakui, H. Takahashi, A. Furusawa, and M. Sasaki, Opt. Express 15, 3568 (2007).
https://doi.org/10.1364/OE.15.003568

[23] P. Marek, H. Jeong, and M. S. Kim, Phys. Rev. A 78, 063811 (2008).
https://doi.org/10.1103/PhysRevA.78.063811

[24] H. Takahashi, K. Wakui, S. Suzuki, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, Phys. Rev. Lett. 101, 233605 (2008).
https://doi.org/10.1103/PhysRevLett.101.233605

[25] K. Huang, H. Le Jeannic, J. Ruaudel, V. B. Verma, M. D. Shaw, F. Marsili, S. W. Nam, E. Wu, H. Zeng, Y.-C. Jeong, R. Filip, O. Morin, and J. Laurat, Phys. Rev. Lett. 115, 023602 (2015).
https://doi.org/10.1103/PhysRevLett.115.023602

[26] D. V. Sychev, A. E. Ulanov, A. A. Pushkina, M. W. Richards, I. A. Fedorov, and A. I. Lvovsky, Nat. Photonics 11, 379 (2017).
https://doi.org/10.1038/nphoton.2017.57

[27] J. Etesse, M. Bouillard, B. Kanseri, and R. Tualle-Brouri, Phys. Rev. Lett. 114, 193602 (2015).
https://doi.org/10.1103/PhysRevLett.114.193602

[28] A. E. Lita, A. J. Miller, and S. W. Nam, Opt. Express 16, 3032 (2008).
https://doi.org/10.1364/OE.16.003032

[29] A. Karimi, Int. J. Quantum Inf 16, 1850003 (2018).
https://doi.org/10.1142/S021974991850003X

[30] N. Quesada, L. G. Helt, J. Izaac, J. M. Arrazola, R. Shahrokhshahi, C. R. Myers, and K. K. Sabapathy, Phys. Rev. A 100, 022341 (2019).
https://doi.org/10.1103/PhysRevA.100.022341

[31] D. Su, C. R. Myers, and K. K. Sabapathy, arXiv:1902.02331.
arXiv:arXiv:1902.02331

[32] D. Su, C. R. Myers, and K. K. Sabapathy, Phys. Rev. A 100, 052301 (2019).
https://doi.org/10.1103/PhysRevA.100.052301

[33] T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, Phys. Rev. A 82, 031802 (2010).
https://doi.org/10.1103/PhysRevA.82.031802

[34] K. T. McCusker and P. G. Kwiat, Phys. Rev. Lett. 103, 163602 (2009).
https://doi.org/10.1103/PhysRevLett.103.163602

[35] T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, Phys. Rev. A 86, 043820 (2012).
https://doi.org/10.1103/PhysRevA.86.043820

[36] R. J. Birrittella, M. El Baz, and C. C. Gerry, J. Opt. Soc. Am. B 35, 1514 (2018).
https://doi.org/10.1364/JOSAB.35.001514

[37] M. Eaton, R. Nehra, and O. Pfister, New J. Phys. 21, 113034 (2019).
https://doi.org/10.1088/1367-2630/ab5330

[38] W. Schleich, M. Pernigo, and F. L. Kien, Phys. Rev. A 44, 2172 (1991).
https://doi.org/10.1103/PhysRevA.44.2172

[39] B. C. Sanders, Phys. Rev. A 45, 6811 (1992).
https://doi.org/10.1103/PhysRevA.45.6811

[40] J. Wenger, M. Hafezi, F. Grosshans, R. Tualle-Brouri, and P. Grangier, Phys. Rev. A 67, 012105 (2003).
https://doi.org/10.1103/PhysRevA.67.012105

[41] H. Jeong, W. Son, M. S. Kim, D. Ahn, and C. Brukner, Phys. Rev. A 67, 012106 (2003).
https://doi.org/10.1103/PhysRevA.67.012106

[42] M. Stobińska, H. Jeong, and T. C. Ralph, Phys. Rev. A 75, 052105 (2007).
https://doi.org/10.1103/PhysRevA.75.052105

[43] S. Haroche, Rev. Mod. Phys. 85, 1083 (2013).
https://doi.org/10.1103/RevModPhys.85.1083

[44] D. J. Wineland, Rev. Mod. Phys. 85, 1103 (2013).
https://doi.org/10.1103/RevModPhys.85.1103

[45] B. Vlastakis, A. Petrenko, N. Ofek, L. Sun, Z. Leghtas, K. Sliwa, Y. Liu, M. Hatridge, J. Blumoff, L. Frunzio, et al., Nat. Commun. 6, 8970 (2015).
https://doi.org/10.1038/ncomms9970%20|

[46] C. Wang, Y. Y. Gao, P. Reinhold, R. W. Heeres, N. Ofek, K. Chou, C. Axline, M. Reagor, J. Blumoff, K. Sliwa, et al., Science 352, 1087 (2016).
https://doi.org/10.1126/science.aaf2941

[47] S. J. van Enk and O. Hirota, Phys. Rev. A 64, 022313 (2001).
https://doi.org/10.1103/PhysRevA.64.022313

[48] H. Jeong, M. S. Kim, and J. Lee, Phys. Rev. A 64, 052308 (2001).
https://doi.org/10.1103/PhysRevA.64.052308

[49] T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, Phys. Rev. A 68, 042319 (2003).
https://doi.org/10.1103/PhysRevA.68.042319

[50] A. Gilchrist, K. Nemoto, W. J. Munro, T. C. Ralph, S. Glancy, S. L. Braunstein, and G. J. Milburn, J. Opt. B: Quantum Semiclass. Opt. 6, S828 (2004).
https://doi.org/10.1088/1464-4266/6/8/032

[51] A. P. Lund, T. C. Ralph, and H. L. Haselgrove, Phys. Rev. Lett. 100, 030503 (2008).
https://doi.org/10.1103/PhysRevLett.100.030503

[52] B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Science 342, 607 (2013).
https://doi.org/10.1126/science.1243289

[53] N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. Girvin, L. Jiang, et al., Nature 536, 441 (2016).
https://doi.org/10.1038/nature18949

[54] Z. Leghtas, G. Kirchmair, B. Vlastakis, R. J. Schoelkopf, M. H. Devoret, and M. Mirrahimi, Phys. Rev. Lett. 111, 120501 (2013).
https://doi.org/10.1103/PhysRevLett.111.120501

[55] M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, New J. Phys. 16, 045014 (2014).
https://doi.org/10.1088/1367-2630/16/4/045014

[56] V. V. Albert, K. Noh, K. Duivenvoorden, D. J. Young, R. T. Brierley, P. Reinhold, C. Vuillot, L. Li, C. Shen, S. M. Girvin, B. M. Terhal, and L. Jiang, Phys. Rev. A 97, 032346 (2018).
https://doi.org/10.1103/PhysRevA.97.032346

[57] W. H. Zurek, Nature 412, 712 (2001).
https://doi.org/10.1038/35089017

[58] G. S. Agarwal and P. K. Pathak, Phys. Rev. A 70, 053813 (2004).
https://doi.org/10.1103/PhysRevA.70.053813

[59] D. A. Dalvit, R. de Matos Filho, and F. Toscano, New J. Phys. 8, 276 (2006).
https://doi.org/10.1088/1367-2630/8/11/276

[60] U. Roy, S. Ghosh, P. K. Panigrahi, and D. Vitali, Phys. Rev. A 80, 052115 (2009).
https://doi.org/10.1103/PhysRevA.80.052115

[61] U. Leonhardt, Measuring the Quantum State of Light (Cambridge University Press, 1997).
https://books.google.ca/books?id=wmsJy1A_cyIC

[62] C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
https://doi.org/10.1103/PhysRevLett.59.2044

[63] R. A. Campos, B. E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
https://doi.org/10.1103/PhysRevA.40.1371

[64] J. R. Johansson, P. D. Nation, and F. Nori, Comput. Phys. Commun. 184, 1234 (2013).
https://doi.org/10.1016/j.cpc.2012.11.019

[65] P. C. Humphreys, B. J. Metcalf, T. Gerrits, T. Hiemstra, A. E. Lita, J. Nunn, S. W. Nam, A. Datta, W. S. Kolthammer, and I. A. Walmsley, New J. Phys. 17, 103044 (2015).
https://doi.org/10.1088/1367-2630/17/10/103044

[66] A. Kenfack and K. Życzkowski, J. Opt. B: Quantum Semiclass. Opt. 6, 396 (2004).
https://doi.org/10.1088/1464-4266/6/10/003

[67] L. A. Howard, T. J. Weinhold, F. Shahandeh, J. Combes, M. R. Vanner, A. G. White, and M. Ringbauer, Phys. Rev. Lett. 123, 020402 (2019).
https://doi.org/10.1103/PhysRevLett.123.020402

[68] M. Ringbauer, T. J. Weinhold, L. Howard, A. White, and M. Vanner, New J. Phys. 20, 053042 (2018).
https://doi.org/10.1088/1367-2630/aabb8d

[69] J. Hastrup, J. S. Neergaard-Nielsen, and U. L. Andersen, Opt. Lett. 45, 640 (2020).
https://doi.org/10.1364/OL.383194

[70] Y. Eto, A. Koshio, A. Ohshiro, J. Sakurai, K. Horie, T. Hirano, and M. Sasaki, Opt. Lett. 36, 4653 (2011).
https://doi.org/10.1364/OL.36.004653

[71] G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, and C. Silberhorn, Phys. Rev. Lett. 116, 143601 (2016).
https://doi.org/10.1103/PhysRevLett.116.143601

[72] T. Eberle, V. Händchen, and R. Schnabel, Opt. Express 21, 11546 (2013).
https://doi.org/10.1364/OE.21.011546

[73] H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 117, 110801 (2016).
https://doi.org/10.1103/PhysRevLett.117.110801

[74] G. S. Thekkadath, D. S. Phillips, J. F. F. Bulmer, W. R. Clements, A. Eckstein, B. A. Bell, J. Lugani, T. A. W. Wolterink, A. Lita, S. W. Nam, T. Gerrits, C. G. Wade, and I. A. Walmsley, arXiv:1908.04765.
arXiv:arXiv:1908.04765

[75] H. M. Vasconcelos, L. Sanz, and S. Glancy, Opt. Lett. 35, 3261 (2010).
https://doi.org/10.1364/OL.35.003261

[76] A. L. Grimsmo, J. Combes, and B. Q. Baragiola, arXiv:1901.08071.
arXiv:arXiv:1901.08071

[77] T. Kiss, U. Herzog, and U. Leonhardt, Phys. Rev. A 52, 2433 (1995).
https://doi.org/10.1103/PhysRevA.52.2433

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