Skip to main content
Log in

Control engineering of continuous-mode single-photon states: a review

  • Review
  • Published:
Control Theory and Technology Aims and scope Submit manuscript

Abstract

In this survey, we present single-photon states of electromagnetic fields, discuss discrete measurements of a single-photon field, show how a linear quantum system responds to a single-photon input, investigate how a coherent feedback network can be used to manipulate the temporal pulse shape of a single-photon state, present single-photon filter and master equations, and finally discuss the generation of Schrödinger cat states by means of photon addition and subtraction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Lvovsky, A. I., Hansen, H., Aichele, T., Benson, O., Mlynek, J., & Schiller, S. (2001). Quantum state reconstruction of the single-photon Fock state. Physical Review Letters, 87(5), 050402.

    Article  Google Scholar 

  2. Yuan, Z., Kardynal, B. E., Stevenson, R. M., Shields, A. J., Lobo, C. J., Cooper, K., Beattie, N. S., Ritchie, D. A., & Pepper, M. (2002). Electrically driven single-photon source. Science, 295(5552), 102–105.

    Article  Google Scholar 

  3. McKeever, J., Boca, A., Boozer, A. D., Miller, R., Buck, J. R., Kuzmich, A., & Kimble, H. J. (2004). Deterministic generation of single photons from one atom trapped in a cavity. Science, 303(5666), 1992–1994.

    Article  Google Scholar 

  4. Houck, A. A., Schuster, D., Gambetta, J., Schreier, J., Johnson, B., Chow, J., Frunzio, L., Majer, J., Devoret, M., Girvin, S., et al. (2007). Generating single microwave photons in a circuit. Nature, 449(7160), 328–331.

    Article  Google Scholar 

  5. O’Brien, J. L., Furusawa, A., & Vučković, J. (2009). Photonic quantum technologies. Nature Photonics, 3(12), 687–695.

    Article  Google Scholar 

  6. Buller, G., & Collins, R. (2009). Single-photon generation and detection. Measurement Science and Technology, 21(1), 012002.

    Article  Google Scholar 

  7. Lvovsky, A. I., & Raymer, M. G. (2009). Continuous-variable optical quantum-state tomography. Reviews of Modern Physics, 81(1), 299.

    Article  Google Scholar 

  8. Santori, C., Fattal, D., & Yamamoto, Y. (2010). Single-photon devices and applications. John Wiley & Sons.

    Google Scholar 

  9. Buckley, S., Rivoire, K., & Vučković, J. (2012). Engineered quantum dot single-photon sources. Reports on Progress in Physics, 75(12), 126503.

    Article  Google Scholar 

  10. Pechal, M., Huthmacher, L., Eichler, C., Zeytinoğlu, S., Abdumalikov, A., Jr., Berger, S., Wallraff, A., & Filipp, S. (2014). Microwave-controlled generation of shaped single photons in circuit quantum electrodynamics. Physical Review X, 4(4), 041010.

    Article  Google Scholar 

  11. Lodahl, P., Mahmoodian, S., & Stobbe, S. (2015). Interfacing single photons and single quantum dots with photonic nanostructures. Reviews of Modern Physics, 87(2), 347.

    Article  MathSciNet  Google Scholar 

  12. Reiserer, A., & Rempe, G. (2015). Cavity-based quantum networks with single atoms and optical photons. Reviews of Modern Physics, 87(4), 1379.

    Article  Google Scholar 

  13. Nurdin, H. I., James, M. R., & Yamamoto, N. (2016). Perfect single device absorber of arbitrary traveling single photon fields with a tunable coupling parameter: A QSDE approach. In: The IEEE 55th Conference on Decision and Control (CDC) (pp. 2513–2518). Las Vegas, NV, USA.

  14. Ogawa, H., Ohdan, H., Miyata, K., Taguchi, M., Makino, K., Yonezawa, H., Yoshikawa, J.-I., & Furusawa, A. (2016). Real-time quadrature measurement of a single-photon wave packet with continuous temporal-mode matching. Physical Review Letters, 116, 233602.

    Article  Google Scholar 

  15. Peng, Z. H., Graaf, S. E. D., Tsai, J. S., & Astafiev, O. V. (2016). Tuneable on-demand single-photon source. Nature Communications, 7(12588). https://doi.org/10.1038/ncomms12588.

  16. Gu, X., Kockum, A. F., Miranowicz, A., Liu, Y.-X., & Nori, F. (2017). Microwave photonics with superconducting quantum circuits. Physics Reports, 718–719, 1–102.

    Article  MathSciNet  MATH  Google Scholar 

  17. Davis, A. O., Thiel, V., Karpiński, M., & Smith, B. J. (2018). Measuring the single-photon temporal-spectral wave function. Physical Review Letters, 121(8), 083602.

    Article  Google Scholar 

  18. Wang, H., Qin, J., Ding, X., Chen, M.-C., Chen, S., You, X., He, Y.-M., Jiang, X., You, L., Wang, Z., et al. (2019). Boson sampling with 20 input photons and a 60-mode interferometer in a \(10^{14}\)-dimensional Hilbert space. Physical Review Letters, 123(25), 250503.

    Article  Google Scholar 

  19. Takase, K., Okada, M., Serikawa, T., Takeda, S., Yoshikawa, J.-I., & Furusawa, A. (2019). Complete temporal mode characterization of non-Gaussian states by a dual homodyne measurement. Physical Review A, 99(3), 033832.

    Article  Google Scholar 

  20. Stobińska, M., Alber, G., & Leuchs, G. (2009). Perfect excitation of a matter qubit by a single photon in free space. EPL (Europhysics Letters), 86(1), 14007.

    Article  Google Scholar 

  21. Wang, Y., Minář, J., Sheridan, L., & Scarani, V. (2011). Efficient excitation of a two-level atom by a single photon in a propagating mode. Physical Review A, 83(6), 063842.

    Article  Google Scholar 

  22. Pan, Y., Zhang, G., & James, M. R. (2016). Analysis and control of quantum finite-level systems driven by single-photon input states. Automatica, 69, 18–23.

    Article  MathSciNet  MATH  Google Scholar 

  23. Rephaeli, E., Shen, J.-T., & Fan, S. (2010). Full inversion of a two-level atom with a single-photon pulse in one-dimensional geometries. Physical Review A, 82(3), 033804.

    Article  Google Scholar 

  24. Gough, J. E., James, M. R., Nurdin, H. I., & Combes, J. (2012). Quantum filtering for systems driven by fields in single-photon states or superposition of coherent states. Physical Review A, 86(4), 043819.

    Article  Google Scholar 

  25. Baragiola, B. Q., Cook, R. L., Brańczyk, A. M., & Combes, J. (2012). N-photon wave packets interacting with an arbitrary quantum system. Physical Review A, 86(1), 013811.

    Article  Google Scholar 

  26. Song, H., Zhang, G., & Xi, Z. (2016). Continuous-mode multiphoton filtering. SIAM Journal on Control and Optimization, 54(3), 1602–1632.

    Article  MathSciNet  MATH  Google Scholar 

  27. Dong, Z., Zhang, G., & Amini, N. H. (2019). Quantum filtering for a two-level atom driven by two counter-propagating photons. Quantum Information Processing, 18(5), 136.

    Article  MathSciNet  Google Scholar 

  28. Dong, Z., Zhang, G., & Amini, N. H. (2019). On the response of a two-level system to two-photon inputs. SIAM Journal on Control and Optimization, 57(5), 3445–3470.

    Article  MathSciNet  MATH  Google Scholar 

  29. Gardiner, C., & Zoller, P. (2004). Quantum noise. Springer.

    MATH  Google Scholar 

  30. Davies, E. B. (1976). Quantum theory of open systems. Academic Press.

    MATH  Google Scholar 

  31. Wiseman, H. M., & Milburn, G. J. (2009). Quantum measurement and control. Cambridge University Press.

    Book  MATH  Google Scholar 

  32. Gough, J., & James, M. R. (2009). The series product and its application to quantum feedforward and feedback networks. IEEE Transactions on Automatic Control, 54(11), 2530–2544.

    Article  MathSciNet  MATH  Google Scholar 

  33. Zhang, G., & James, M. R. (2012). Quantum feedback networks and control: a brief survey. Chinese Science Bulletin, 57(18), 2200–2214.

    Article  Google Scholar 

  34. Gough, J. E., & Zhang, G. (2015). On realization theory of quantum linear systems. Automatica, 59, 139–151.

    Article  MathSciNet  MATH  Google Scholar 

  35. Combes, J., Kerckhoff, J., & Sarovar, M. (2017). The SLH framework for modeling quantum input-output networks. Advances in Physics: X, 2(3), 784–888.

    Google Scholar 

  36. Zhang, J., Liu, Y.-X., Wu, R.-B., Jacobs, K., & Nori, F. (2017). Quantum feedback: theory, experiments, and applications. Physics Reports, 679, 1–60.

    Article  MathSciNet  MATH  Google Scholar 

  37. Nurdin, H. I., & Yamamoto, N. (2017). Linear dynamical quantum systems-analysis, synthesis, and control. Berlin: Springer.

    MATH  Google Scholar 

  38. Zhang, G., Grivopoulos, S., Petersen, I. R., & Gough, J. E. (2018). The Kalman decomposition for linear quantum systems. IEEE Transactions on Automatic Control, 63(2), 331–346.

    Article  MathSciNet  MATH  Google Scholar 

  39. Gardiner, C. W., & Collett, M. J. (1985). Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation. Physical Review A, 31(6), 3761.

    Article  MathSciNet  Google Scholar 

  40. Blow, K., Loudon, R., Phoenix, S. J., & Shepherd, T. (1990). Continuum fields in quantum optics. Physical Review A, 42(7), 4102.

    Article  Google Scholar 

  41. Fan, S., Kocabas, S. E., & Shen, J. T. (2010). Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit. Physical Review A, 82, 063821.

    Article  Google Scholar 

  42. Fischer, K. A., Trivedi, R., Ramasesh, V., Siddiqi, I., & Vučković, J. (2018). Scattering into one-dimensional waveguides from a coherently-driven quantum-optical system. Quantum, 2, 69.

    Article  Google Scholar 

  43. Tezak, N., Niederberger, A., Pavlichin, D. S., Sarma, G., & Mabuchi, H. (2012). Specification of photonic circuits using quantum hardware description language. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 370(1979), 5270–5290.

    Article  MathSciNet  MATH  Google Scholar 

  44. Qin, Z., Prasad, A. S., Brannan, T., MacRae, A., Lezama, A., & Lvovsky, A. (2015). Complete temporal characterization of a single photon. Light: Science & Applications, 4(6), e298–e298.

    Article  Google Scholar 

  45. Walls, D. F., & Milburn, G. J. (2007). Quantum optics. Springer.

    MATH  Google Scholar 

  46. Loudon, R. (2000). The quantum theory of light. Oxford University Press.

    MATH  Google Scholar 

  47. Yamamoto, N., & James, M. R. (2014). Zero-dynamics principle for perfect quantum memory in linear networks. New Journal of Physics, 16(7), 073032.

    Article  MathSciNet  MATH  Google Scholar 

  48. Bachor, H.-A., & Ralph, T. C. (2004). A guide to experiments in quantum optics. Wiley.

    Book  Google Scholar 

  49. Gough, J. E., & Zhang, G. (2015). Generating nonclassical quantum input field states with modulating filters. EPJ Quantum Technology, 2, 2–15.

    Article  Google Scholar 

  50. Dong, Z., Cui, L., Zhang, G., & Fu, H. (2016). Wigner spectrum and coherent feedback control of continuous-mode single-photon Fock states. Journal of Physics A: Mathematical and Theoretical, 49(43), 435301.

    Article  MathSciNet  MATH  Google Scholar 

  51. Titulaer, U., & Glauber, R. (1966). Density operators for coherent fields. Physical Review, 145(4), 1041.

    Article  Google Scholar 

  52. Raymer, M. G., & Walmsley, I. A. (2020). Temporal modes in quantum optics: then and now. Physica Scripta, 95(6), 064002.

    Article  Google Scholar 

  53. Milburn, G. J. (2008). Coherent control of single photon states. The European Physical Journal Special Topics, 159, 113–117.

    Article  Google Scholar 

  54. Hassani, S. (2013). Mathematical physics: A modern introduction to its foundations. Springer Science & Business Media.

    Book  MATH  Google Scholar 

  55. Zhang, G., & James, M. R. (2013). On the response of quantum linear systems to single photon input fields. IEEE Transactions on Automatic Control, 58(5), 1221–1235.

    Article  MathSciNet  MATH  Google Scholar 

  56. Gough, J. E., James, M., & Nurdin, H. (2010). Squeezing components in linear quantum feedback networks. Physical Review A, 81(2), 023804.

    Article  Google Scholar 

  57. Zhang, G., & James, M. R. (2011). Direct and indirect couplings in coherent feedback control of linear quantum systems. IEEE Transactions on Automatic Control, 56, 1535–1550.

    Article  MathSciNet  MATH  Google Scholar 

  58. Zhang, G., Petersen, I. R., & Li, J. (2020). Structural characterization of linear quantum systems with application to back-action evading measurement. IEEE Transactions on Automatic Control, 65(7), 3157–3163.

    Article  MathSciNet  MATH  Google Scholar 

  59. James, M. R., Nurdin, H. I., & Petersen, I. R. (2008). \({H}^\infty\) control of linear quantum stochastic systems. IEEE Transactions on Automatic Control, 53(8), 1787–1803.

    Article  MathSciNet  MATH  Google Scholar 

  60. Nurdin, H. I., James, M. R., & Doherty, A. C. (2009). Network synthesis of linear dynamical quantum stochastic systems. SIAM Journal on Control and Optimization, 48(4), 2686–2718.

    Article  MathSciNet  MATH  Google Scholar 

  61. Le Page, W. R. (1980). Complex variables and the Laplace transform for engineers. Dover Publications.

    Google Scholar 

  62. Zhang, G. (2014). Analysis of quantum linear systems’ response to multi-photon states. Automatica, 50(2), 442–451.

    Article  MathSciNet  MATH  Google Scholar 

  63. Zhang, G. (2017). Dynamical analysis of quantum linear systems driven by multi-channel multi-photon states. Automatica, 83, 186–198.

    Article  MathSciNet  MATH  Google Scholar 

  64. Gough, J. E., James, M. R., & Nurdin, H. I. (2013). Quantum filtering for systems driven by fields in single photon states and superposition of coherent states using non-markovian embeddings. Quantum Information Processing, 12(3), 1469–1499.

    Article  MathSciNet  MATH  Google Scholar 

  65. Baragiola, B. Q., & Combes, J. (2017). Quantum trajectories for propagating Fock states. Physical Review A, 96(2), 023819.

    Article  Google Scholar 

  66. Song, H., Kuntz, K. B., & Huntington, E. H. (2013). Limitations on the quantum non-Gaussian characteristic of Schrödinger kitten state generation. New Journal of Physics, 15(2), 023042.

    Article  MathSciNet  Google Scholar 

  67. Belavkin, V. (1980). Quantum filtering of markov signals with white quantum noise. Elektronika, 25, 1445–1453.

    Google Scholar 

  68. Belavkin, V. P. (1989). Nondemolition measurements, nonlinear filtering and dynamic programming of quantum stochastic processes. In: Modeling and control of systems (pp. 245–265). Springer.

  69. Plenio, M. B., & Knight, P. L. (1998). The quantum-jump approach to dissipative dynamics in quantum optics. Reviews of Modern Physics, 70, 101–144.

    Article  Google Scholar 

  70. van Handel, R., Stockton, J., & Mabuchi, H. (2005). Feedback control of quantum state reduction. IEEE Transactions on Automatic Control, 50(6), 768–780.

    Article  MathSciNet  MATH  Google Scholar 

  71. Bouten, L., van Handel, R., & James, M. R. (2007). An introduction to quantum filtering. SIAM Journal on Control and Optimization, 46(6), 2199–2241.

    Article  MathSciNet  MATH  Google Scholar 

  72. Barchielli, A., & Gregoratti, M. (2009). Quantum trajectories and measurements in continuous time: The diffusive case. Springer.

    Book  MATH  Google Scholar 

  73. Rouchon, P., & Ralph, J. F. (2015). Efficient quantum filtering for quantum feedback control. Physical Review A, 91(1), 012118.

    Article  MathSciNet  Google Scholar 

  74. Dabrowska, A., Sarbicki, G., & Chruściński, D. (2017). Quantum trajectories for a system interacting with environment in a single-photon state: Counting and diffusive processes. Physical Review A, 96(5), 053819.

    Article  Google Scholar 

  75. Gough, J.E. (2018). An introduction to quantum filtering, arXiv Preprint, arXiv:1804.09086.

  76. Gao, Q., Zhang, G., & Petersen, I. R. (2019). An exponential quantum projection filter for open quantum systems. Automatica, 99, 59–68.

    Article  MathSciNet  MATH  Google Scholar 

  77. Gao, Q., Zhang, G., & Petersen, I. R. (2020). An improved quantum projection filter. Automatica, 112, 108716.

    Article  MathSciNet  MATH  Google Scholar 

  78. Dabrowska, A. M. (2020). From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket. JOSA B, 37(4), 1240–1248.

    Article  Google Scholar 

  79. Dong, Z., Zhang, G., & Amini, N. H. (2018). Single-photon quantum filtering with multiple measurements. International Journal of Adaptive Control and Signal Processing, 32(3), 528–546.

    Article  MathSciNet  MATH  Google Scholar 

  80. Serafini, A., De Siena, S., Illuminati, F., & Paris, M. G. (2004). Minimum decoherence cat-like states in Gaussian noisy channels. Journal of Optics B: Quantum and Semiclassical Optics, 6(6), S591.

    Article  Google Scholar 

  81. Brańczyk, A. M., & Ralph, T. (2008). Teleportation using squeezed single photons. Physical Review A, 78(5), 052304.

    Article  Google Scholar 

  82. Neergaard-Nielsen, J. S., Eto, Y., Lee, C.-W., Jeong, H., & Sasaki, M. (2013). Quantum tele-amplification with a continuous-variable superposition state. Nature Photonics, 7(6), 439–443.

    Article  Google Scholar 

  83. Gheri, K., Ellinger, K., Pellizzari, T., & Zoller, P. (1998). Photon-wavepackets as flying quantum bits. Fortschritte der Physik, 46, 401–415.

    Article  Google Scholar 

  84. Fabre, C., & Treps, N. (2020). Modes and states in quantum optics. Reviews of Modern Physics, 92(3), 035005.

    Article  MathSciNet  Google Scholar 

  85. Zhong, H.-S., Wang, H., Deng, Y.-H., Chen, M.-C., Peng, L.-C., Luo, Y.-H., Qin, J., Wu, D., Ding, X., Hu, Y., et al. (2020). Quantum computational advantage using photons. Science, 370(6523), 1460–1463.

    Article  Google Scholar 

  86. Asavanant, W., Takase, K., Fukui, K., Endo, M., Yoshikawa, J.-I., & Furusawa, A. (2021). Wave-function engineering via conditional quantum teleportation with a non-gaussian entanglement resource. Physical Review A, 103(4), 043701.

    Article  MathSciNet  Google Scholar 

  87. Ralph, T. C., Gilchrist, A., Milburn, G. J., Munro, W. J., & Glancy, S. (2003). Quantum computation with optical coherent states. Physical Review A, 68(4), 042319.

    Article  Google Scholar 

  88. Ourjoumtsev, A., Jeong, H., Tualle-Brouri, R., & Grangier, P. (2007). Generation of optical Schrödinger cats from photon number states. Nature, 448(7155), 784–786.

    Article  Google Scholar 

  89. Gerrits, T., Glancy, S., Clement, T. S., Calkins, B., Lita, A. E., Miller, A. J., Migdall, A. L., Nam, S. W., Mirin, R. P., & Knill, E. (2010). Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum. Physical Review A, 82(3), 031802.

    Article  Google Scholar 

  90. Huang, K., Le Jeannic, H., Ruaudel, J., Verma, V., Shaw, M., Marsili, F., Nam, S., Wu, E., Zeng, H., Jeong, Y.-C., et al. (2015). Optical synthesis of large-amplitude squeezed coherent-state superpositions with minimal resources. Physical Review Letters, 115(2), 023602.

    Article  Google Scholar 

  91. Etesse, J., Bouillard, M., Kanseri, B., & Tualle-Brouri, R. (2015). Experimental generation of squeezed cat states with an operation allowing iterative growth. Physical Review Letters, 114(19), 193602.

    Article  Google Scholar 

  92. Sychev, D. V., Ulanov, A. E., Pushkina, A. A., Richards, M. W., Fedorov, I. A., & Lvovsky, A. I. (2017). Enlargement of optical Schrödinger’s cat states. Nature Photonics, 11(6), 379.

    Article  Google Scholar 

  93. Oh, C., & Jeong, H. (2018). Efficient amplification of superpositions of coherent states using input states with different parities. JOSA B, 35(11), 2933–2939.

    Article  Google Scholar 

  94. Eaton, M., Nehra, R., & Pfister, O. (2019). Non-Gaussian and Gottesman-Kitaev-Preskill state preparation by photon catalysis. New Journal of Physics, 21(11), 113034.

    Article  MathSciNet  Google Scholar 

  95. Mikheev, E. V., Pugin, A. S., Kuts, D. A., Podoshvedov, S. A., & An, N. B. (2019). Efficient production of large-size optical Schrödinger cat states. Scientific Reports, 9(1), 1–15.

    Article  Google Scholar 

  96. Takase, K., Yoshikawa, J.-I., Asavanant, W., Endo, M., & Furusawa, A. (2021). Generation of optical Schrödinger cat states by generalized photon subtraction. Physical Review A, 103(1), 013710.

    Article  Google Scholar 

  97. Dong, Z., Cui, W., Zhang, G. (2020). On the dynamics of a quantum coherent feedback network of cavity-mediated double quantum dot qubits, arXiv Print, arXiv:2004.03870.

  98. Breitenbach, T., & Borzì, A. (2020). A sequential quadratic hamiltonian scheme for solving non-smooth quantum control problems with sparsity. Journal of Computational and Applied Mathematics, 369, 112583.

    Article  MathSciNet  MATH  Google Scholar 

  99. Ciaramella, G., & Borzi, A. (2016). Quantum optimal control problems with a sparsity cost functional. Numerical Functional Analysis and Optimization, 37(8), 938–965.

    Article  MathSciNet  MATH  Google Scholar 

  100. Borzì, A., Ciaramella, G., & Sprengel, M. (2017). Formulation and numerical solution of quantum control problems. SIAM.

    Book  MATH  Google Scholar 

Download references

Acknowledgements

The author thanks financial support from the Hong Kong Research Grant Council (Nos. 15208418, 15203619), the Shenzhen Fundamental Research Fund, China (No. JCYJ20190813165207290), and the CAS AMSS-polyU Joint Laboratory of Applied Mathematics.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guofeng Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, G. Control engineering of continuous-mode single-photon states: a review. Control Theory Technol. 19, 544–562 (2021). https://doi.org/10.1007/s11768-021-00059-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-021-00059-7

Keywords

Navigation