Interaction between a single photon and a weak coherent state mediated by a quantum emitter
Main Article Content
Abstract
Photon-photon interaction, an essential ingredient for optical quantum technologies, is indirect actually, i.e., often mediated via a nonlinear medium. In this work, we consider a single photon interacting with a weak coherent state in a one-dimensional waveguide coupled to a two-level quantum emitter. We present a general input-output framework that applies to an arbitrary input Fock state and various types of quantum emitters. We then use this to compute the relevant scattering processes between the single photon and the weak coherent state. We analyse
in detail the characteristics of the output state taking into account the continuous-mode nature of the input and output states which are treated as appropriate photon wavepackets.
Article Details
Keywords
Waveguide quantum electrodynamics, quantum emiiters, photonphoton interaction.
References
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[23] Brod, Daniel J., Combes, Joshua, and Gea-Banacloche, Julio. Two photons co- and counterpropagating through N cross-Kerr sites. Phys. Rev. A, 94:023833, Aug 2016.
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[28] T P Spiller, Kae Nemoto, Samuel L Braunstein, W J Munro, P van Loock, and G J Milburn. Quantum computation by communication. New Journal of Physics, 8(2):30, feb 2006.
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[31] Gea-Banacloche, Julio. Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets. Phys. Rev. A, 81:043823, Apr 2010.
[32] He, Bing, Lin, Qing, and Simon, Christoph. Cross-Kerr nonlinearity between continuous-mode coherent states and single photons. Phys. Rev. A, 83:053826, May 2011.
[33] He, Bing, MacRae, Andrew, Han, Yang, Lvovsky, A. I., and Simon, Christoph. Transverse multimode effects on the performance of photon-photon gates. Phys. Rev. A, 83:022312, Feb 2011.
[34] Le, Dat Thanh, Asavanant, Warit, and An, Nguyen Ba. Heralded preparation of polarization entanglement via quantum scissors. Phys. Rev. A, 104:012612, Jul 2021.
[35] Dat Thanh Le, Cao Thi Bich, and Nguyen Ba An. Feasible and economical scheme to entangle a polarized coherent state and a polarized photon. Optik, 225:165820, 2021.
[36] Furusawa, Akira and Van Loock, Peter. Quantum teleportation and entanglement: a hybrid approach to optical quantum information processing. John Wiley & Sons, 2011.
[37] Takeda, Shuntaro and Mizuta, Takahiro, Fuwa, Maria, van Loock, Peter, and Furusawa, Akira. Deterministic quantum teleportation of photonic quantum bits by a hybrid technique. Nature, 500(7462):315–318, 2013.
[38] Andersen, Ulrik L., Neergaard-Nielsen, Jonas S., van Loock, Peter, and Furusawa, Akira. Hybrid discrete- and continuous-variable quantum information. Nature Physics, 11(9):713–719, 2015.
[39] Gerry, Christopher C and Knight, Peter L. Introductory quantum optics. Cambridge university press, 2023.
[40] Fan, Bixuan, Kockum, Anton F., Combes, Joshua, Johansson, G¨oran, Hoi, Io-chun, Wilson, C. M., Delsing, Per, Milburn, G.
J., and Stace, Thomas M. Breakdown of the Cross-Kerr Scheme for Photon Counting. Phys. Rev. Lett., 110:053601, Jan 2013.
[41] Shi, Tao, Chang, Darrick E., and Cirac, J. Ignacio. Multiphotonscattering theory and generalized master equations. Phys. Rev. A, 92:053834, Nov 2015.
[42] Joseph Kerckhoff Joshua Combes and Mohan Sarovar. The SLH framework for modeling quantum input-output networks. Advances in Physics: X, 2(3):784–888, 2017.
[43] Gardiner, Crispin and Zoller, Peter. Quantum noise: a handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics. Springer, Berlin, 2004.
[44] Shanshan Xu. Theory of few-photon quantum scattering in nanophotonic structures. PhD thesis, Stanford University, 2017.
[45] Loudon, Rodney. The quantum theory of light. OUP Oxford, 2000.
[46] Vinu, Athul and Roy, Dibyendu. Single photons versus coherent-state input in waveguide quantum electrodynamics: Light scattering, Kerr, and cross-Kerr effect. Phys. Rev. A, 107:023704, Feb 2023.
[2] Nielsen, Michael A and Chuang, Isaac L. Quantum computation and quantum information. Cambridge university press, 2010.
[3] Knill, E., Laflamme, R., and Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature, 409(6816):46–52, 2001.
[4] Briegel, H. J., Browne, D. E., D¨ur, W., Raussendorf, R., and Van den Nest, M. Measurement-based quantum computation. Nature Physics, 5(1):19–26, 2009.
[5] Lukin, M. D. Colloquium: Trapping and manipulating photon states in atomic ensembles. Rev. Mod. Phys., 75:457–472, Apr 2003.
[6] Lodahl, Peter, Mahmoodian, Sahand, and Stobbe, Søren. Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys., 87:347–400, May 2015.
[7] Vetsch, E., Reitz, D., Sagu´e, G., Schmidt, R., Dawkins, S. T., and Rauschenbeutel, A. Optical Interface Created by Laser-Cooled Atoms Trapped in the Evanescent Field Surrounding an Optical Nanofiber. Phys. Rev. Lett., 104:203603, May 2010.
[8] Corzo, Neil V., Gouraud, Baptiste, Chandra, Aveek, Goban, Akihisa, Sheremet, Alexandra S., Kupriyanov, Dmitriy V., and Laurat, Julien. Large Bragg Reflection from One-Dimensional Chains of Trapped Atoms Near a Nanoscale Waveguide. Phys. Rev. Lett., 117:133603, Sep 2016.
[9] Lund-Hansen, T., Stobbe, S., Julsgaard, B., Thyrrestrup, H., S¨unner, T., Kamp, M., Forchel, A., and Lodahl, P. Experimental Realization of Highly Efficient Broadband Coupling of Single Quantum Dots to a Photonic Crystal Waveguide. Phys. Rev. Lett., 101:113903, Sep 2008.
[10] Arcari, M., S¨ollner, I., Javadi, A. andLindskov Hansen, S., Mahmoodian, S., Liu, J., Thyrrestrup, H., Lee, E. H., Song, J. D., Stobbe, S., and Lodahl, P. Near-Unity Coupling Efficiency of a Quantum Emitter to a Photonic Crystal Waveguide. Phys. Rev. Lett., 113:093603, Aug 2014.
[11] O. Astafiev , A. M. Zagoskin , A. A. Abdumalikov , Yu. A. Pashkin , T. Yamamoto , K. Inomata , Y. Nakamura , and J.
S. Tsai. Resonance Fluorescence of a Single Artificial Atom. Science, 327(5967):840–843, 2010.
[12] Arjan F. van Loo , Arkady Fedorov , Kevin Lalumi`ere , Barry C. Sanders , Alexandre Blais , and Andreas Wallraff. Photon-Mediated Interactions Between Distant Artificial Atoms. Science, 342(6165): 1494–1496, 2013.
[13] Sheremet, Alexandra S., Petrov, Mihail I., Iorsh, Ivan V., Poshakinskiy, Alexander V., and Poddubny, Alexander N. Waveguide quantum electrodynamics: Collective radiance and photon-photon correlations. Rev. Mod. Phys., 95:015002, Mar 2023.
[14] Roy, Dibyendu, Wilson, C. M., and Firstenberg, Ofer. Colloquium: Strongly interacting photons in one-dimensional continuum. Rev. Mod. Phys., 89:021001, May 2017.
[15] Chang, Darrick E., Sørensen, Anders S., Demler, Eugene A., and Lukin, Mikhail D. A single-photon transistor using nanoscale surface plasmons. Nature Physics, 3(11):807–812, 2007.
[16] Abdumalikov, A. A., Astafiev, O., Zagoskin, A. M., Pashkin, Yu. A., Nakamura, Y., and Tsai, J. S. Electromagnetically Induced
Transparency on a Single Artificial Atom. Phys. Rev. Lett., 104:193601, May 2010.
[17] Peyronel, Thibault, Firstenberg, Ofer, Liang, Qi-Yu, Hofferberth, Sebastian, Gorshkov, Alexey V., Pohl, Thomas, Lukin,
Mikhail D., and Vuleti´c, Vladan. Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature, 488(7409):57–60, 2012.
[18] Firstenberg, Ofer, Peyronel, Thibault, Liang, Qi-Yu, Gorshkov, Alexey V., Lukin, Mikhail D., and Vuleti´c, Vladan. Attractive photons in a quantum nonlinear medium. Nature, 502(7469):71–75, 2013.
[19] J. T. Shen and Shanhui Fan. Coherent photon transport from spontaneous emission in one-dimensional waveguides. Opt. Lett., 30(15):2001–2003, Aug 2005.
[20] Shen, Jung-Tsung and Fan, Shanhui. Strongly Correlated Two-Photon Transport in a One-Dimensional Waveguide Coupled to a Two-Level System. Phys. Rev. Lett., 98:153003, Apr 2007.
[21] Shen, Jung-Tsung and Fan, Shanhui. Strongly correlated multiparticle transport in one dimension through a quantum impurity. Phys. Rev. A, 76:062709, Dec 2007.
[22] Tommaso Caneva , Marco T Manzoni, Tao Shi, James S Douglas, J Ignacio Cirac, and Darrick E Chang. Quantum dynamics of propagating photons with strong interactions: a generalized input–output formalism. New Journal of Physics, 17(11):113001, Oct 2015.
[23] Brod, Daniel J., Combes, Joshua, and Gea-Banacloche, Julio. Two photons co- and counterpropagating through N cross-Kerr sites. Phys. Rev. A, 94:023833, Aug 2016.
[24] Brod, Daniel J. and Combes, Joshua. Passive CPHASE Gate via Cross-Kerr Nonlinearities. Phys. Rev. Lett., 117:080502, Aug 2016.
[25] Fan, Shanhui , Kocaba¸s, S¸¨ukr¨u Ekin , and Shen, Jung-Tsung. Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit. Phys. Rev. A, 82:063821, Dec 2010.
[26] Zheng, Huaixiu, Gauthier, Daniel J., and Baranger, Harold U. Waveguide QED: Many-body bound-state effects in coherent and Fock-state scattering from a two-level system. Phys. Rev. A, 82:063816, Dec 2010.
[27] Nemoto, Kae and Munro, W. J. Nearly Deterministic Linear Optical Controlled-NOT Gate. Phys. Rev. Lett., 93:250502, Dec 2004.
[28] T P Spiller, Kae Nemoto, Samuel L Braunstein, W J Munro, P van Loock, and G J Milburn. Quantum computation by communication. New Journal of Physics, 8(2):30, feb 2006.
[29] Shapiro, Jeffrey H. Single-photon Kerr nonlinearities do not help quantum computation. Phys. Rev. A, 73:062305, Jun 2006.
[30] Shapiro, Jeffrey H. and Bondurant, Roy S. Qubit degradation due to cross-phase-modulation photon-number measurement. Phys. Rev. A, 73:022301, Feb 2006.
[31] Gea-Banacloche, Julio. Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets. Phys. Rev. A, 81:043823, Apr 2010.
[32] He, Bing, Lin, Qing, and Simon, Christoph. Cross-Kerr nonlinearity between continuous-mode coherent states and single photons. Phys. Rev. A, 83:053826, May 2011.
[33] He, Bing, MacRae, Andrew, Han, Yang, Lvovsky, A. I., and Simon, Christoph. Transverse multimode effects on the performance of photon-photon gates. Phys. Rev. A, 83:022312, Feb 2011.
[34] Le, Dat Thanh, Asavanant, Warit, and An, Nguyen Ba. Heralded preparation of polarization entanglement via quantum scissors. Phys. Rev. A, 104:012612, Jul 2021.
[35] Dat Thanh Le, Cao Thi Bich, and Nguyen Ba An. Feasible and economical scheme to entangle a polarized coherent state and a polarized photon. Optik, 225:165820, 2021.
[36] Furusawa, Akira and Van Loock, Peter. Quantum teleportation and entanglement: a hybrid approach to optical quantum information processing. John Wiley & Sons, 2011.
[37] Takeda, Shuntaro and Mizuta, Takahiro, Fuwa, Maria, van Loock, Peter, and Furusawa, Akira. Deterministic quantum teleportation of photonic quantum bits by a hybrid technique. Nature, 500(7462):315–318, 2013.
[38] Andersen, Ulrik L., Neergaard-Nielsen, Jonas S., van Loock, Peter, and Furusawa, Akira. Hybrid discrete- and continuous-variable quantum information. Nature Physics, 11(9):713–719, 2015.
[39] Gerry, Christopher C and Knight, Peter L. Introductory quantum optics. Cambridge university press, 2023.
[40] Fan, Bixuan, Kockum, Anton F., Combes, Joshua, Johansson, G¨oran, Hoi, Io-chun, Wilson, C. M., Delsing, Per, Milburn, G.
J., and Stace, Thomas M. Breakdown of the Cross-Kerr Scheme for Photon Counting. Phys. Rev. Lett., 110:053601, Jan 2013.
[41] Shi, Tao, Chang, Darrick E., and Cirac, J. Ignacio. Multiphotonscattering theory and generalized master equations. Phys. Rev. A, 92:053834, Nov 2015.
[42] Joseph Kerckhoff Joshua Combes and Mohan Sarovar. The SLH framework for modeling quantum input-output networks. Advances in Physics: X, 2(3):784–888, 2017.
[43] Gardiner, Crispin and Zoller, Peter. Quantum noise: a handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics. Springer, Berlin, 2004.
[44] Shanshan Xu. Theory of few-photon quantum scattering in nanophotonic structures. PhD thesis, Stanford University, 2017.
[45] Loudon, Rodney. The quantum theory of light. OUP Oxford, 2000.
[46] Vinu, Athul and Roy, Dibyendu. Single photons versus coherent-state input in waveguide quantum electrodynamics: Light scattering, Kerr, and cross-Kerr effect. Phys. Rev. A, 107:023704, Feb 2023.