Abstract

Stimulated emission can be defined as the process when an incoming photon stimulates an additional quantum of energy from an atom into the same electromagnetic mode as the impinging photon. Hence, the two outgoing photons are identical. In a waveguide or free space, this intuition is typically found through Fermi’s Golden rule, however, this does not properly account for the wave-like nature of the photons. Here, I present an exact solution to stimulated emission from a quantum two-level atom that properly accounts for the incoming and outgoing electromagnetic modes. This result is valid over a huge range of incident photon numbers. For a single incident photon, it shows how the photon must properly mode match the two-level system to cause stimulated emission. For a Fock state drive with large photon number, the exact solution shows how a two-level system Rabi oscillates with the traveling Fock mode as it passes by. I additionally use the same formalism to show that stimulated emission by a coherent pulse cannot be understood as an additional photon being emitted into the incident coherent state because the two-level system’s state factorizes with the electromagnetic field’s coherent state. Recent advances in superconducting circuits make them an ideal platform to test these predictions.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. H. J. Carmichael, Statistical Methods in Quantum Optics 2: Non-Classical Fields (Springer Science & Business Media, 2009).
  2. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, 1998) p. 678.
  3. R. Shankar, Principles of Quantum Mechanics (Springer Science & Business Media, 2012).
  4. D. Valente, Y. Li, J.-P. Poizat, J.-M. Gérard, L. Kwek, M. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
    [Crossref]
  5. E. Mascarenhas, M. Santos, A. Auffèves, and D. Gerace, “Quantum rectifier in a one-dimensional photonic channel,” Phys. Rev. A 93, 043821 (2016).
    [Crossref]
  6. D. Roy, C. M. Wilson, and O. Firstenberg, “Colloquium: Strongly interacting photons in one-dimensional continuum,” Rev. Mod. Phys. 89, 021001 (2017).
    [Crossref]
  7. Y. Pan, D. Dong, and G. Zhang, “Exact analysis of the response of quantum systems to two-photons using a QSDE approach,” New J. Phys. 18, 033004 (2016).
    [Crossref]
  8. A. Nysteen, P. T. Kristensen, D. P. McCutcheon, P. Kaer, and J. Mørk, “Scattering of two photons on a quantum emitter in a one-dimensional waveguide: exact dynamics and induced correlations,” New J. Phys. 17, 023030 (2015).
    [Crossref]
  9. E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
    [Crossref] [PubMed]
  10. A. F. Koenderink, A. Alù, and A. Polman, “Nanophotonics: shrinking light-based technology,” Science 348, 516–521 (2015).
    [Crossref] [PubMed]
  11. X. Gu, A. F. Kockum, A. Miranowicz, Y. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
    [Crossref]
  12. P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473 (2017).
    [Crossref] [PubMed]
  13. P. Senellart, G. Solomon, and A. White, “High-performance semiconductor quantum-dot single-photon sources,” Nat. Nanotechnol. 12, 1026 (2017).
    [Crossref] [PubMed]
  14. C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, vol. 56 (Springer Science & Business Media, 2004).
  15. C. Gardiner and M. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761 (1985).
    [Crossref]
  16. C. Gardiner, A. Parkins, and P. Zoller, “Wave-function quantum stochastic differential equations and quantum-jump simulation methods,” Phys. Rev. A 46, 4363 (1992).
    [Crossref] [PubMed]
  17. L. Li, M. J. Hall, and H. M. Wiseman, “Concepts of quantum non-markovianity: a hierarchy,” (2018), in press.
  18. J. Gough, “Quantum stratonovich calculus and the quantum Wong-Zakai theorem,” J. Math. Phys. 47, 113509 (2006).
    [Crossref]
  19. R. Loudon, The Quantum Theory of Light (OUPOxford, 2000).
  20. B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
    [Crossref]
  21. S. Xu and S. Fan, “Input-output formalism for few-photon transport: A systematic treatment beyond two photons,” Phys. Rev. A 91, 043845 (2015).
    [Crossref]
  22. B. Mollow, “Stimulated emission and absorption near resonance for driven systems,” Phys. Rev. A 5, 2217 (1972).
    [Crossref]
  23. D. Valente, S. Portolan, G. Nogues, J.-P. Poizat, M. Richard, J.-M. Gérard, M. Santos, and A. Auffèves, “Monitoring stimulated emission at the single-photon level in one-dimensional atoms,” Phys. Rev. A 85, 023811 (2012).
    [Crossref]
  24. K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, C. Dory, J. J. Finley, J. Vučković, and K. Müller, “Signatures of two-photon pulses from a quantum two-level system,” Nat. Phys. 13, 649 (2017).
    [Crossref]
  25. G. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492 (1991).
    [Crossref] [PubMed]
  26. R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “Implementing a universal gate set on a logical qubit encoded in an oscillator,” Nat. Commun. 8, 94 (2017).
    [Crossref] [PubMed]
  27. C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
    [Crossref]
  28. C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
    [Crossref] [PubMed]
  29. C. Lang, C. Eichler, L. Steffen, J. Fink, M. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in hong–ou–mandel experiments at microwave frequencies,” Nat. Phys. 9, 345 (2013).
    [Crossref]
  30. J. Gambetta, A. Houck, and A. Blais, “Superconducting qubit with Purcell protection and tunable coupling,” Phys. Rev. Lett. 106, 030502 (2011).
    [Crossref] [PubMed]
  31. V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222 (2011).
    [Crossref]
  32. A. Silberfarb and I. H. Deutsch, “Continuous measurement with traveling-wave probes,” Phys. Rev. A 68, 013817 (2003).
    [Crossref]

2018 (1)

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

2017 (6)

K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, C. Dory, J. J. Finley, J. Vučković, and K. Müller, “Signatures of two-photon pulses from a quantum two-level system,” Nat. Phys. 13, 649 (2017).
[Crossref]

R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “Implementing a universal gate set on a logical qubit encoded in an oscillator,” Nat. Commun. 8, 94 (2017).
[Crossref] [PubMed]

D. Roy, C. M. Wilson, and O. Firstenberg, “Colloquium: Strongly interacting photons in one-dimensional continuum,” Rev. Mod. Phys. 89, 021001 (2017).
[Crossref]

X. Gu, A. F. Kockum, A. Miranowicz, Y. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
[Crossref]

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473 (2017).
[Crossref] [PubMed]

P. Senellart, G. Solomon, and A. White, “High-performance semiconductor quantum-dot single-photon sources,” Nat. Nanotechnol. 12, 1026 (2017).
[Crossref] [PubMed]

2016 (2)

Y. Pan, D. Dong, and G. Zhang, “Exact analysis of the response of quantum systems to two-photons using a QSDE approach,” New J. Phys. 18, 033004 (2016).
[Crossref]

E. Mascarenhas, M. Santos, A. Auffèves, and D. Gerace, “Quantum rectifier in a one-dimensional photonic channel,” Phys. Rev. A 93, 043821 (2016).
[Crossref]

2015 (3)

A. F. Koenderink, A. Alù, and A. Polman, “Nanophotonics: shrinking light-based technology,” Science 348, 516–521 (2015).
[Crossref] [PubMed]

S. Xu and S. Fan, “Input-output formalism for few-photon transport: A systematic treatment beyond two photons,” Phys. Rev. A 91, 043845 (2015).
[Crossref]

A. Nysteen, P. T. Kristensen, D. P. McCutcheon, P. Kaer, and J. Mørk, “Scattering of two photons on a quantum emitter in a one-dimensional waveguide: exact dynamics and induced correlations,” New J. Phys. 17, 023030 (2015).
[Crossref]

2013 (1)

C. Lang, C. Eichler, L. Steffen, J. Fink, M. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in hong–ou–mandel experiments at microwave frequencies,” Nat. Phys. 9, 345 (2013).
[Crossref]

2012 (4)

D. Valente, S. Portolan, G. Nogues, J.-P. Poizat, M. Richard, J.-M. Gérard, M. Santos, and A. Auffèves, “Monitoring stimulated emission at the single-photon level in one-dimensional atoms,” Phys. Rev. A 85, 023811 (2012).
[Crossref]

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[Crossref] [PubMed]

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

D. Valente, Y. Li, J.-P. Poizat, J.-M. Gérard, L. Kwek, M. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[Crossref]

2011 (3)

J. Gambetta, A. Houck, and A. Blais, “Superconducting qubit with Purcell protection and tunable coupling,” Phys. Rev. Lett. 106, 030502 (2011).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222 (2011).
[Crossref]

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

2006 (1)

J. Gough, “Quantum stratonovich calculus and the quantum Wong-Zakai theorem,” J. Math. Phys. 47, 113509 (2006).
[Crossref]

2003 (1)

A. Silberfarb and I. H. Deutsch, “Continuous measurement with traveling-wave probes,” Phys. Rev. A 68, 013817 (2003).
[Crossref]

1992 (1)

C. Gardiner, A. Parkins, and P. Zoller, “Wave-function quantum stochastic differential equations and quantum-jump simulation methods,” Phys. Rev. A 46, 4363 (1992).
[Crossref] [PubMed]

1991 (1)

G. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492 (1991).
[Crossref] [PubMed]

1985 (1)

C. Gardiner and M. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761 (1985).
[Crossref]

1972 (1)

B. Mollow, “Stimulated emission and absorption near resonance for driven systems,” Phys. Rev. A 5, 2217 (1972).
[Crossref]

Abdumalikov, A.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

Agarwal, G.

G. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492 (1991).
[Crossref] [PubMed]

Alù, A.

A. F. Koenderink, A. Alù, and A. Polman, “Nanophotonics: shrinking light-based technology,” Science 348, 516–521 (2015).
[Crossref] [PubMed]

Auffèves, A.

E. Mascarenhas, M. Santos, A. Auffèves, and D. Gerace, “Quantum rectifier in a one-dimensional photonic channel,” Phys. Rev. A 93, 043821 (2016).
[Crossref]

D. Valente, Y. Li, J.-P. Poizat, J.-M. Gérard, L. Kwek, M. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[Crossref]

D. Valente, S. Portolan, G. Nogues, J.-P. Poizat, M. Richard, J.-M. Gérard, M. Santos, and A. Auffèves, “Monitoring stimulated emission at the single-photon level in one-dimensional atoms,” Phys. Rev. A 85, 023811 (2012).
[Crossref]

Axline, C. J.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

Baragiola, B. Q.

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

Baur, M.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

Blais, A.

C. Lang, C. Eichler, L. Steffen, J. Fink, M. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in hong–ou–mandel experiments at microwave frequencies,” Nat. Phys. 9, 345 (2013).
[Crossref]

J. Gambetta, A. Houck, and A. Blais, “Superconducting qubit with Purcell protection and tunable coupling,” Phys. Rev. Lett. 106, 030502 (2011).
[Crossref] [PubMed]

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

Bozyigit, D.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

Branczyk, A. M.

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

Burkhart, L. D.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

Campagne-Ibarcq, P.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

Carmichael, H. J.

H. J. Carmichael, Statistical Methods in Quantum Optics 2: Non-Classical Fields (Springer Science & Business Media, 2009).

Chou, K.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, 1998) p. 678.

Collett, M.

C. Gardiner and M. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761 (1985).
[Crossref]

Combes, J.

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

Cook, R. L.

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

Da Silva, M.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

Deutsch, I. H.

A. Silberfarb and I. H. Deutsch, “Continuous measurement with traveling-wave probes,” Phys. Rev. A 68, 013817 (2003).
[Crossref]

Devoret, M. H.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “Implementing a universal gate set on a logical qubit encoded in an oscillator,” Nat. Commun. 8, 94 (2017).
[Crossref] [PubMed]

Dong, D.

Y. Pan, D. Dong, and G. Zhang, “Exact analysis of the response of quantum systems to two-photons using a QSDE approach,” New J. Phys. 18, 033004 (2016).
[Crossref]

Dory, C.

K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, C. Dory, J. J. Finley, J. Vučković, and K. Müller, “Signatures of two-photon pulses from a quantum two-level system,” Nat. Phys. 13, 649 (2017).
[Crossref]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, 1998) p. 678.

Eichler, C.

C. Lang, C. Eichler, L. Steffen, J. Fink, M. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in hong–ou–mandel experiments at microwave frequencies,” Nat. Phys. 9, 345 (2013).
[Crossref]

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

Fan, S.

S. Xu and S. Fan, “Input-output formalism for few-photon transport: A systematic treatment beyond two photons,” Phys. Rev. A 91, 043845 (2015).
[Crossref]

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[Crossref] [PubMed]

Filipp, S.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

Fink, J.

C. Lang, C. Eichler, L. Steffen, J. Fink, M. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in hong–ou–mandel experiments at microwave frequencies,” Nat. Phys. 9, 345 (2013).
[Crossref]

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

Finley, J. J.

K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, C. Dory, J. J. Finley, J. Vučković, and K. Müller, “Signatures of two-photon pulses from a quantum two-level system,” Nat. Phys. 13, 649 (2017).
[Crossref]

Firstenberg, O.

D. Roy, C. M. Wilson, and O. Firstenberg, “Colloquium: Strongly interacting photons in one-dimensional continuum,” Rev. Mod. Phys. 89, 021001 (2017).
[Crossref]

Fischer, K. A.

K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, C. Dory, J. J. Finley, J. Vučković, and K. Müller, “Signatures of two-photon pulses from a quantum two-level system,” Nat. Phys. 13, 649 (2017).
[Crossref]

Frunzio, L.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “Implementing a universal gate set on a logical qubit encoded in an oscillator,” Nat. Commun. 8, 94 (2017).
[Crossref] [PubMed]

Gambetta, J.

J. Gambetta, A. Houck, and A. Blais, “Superconducting qubit with Purcell protection and tunable coupling,” Phys. Rev. Lett. 106, 030502 (2011).
[Crossref] [PubMed]

Gardiner, C.

C. Gardiner, A. Parkins, and P. Zoller, “Wave-function quantum stochastic differential equations and quantum-jump simulation methods,” Phys. Rev. A 46, 4363 (1992).
[Crossref] [PubMed]

C. Gardiner and M. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761 (1985).
[Crossref]

C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, vol. 56 (Springer Science & Business Media, 2004).

Gerace, D.

E. Mascarenhas, M. Santos, A. Auffèves, and D. Gerace, “Quantum rectifier in a one-dimensional photonic channel,” Phys. Rev. A 93, 043821 (2016).
[Crossref]

Gérard, J.-M.

D. Valente, Y. Li, J.-P. Poizat, J.-M. Gérard, L. Kwek, M. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[Crossref]

D. Valente, S. Portolan, G. Nogues, J.-P. Poizat, M. Richard, J.-M. Gérard, M. Santos, and A. Auffèves, “Monitoring stimulated emission at the single-photon level in one-dimensional atoms,” Phys. Rev. A 85, 023811 (2012).
[Crossref]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222 (2011).
[Crossref]

Girvin, S.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

Gough, J.

J. Gough, “Quantum stratonovich calculus and the quantum Wong-Zakai theorem,” J. Math. Phys. 47, 113509 (2006).
[Crossref]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, 1998) p. 678.

Gu, X.

X. Gu, A. F. Kockum, A. Miranowicz, Y. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
[Crossref]

Hall, M. J.

L. Li, M. J. Hall, and H. M. Wiseman, “Concepts of quantum non-markovianity: a hierarchy,” (2018), in press.

Hanschke, L.

K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, C. Dory, J. J. Finley, J. Vučković, and K. Müller, “Signatures of two-photon pulses from a quantum two-level system,” Nat. Phys. 13, 649 (2017).
[Crossref]

Heeres, R. W.

R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “Implementing a universal gate set on a logical qubit encoded in an oscillator,” Nat. Commun. 8, 94 (2017).
[Crossref] [PubMed]

Houck, A.

J. Gambetta, A. Houck, and A. Blais, “Superconducting qubit with Purcell protection and tunable coupling,” Phys. Rev. Lett. 106, 030502 (2011).
[Crossref] [PubMed]

Jiang, L.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “Implementing a universal gate set on a logical qubit encoded in an oscillator,” Nat. Commun. 8, 94 (2017).
[Crossref] [PubMed]

Kaer, P.

A. Nysteen, P. T. Kristensen, D. P. McCutcheon, P. Kaer, and J. Mørk, “Scattering of two photons on a quantum emitter in a one-dimensional waveguide: exact dynamics and induced correlations,” New J. Phys. 17, 023030 (2015).
[Crossref]

Kockum, A. F.

X. Gu, A. F. Kockum, A. Miranowicz, Y. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
[Crossref]

Koenderink, A. F.

A. F. Koenderink, A. Alù, and A. Polman, “Nanophotonics: shrinking light-based technology,” Science 348, 516–521 (2015).
[Crossref] [PubMed]

Kristensen, P. T.

A. Nysteen, P. T. Kristensen, D. P. McCutcheon, P. Kaer, and J. Mørk, “Scattering of two photons on a quantum emitter in a one-dimensional waveguide: exact dynamics and induced correlations,” New J. Phys. 17, 023030 (2015).
[Crossref]

Kwek, L.

D. Valente, Y. Li, J.-P. Poizat, J.-M. Gérard, L. Kwek, M. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[Crossref]

Lang, C.

C. Lang, C. Eichler, L. Steffen, J. Fink, M. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in hong–ou–mandel experiments at microwave frequencies,” Nat. Phys. 9, 345 (2013).
[Crossref]

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

Li, L.

L. Li, M. J. Hall, and H. M. Wiseman, “Concepts of quantum non-markovianity: a hierarchy,” (2018), in press.

Li, Y.

D. Valente, Y. Li, J.-P. Poizat, J.-M. Gérard, L. Kwek, M. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[Crossref]

Liu, Y.

X. Gu, A. F. Kockum, A. Miranowicz, Y. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
[Crossref]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222 (2011).
[Crossref]

Lodahl, P.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473 (2017).
[Crossref] [PubMed]

Loudon, R.

R. Loudon, The Quantum Theory of Light (OUPOxford, 2000).

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222 (2011).
[Crossref]

Mahmoodian, S.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473 (2017).
[Crossref] [PubMed]

Mascarenhas, E.

E. Mascarenhas, M. Santos, A. Auffèves, and D. Gerace, “Quantum rectifier in a one-dimensional photonic channel,” Phys. Rev. A 93, 043821 (2016).
[Crossref]

McCutcheon, D. P.

A. Nysteen, P. T. Kristensen, D. P. McCutcheon, P. Kaer, and J. Mørk, “Scattering of two photons on a quantum emitter in a one-dimensional waveguide: exact dynamics and induced correlations,” New J. Phys. 17, 023030 (2015).
[Crossref]

Miranowicz, A.

X. Gu, A. F. Kockum, A. Miranowicz, Y. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
[Crossref]

Mollow, B.

B. Mollow, “Stimulated emission and absorption near resonance for driven systems,” Phys. Rev. A 5, 2217 (1972).
[Crossref]

Mørk, J.

A. Nysteen, P. T. Kristensen, D. P. McCutcheon, P. Kaer, and J. Mørk, “Scattering of two photons on a quantum emitter in a one-dimensional waveguide: exact dynamics and induced correlations,” New J. Phys. 17, 023030 (2015).
[Crossref]

Müller, K.

K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, C. Dory, J. J. Finley, J. Vučković, and K. Müller, “Signatures of two-photon pulses from a quantum two-level system,” Nat. Phys. 13, 649 (2017).
[Crossref]

Nogues, G.

D. Valente, S. Portolan, G. Nogues, J.-P. Poizat, M. Richard, J.-M. Gérard, M. Santos, and A. Auffèves, “Monitoring stimulated emission at the single-photon level in one-dimensional atoms,” Phys. Rev. A 85, 023811 (2012).
[Crossref]

Nori, F.

X. Gu, A. F. Kockum, A. Miranowicz, Y. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
[Crossref]

Nysteen, A.

A. Nysteen, P. T. Kristensen, D. P. McCutcheon, P. Kaer, and J. Mørk, “Scattering of two photons on a quantum emitter in a one-dimensional waveguide: exact dynamics and induced correlations,” New J. Phys. 17, 023030 (2015).
[Crossref]

Ofek, N.

R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “Implementing a universal gate set on a logical qubit encoded in an oscillator,” Nat. Commun. 8, 94 (2017).
[Crossref] [PubMed]

Pan, Y.

Y. Pan, D. Dong, and G. Zhang, “Exact analysis of the response of quantum systems to two-photons using a QSDE approach,” New J. Phys. 18, 033004 (2016).
[Crossref]

Parkins, A.

C. Gardiner, A. Parkins, and P. Zoller, “Wave-function quantum stochastic differential equations and quantum-jump simulation methods,” Phys. Rev. A 46, 4363 (1992).
[Crossref] [PubMed]

Pfaff, W.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

Pichler, H.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473 (2017).
[Crossref] [PubMed]

Poizat, J.-P.

D. Valente, S. Portolan, G. Nogues, J.-P. Poizat, M. Richard, J.-M. Gérard, M. Santos, and A. Auffèves, “Monitoring stimulated emission at the single-photon level in one-dimensional atoms,” Phys. Rev. A 85, 023811 (2012).
[Crossref]

D. Valente, Y. Li, J.-P. Poizat, J.-M. Gérard, L. Kwek, M. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[Crossref]

Polman, A.

A. F. Koenderink, A. Alù, and A. Polman, “Nanophotonics: shrinking light-based technology,” Science 348, 516–521 (2015).
[Crossref] [PubMed]

Portolan, S.

D. Valente, S. Portolan, G. Nogues, J.-P. Poizat, M. Richard, J.-M. Gérard, M. Santos, and A. Auffèves, “Monitoring stimulated emission at the single-photon level in one-dimensional atoms,” Phys. Rev. A 85, 023811 (2012).
[Crossref]

Rauschenbeutel, A.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473 (2017).
[Crossref] [PubMed]

Reinhold, P.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “Implementing a universal gate set on a logical qubit encoded in an oscillator,” Nat. Commun. 8, 94 (2017).
[Crossref] [PubMed]

Rephaeli, E.

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[Crossref] [PubMed]

Richard, M.

D. Valente, S. Portolan, G. Nogues, J.-P. Poizat, M. Richard, J.-M. Gérard, M. Santos, and A. Auffèves, “Monitoring stimulated emission at the single-photon level in one-dimensional atoms,” Phys. Rev. A 85, 023811 (2012).
[Crossref]

Roy, D.

D. Roy, C. M. Wilson, and O. Firstenberg, “Colloquium: Strongly interacting photons in one-dimensional continuum,” Rev. Mod. Phys. 89, 021001 (2017).
[Crossref]

Santos, M.

E. Mascarenhas, M. Santos, A. Auffèves, and D. Gerace, “Quantum rectifier in a one-dimensional photonic channel,” Phys. Rev. A 93, 043821 (2016).
[Crossref]

D. Valente, Y. Li, J.-P. Poizat, J.-M. Gérard, L. Kwek, M. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[Crossref]

D. Valente, S. Portolan, G. Nogues, J.-P. Poizat, M. Richard, J.-M. Gérard, M. Santos, and A. Auffèves, “Monitoring stimulated emission at the single-photon level in one-dimensional atoms,” Phys. Rev. A 85, 023811 (2012).
[Crossref]

Schneeweiss, P.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473 (2017).
[Crossref] [PubMed]

Schoelkopf, R. J.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “Implementing a universal gate set on a logical qubit encoded in an oscillator,” Nat. Commun. 8, 94 (2017).
[Crossref] [PubMed]

Senellart, P.

P. Senellart, G. Solomon, and A. White, “High-performance semiconductor quantum-dot single-photon sources,” Nat. Nanotechnol. 12, 1026 (2017).
[Crossref] [PubMed]

Shankar, R.

R. Shankar, Principles of Quantum Mechanics (Springer Science & Business Media, 2012).

Silberfarb, A.

A. Silberfarb and I. H. Deutsch, “Continuous measurement with traveling-wave probes,” Phys. Rev. A 68, 013817 (2003).
[Crossref]

Simmet, T.

K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, C. Dory, J. J. Finley, J. Vučković, and K. Müller, “Signatures of two-photon pulses from a quantum two-level system,” Nat. Phys. 13, 649 (2017).
[Crossref]

Solomon, G.

P. Senellart, G. Solomon, and A. White, “High-performance semiconductor quantum-dot single-photon sources,” Nat. Nanotechnol. 12, 1026 (2017).
[Crossref] [PubMed]

Steffen, L.

C. Lang, C. Eichler, L. Steffen, J. Fink, M. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in hong–ou–mandel experiments at microwave frequencies,” Nat. Phys. 9, 345 (2013).
[Crossref]

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

Stobbe, S.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473 (2017).
[Crossref] [PubMed]

Tara, K.

G. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492 (1991).
[Crossref] [PubMed]

Valente, D.

D. Valente, Y. Li, J.-P. Poizat, J.-M. Gérard, L. Kwek, M. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[Crossref]

D. Valente, S. Portolan, G. Nogues, J.-P. Poizat, M. Richard, J.-M. Gérard, M. Santos, and A. Auffèves, “Monitoring stimulated emission at the single-photon level in one-dimensional atoms,” Phys. Rev. A 85, 023811 (2012).
[Crossref]

Volz, J.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473 (2017).
[Crossref] [PubMed]

Vuckovic, J.

K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, C. Dory, J. J. Finley, J. Vučković, and K. Müller, “Signatures of two-photon pulses from a quantum two-level system,” Nat. Phys. 13, 649 (2017).
[Crossref]

Wallraff, A.

C. Lang, C. Eichler, L. Steffen, J. Fink, M. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in hong–ou–mandel experiments at microwave frequencies,” Nat. Phys. 9, 345 (2013).
[Crossref]

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

White, A.

P. Senellart, G. Solomon, and A. White, “High-performance semiconductor quantum-dot single-photon sources,” Nat. Nanotechnol. 12, 1026 (2017).
[Crossref] [PubMed]

Wierzbowski, J.

K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, C. Dory, J. J. Finley, J. Vučković, and K. Müller, “Signatures of two-photon pulses from a quantum two-level system,” Nat. Phys. 13, 649 (2017).
[Crossref]

Wilson, C. M.

D. Roy, C. M. Wilson, and O. Firstenberg, “Colloquium: Strongly interacting photons in one-dimensional continuum,” Rev. Mod. Phys. 89, 021001 (2017).
[Crossref]

Wiseman, H. M.

L. Li, M. J. Hall, and H. M. Wiseman, “Concepts of quantum non-markovianity: a hierarchy,” (2018), in press.

Woolley, M.

C. Lang, C. Eichler, L. Steffen, J. Fink, M. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in hong–ou–mandel experiments at microwave frequencies,” Nat. Phys. 9, 345 (2013).
[Crossref]

Xu, S.

S. Xu and S. Fan, “Input-output formalism for few-photon transport: A systematic treatment beyond two photons,” Phys. Rev. A 91, 043845 (2015).
[Crossref]

Zhang, G.

Y. Pan, D. Dong, and G. Zhang, “Exact analysis of the response of quantum systems to two-photons using a QSDE approach,” New J. Phys. 18, 033004 (2016).
[Crossref]

Zhang, M.

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

Zoller, P.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473 (2017).
[Crossref] [PubMed]

C. Gardiner, A. Parkins, and P. Zoller, “Wave-function quantum stochastic differential equations and quantum-jump simulation methods,” Phys. Rev. A 46, 4363 (1992).
[Crossref] [PubMed]

C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, vol. 56 (Springer Science & Business Media, 2004).

J. Math. Phys. (1)

J. Gough, “Quantum stratonovich calculus and the quantum Wong-Zakai theorem,” J. Math. Phys. 47, 113509 (2006).
[Crossref]

Nat. Commun. (1)

R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “Implementing a universal gate set on a logical qubit encoded in an oscillator,” Nat. Commun. 8, 94 (2017).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

P. Senellart, G. Solomon, and A. White, “High-performance semiconductor quantum-dot single-photon sources,” Nat. Nanotechnol. 12, 1026 (2017).
[Crossref] [PubMed]

Nat. Photonics (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222 (2011).
[Crossref]

Nat. Phys. (3)

C. Lang, C. Eichler, L. Steffen, J. Fink, M. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in hong–ou–mandel experiments at microwave frequencies,” Nat. Phys. 9, 345 (2013).
[Crossref]

C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, “On-demand quantum state transfer and entanglement between remote microwave cavity memories,” Nat. Phys. 14, 705 (2018).
[Crossref]

K. A. Fischer, L. Hanschke, J. Wierzbowski, T. Simmet, C. Dory, J. J. Finley, J. Vučković, and K. Müller, “Signatures of two-photon pulses from a quantum two-level system,” Nat. Phys. 13, 649 (2017).
[Crossref]

Nature (1)

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473 (2017).
[Crossref] [PubMed]

New J. Phys. (3)

D. Valente, Y. Li, J.-P. Poizat, J.-M. Gérard, L. Kwek, M. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[Crossref]

Y. Pan, D. Dong, and G. Zhang, “Exact analysis of the response of quantum systems to two-photons using a QSDE approach,” New J. Phys. 18, 033004 (2016).
[Crossref]

A. Nysteen, P. T. Kristensen, D. P. McCutcheon, P. Kaer, and J. Mørk, “Scattering of two photons on a quantum emitter in a one-dimensional waveguide: exact dynamics and induced correlations,” New J. Phys. 17, 023030 (2015).
[Crossref]

Phys. Rep. (1)

X. Gu, A. F. Kockum, A. Miranowicz, Y. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
[Crossref]

Phys. Rev. A (9)

C. Gardiner and M. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761 (1985).
[Crossref]

C. Gardiner, A. Parkins, and P. Zoller, “Wave-function quantum stochastic differential equations and quantum-jump simulation methods,” Phys. Rev. A 46, 4363 (1992).
[Crossref] [PubMed]

E. Mascarenhas, M. Santos, A. Auffèves, and D. Gerace, “Quantum rectifier in a one-dimensional photonic channel,” Phys. Rev. A 93, 043821 (2016).
[Crossref]

G. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492 (1991).
[Crossref] [PubMed]

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

S. Xu and S. Fan, “Input-output formalism for few-photon transport: A systematic treatment beyond two photons,” Phys. Rev. A 91, 043845 (2015).
[Crossref]

B. Mollow, “Stimulated emission and absorption near resonance for driven systems,” Phys. Rev. A 5, 2217 (1972).
[Crossref]

D. Valente, S. Portolan, G. Nogues, J.-P. Poizat, M. Richard, J.-M. Gérard, M. Santos, and A. Auffèves, “Monitoring stimulated emission at the single-photon level in one-dimensional atoms,” Phys. Rev. A 85, 023811 (2012).
[Crossref]

A. Silberfarb and I. H. Deutsch, “Continuous measurement with traveling-wave probes,” Phys. Rev. A 68, 013817 (2003).
[Crossref]

Phys. Rev. Lett. (3)

J. Gambetta, A. Houck, and A. Blais, “Superconducting qubit with Purcell protection and tunable coupling,” Phys. Rev. Lett. 106, 030502 (2011).
[Crossref] [PubMed]

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. Fink, A. Abdumalikov, M. Baur, S. Filipp, M. Da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[Crossref] [PubMed]

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

D. Roy, C. M. Wilson, and O. Firstenberg, “Colloquium: Strongly interacting photons in one-dimensional continuum,” Rev. Mod. Phys. 89, 021001 (2017).
[Crossref]

Science (1)

A. F. Koenderink, A. Alù, and A. Polman, “Nanophotonics: shrinking light-based technology,” Science 348, 516–521 (2015).
[Crossref] [PubMed]

Other (6)

H. J. Carmichael, Statistical Methods in Quantum Optics 2: Non-Classical Fields (Springer Science & Business Media, 2009).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, 1998) p. 678.

R. Shankar, Principles of Quantum Mechanics (Springer Science & Business Media, 2012).

L. Li, M. J. Hall, and H. M. Wiseman, “Concepts of quantum non-markovianity: a hierarchy,” (2018), in press.

R. Loudon, The Quantum Theory of Light (OUPOxford, 2000).

C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, vol. 56 (Springer Science & Business Media, 2004).

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Figures (4)

Fig. 1
Fig. 1 Illustration of stimulated emission from a two-level system, initially prepared in its excited state |e〉 and coupled to a unidirectional (chiral) waveguide at rate γ. A Fock state |nξ〉 has the potential to stimulate emission of a photon from a two-level system into the mode ξ. A coherent pulse driving the two-level atom cannot be thought of as stimulating emission into the same mode as the pulse.
Fig. 2
Fig. 2 Probability for an n photon Fock state in an exponentially decaying mode ξ with length τ to stimulate emission from a quantum two-level system. Dashed line shows idealized model for large photon number and short pulses.
Fig. 3
Fig. 3 Rabi oscillations of a quantum between the two-level system and a stimulated Fock mode, as seen in the probabilities Pstim(t) = |〈n+ 1 ξ , g|U(t)|nξ, e〉|2 and P0(t) = |〈nξ, e|U(t)|nξ, e〉|2. The driving Fock mode has a pulse width τ = 0.01/γ. (a)–(d) show drive by Fock states of different photon number.
Fig. 4
Fig. 4 We defined the probability of stimulated emission as Pstim = |〈n + 1 ξ , g|S|nξ, e〉|2, however, the projection onto a different Fock mode than the incident one could potentially be larger. Here, we consider Projection = |〈n + 1ξ,τ′, g|S|nξ,τ, e〉|2 where the state is driven by a pulse of width τ = 1/3γ, but the pulse width τ′ of the state projected onto is variable.

Equations (39)

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H atom = ω 0 σ σ
H EM = i d t b ( t ) t b ( t )
V ( t ) = i γ ( σ b ˜ ( t ) σ b ˜ ( t ) ) ;
d U ( t ) = i V ( t ) ° U ( t ) .
d U ( t ) = ( γ σ d B t γ σ d B t γ 2 σ σ d t ) U ( t )
U ( t ) = 𝒯 exp ( 0 t { γ σ d B t γ σ d B t γ 2 σ σ d t } )
| n ξ = ( d s ξ ( s ) b ˜ ( s ) ) n ξ | vac / n ξ ! .
P stim ( t ) = | n + 1 ξ , g | U ( t ) | n ξ , e | 2 .
P stim ( t ) = | n + 1 ξ , g | [ p = 1 0 t t 1 t t p 1 t e γ σ σ t p / 2 × Π i = 1 p e γ σ σ t i / 2 ( γ σ d B t i γ σ d B t i ) e γ σ σ t i / 2 ] | n ξ , e | 2
= | n + 1 ξ | [ p = 0 n ξ ( 1 ) p 0 t t 1 t t 2 p t e γ t 2 p + 1 / 2 γ d B t 2 p + 1 × Π i = 1 p e γ ( t 2 i t 2 i 1 ) / 2 γ d B t 2 i d B t 2 i 1 ] | n ξ | 2
= | p = 0 n ξ ( 1 ) p n ξ + 1 n ξ ! ( n ξ p ) ! F p ( t ) ( γ ) 2 p + 1 | 2
F p ( t ) = 0 t t 1 t t 2 p t ξ * ( t 2 p + 1 ) e γ t 2 p + 1 / 2 d t 2 p + 1 × i = 1 p ξ ( t 2 i ) ξ * ( t 2 i 1 ) e γ ( t 2 i t 2 i 1 ) / 2 d t 2 i d t 2 i 1 ,
P stim = | n + 1 ξ , g | S | n ξ , e | 2 ,
ξ ( t ) = e t / 2 τ Θ ( t ) / τ ,
lim t F p ( t ) 2 p + 1 p ! ( τ ) 2 p + 1 k = 0 p ( 2 k + 1 + γ τ ) .
n ξ + 1 n ξ ! ( n ξ p ) ! ( n ξ ) 2 p + 1
lim t F p ( t ) ( 4 τ ) 2 p + 1 ( 2 p + 1 ) !
P stim sin 2 ( 4 γ τ n ξ ) .
| Ψ scatter = S | n ξ , e
= e i ϕ stim P stim | ψ stim + P 0 | ψ other
| ψ other = d s 1 d s 2 d s n ξ + 1 ζ ( s 1 , s 2 , , s n ξ + 1 ) b ˜ ( s 1 ) b ˜ ( s 2 ) b ˜ ( s n ξ + 1 ) | vac , g / ( n ξ + 1 ) !
| ψ other γ d s e γ s / 2 b ( s ) | n ξ , g / n ξ + 1
P 0 = | n ξ , e | U ( T ) | n ξ , e | 2
cos 2 ( 4 γ τ n ξ )
F p ( t ) 4 τ 2 p + 1 ( 2 p + 1 ) ! e 2 p + 1 2 τ t ( 1 + e t / 2 τ ) 2 p + 1
P 0 ( t ) = | n ξ , e | U ( t ) | n ξ , e | 2
= | p = 0 n ξ ( 1 ) p n ξ ! ( n ξ p ) ! G p ( t ) ( γ ) 2 p | 2
G p ( t ) 4 τ 2 p ( 2 p ) ! e 2 p 2 τ t ( 1 + e t / 2 τ ) 2 p .
| α = exp ( { α ( s ) b ˜ ( s ) α * ( s ) b ˜ ( s ) } d s ) | vac ,
d B t | α = d t α ( t ) | α .
β | ψ ( t ) = β | U ( t ) | α | e
β | ψ ( t ) = 𝒯 e 0 t { γ β * ( t ) σ γ α ( t ) σ γ 2 σ σ } d t | e β | α .
Ψ scatter ( τ 1 , τ 2 ) = γ 3 ( e 3 γ τ 1 + γ τ 2 2 Θ ( 0 τ 2 τ 1 ) + e 3 γ τ 2 + γ τ 1 2 Θ ( 0 τ 1 τ 2 ) ) .
ψ Fock ( s 1 , s 2 ) = 1 τ 2 e s 1 + s 2 2 τ Θ ( s 1 ) Θ ( s 2 )
Projection = | ψ Fock | Ψ scatter | 2
= d s 1 d s 2 ( ψ Fock * ( s 1 , s 2 ) Ψ scatter ( s 1 , s 2 ) + ψ Fock * ( s 1 , s 2 ) Ψ scatter ( s 2 , s 1 ) ) .
ξ ( t ) = 1 / T Θ ( 0 t < T ) ,
P stim ( t ) sin 2 ( t γ T n ξ ) Θ ( 0 t < T ) + sin 2 ( γ T n ξ ) Θ ( T t )
P 0 ( t ) cos 2 ( t γ T n ξ ) Θ ( 0 t < T ) + cos 2 ( γ T n ξ ) Θ ( T t ) .

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