Abstract

We show that detection of single photons is not subject to the fundamental limitations that accompany quantum linear amplification of bosonic mode amplitudes, even though a photodetector does amplify a few-photon input signal to a macroscopic output signal. Alternative limits are derived for nonlinear photon-number amplification schemes with optimistic implications for single-photon detection. Four commutator-preserving transformations are presented: one idealized (which is optimal) and three more realistic (less than optimal). Our description makes clear that nonlinear amplification takes place, in general, at a different frequency ω′ than the frequency ω of the input photons. This can be exploited to suppress thermal noise and dark counts past what is possible with linear amplification up to a fundamental limit imposed by nonlinear amplification into a single bosonic mode.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Improved analog optical link performance with quantum phase amplification

Roy S. Bondurant
Opt. Lett. 25(9) 649-650 (2000)

Overcoming the diffraction limit by multi-photon interference: a tutorial

Joachim Stöhr
Adv. Opt. Photon. 11(1) 215-313 (2019)

References

  • View by:
  • |
  • |
  • |

  1. C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817–1839 (1982).
    [Crossref]
  2. This could be a mode internal to the detector.
  3. A. Metelmann and A. Clerk, “Quantum-Limited Amplification via Reservoir Engineering,” Phys. Rev. Lett. 112, 133904 (2014).
    [Crossref] [PubMed]
  4. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement, and amplification,” Rev. Mod. Phys. 82, 1155–1208 (2010).
    [Crossref]
  5. U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
    [Crossref]
  6. L.-P. Yang and Z. Jacob, “Quantum critical detector: amplifying weak signals using discontinuous quantum phase transitions,” Opt. Express 27, 10482–10494 (2019).
    [Crossref] [PubMed]
  7. S. M. Young, M. Sarovar, and F. Léonard, “General modeling framework for quantum photodetectors,” Phys. Rev. A 98, 063835 (2018).
    [Crossref]
  8. S. M. Young, M. Sarovar, and F. Léonard, “Fundamental limits to single-photon detection determined by quantum coherence and backaction,” Phys. Rev. A 97, 033836 (2018).
    [Crossref]
  9. S. J. van Enk, “Photodetector figures of merit in terms of POVMs,” J. Phys. Comm. 1, 045001 (2017).
    [Crossref]
  10. E. S. Matekole, H. Lee, and J. P. Dowling, “Limits to atom-vapor-based room-temperature photon-number-resolving detection,” Phys. Rev. A 98, 033829 (2018).
    [Crossref]
  11. F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
    [Crossref]
  12. E. E. Wollman, V. B. Verma, A. D. Beyer, R. M. Briggs, B. Korzh, J. P. Allmaras, F. Marsili, A. E. Lita, R. Mirin, and S. Nam, “UV superconducting nanowire single-photon detectors with high efficiency, low noise, and 4K operating temperature,” Opt. Express 25, 26792–26801 (2017).
    [Crossref] [PubMed]
  13. H. P. Yuen, “Generation, detection, and application of high-intensity photon-number-eigenstate fields,” Phys. Rev. Lett. 56, 2176–2179 (1986).
    [Crossref] [PubMed]
  14. S.-T. Ho and H. P. Yuen, “Scheme for realizing a photon number amplifier,” Opt. Lett. 19, 61–63 (1994).
    [Crossref] [PubMed]
  15. H. P. Yuen, “Quantum amplifiers, quantum duplicators and quantum cryptography,” Quantum Semiclass. Opt.: J. Eur. Opt. Soc. Part B 8, 939 (1996).
    [Crossref]
  16. G. D’Ariano, “Hamiltonians for the photon-number-phase amplifiers,” Phys. Rev. A 45, 3224–3227 (1992).
    [Crossref]
  17. G. D’Ariano, C. Macchiavello, N. Sterpi, and H. Yuen, “Quantum phase amplification,” Phys. Rev. A 54, 4712–4718 (1996).
    [Crossref]
  18. G. Björk, J. Söderholm, and A. Karlsson, “Superposition-preserving photon-number amplifier,” Phys. Rev. A 57, 650–658 (1998).
    [Crossref]
  19. The transformation in Eq. (2) can be realized only when M ≥ Gn. There is always such a restriction on amplification relations; the energy transferred to reservoir 2 must come from somewhere.
  20. H. G. Dehmelt, “Proposed 1014 δv<v laser fluorescence spectroscopy on Tl + ion mono-oscillator II,” Bull. Am. Phys. Soc. 20, 60 (1975).
  21. D. Wineland, J. Bergquist, W. M. Itano, and R. Drullinger, “Double-resonance and optical-pumping experiments on electromagnetically confined, laser-cooled ions,” Opt. Lett. 5, 245–247 (1980).
    [Crossref] [PubMed]
  22. J. Bergquist, R. G. Hulet, W. M. Itano, and D. Wineland, “Observation of quantum jumps in a single atom,” Phys. Rev. Lett. 57, 1699–1702 (1986).
    [Crossref] [PubMed]
  23. The construction of physically implementable transformations such as Eq. (3) (and transformations including higher powers of the input photon number operator) are highly constrained by two conditions: that the spectrum of the operator-representation be ℕ0 (the natural numbers including zero) and that the commutator be preserved [14]. From these conditions, in Eq. (3) we need at least one term with a number operator on the right with a prefactor of one. Additional reservoirs with arbitrary prefactors are allowed but they will carry additional noise and decrease the SNR.
  24. Phase randomization is necessary for optimal amplification and measurement of photon number due to number-phase uncertainty. Indeed, amplification of photon number deamplifies phase and vice versa, see [17].
  25. D. Pegg and S. Barnett, “Phase properties of the quantized single-mode electromagnetic field,” Phys. Rev. A 39, 1665–1675 (1989).
    [Crossref]
  26. Note the dimension of both input and output mode Hilbert spaces are s + 1; they necessarily match in the Heisenberg picture.
  27. C. M. Caves, J. Combes, Z. Jiang, and S. Pandey, “Quantum limits on phase-preserving linear amplifiers,” Phys. Rev. A 86, 063802 (2012).
    [Crossref]
  28. R. Nehra, C.-H. Chang, A. Beling, and O. Pfister, “Photon-number-resolving segmented avalanche-photodiode detectors,” e-print arXiv:1708.09015 [physics.ins-det] (2017).
  29. Q. Yu, K. Sun, Q. Li, and A. Beling, “Segmented waveguide photodetector with 90% quantum efficiency,” Opt. Express 26, 12499–12505 (2018).
    [Crossref] [PubMed]
  30. L. V. Keldysh and A. N. Kozlov, “Collective properties of excitons in semiconductors,” Sov. Phys. JETP 27, 521–528 (1968).
  31. M. H. Devoret and R. J. Schoelkopf, “Amplifying quantum signals with the single-electron transistor,” Nature 406, 1039–1046 (2000).
    [Crossref] [PubMed]
  32. B. Laikhtman, “Are excitons really bosons?” J. Phys.: Condens. Matter 19, 295214 (2007).
  33. M. Combescot, O. Betbeder-Matibet, and R. Combescot, “Exciton-exciton scattering: Composite boson versus elementary boson,” Phys. Rev. B 75, 174305 (2007).
    [Crossref]
  34. One way around this limitation is for the incident photons to only interact with a single symmetrized collective degree of freedom of many fermions, on which a measurement is then made. In this idealized case, this collective degree of freedom plays the role of a single bosonic mode and amplification could still be described by Eq. (5) and photon number amplification is improved past the limit for linear fermionic amplification [5].
  35. The signal-to-noise ratios Eqs. (22) and (23) for linear amplification become infinite at G = 1 simply because there is no noise when both G = 1 and Δna = 0.
  36. We find the linear dependence on G resulting from single-shot single-mode amplification holds for transformations describing higher-order amplification of photon number operator, again subject to the constraints of [23].
  37. The space is further filled in by considering nonlinear amplification where G excitations are distributed into G′ > G modes so that ancillary modes contribute only to the noise and not to the signal. In this case, we find that the SNR goes to 0 as G′ → ∞; the effect of additional noise modes is always to reduce the SNR and move us away from the optimal SNR in Eq. (24).
  38. Photon-number resolved photo detection can be achieved by multiplexing an n-photon signal to many (N ≫ n) single photon detectors [28], each satisfying Eq. (28) independently. However, this means an additional noise mode will be added with each splitting of the signal, decreasing the integrated signal-to-noise ratio. To avoid added noise a nonlinear multi-photon filtering process could be used, but for this a full S-matrix treatment must be used, see [45–47].
  39. See, for example, [48]. The result is that, instead of certain frequencies, it is certain spectral “Schmidt modes” that are detected perfectly.
  40. Tz. B. Propp and S. J. van Enk, “Quantum networks for single photon detection,” e-print arXiv:1901.09974 [quant-ph] (2019).
  41. J. Dowling. Private communication.
  42. Tz. B. Propp and S. J. van Enk, “POVMs for photo detection,” in preparation.
  43. M. S. Ünlü and S. Strite, “Resonant cavity enhanced photonic devices,” J. Appl. Phys. 78, 607–639 (1995).
    [Crossref]
  44. A. Imamoḡlu, “High efficiency photon counting using stored light,” Phys. Rev. Lett. 89, 163602 (2002).
    [Crossref]

2019 (1)

2018 (4)

S. M. Young, M. Sarovar, and F. Léonard, “General modeling framework for quantum photodetectors,” Phys. Rev. A 98, 063835 (2018).
[Crossref]

S. M. Young, M. Sarovar, and F. Léonard, “Fundamental limits to single-photon detection determined by quantum coherence and backaction,” Phys. Rev. A 97, 033836 (2018).
[Crossref]

E. S. Matekole, H. Lee, and J. P. Dowling, “Limits to atom-vapor-based room-temperature photon-number-resolving detection,” Phys. Rev. A 98, 033829 (2018).
[Crossref]

Q. Yu, K. Sun, Q. Li, and A. Beling, “Segmented waveguide photodetector with 90% quantum efficiency,” Opt. Express 26, 12499–12505 (2018).
[Crossref] [PubMed]

2017 (2)

2014 (1)

A. Metelmann and A. Clerk, “Quantum-Limited Amplification via Reservoir Engineering,” Phys. Rev. Lett. 112, 133904 (2014).
[Crossref] [PubMed]

2013 (1)

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

2012 (1)

C. M. Caves, J. Combes, Z. Jiang, and S. Pandey, “Quantum limits on phase-preserving linear amplifiers,” Phys. Rev. A 86, 063802 (2012).
[Crossref]

2010 (1)

A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement, and amplification,” Rev. Mod. Phys. 82, 1155–1208 (2010).
[Crossref]

2007 (2)

B. Laikhtman, “Are excitons really bosons?” J. Phys.: Condens. Matter 19, 295214 (2007).

M. Combescot, O. Betbeder-Matibet, and R. Combescot, “Exciton-exciton scattering: Composite boson versus elementary boson,” Phys. Rev. B 75, 174305 (2007).
[Crossref]

2004 (1)

U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
[Crossref]

2002 (1)

A. Imamoḡlu, “High efficiency photon counting using stored light,” Phys. Rev. Lett. 89, 163602 (2002).
[Crossref]

2000 (1)

M. H. Devoret and R. J. Schoelkopf, “Amplifying quantum signals with the single-electron transistor,” Nature 406, 1039–1046 (2000).
[Crossref] [PubMed]

1998 (1)

G. Björk, J. Söderholm, and A. Karlsson, “Superposition-preserving photon-number amplifier,” Phys. Rev. A 57, 650–658 (1998).
[Crossref]

1996 (2)

H. P. Yuen, “Quantum amplifiers, quantum duplicators and quantum cryptography,” Quantum Semiclass. Opt.: J. Eur. Opt. Soc. Part B 8, 939 (1996).
[Crossref]

G. D’Ariano, C. Macchiavello, N. Sterpi, and H. Yuen, “Quantum phase amplification,” Phys. Rev. A 54, 4712–4718 (1996).
[Crossref]

1995 (1)

M. S. Ünlü and S. Strite, “Resonant cavity enhanced photonic devices,” J. Appl. Phys. 78, 607–639 (1995).
[Crossref]

1994 (1)

1992 (1)

G. D’Ariano, “Hamiltonians for the photon-number-phase amplifiers,” Phys. Rev. A 45, 3224–3227 (1992).
[Crossref]

1989 (1)

D. Pegg and S. Barnett, “Phase properties of the quantized single-mode electromagnetic field,” Phys. Rev. A 39, 1665–1675 (1989).
[Crossref]

1986 (2)

J. Bergquist, R. G. Hulet, W. M. Itano, and D. Wineland, “Observation of quantum jumps in a single atom,” Phys. Rev. Lett. 57, 1699–1702 (1986).
[Crossref] [PubMed]

H. P. Yuen, “Generation, detection, and application of high-intensity photon-number-eigenstate fields,” Phys. Rev. Lett. 56, 2176–2179 (1986).
[Crossref] [PubMed]

1982 (1)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817–1839 (1982).
[Crossref]

1980 (1)

1975 (1)

H. G. Dehmelt, “Proposed 1014 δv<v laser fluorescence spectroscopy on Tl + ion mono-oscillator II,” Bull. Am. Phys. Soc. 20, 60 (1975).

1968 (1)

L. V. Keldysh and A. N. Kozlov, “Collective properties of excitons in semiconductors,” Sov. Phys. JETP 27, 521–528 (1968).

Allmaras, J. P.

Baek, B.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Barnett, S.

D. Pegg and S. Barnett, “Phase properties of the quantized single-mode electromagnetic field,” Phys. Rev. A 39, 1665–1675 (1989).
[Crossref]

Beling, A.

Q. Yu, K. Sun, Q. Li, and A. Beling, “Segmented waveguide photodetector with 90% quantum efficiency,” Opt. Express 26, 12499–12505 (2018).
[Crossref] [PubMed]

R. Nehra, C.-H. Chang, A. Beling, and O. Pfister, “Photon-number-resolving segmented avalanche-photodiode detectors,” e-print arXiv:1708.09015 [physics.ins-det] (2017).

Bergquist, J.

Betbeder-Matibet, O.

M. Combescot, O. Betbeder-Matibet, and R. Combescot, “Exciton-exciton scattering: Composite boson versus elementary boson,” Phys. Rev. B 75, 174305 (2007).
[Crossref]

Beyer, A. D.

Björk, G.

G. Björk, J. Söderholm, and A. Karlsson, “Superposition-preserving photon-number amplifier,” Phys. Rev. A 57, 650–658 (1998).
[Crossref]

Briggs, R. M.

Caves, C. M.

C. M. Caves, J. Combes, Z. Jiang, and S. Pandey, “Quantum limits on phase-preserving linear amplifiers,” Phys. Rev. A 86, 063802 (2012).
[Crossref]

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817–1839 (1982).
[Crossref]

Chang, C.-H.

R. Nehra, C.-H. Chang, A. Beling, and O. Pfister, “Photon-number-resolving segmented avalanche-photodiode detectors,” e-print arXiv:1708.09015 [physics.ins-det] (2017).

Clerk, A.

A. Metelmann and A. Clerk, “Quantum-Limited Amplification via Reservoir Engineering,” Phys. Rev. Lett. 112, 133904 (2014).
[Crossref] [PubMed]

Clerk, A. A.

A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement, and amplification,” Rev. Mod. Phys. 82, 1155–1208 (2010).
[Crossref]

Combes, J.

C. M. Caves, J. Combes, Z. Jiang, and S. Pandey, “Quantum limits on phase-preserving linear amplifiers,” Phys. Rev. A 86, 063802 (2012).
[Crossref]

Combescot, M.

M. Combescot, O. Betbeder-Matibet, and R. Combescot, “Exciton-exciton scattering: Composite boson versus elementary boson,” Phys. Rev. B 75, 174305 (2007).
[Crossref]

Combescot, R.

M. Combescot, O. Betbeder-Matibet, and R. Combescot, “Exciton-exciton scattering: Composite boson versus elementary boson,” Phys. Rev. B 75, 174305 (2007).
[Crossref]

D’Ariano, G.

G. D’Ariano, C. Macchiavello, N. Sterpi, and H. Yuen, “Quantum phase amplification,” Phys. Rev. A 54, 4712–4718 (1996).
[Crossref]

G. D’Ariano, “Hamiltonians for the photon-number-phase amplifiers,” Phys. Rev. A 45, 3224–3227 (1992).
[Crossref]

Dehmelt, H. G.

H. G. Dehmelt, “Proposed 1014 δv<v laser fluorescence spectroscopy on Tl + ion mono-oscillator II,” Bull. Am. Phys. Soc. 20, 60 (1975).

Devoret, M. H.

A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement, and amplification,” Rev. Mod. Phys. 82, 1155–1208 (2010).
[Crossref]

M. H. Devoret and R. J. Schoelkopf, “Amplifying quantum signals with the single-electron transistor,” Nature 406, 1039–1046 (2000).
[Crossref] [PubMed]

Dowling, J. P.

E. S. Matekole, H. Lee, and J. P. Dowling, “Limits to atom-vapor-based room-temperature photon-number-resolving detection,” Phys. Rev. A 98, 033829 (2018).
[Crossref]

Dowling., J.

J. Dowling. Private communication.

Drullinger, R.

Gavish, U.

U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
[Crossref]

Gerrits, T.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Girvin, S. M.

A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement, and amplification,” Rev. Mod. Phys. 82, 1155–1208 (2010).
[Crossref]

Harrington, S.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Ho, S.-T.

Hulet, R. G.

J. Bergquist, R. G. Hulet, W. M. Itano, and D. Wineland, “Observation of quantum jumps in a single atom,” Phys. Rev. Lett. 57, 1699–1702 (1986).
[Crossref] [PubMed]

Imamo?lu, A.

A. Imamoḡlu, “High efficiency photon counting using stored light,” Phys. Rev. Lett. 89, 163602 (2002).
[Crossref]

Imry, Y.

U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
[Crossref]

Itano, W. M.

Jacob, Z.

Jiang, Z.

C. M. Caves, J. Combes, Z. Jiang, and S. Pandey, “Quantum limits on phase-preserving linear amplifiers,” Phys. Rev. A 86, 063802 (2012).
[Crossref]

Karlsson, A.

G. Björk, J. Söderholm, and A. Karlsson, “Superposition-preserving photon-number amplifier,” Phys. Rev. A 57, 650–658 (1998).
[Crossref]

Keldysh, L. V.

L. V. Keldysh and A. N. Kozlov, “Collective properties of excitons in semiconductors,” Sov. Phys. JETP 27, 521–528 (1968).

Korzh, B.

Kozlov, A. N.

L. V. Keldysh and A. N. Kozlov, “Collective properties of excitons in semiconductors,” Sov. Phys. JETP 27, 521–528 (1968).

Laikhtman, B.

B. Laikhtman, “Are excitons really bosons?” J. Phys.: Condens. Matter 19, 295214 (2007).

Lee, H.

E. S. Matekole, H. Lee, and J. P. Dowling, “Limits to atom-vapor-based room-temperature photon-number-resolving detection,” Phys. Rev. A 98, 033829 (2018).
[Crossref]

Léonard, F.

S. M. Young, M. Sarovar, and F. Léonard, “Fundamental limits to single-photon detection determined by quantum coherence and backaction,” Phys. Rev. A 97, 033836 (2018).
[Crossref]

S. M. Young, M. Sarovar, and F. Léonard, “General modeling framework for quantum photodetectors,” Phys. Rev. A 98, 063835 (2018).
[Crossref]

Li, Q.

Lita, A.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Lita, A. E.

Macchiavello, C.

G. D’Ariano, C. Macchiavello, N. Sterpi, and H. Yuen, “Quantum phase amplification,” Phys. Rev. A 54, 4712–4718 (1996).
[Crossref]

Marquardt, F.

A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement, and amplification,” Rev. Mod. Phys. 82, 1155–1208 (2010).
[Crossref]

Marsili, F.

E. E. Wollman, V. B. Verma, A. D. Beyer, R. M. Briggs, B. Korzh, J. P. Allmaras, F. Marsili, A. E. Lita, R. Mirin, and S. Nam, “UV superconducting nanowire single-photon detectors with high efficiency, low noise, and 4K operating temperature,” Opt. Express 25, 26792–26801 (2017).
[Crossref] [PubMed]

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Matekole, E. S.

E. S. Matekole, H. Lee, and J. P. Dowling, “Limits to atom-vapor-based room-temperature photon-number-resolving detection,” Phys. Rev. A 98, 033829 (2018).
[Crossref]

Metelmann, A.

A. Metelmann and A. Clerk, “Quantum-Limited Amplification via Reservoir Engineering,” Phys. Rev. Lett. 112, 133904 (2014).
[Crossref] [PubMed]

Mirin, R.

E. E. Wollman, V. B. Verma, A. D. Beyer, R. M. Briggs, B. Korzh, J. P. Allmaras, F. Marsili, A. E. Lita, R. Mirin, and S. Nam, “UV superconducting nanowire single-photon detectors with high efficiency, low noise, and 4K operating temperature,” Opt. Express 25, 26792–26801 (2017).
[Crossref] [PubMed]

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Nam, S.

Nam, S. W.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Nehra, R.

R. Nehra, C.-H. Chang, A. Beling, and O. Pfister, “Photon-number-resolving segmented avalanche-photodiode detectors,” e-print arXiv:1708.09015 [physics.ins-det] (2017).

Pandey, S.

C. M. Caves, J. Combes, Z. Jiang, and S. Pandey, “Quantum limits on phase-preserving linear amplifiers,” Phys. Rev. A 86, 063802 (2012).
[Crossref]

Pegg, D.

D. Pegg and S. Barnett, “Phase properties of the quantized single-mode electromagnetic field,” Phys. Rev. A 39, 1665–1675 (1989).
[Crossref]

Pfister, O.

R. Nehra, C.-H. Chang, A. Beling, and O. Pfister, “Photon-number-resolving segmented avalanche-photodiode detectors,” e-print arXiv:1708.09015 [physics.ins-det] (2017).

Propp, Tz. B.

Tz. B. Propp and S. J. van Enk, “POVMs for photo detection,” in preparation.

Tz. B. Propp and S. J. van Enk, “Quantum networks for single photon detection,” e-print arXiv:1901.09974 [quant-ph] (2019).

Sarovar, M.

S. M. Young, M. Sarovar, and F. Léonard, “Fundamental limits to single-photon detection determined by quantum coherence and backaction,” Phys. Rev. A 97, 033836 (2018).
[Crossref]

S. M. Young, M. Sarovar, and F. Léonard, “General modeling framework for quantum photodetectors,” Phys. Rev. A 98, 063835 (2018).
[Crossref]

Schoelkopf, R. J.

A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement, and amplification,” Rev. Mod. Phys. 82, 1155–1208 (2010).
[Crossref]

M. H. Devoret and R. J. Schoelkopf, “Amplifying quantum signals with the single-electron transistor,” Nature 406, 1039–1046 (2000).
[Crossref] [PubMed]

Shaw, M. D.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Söderholm, J.

G. Björk, J. Söderholm, and A. Karlsson, “Superposition-preserving photon-number amplifier,” Phys. Rev. A 57, 650–658 (1998).
[Crossref]

Stern, J.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Sterpi, N.

G. D’Ariano, C. Macchiavello, N. Sterpi, and H. Yuen, “Quantum phase amplification,” Phys. Rev. A 54, 4712–4718 (1996).
[Crossref]

Strite, S.

M. S. Ünlü and S. Strite, “Resonant cavity enhanced photonic devices,” J. Appl. Phys. 78, 607–639 (1995).
[Crossref]

Sun, K.

Ünlü, M. S.

M. S. Ünlü and S. Strite, “Resonant cavity enhanced photonic devices,” J. Appl. Phys. 78, 607–639 (1995).
[Crossref]

van Enk, S. J.

S. J. van Enk, “Photodetector figures of merit in terms of POVMs,” J. Phys. Comm. 1, 045001 (2017).
[Crossref]

Tz. B. Propp and S. J. van Enk, “POVMs for photo detection,” in preparation.

Tz. B. Propp and S. J. van Enk, “Quantum networks for single photon detection,” e-print arXiv:1901.09974 [quant-ph] (2019).

Vayshenker, I.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Verma, V.

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Verma, V. B.

Wineland, D.

Wollman, E. E.

Yang, L.-P.

Young, S. M.

S. M. Young, M. Sarovar, and F. Léonard, “Fundamental limits to single-photon detection determined by quantum coherence and backaction,” Phys. Rev. A 97, 033836 (2018).
[Crossref]

S. M. Young, M. Sarovar, and F. Léonard, “General modeling framework for quantum photodetectors,” Phys. Rev. A 98, 063835 (2018).
[Crossref]

Yu, Q.

Yuen, H.

G. D’Ariano, C. Macchiavello, N. Sterpi, and H. Yuen, “Quantum phase amplification,” Phys. Rev. A 54, 4712–4718 (1996).
[Crossref]

Yuen, H. P.

H. P. Yuen, “Quantum amplifiers, quantum duplicators and quantum cryptography,” Quantum Semiclass. Opt.: J. Eur. Opt. Soc. Part B 8, 939 (1996).
[Crossref]

S.-T. Ho and H. P. Yuen, “Scheme for realizing a photon number amplifier,” Opt. Lett. 19, 61–63 (1994).
[Crossref] [PubMed]

H. P. Yuen, “Generation, detection, and application of high-intensity photon-number-eigenstate fields,” Phys. Rev. Lett. 56, 2176–2179 (1986).
[Crossref] [PubMed]

Yurke, B.

U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
[Crossref]

Bull. Am. Phys. Soc. (1)

H. G. Dehmelt, “Proposed 1014 δv<v laser fluorescence spectroscopy on Tl + ion mono-oscillator II,” Bull. Am. Phys. Soc. 20, 60 (1975).

J. Appl. Phys. (1)

M. S. Ünlü and S. Strite, “Resonant cavity enhanced photonic devices,” J. Appl. Phys. 78, 607–639 (1995).
[Crossref]

J. Phys. Comm. (1)

S. J. van Enk, “Photodetector figures of merit in terms of POVMs,” J. Phys. Comm. 1, 045001 (2017).
[Crossref]

J. Phys.: Condens. Matter (1)

B. Laikhtman, “Are excitons really bosons?” J. Phys.: Condens. Matter 19, 295214 (2007).

Nat. Photonics (1)

F. Marsili, V. Verma, J. Stern, S. Harrington, A. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Nature (1)

M. H. Devoret and R. J. Schoelkopf, “Amplifying quantum signals with the single-electron transistor,” Nature 406, 1039–1046 (2000).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (8)

D. Pegg and S. Barnett, “Phase properties of the quantized single-mode electromagnetic field,” Phys. Rev. A 39, 1665–1675 (1989).
[Crossref]

C. M. Caves, J. Combes, Z. Jiang, and S. Pandey, “Quantum limits on phase-preserving linear amplifiers,” Phys. Rev. A 86, 063802 (2012).
[Crossref]

E. S. Matekole, H. Lee, and J. P. Dowling, “Limits to atom-vapor-based room-temperature photon-number-resolving detection,” Phys. Rev. A 98, 033829 (2018).
[Crossref]

S. M. Young, M. Sarovar, and F. Léonard, “General modeling framework for quantum photodetectors,” Phys. Rev. A 98, 063835 (2018).
[Crossref]

S. M. Young, M. Sarovar, and F. Léonard, “Fundamental limits to single-photon detection determined by quantum coherence and backaction,” Phys. Rev. A 97, 033836 (2018).
[Crossref]

G. D’Ariano, “Hamiltonians for the photon-number-phase amplifiers,” Phys. Rev. A 45, 3224–3227 (1992).
[Crossref]

G. D’Ariano, C. Macchiavello, N. Sterpi, and H. Yuen, “Quantum phase amplification,” Phys. Rev. A 54, 4712–4718 (1996).
[Crossref]

G. Björk, J. Söderholm, and A. Karlsson, “Superposition-preserving photon-number amplifier,” Phys. Rev. A 57, 650–658 (1998).
[Crossref]

Phys. Rev. B (1)

M. Combescot, O. Betbeder-Matibet, and R. Combescot, “Exciton-exciton scattering: Composite boson versus elementary boson,” Phys. Rev. B 75, 174305 (2007).
[Crossref]

Phys. Rev. D (1)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817–1839 (1982).
[Crossref]

Phys. Rev. Lett. (5)

A. Metelmann and A. Clerk, “Quantum-Limited Amplification via Reservoir Engineering,” Phys. Rev. Lett. 112, 133904 (2014).
[Crossref] [PubMed]

J. Bergquist, R. G. Hulet, W. M. Itano, and D. Wineland, “Observation of quantum jumps in a single atom,” Phys. Rev. Lett. 57, 1699–1702 (1986).
[Crossref] [PubMed]

U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
[Crossref]

H. P. Yuen, “Generation, detection, and application of high-intensity photon-number-eigenstate fields,” Phys. Rev. Lett. 56, 2176–2179 (1986).
[Crossref] [PubMed]

A. Imamoḡlu, “High efficiency photon counting using stored light,” Phys. Rev. Lett. 89, 163602 (2002).
[Crossref]

Quantum Semiclass. Opt.: J. Eur. Opt. Soc. Part B (1)

H. P. Yuen, “Quantum amplifiers, quantum duplicators and quantum cryptography,” Quantum Semiclass. Opt.: J. Eur. Opt. Soc. Part B 8, 939 (1996).
[Crossref]

Rev. Mod. Phys. (1)

A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement, and amplification,” Rev. Mod. Phys. 82, 1155–1208 (2010).
[Crossref]

Sov. Phys. JETP (1)

L. V. Keldysh and A. N. Kozlov, “Collective properties of excitons in semiconductors,” Sov. Phys. JETP 27, 521–528 (1968).

Other (15)

R. Nehra, C.-H. Chang, A. Beling, and O. Pfister, “Photon-number-resolving segmented avalanche-photodiode detectors,” e-print arXiv:1708.09015 [physics.ins-det] (2017).

Note the dimension of both input and output mode Hilbert spaces are s + 1; they necessarily match in the Heisenberg picture.

One way around this limitation is for the incident photons to only interact with a single symmetrized collective degree of freedom of many fermions, on which a measurement is then made. In this idealized case, this collective degree of freedom plays the role of a single bosonic mode and amplification could still be described by Eq. (5) and photon number amplification is improved past the limit for linear fermionic amplification [5].

The signal-to-noise ratios Eqs. (22) and (23) for linear amplification become infinite at G = 1 simply because there is no noise when both G = 1 and Δna = 0.

We find the linear dependence on G resulting from single-shot single-mode amplification holds for transformations describing higher-order amplification of photon number operator, again subject to the constraints of [23].

The space is further filled in by considering nonlinear amplification where G excitations are distributed into G′ > G modes so that ancillary modes contribute only to the noise and not to the signal. In this case, we find that the SNR goes to 0 as G′ → ∞; the effect of additional noise modes is always to reduce the SNR and move us away from the optimal SNR in Eq. (24).

Photon-number resolved photo detection can be achieved by multiplexing an n-photon signal to many (N ≫ n) single photon detectors [28], each satisfying Eq. (28) independently. However, this means an additional noise mode will be added with each splitting of the signal, decreasing the integrated signal-to-noise ratio. To avoid added noise a nonlinear multi-photon filtering process could be used, but for this a full S-matrix treatment must be used, see [45–47].

See, for example, [48]. The result is that, instead of certain frequencies, it is certain spectral “Schmidt modes” that are detected perfectly.

Tz. B. Propp and S. J. van Enk, “Quantum networks for single photon detection,” e-print arXiv:1901.09974 [quant-ph] (2019).

J. Dowling. Private communication.

Tz. B. Propp and S. J. van Enk, “POVMs for photo detection,” in preparation.

This could be a mode internal to the detector.

The construction of physically implementable transformations such as Eq. (3) (and transformations including higher powers of the input photon number operator) are highly constrained by two conditions: that the spectrum of the operator-representation be ℕ0 (the natural numbers including zero) and that the commutator be preserved [14]. From these conditions, in Eq. (3) we need at least one term with a number operator on the right with a prefactor of one. Additional reservoirs with arbitrary prefactors are allowed but they will carry additional noise and decrease the SNR.

Phase randomization is necessary for optimal amplification and measurement of photon number due to number-phase uncertainty. Indeed, amplification of photon number deamplifies phase and vice versa, see [17].

The transformation in Eq. (2) can be realized only when M ≥ Gn. There is always such a restriction on amplification relations; the energy transferred to reservoir 2 must come from somewhere.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1 An input photon with frequency ω undergoes amplification into a macroscopic signal via electron-shelving [20–22]: when an on-resonance photon is absorbed, an atom (modeled here as a three-level system) enters the first excited state and a laser tuned to the second transition frequency ωLω′ induces fluorescence. If there are multiple input photons, they are absorbed by multiple atoms and the fluorescence signal is increased proportionally. The number of fluorescence modes may be reduced by using a high-Q cavity so that amplification moves towards the ideal transformation given in Eq. (2).

Equations (29)

Equations on this page are rendered with MathJax. Learn more.

a ^ out = G a ^ in + G 1 b ^ in + ,
| n a | M 1 | N 2 | n a | M G n 1 | N + G n 2 .
b ^ out + b ^ out = b ^ in + b ^ in + G a ^ in + a ^ in .
| n a | E S | 0 a | E + n ω S .
b ^ out = S ^ ( b ^ + b ^ ) in + G ( a ^ + a ^ ) in ,
S ^ | N = e i ϕ | N 1 for s N > 0 ,
H ^ = i κ ( a ^ b ^ a ^ + b ^ + )
b ^ k out = S ^ k ( b ^ + b ^ ) k in + ( a ^ + a ^ ) in , k = 1 G .
I ^ out = k = 1 G ( b ^ + b ^ ) k out = k = 1 G ( b ^ + b ^ ) k in + G ( a ^ + a ^ ) in .
( b ^ + b ^ ) N out = k = 1 N g N k ( b ^ + b ^ ) k in + G ( a ^ + a ^ ) in
I ^ out = k N = 1 G ( b ^ + b ^ ) k N out = n = 1 N k n = 1 g n ( b ^ + b ^ ) k n in + G ( a ^ + a ^ ) in
( b ^ + b ^ ) in = n ¯ b ; ( b ^ + b ^ ) in 2 = n ¯ b 2 + Δ n b 2
( a ^ + a ^ ) in = n ¯ a ; ( a ^ + a ^ ) in 2 = n ¯ a 2 + Δ n a 2 .
f ( a ^ , a ^ + ) g ( b ^ , b ^ + ) = f ( a ^ , a ^ + ) g ( b ^ , b ^ + )
σ ( a ^ + a ^ ) out 2 = G 2 Δ n a 2 + ( G 1 ) 2 Δ n b 2 + G ( G 1 ) ( 2 n ¯ a n ¯ b + n ¯ a + n ¯ b + 1 ) .
a ^ out = G a ^ in + G 1 a ^ in + .
σ ( a ^ + a ^ ) out 2 = ( 6 G ( G 1 ) + 1 ) Δ n a 2 + 2 G ( G 1 ) ( n ¯ a 2 + n ¯ a + 1 ) .
σ ( b ^ + b ^ ) out 2 = Δ n b 2 + G 2 Δ n a 2 .
σ I ^ out 2 = G Δ n b 2 + G 2 Δ n a 2 ,
σ ( b ^ + b ^ ) out 2 = G 2 1 g 2 1 Δ n b 2 + G 2 Δ n a 2
σ I ^ out 2 = G G 1 g 1 Δ n b 2 + G 2 Δ n a 2
SNR PhaseInsensitive G G 1 n a Δ n b
SNR PhaseSensitive 2 G 1 2 G ( G 1 ) n a
SNR SingleMode = G n a Δ n b
SNR GModes = G n a G Δ n b = G n a Δ n b .
SNR MultiStepSingleMode = G g 2 1 n a G 2 1 Δ n b
SNR MultiStepMultiMode = G ( g 1 ) n a G 1 Δ n b .
a ^ out ( ω ) = T ( ω ) a ^ in ( ω ) + R ( ω ) c ^ in ( ω )
b ^ out + ( ω ) b ^ out ( ω ) = b ^ in + ( ω ) b ^ in ( ω ) + G a ^ out + ( ω ) a ^ out ( ω ) .

Metrics