Abstract

In a previous article [Astron. Astrophys. 561, A118 (2014)], we suggested a method to overcome the diffraction limit behind a telescope. We discuss and extend recent numerical simulations and test whether it is indeed possible to use photon amplification to enhance the angular resolution of a telescope or a microscope beyond the diffraction limit. An essential addition is the proposal to select events with an above-average ratio of stimulated to spontaneous photons. The analysis shows that the diffraction limit of a telescope is surpassed by a factor of 10 for an amplifier gain of 200, if the analysis is restricted to a tenth of the incoming astronomical photons. A gain of 70 is sufficient with a hundredth of the photons. More simulations must be performed to account for the bunching of spontaneous photons.

© 2016 Optical Society of America

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References

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2016 (1)

2014 (1)

A. Kellerer, Astron. Astrophys. 561, A118 (2014).
[Crossref]

2011 (1)

A. Zavatta, J. Fiurasek, and M. Bellini, Nat. Photonics 5, 52 (2011).
[Crossref]

2010 (1)

M. A. Usuga, C. R. Muller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, Nat. Phys. 6, 767 (2010).
[Crossref]

2007 (1)

S. W. Hell, Science 316, 1153 (2007).
[Crossref]

2004 (1)

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, Eur. Phys. J. D 28, 447 (2004).
[Crossref]

1998 (1)

L.-M. Duan and G.-C. Guo, Phys. Rev. Lett. 80, 4999 (1998).
[Crossref]

1994 (1)

1983 (1)

L. Mandel, Nature 304, 188 (1983).
[Crossref]

1982 (3)

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[Crossref]

P. W. Milonni and M. L. Hardies, Phys. Lett. A 92, 321 (1982).
[Crossref]

W. K. Wootters and W. H. Zurek, Nature 299, 802 (1982).
[Crossref]

1957 (1)

K. Shimoda, H. Takahasi, and C. Townes, J. Phys. Soc. Jpn. 12, 686 (1957).
[Crossref]

Andersen, U. L.

M. A. Usuga, C. R. Muller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, Nat. Phys. 6, 767 (2010).
[Crossref]

Bellini, M.

A. Zavatta, J. Fiurasek, and M. Bellini, Nat. Photonics 5, 52 (2011).
[Crossref]

Caves, C. M.

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[Crossref]

Devaux, F.

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, Eur. Phys. J. D 28, 447 (2004).
[Crossref]

Duan, L.-M.

L.-M. Duan and G.-C. Guo, Phys. Rev. Lett. 80, 4999 (1998).
[Crossref]

Fanjoux, G.

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, Eur. Phys. J. D 28, 447 (2004).
[Crossref]

Filip, R.

M. A. Usuga, C. R. Muller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, Nat. Phys. 6, 767 (2010).
[Crossref]

Fiurasek, J.

A. Zavatta, J. Fiurasek, and M. Bellini, Nat. Photonics 5, 52 (2011).
[Crossref]

Guo, G.-C.

L.-M. Duan and G.-C. Guo, Phys. Rev. Lett. 80, 4999 (1998).
[Crossref]

Hardies, M. L.

P. W. Milonni and M. L. Hardies, Phys. Lett. A 92, 321 (1982).
[Crossref]

Haus, H. A.

H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, 2000), pp. 305–344.

Hell, S. W.

S. W. Hell, Science 316, 1153 (2007).
[Crossref]

Kellerer, A.

A. Kellerer, Astron. Astrophys. 561, A118 (2014).
[Crossref]

Kurek, A. R.

Lantz, E.

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, Eur. Phys. J. D 28, 447 (2004).
[Crossref]

Leuchs, G.

M. A. Usuga, C. R. Muller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, Nat. Phys. 6, 767 (2010).
[Crossref]

Lund, A. P.

T. C. Ralph and A. P. Lund, Proceedings of the 9th International Conference on Quantum Communication Measurement and Computing (American Institute of Physics, 2009), pp. 155–160.

Mandel, L.

L. Mandel, Nature 304, 188 (1983).
[Crossref]

Marek, P.

M. A. Usuga, C. R. Muller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, Nat. Phys. 6, 767 (2010).
[Crossref]

Marquardt, C.

M. A. Usuga, C. R. Muller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, Nat. Phys. 6, 767 (2010).
[Crossref]

Milonni, P. W.

P. W. Milonni and M. L. Hardies, Phys. Lett. A 92, 321 (1982).
[Crossref]

Mosset, A.

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, Eur. Phys. J. D 28, 447 (2004).
[Crossref]

Muller, C. R.

M. A. Usuga, C. R. Muller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, Nat. Phys. 6, 767 (2010).
[Crossref]

Pieta, T.

Pollo, A.

Popowicz, A.

Prasad, S.

Ralph, T. C.

T. C. Ralph and A. P. Lund, Proceedings of the 9th International Conference on Quantum Communication Measurement and Computing (American Institute of Physics, 2009), pp. 155–160.

Shimoda, K.

K. Shimoda, H. Takahasi, and C. Townes, J. Phys. Soc. Jpn. 12, 686 (1957).
[Crossref]

Stebel, T.

Takahasi, H.

K. Shimoda, H. Takahasi, and C. Townes, J. Phys. Soc. Jpn. 12, 686 (1957).
[Crossref]

Townes, C.

K. Shimoda, H. Takahasi, and C. Townes, J. Phys. Soc. Jpn. 12, 686 (1957).
[Crossref]

Usuga, M. A.

M. A. Usuga, C. R. Muller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, Nat. Phys. 6, 767 (2010).
[Crossref]

Wittmann, C.

M. A. Usuga, C. R. Muller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, Nat. Phys. 6, 767 (2010).
[Crossref]

Wootters, W. K.

W. K. Wootters and W. H. Zurek, Nature 299, 802 (1982).
[Crossref]

Zavatta, A.

A. Zavatta, J. Fiurasek, and M. Bellini, Nat. Photonics 5, 52 (2011).
[Crossref]

Zurek, W. H.

W. K. Wootters and W. H. Zurek, Nature 299, 802 (1982).
[Crossref]

Astron. Astrophys. (1)

A. Kellerer, Astron. Astrophys. 561, A118 (2014).
[Crossref]

Eur. Phys. J. D (1)

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, Eur. Phys. J. D 28, 447 (2004).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Phys. Soc. Jpn. (1)

K. Shimoda, H. Takahasi, and C. Townes, J. Phys. Soc. Jpn. 12, 686 (1957).
[Crossref]

Nat. Photonics (1)

A. Zavatta, J. Fiurasek, and M. Bellini, Nat. Photonics 5, 52 (2011).
[Crossref]

Nat. Phys. (1)

M. A. Usuga, C. R. Muller, C. Wittmann, P. Marek, R. Filip, C. Marquardt, G. Leuchs, and U. L. Andersen, Nat. Phys. 6, 767 (2010).
[Crossref]

Nature (2)

W. K. Wootters and W. H. Zurek, Nature 299, 802 (1982).
[Crossref]

L. Mandel, Nature 304, 188 (1983).
[Crossref]

Opt. Lett. (1)

Phys. Lett. A (1)

P. W. Milonni and M. L. Hardies, Phys. Lett. A 92, 321 (1982).
[Crossref]

Phys. Rev. D (1)

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[Crossref]

Phys. Rev. Lett. (1)

L.-M. Duan and G.-C. Guo, Phys. Rev. Lett. 80, 4999 (1998).
[Crossref]

Science (1)

S. W. Hell, Science 316, 1153 (2007).
[Crossref]

Other (2)

H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, 2000), pp. 305–344.

T. C. Ralph and A. P. Lund, Proceedings of the 9th International Conference on Quantum Communication Measurement and Computing (American Institute of Physics, 2009), pp. 155–160.

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Figures (4)

Fig. 1.
Fig. 1.

Amplifier medium placed behind a telescope. The surfaces of the amplifier and telescope pupil are assumed equal to simplify the notations, but in actuality the amplifier surface can be made substantially smaller than the pupil.

Fig. 2.
Fig. 2.

Rms deviation of the position estimate. The number of stimulated photons either follow a Poisson distribution or the actual distribution indicated by Eq. (4): Modes 1 and 2 in the text.

Fig. 3.
Fig. 3.

Rms deviation of the position estimate as a function of amplifier gain. The analysis is restricted to a percentage of sets with highest photon density (Modes 2–4 in the text).

Fig. 4.
Fig. 4.

Rms deviation of the position estimate as a function of the fraction of events kept for the analysis and for different amplifier gains.

Equations (7)

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

n = s S I ,
m = π θ 0 2 4 · I 4 π · A Δ t .
m n = 0.74 π 2 7.3 .
p st ( n ) = ( 1 1 g ) n 1 g ,
p sp ( n ) = exp ( m ) m n n ! .
m = 7.3 ( g 1 ) ( α θ 0 ) 2 ,
f ( θ ) = ( 2 J 1 ( π D θ / λ ) π D θ / λ ) 2 = ( 2 J 1 ( 2.44 π θ / θ 0 ) 2.44 π θ / θ 0 ) 2 ,

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