Abstract

We examine nonclassical properties of the field states generated by applying a photon annihilation-then-creation operation (AC) and a creation-then-annihilation operation (CA) to the thermal and coherent states. Effects of repeated applications of AC and of CA are also studied. We also discuss experimental schemes to realize AC and CA with a cavity system using atom-field interactions.

© 2009 Optical Society of America

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  1. M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B: At. Mol. Opt. Phys. 41, 133001 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485-488 (1992).
    [CrossRef] [PubMed]
  4. A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660-662 (2004).
    [CrossRef] [PubMed]
  5. A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
    [CrossRef]
  6. A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
    [CrossRef]
  7. V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
    [CrossRef] [PubMed]
  8. M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
    [CrossRef]
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  12. R. Jozsa, “Fidelity for mixed quantum states,” J. Mod. Opt. 41, 2315-2323 (1994).
    [CrossRef]
  13. Q. Sun, M. Al-Amri, and M. S. Zubairy, “Probing the quantum commutation rules through cavity QED,” Phys. Rev. A 78, 043801 (2008).
    [CrossRef]
  14. Y. Yang and F. L. Li, “Nonclassicality of photon-subtracted and photon-added-then-subtracted Gaussian states,” J. Opt. Soc. Am. B 26, 830-835 (2009).
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2009

2008

Q. Sun, M. Al-Amri, and M. S. Zubairy, “Probing the quantum commutation rules through cavity QED,” Phys. Rev. A 78, 043801 (2008).
[CrossRef]

M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B: At. Mol. Opt. Phys. 41, 133001 (2008).
[CrossRef]

M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
[CrossRef]

2007

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
[CrossRef] [PubMed]

2005

A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
[CrossRef]

2004

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660-662 (2004).
[CrossRef] [PubMed]

1995

H. W. Lee, “Theory and application of the quantum phase-space distribution functions,” Phys. Rep. 259, 147-211 (1995).
[CrossRef]

1994

R. Jozsa, “Fidelity for mixed quantum states,” J. Mod. Opt. 41, 2315-2323 (1994).
[CrossRef]

1992

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485-488 (1992).
[CrossRef] [PubMed]

1991

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492-497 (1991).
[CrossRef] [PubMed]

C. T. Lee, “Measure of the nonclassicality of nonclassical states,” Phys. Rev. A 44, R2775-R2778 (1991).
[CrossRef] [PubMed]

1979

1932

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485-488 (1992).
[CrossRef] [PubMed]

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492-497 (1991).
[CrossRef] [PubMed]

Al-Amri, M.

Q. Sun, M. Al-Amri, and M. S. Zubairy, “Probing the quantum commutation rules through cavity QED,” Phys. Rev. A 78, 043801 (2008).
[CrossRef]

Bellini, M.

M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
[CrossRef]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
[CrossRef] [PubMed]

A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660-662 (2004).
[CrossRef] [PubMed]

Jeong, H.

M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
[CrossRef]

Jozsa, R.

R. Jozsa, “Fidelity for mixed quantum states,” J. Mod. Opt. 41, 2315-2323 (1994).
[CrossRef]

Kim, J.

Kim, M. S.

M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B: At. Mol. Opt. Phys. 41, 133001 (2008).
[CrossRef]

M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
[CrossRef]

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
[CrossRef] [PubMed]

Lee, C. T.

C. T. Lee, “Measure of the nonclassicality of nonclassical states,” Phys. Rev. A 44, R2775-R2778 (1991).
[CrossRef] [PubMed]

Lee, H. W.

H. W. Lee, “Theory and application of the quantum phase-space distribution functions,” Phys. Rep. 259, 147-211 (1995).
[CrossRef]

Lee, J.

Li, F. L.

Mandel, L.

Nha, H.

Parigi, V.

M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
[CrossRef]

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
[CrossRef] [PubMed]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

Sun, Q.

Q. Sun, M. Al-Amri, and M. S. Zubairy, “Probing the quantum commutation rules through cavity QED,” Phys. Rev. A 78, 043801 (2008).
[CrossRef]

Tara, K.

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485-488 (1992).
[CrossRef] [PubMed]

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492-497 (1991).
[CrossRef] [PubMed]

Viciani, S.

A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660-662 (2004).
[CrossRef] [PubMed]

Wigner, E.

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932).
[CrossRef]

Yang, Y.

Zavatta, A.

M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
[CrossRef]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
[CrossRef] [PubMed]

A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660-662 (2004).
[CrossRef] [PubMed]

Zubairy, M. S.

Q. Sun, M. Al-Amri, and M. S. Zubairy, “Probing the quantum commutation rules through cavity QED,” Phys. Rev. A 78, 043801 (2008).
[CrossRef]

J. Mod. Opt.

R. Jozsa, “Fidelity for mixed quantum states,” J. Mod. Opt. 41, 2315-2323 (1994).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B: At. Mol. Opt. Phys.

M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B: At. Mol. Opt. Phys. 41, 133001 (2008).
[CrossRef]

Opt. Lett.

Phys. Rep.

H. W. Lee, “Theory and application of the quantum phase-space distribution functions,” Phys. Rep. 259, 147-211 (1995).
[CrossRef]

Phys. Rev.

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932).
[CrossRef]

Phys. Rev. A

A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
[CrossRef]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492-497 (1991).
[CrossRef] [PubMed]

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485-488 (1992).
[CrossRef] [PubMed]

Q. Sun, M. Al-Amri, and M. S. Zubairy, “Probing the quantum commutation rules through cavity QED,” Phys. Rev. A 78, 043801 (2008).
[CrossRef]

C. T. Lee, “Measure of the nonclassicality of nonclassical states,” Phys. Rev. A 44, R2775-R2778 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett.

M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008).
[CrossRef]

Science

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660-662 (2004).
[CrossRef] [PubMed]

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Mandel Q factor of the states ρ AC (dashed curve) and ρ CA (solid curve) vs. n ¯ , the mean photon number of the initial thermal state.

Fig. 2
Fig. 2

Wigner distribution of (a) the state ρ AC and (b) the state ρ CA for the case n ¯ = 0.57 . x = 1 2 ( α + α * ) and y = 1 2 i ( α α * ) .

Fig. 3
Fig. 3

Mandel Q factor of the states ρ AC k = 20 (dashed curve) and ρ CA k = 20 (solid curve) versus n ¯ .

Fig. 4
Fig. 4

Fidelity between the states ρ AC k and ρ CA k versus k for the case n ¯ = 0.57 .

Fig. 5
Fig. 5

Mandel Q factor of the states α AC (dashed curve) and α CA (solid curve) versus α 2 , the mean photon number of the initial coherent state.

Fig. 6
Fig. 6

Wigner distribution of (a) the state α AC and (b) the state α CA for the case α 2 = 0.57 . x = 1 2 ( α + α * ) and y = 1 2 i ( α α * ) .

Fig. 7
Fig. 7

Mandel Q factor of the states α AC k = 20 (dashed curve) and α CA k = 20 (solid curve) versus α 2 .

Fig. 8
Fig. 8

Fidelity between the states α AC k and α CA k versus k for the case α 2 = 0.57 .

Fig. 9
Fig. 9

The success probability P 1 (solid curve) and the fidelity F 1 (dashed curve) versus α 2 , the mean photon number of the initial coherent state. The interaction times t 1 and t 2 are chosen such that α g t 1 = α g t 2 = π 2 .

Equations (19)

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n ̂ C n ̂ = ( Δ n ̂ ) 2 n ̂ + 1 + 1 ,
n ̂ A n ̂ = ( Δ n ̂ ) 2 n ̂ 1 ,
ρ = n = 0 n ¯ n ( 1 + n ¯ ) n + 1 n n ,
ρ AC = N { a ̂ + a ̂ ρ a ̂ + a ̂ } = a ̂ + a ̂ ρ a ̂ + a ̂ Tr { a ̂ + a ̂ ρ a ̂ + a ̂ } = 1 ( 1 + 2 n ¯ ) ( 1 + n ¯ ) n ¯ n = 0 n ¯ n n 2 ( 1 + n ¯ ) n n n ,
ρ CA = N { a ̂ a ̂ + ρ a ̂ a ̂ + } = a ̂ a ̂ + ρ a ̂ a ̂ + Tr { a ̂ a ̂ + ρ a ̂ a ̂ + } = 1 ( 1 + 2 n ¯ ) ( 1 + n ¯ ) 2 n = 0 n ¯ n ( n + 1 ) 2 ( 1 + n ¯ ) n n n .
ρ AC k = N { ( a ̂ + a ̂ ) k ρ ( a ̂ + a ̂ ) k } = 1 L i 2 k ( n ¯ 1 + n ¯ ) n = 0 n ¯ n n 2 k ( 1 + n ¯ ) n n n ,
ρ CA k = N { ( a ̂ a ̂ + ) k ρ ( a ̂ a ̂ + ) k } = 1 L i 2 k ( n ¯ 1 + n ¯ ) n = 0 n ¯ n + 1 ( n + 1 ) 2 k ( 1 + n ¯ ) n + 1 n n ,
n ̂ AC k = L i 2 k 1 ( n ¯ 1 + n ¯ ) L i 2 k ( n ¯ 1 + n ¯ ) = n ̂ CA k + 1 ,
[ ( Δ n ̂ ) 2 ] AC k = [ ( Δ n ̂ ) 2 ] CA k = L i 2 k 2 ( n ¯ 1 + n ¯ ) L i 2 k ( n ¯ 1 + n ¯ ) ( L i 2 k 1 ( n ¯ 1 + n ¯ ) L i 2 k ( n ¯ 1 + n ¯ ) ) 2 .
α AC = N { a ̂ + a ̂ α } = a ̂ + a ̂ α α a ̂ + a ̂ a ̂ + a ̂ α ,
α CA = N { a ̂ a ̂ + α } = a ̂ a ̂ + α α a ̂ a ̂ + a ̂ a ̂ + α .
α AC k = N { ( a ̂ + a ̂ ) k α } ,
α CA k = N { ( a ̂ a ̂ + ) k α } .
ψ 1 = N { n = 1 sin ( n g t 1 ) sin ( n g t 2 ) C n n } ,
ψ AC = N { a ̂ + a ̂ ψ i } = N { n = 1 n C n n }
ψ 2 = N { n = 0 sin ( n + 1 g t 1 ) sin ( n + 1 g t 2 ) C n n } ,
ψ CA = N { a ̂ a ̂ + ψ i } = N { n = 0 ( n + 1 ) C n n } .
P 1 = n = 1 sin 2 ( n g t 1 ) sin 2 ( n g t 2 ) C n 2 ,
P 2 = n = 0 sin 2 ( n + 1 g t 1 ) sin 2 ( n + 1 g t 2 ) C n 2 .

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