Abstract

We study the application of photon-subtracted two-mode squeezed vacuum states (TMSVS), where identical photon numbers are subtracted from each beam, to the problem of quantum optical interferometry with the photon-number parity measurements scheme. Previously, Anisimov et al. [Phys. Rev. Lett. 104, 103602 (2010)] have studied the prospect of using the TMSVS for parity measurements based interferometry. However, the joint photon number distribution of this state before beam splitting is thermal-like in each mode, meaning that its statistics are super-Poissonian and that the most probable state of the field is the double vacuum and that the average photon number is low. Furthermore, with these states the sensitivity of the phase-shift measurement is extremely sensitive to the size of the phase shift to be measured for large average photon numbers. The simultaneous subtraction of 1, 2, or 3 photons from each mode has the effects of increasing the average photon numbers of each mode and rendering the statistics nearly Poissonian and in some cases sub-Poissonian. We show that phase uncertainties for such states are less sensitive to the phase shift itself at large average photon numbers. We also show that the photon-subtracted TMSVS also lead to increased resolution.

© 2012 Optical Society of America

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  1. J. P. Dowling, “Quantum optical metrology-the lowdown on high-NOON states,” Contemp. Phys. 49, 125–143 (2008), and references therein.
    [CrossRef]
  2. C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010), and references therein.
    [CrossRef]
  3. C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum optical Fredkin gate,” Phys. Rev. A 64, 06314 (2001).
    [CrossRef]
  4. C. C. Gerry, A. Benmoussa, and R. A. Campos, “Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry,” Phys. Rev. A 66, 013804 (2002).
    [CrossRef]
  5. M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
    [CrossRef]
  6. R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).
    [CrossRef]
  7. P. M. Anisimov, G. M. Raterman, S. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
    [CrossRef]
  8. C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
    [CrossRef]
  9. G. S. Agarwal, “Generation of pair coherent states and squeezing via the competition of four-wave mixing and amplified spontaneous emission,” Phys. Rev. Lett. 57, 827–830 (1986).
    [CrossRef]
  10. G. S. Agarwal, “Nonclassical statistics of fields in pair coherent states,” J. Opt. Soc. Am. B 5, 1940–1947 (1988).
    [CrossRef]
  11. 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]
  12. M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
    [CrossRef]
  13. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
    [CrossRef]
  14. T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
    [CrossRef]
  15. A. Luis, “Paradoxical evolution of the number of photons in the Jaynes-Cummings model,” J. Opt. Soc. Am. B 24, 2619 (2007). Subtracting photons can sometimes raise the average photon number. For the state |ψ〉=(|1〉+|11〉)/2 the average photon number is 6, but the state obtained by the action of the annihilation operator, a^|ψ〉, after renormalization, the average photon number has increased to 9.17.
    [CrossRef]
  16. H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
    [CrossRef]
  17. R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
    [CrossRef]
  18. D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).
    [CrossRef]
  19. L. Mandel, “Sub-Poissonian photon statistics is resonance fluorescence,” Opt. Lett. 4, 205–207 (1979).
    [CrossRef]
  20. R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
    [CrossRef]
  21. V. Bužek and M. Hillery, “Quantum disentanglement and phase measurement,” Czech. J. Phys. 45, 711–725 (1995).
    [CrossRef]
  22. B. Böhmer and U. Leonhardt, “Correlation interferometer for squeezed light,” Opt. Commun. 118, 181–185 (1995).
    [CrossRef]
  23. A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
    [CrossRef]
  24. K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
    [CrossRef]

2010 (4)

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010), and references therein.
[CrossRef]

P. M. Anisimov, G. M. Raterman, S. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[CrossRef]

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

2008 (1)

J. P. Dowling, “Quantum optical metrology-the lowdown on high-NOON states,” Contemp. Phys. 49, 125–143 (2008), and references therein.
[CrossRef]

2007 (3)

A. Luis, “Paradoxical evolution of the number of photons in the Jaynes-Cummings model,” J. Opt. Soc. Am. B 24, 2619 (2007). Subtracting photons can sometimes raise the average photon number. For the state |ψ〉=(|1〉+|11〉)/2 the average photon number is 6, but the state obtained by the action of the annihilation operator, a^|ψ〉, after renormalization, the average photon number has increased to 9.17.
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[CrossRef]

2006 (1)

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

2005 (1)

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).
[CrossRef]

2004 (2)

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

2003 (1)

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).
[CrossRef]

2002 (1)

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry,” Phys. Rev. A 66, 013804 (2002).
[CrossRef]

2001 (1)

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum optical Fredkin gate,” Phys. Rev. A 64, 06314 (2001).
[CrossRef]

1997 (1)

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

1995 (2)

V. Bužek and M. Hillery, “Quantum disentanglement and phase measurement,” Czech. J. Phys. 45, 711–725 (1995).
[CrossRef]

B. Böhmer and U. Leonhardt, “Correlation interferometer for squeezed light,” Opt. Commun. 118, 181–185 (1995).
[CrossRef]

1993 (1)

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[CrossRef]

1991 (1)

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]

1989 (1)

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef]

1988 (1)

1986 (1)

G. S. Agarwal, “Generation of pair coherent states and squeezing via the competition of four-wave mixing and amplified spontaneous emission,” Phys. Rev. Lett. 57, 827–830 (1986).
[CrossRef]

1979 (1)

Agarwal, G. S.

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]

G. S. Agarwal, “Nonclassical statistics of fields in pair coherent states,” J. Opt. Soc. Am. B 5, 1940–1947 (1988).
[CrossRef]

G. S. Agarwal, “Generation of pair coherent states and squeezing via the competition of four-wave mixing and amplified spontaneous emission,” Phys. Rev. Lett. 57, 827–830 (1986).
[CrossRef]

Anhut, T.

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

Anisimov, P. M.

P. M. Anisimov, G. M. Raterman, S. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[CrossRef]

Benmoussa, A.

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).
[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry,” Phys. Rev. A 66, 013804 (2002).
[CrossRef]

Böhmer, B.

B. Böhmer and U. Leonhardt, “Correlation interferometer for squeezed light,” Opt. Commun. 118, 181–185 (1995).
[CrossRef]

Burnett, K.

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[CrossRef]

Bužek, V.

V. Bužek and M. Hillery, “Quantum disentanglement and phase measurement,” Czech. J. Phys. 45, 711–725 (1995).
[CrossRef]

Calkins, B.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

Campos, R. A.

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).
[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry,” Phys. Rev. A 66, 013804 (2002).
[CrossRef]

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum optical Fredkin gate,” Phys. Rev. A 64, 06314 (2001).
[CrossRef]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef]

Carmichael, H. J.

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

Cerf, N. J.

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

Chiruvelli, S.

P. M. Anisimov, G. M. Raterman, S. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[CrossRef]

Clement, T. S.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

Dakna, M.

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

Dantan, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

Dowling, J. P.

P. M. Anisimov, G. M. Raterman, S. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[CrossRef]

J. P. Dowling, “Quantum optical metrology-the lowdown on high-NOON states,” Contemp. Phys. 49, 125–143 (2008), and references therein.
[CrossRef]

Fiurášek, J.

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

García-Patrón, R.

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

Gerrits, T.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

Gerry, C. C.

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
[CrossRef]

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010), and references therein.
[CrossRef]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).
[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry,” Phys. Rev. A 66, 013804 (2002).
[CrossRef]

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum optical Fredkin gate,” Phys. Rev. A 64, 06314 (2001).
[CrossRef]

Gilchrist, A.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[CrossRef]

Glancy, S.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

Grangier, P.

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

Grangier, Ph.

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

Hillery, M.

V. Bužek and M. Hillery, “Quantum disentanglement and phase measurement,” Czech. J. Phys. 45, 711–725 (1995).
[CrossRef]

Holland, M. J.

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[CrossRef]

Huver, S. D.

P. M. Anisimov, G. M. Raterman, S. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[CrossRef]

Knill, E.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

Knöll, L.

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

Laurat, J.

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

Lee, H.

P. M. Anisimov, G. M. Raterman, S. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[CrossRef]

Leonhardt, U.

B. Böhmer and U. Leonhardt, “Correlation interferometer for squeezed light,” Opt. Commun. 118, 181–185 (1995).
[CrossRef]

Lita, A. E.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).
[CrossRef]

Luis, A.

Mandel, L.

Migdal, A. L.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

Miller, A. J.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).
[CrossRef]

Mimih, J.

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010), and references therein.
[CrossRef]

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
[CrossRef]

Mirin, R. P.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

Nam, S.

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).
[CrossRef]

Nam, S. W.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

Nha, H.

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

O’Brien, J. L.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[CrossRef]

Opatrný, T.

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

Ourjoumtsev, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

Plick, W. N.

P. M. Anisimov, G. M. Raterman, S. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[CrossRef]

Pregnell, K. L.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[CrossRef]

Prevedel, R.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[CrossRef]

Pryde, G. J.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[CrossRef]

Raterman, G. M.

P. M. Anisimov, G. M. Raterman, S. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[CrossRef]

Resch, K. J.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[CrossRef]

Rosenberg, D.

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).
[CrossRef]

Saleh, B. E. A.

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef]

Schwall, R. E.

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).
[CrossRef]

Tara, K.

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]

Teich, M. C.

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef]

Tualle-Bouri, R.

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

Tualle-Brouri, R.

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

Welsch, D-G.

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

Wenger, J.

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

White, A. G.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[CrossRef]

Contemp. Phys. (2)

J. P. Dowling, “Quantum optical metrology-the lowdown on high-NOON states,” Contemp. Phys. 49, 125–143 (2008), and references therein.
[CrossRef]

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010), and references therein.
[CrossRef]

Czech. J. Phys. (1)

V. Bužek and M. Hillery, “Quantum disentanglement and phase measurement,” Czech. J. Phys. 45, 711–725 (1995).
[CrossRef]

IEEE Trans. Appl. Supercond. (1)

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

B. Böhmer and U. Leonhardt, “Correlation interferometer for squeezed light,” Opt. Commun. 118, 181–185 (1995).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (8)

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[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]

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum optical Fredkin gate,” Phys. Rev. A 64, 06314 (2001).
[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry,” Phys. Rev. A 66, 013804 (2002).
[CrossRef]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).
[CrossRef]

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[CrossRef]

Phys. Rev. Lett. (7)

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[CrossRef]

G. S. Agarwal, “Generation of pair coherent states and squeezing via the competition of four-wave mixing and amplified spontaneous emission,” Phys. Rev. Lett. 57, 827–830 (1986).
[CrossRef]

P. M. Anisimov, G. M. Raterman, S. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[CrossRef]

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
[CrossRef]

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).
[CrossRef]

Science (1)

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Diagram of the proposed experiment with a downconverter producing two-mode squeezed vacuum states from which photons are subtracted from each mode.

Fig. 2.
Fig. 2.

Plot of PBBS1(n,m) versus n and m for z=0.7 for (a) l=0, (b) l=1, (c) l=2, and (d) l=3.

Fig. 3.
Fig. 3.

Plot the total average photon number 2N¯ versus the parameter |z| for l=0, 1, 2, and 3.

Fig. 4.
Fig. 4.

Plot of Qa versus |z| for l=0, 1, 2 and 3.

Fig. 5.
Fig. 5.

Plot of PABS1(n,m) for the same |z|=0.7 for (a) l=0, (b) l=1, (c) l=2, and (d) l=3.

Fig. 6.
Fig. 6.

Plot of S versus |z| for l=0, 1, 2, 3, for (a) before and (b) after beam splitting.

Fig. 7.
Fig. 7.

Plot Π^b(φ) versus φ for |z|=0.7 for (a) l=0, (b) l=1, (c) l=2, and (d) l=3.

Fig. 8.
Fig. 8.

Plot of Δφ versus the total average photon number of the two modes given by 2N¯ for (a) l=0, (b) l=1, (c) l=2, and (d) l=3, taking φ=104.

Fig. 9.
Fig. 9.

Plot of Δφ versus the total average photon number of the two modes given by 2N¯ for (a) l=0, (b) l=1, (c) l=2, and (d) l=3, taking φ=0.05.

Equations (15)

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

|z=(1|z|2)1/2n=0zn|na|nb,
|z,l=n=lBn(l)|nla|nlb,
Bn(l)=Nl(n!(nl)!)zn,Nl=[n=0|z|2n(n!(nl)!)2]1/2.
|z,l=N=0DN(l)|Na|Nb,
DN(l)=Nl((N+l)!N!)zN+l.
PBBS1(n,m)=|n,m|z,la,b|2=|DN(l)δn,Nδm,N|2
N¯=N=0N|DN(l)|2,
Qa=(a^a^)2a^a^2a^a^a^a^.
|out,BS1=U^BS1|z,l=N=0k=0NDN(l)AkN|2ka|2N2kb,
AkN=(1)Nk[(2kk)(2N2kNk)(12)2N]1/2.
U^BS1|Na|Nb=k=0NAkN|2ka|2N2kb.
PABS1(n,m)=|n,m|out,BS1|2=|N=0k=0NDN(l)AkNδn,2kδm,2n2k|2,
|ψ(φ)=U^(φ)|out,BS1=N=0k=0Neiφ(2N2k)DN(l)AkN|2ka|2N2kb.
Π^b(φ)=ψ(φ)|U^BS2Π^bU^BS2|ψ(φ)=N=0|DN(l)|2PN[cos(2φ)],
Δφ=ΔΠb|Π^b(φ)/φ|=1Π^b(φ)2|Π^b(φ)/φ|,

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