Abstract

A method for time differentiation based on a Babinet-Soleil-Bravais compensator is introduced. The complex transfer function of the device is measured using polarization spectral interferometry. Time differentiation of both the pulse field and pulse envelope are demonstrated over a spectral width of about 100 THz with a measured overlap with the objective mode greater than 99.8%. This pulse shaping technique is shown to be perfectly suited to time metrology at the quantum limit.

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  1. J. Abadie, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys.7, 962–965 (2011).
    [CrossRef]
  2. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett.96, 010401 (2006).
    [CrossRef] [PubMed]
  3. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D23, 1693–1708 (1981).
    [CrossRef]
  4. C. W. Helstrom, Quantum detection and estimation theory (Academic Press, 1976).
  5. S. L. Braunstein and C. M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett.72, 3439–3443 (1994).
    [CrossRef] [PubMed]
  6. B. M. Escher, R. L. de Matos Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys.7, 406–411 (2011).
    [CrossRef]
  7. V. Delaubert, N. Treps, C. Fabre, H.-A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett.81, 44001 (2008).
    [CrossRef]
  8. O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, and C. Fabre, “Ultimate sensitivity of precision measurements with intense Gaussian quantum light: a multimodal approach,” Phys. Rev. A85,(2012).
    [CrossRef]
  9. B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett.101, 123601 (2008).
    [CrossRef] [PubMed]
  10. A.M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instr.71, 1929–1960 (2000).
    [CrossRef]
  11. A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B43, 103001 (2010).
    [CrossRef]
  12. A.M. Weiner, “Ultrafast optical pulse shaping: A tutorial review,” Opt. Comm.284, 3669–3692 (2011).
    [CrossRef]
  13. F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys.130, 034302 (2009).
    [CrossRef] [PubMed]
  14. P. Jian, O. Pinel, C. Fabre, B. Lamine, and N. Treps, “Real-time displacement measurement immune from atmospheric parameters using optical frequency combs,” Opt. Express20, 27133–27146 (2012).
    [CrossRef] [PubMed]
  15. M. A. Preciado and M. A. Muriel, “Design of an ultrafast all-optical differentiator based on a fiber Bragg grating in transmission,” Opt. Lett.33, 2458–2460 (2008).
    [CrossRef] [PubMed]
  16. Y. Park, J. Azana, and R. Slavik, “Ultrafast all-optical first- and higher-order differentiators based on interferometers,” Opt. Lett.32, 710–712 (2007).
    [CrossRef] [PubMed]
  17. F. X. Li, Y. W. Park, and J. Azana, “Complete temporal pulse characterization based an phase reconstruction using optical ultrafast differentiation (PROUD),” Opt. Lett.32, 3364–3366 (2007).
    [CrossRef] [PubMed]
  18. C. Dorrer and F. Salin, “Characterization of spectral phase modulation by classical and polarization spectral interferometry,” J. Opt. Soc. Am. B15, 2331–2337 (1998).
    [CrossRef]
  19. D. Brida, C. Manzoni, and G. Cerullo, “Phase-locked pulses for two-dimensional spectroscopy by a birefringent delay line,” Opt. Lett.37, 3027–3029 (2012).
    [CrossRef] [PubMed]
  20. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B12, 2467–2474 (1995).
    [CrossRef]
  21. C. Dorrer, N. Belabas, J. P. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B17, 1795–1802 (2000).
    [CrossRef]

2012 (3)

2011 (3)

A.M. Weiner, “Ultrafast optical pulse shaping: A tutorial review,” Opt. Comm.284, 3669–3692 (2011).
[CrossRef]

J. Abadie, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys.7, 962–965 (2011).
[CrossRef]

B. M. Escher, R. L. de Matos Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys.7, 406–411 (2011).
[CrossRef]

2010 (1)

A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B43, 103001 (2010).
[CrossRef]

2009 (1)

F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys.130, 034302 (2009).
[CrossRef] [PubMed]

2008 (3)

M. A. Preciado and M. A. Muriel, “Design of an ultrafast all-optical differentiator based on a fiber Bragg grating in transmission,” Opt. Lett.33, 2458–2460 (2008).
[CrossRef] [PubMed]

B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett.101, 123601 (2008).
[CrossRef] [PubMed]

V. Delaubert, N. Treps, C. Fabre, H.-A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett.81, 44001 (2008).
[CrossRef]

2007 (2)

2006 (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett.96, 010401 (2006).
[CrossRef] [PubMed]

2000 (2)

1998 (1)

1995 (1)

1994 (1)

S. L. Braunstein and C. M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett.72, 3439–3443 (1994).
[CrossRef] [PubMed]

1981 (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D23, 1693–1708 (1981).
[CrossRef]

Abadie, J.

J. Abadie, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys.7, 962–965 (2011).
[CrossRef]

Azana, J.

Bachor, H.-A.

V. Delaubert, N. Treps, C. Fabre, H.-A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett.81, 44001 (2008).
[CrossRef]

Belabas, N.

Braun, D.

O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, and C. Fabre, “Ultimate sensitivity of precision measurements with intense Gaussian quantum light: a multimodal approach,” Phys. Rev. A85,(2012).
[CrossRef]

Braunstein, S. L.

S. L. Braunstein and C. M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett.72, 3439–3443 (1994).
[CrossRef] [PubMed]

Brida, D.

Caves, C. M.

S. L. Braunstein and C. M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett.72, 3439–3443 (1994).
[CrossRef] [PubMed]

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D23, 1693–1708 (1981).
[CrossRef]

Cerullo, G.

Chatel, B.

A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B43, 103001 (2010).
[CrossRef]

Chériaux, G.

Davidovich, L.

B. M. Escher, R. L. de Matos Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys.7, 406–411 (2011).
[CrossRef]

de Matos Filho, R. L.

B. M. Escher, R. L. de Matos Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys.7, 406–411 (2011).
[CrossRef]

Delaubert, V.

V. Delaubert, N. Treps, C. Fabre, H.-A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett.81, 44001 (2008).
[CrossRef]

Dorrer, C.

Escher, B. M.

B. M. Escher, R. L. de Matos Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys.7, 406–411 (2011).
[CrossRef]

Fabre, C.

O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, and C. Fabre, “Ultimate sensitivity of precision measurements with intense Gaussian quantum light: a multimodal approach,” Phys. Rev. A85,(2012).
[CrossRef]

P. Jian, O. Pinel, C. Fabre, B. Lamine, and N. Treps, “Real-time displacement measurement immune from atmospheric parameters using optical frequency combs,” Opt. Express20, 27133–27146 (2012).
[CrossRef] [PubMed]

B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett.101, 123601 (2008).
[CrossRef] [PubMed]

V. Delaubert, N. Treps, C. Fabre, H.-A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett.81, 44001 (2008).
[CrossRef]

Fade, J.

O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, and C. Fabre, “Ultimate sensitivity of precision measurements with intense Gaussian quantum light: a multimodal approach,” Phys. Rev. A85,(2012).
[CrossRef]

Feurer, T.

F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys.130, 034302 (2009).
[CrossRef] [PubMed]

Frei, F.

F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys.130, 034302 (2009).
[CrossRef] [PubMed]

Galler, A.

F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys.130, 034302 (2009).
[CrossRef] [PubMed]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett.96, 010401 (2006).
[CrossRef] [PubMed]

Helstrom, C. W.

C. W. Helstrom, Quantum detection and estimation theory (Academic Press, 1976).

Jian, P.

O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, and C. Fabre, “Ultimate sensitivity of precision measurements with intense Gaussian quantum light: a multimodal approach,” Phys. Rev. A85,(2012).
[CrossRef]

P. Jian, O. Pinel, C. Fabre, B. Lamine, and N. Treps, “Real-time displacement measurement immune from atmospheric parameters using optical frequency combs,” Opt. Express20, 27133–27146 (2012).
[CrossRef] [PubMed]

Joffre, M.

Lamine, B.

Lepetit, L.

Li, F. X.

Likforman, J. P.

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett.96, 010401 (2006).
[CrossRef] [PubMed]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett.96, 010401 (2006).
[CrossRef] [PubMed]

Manzoni, C.

Monmayrant, A.

A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B43, 103001 (2010).
[CrossRef]

Muriel, M. A.

Park, Y.

Park, Y. W.

Pinel, O.

P. Jian, O. Pinel, C. Fabre, B. Lamine, and N. Treps, “Real-time displacement measurement immune from atmospheric parameters using optical frequency combs,” Opt. Express20, 27133–27146 (2012).
[CrossRef] [PubMed]

O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, and C. Fabre, “Ultimate sensitivity of precision measurements with intense Gaussian quantum light: a multimodal approach,” Phys. Rev. A85,(2012).
[CrossRef]

Preciado, M. A.

Réfrégier, P.

V. Delaubert, N. Treps, C. Fabre, H.-A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett.81, 44001 (2008).
[CrossRef]

Salin, F.

Slavik, R.

Treps, N.

P. Jian, O. Pinel, C. Fabre, B. Lamine, and N. Treps, “Real-time displacement measurement immune from atmospheric parameters using optical frequency combs,” Opt. Express20, 27133–27146 (2012).
[CrossRef] [PubMed]

O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, and C. Fabre, “Ultimate sensitivity of precision measurements with intense Gaussian quantum light: a multimodal approach,” Phys. Rev. A85,(2012).
[CrossRef]

B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett.101, 123601 (2008).
[CrossRef] [PubMed]

V. Delaubert, N. Treps, C. Fabre, H.-A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett.81, 44001 (2008).
[CrossRef]

Weber, S.

A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B43, 103001 (2010).
[CrossRef]

Weiner, A.M.

A.M. Weiner, “Ultrafast optical pulse shaping: A tutorial review,” Opt. Comm.284, 3669–3692 (2011).
[CrossRef]

A.M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instr.71, 1929–1960 (2000).
[CrossRef]

Europhys. Lett. (1)

V. Delaubert, N. Treps, C. Fabre, H.-A. Bachor, and P. Réfrégier, “Quantum limits in image processing,” Europhys. Lett.81, 44001 (2008).
[CrossRef]

J. Chem. Phys. (1)

F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys.130, 034302 (2009).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (3)

J. Phys. B (1)

A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B43, 103001 (2010).
[CrossRef]

Nat. Phys. (2)

B. M. Escher, R. L. de Matos Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,” Nat. Phys.7, 406–411 (2011).
[CrossRef]

J. Abadie, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys.7, 962–965 (2011).
[CrossRef]

Opt. Comm. (1)

A.M. Weiner, “Ultrafast optical pulse shaping: A tutorial review,” Opt. Comm.284, 3669–3692 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, and C. Fabre, “Ultimate sensitivity of precision measurements with intense Gaussian quantum light: a multimodal approach,” Phys. Rev. A85,(2012).
[CrossRef]

Phys. Rev. D (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D23, 1693–1708 (1981).
[CrossRef]

Phys. Rev. Lett. (3)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett.96, 010401 (2006).
[CrossRef] [PubMed]

B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett.101, 123601 (2008).
[CrossRef] [PubMed]

S. L. Braunstein and C. M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett.72, 3439–3443 (1994).
[CrossRef] [PubMed]

Rev. Sci. Instr. (1)

A.M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instr.71, 1929–1960 (2000).
[CrossRef]

Other (1)

C. W. Helstrom, Quantum detection and estimation theory (Academic Press, 1976).

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. A linearly polarized pulse 0(t)x⃗ is sent through a Babinet-Soleil-Bravais compensator (BSB) rotated by 45° to produce a pair of orthogonally polarized pulses ℰ⃗′(t) with a relative time delay τ. For phase measurements, a large time delay τFTSI is introduced between the two pulses of interest, polarized along x⃗ and y⃗, with a birefringent crystal aligned on x⃗. An analyzer at 45° allows recording the interference spectrum between the two pulses.

Fig. 2
Fig. 2

Time differentiation of the pulse field. (a) Power spectrum measured along the x (blue solid line) and y polarizations (red dashed line), corresponding respectively to un-shaped and shaped pulses. (b) Measured ratio of the field amplitudes (blue solid line), as compared to the objective (back solid line) and calculation (red dashed line).

Fig. 3
Fig. 3

(a) Fraction of the interference spectrum between the unshaped and shaped pulses, measured with and without the BSB compensator. (b) Spectral phase retrieved using FTSI.

Fig. 4
Fig. 4

Time differentiation of the pulse envelope. (a) Power spectrum measured along the y (blue solid line) and x polarizations (red dashed line), corresponding respectively to unshaped and shaped pulses. (b) Measured ratio of the field amplitudes (blue solid line), as compared to the objective (back solid line) and calculation (red dashed line).

Fig. 5
Fig. 5

Spectral phase retrieved using polarization spectral interferometry, evidencing the π phase jump when the term (ωω0) changes sign.

Equations (12)

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1 ( t ) = T 1 d d t ,
2 ( t ) = T 2 d A ( t ) d t exp ( i ω 0 t ) .
1 ( ω ) = i ω T 1 ( ω )
2 ( ω ) = i ( ω ω 0 ) T 2 ( ω ) .
1 2 ( t + τ / 2 ) 1 2 ( t τ / 2 ) τ 2 d d t .
1 2 ( t + τ / 2 ) 1 2 ( t τ / 2 ) τ 2 d A d t exp ( i ω 0 t ) .
( ω ) = 0 ( ω ) 2 exp ( i k o ( ω ) L ) o + 0 ( ω ) 2 exp ( i k e ( ω ) L ) e
( ω ) = 0 ( ω ) e i φ ( ω ) ( cos ( δ k ( ω ) L 2 ) x + i sin ( δ k ( ω ) L 2 ) y )
( ω ) 0 ( ω ) e i φ ( ω ) ( x + i δ k ( ω ) L 2 y )
ω 1 = ω 0 δ k ( ω 0 ) δ k ( ω 0 ) = δ n g ( ω 0 ) δ n ( ω 0 ) δ n g ( ω 0 ) ω 0
( ω ) ( 1 ) n 0 ( ω ) e i φ ( ω ) ( x + i ( ω ω 0 ) δ k ( ω 0 ) L 2 y )
( ω ) = i 0 ( ω ) e i φ ( ω ) ( i ( ω ω 0 ) δ k ( ω 0 ) L 2 x + y )

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