Abstract

We describe a new scheme to induce large contrast (nearly 50%) absorption resonances using three co-propagating fields which interact with a three-level Λ-system (obtained by the D 2 transition of 87 Rb atoms) in an N-configuration scheme. A single mode laser which couples the upper ground state to the excited state of 87 Rb is phase modulated at half the hyperfine splitting frequency. The resultant three line spectrum interacts with the atomic vapor yielding a population transfer which increases the absorption by an amount which depends on the carrier to modulation side band intensity ratio.

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  1. E. Arimondo, “Coherent population trapping in laser spectroscopy,” in “Progress in Optics ,” vol. XXXV, E. Wolf, ed. (Elsevier, 1996), pp. 257–354.
    [CrossRef]
  2. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
    [CrossRef]
  3. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, 1997).
  4. M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
    [CrossRef]
  5. H. Schmidt and A. Imamogdlu, “Giant kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
    [CrossRef] [PubMed]
  6. S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
    [CrossRef]
  7. M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
    [CrossRef]
  8. A. Lezama, S. Barreiro, and A. M. Akulshin, “Electromagnetically induced absorption,” Phys. Rev. A 59, 4732–4735 (1999).
    [CrossRef]
  9. A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A 61, 011802 (1999).
    [CrossRef]
  10. A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, “Observation of a three-photon electromagnetically induced transparency in hot atomic vapor,” Phys. Rev. A 65, 043817 (2002).
    [CrossRef]
  11. S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, “Three-photon-absorption resonance for all-optical atomic clocks,” Phys. Rev. A 72, 011801 (2005).
    [CrossRef]
  12. I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “Cancellation of light shifts in an N-resonance clock,” Opt. Lett. 31, 622–624 (2006).
    [CrossRef] [PubMed]
  13. I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “Comparison of 87Rb N-resonances for D1 and D2 transitions,” Opt. Lett. 31, 2353–2355 (2006).
    [CrossRef] [PubMed]
  14. C. Hancox, M. Hohensee, M. Crescimanno, D. F. Phillips, and R. L. Walsworth, “Lineshape asymmetry for joint coherent population trapping and three-photon N resonances,” Opt. Lett. 33, 1536–1538 (2008).
    [CrossRef] [PubMed]
  15. J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, “On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards,” IEEE Trans. Instrum. Meas. 52, 822–831 (2003).
    [CrossRef]
  16. Y. Yoshikawa, T. Umeki, T. Mukae, Y. Torii, and T. Kuga, “Frequency stabilization of a laser diode with use of Light-Induced birefringence in an atomic vapor,” Appl. Opt. 42, 6645–6649 (2003).
    [CrossRef] [PubMed]
  17. J. H. Shirley, “Solution of the schrödinger equation with a hamiltonian periodic in time,” Phys. Rev. 138, B979–B987 (1965).
    [CrossRef]
  18. D. R. Masson, “Schrödinger’s equation and continued fractions,” Int. J. Quantum Chem. 32, 699–712 (1987).
    [CrossRef]
  19. S. M. Tan, “A computational toolbox for quantum and atomic optics,” J. Opt. B: Quantum Semiclass. Opt. 1, 424–432 (1999).
    [CrossRef]
  20. S. Knappe, J. Kitching, L. Hollberg, and R. Wynands, “Temperature dependence of coherent population trapping resonances,” Appl. Phys. B 74, 217–222 (2002).
    [CrossRef]

2008 (1)

2006 (2)

2005 (1)

S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, “Three-photon-absorption resonance for all-optical atomic clocks,” Phys. Rev. A 72, 011801 (2005).
[CrossRef]

2003 (2)

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, “On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards,” IEEE Trans. Instrum. Meas. 52, 822–831 (2003).
[CrossRef]

Y. Yoshikawa, T. Umeki, T. Mukae, Y. Torii, and T. Kuga, “Frequency stabilization of a laser diode with use of Light-Induced birefringence in an atomic vapor,” Appl. Opt. 42, 6645–6649 (2003).
[CrossRef] [PubMed]

2002 (2)

S. Knappe, J. Kitching, L. Hollberg, and R. Wynands, “Temperature dependence of coherent population trapping resonances,” Appl. Phys. B 74, 217–222 (2002).
[CrossRef]

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, “Observation of a three-photon electromagnetically induced transparency in hot atomic vapor,” Phys. Rev. A 65, 043817 (2002).
[CrossRef]

2001 (1)

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
[CrossRef]

1999 (4)

A. Lezama, S. Barreiro, and A. M. Akulshin, “Electromagnetically induced absorption,” Phys. Rev. A 59, 4732–4735 (1999).
[CrossRef]

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A 61, 011802 (1999).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
[CrossRef]

S. M. Tan, “A computational toolbox for quantum and atomic optics,” J. Opt. B: Quantum Semiclass. Opt. 1, 424–432 (1999).
[CrossRef]

1998 (1)

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[CrossRef]

1996 (1)

1987 (1)

D. R. Masson, “Schrödinger’s equation and continued fractions,” Int. J. Quantum Chem. 32, 699–712 (1987).
[CrossRef]

1965 (1)

J. H. Shirley, “Solution of the schrödinger equation with a hamiltonian periodic in time,” Phys. Rev. 138, B979–B987 (1965).
[CrossRef]

Akulshin, A. M.

A. Lezama, S. Barreiro, and A. M. Akulshin, “Electromagnetically induced absorption,” Phys. Rev. A 59, 4732–4735 (1999).
[CrossRef]

Arimondo, E.

E. Arimondo, “Coherent population trapping in laser spectroscopy,” in “Progress in Optics ,” vol. XXXV, E. Wolf, ed. (Elsevier, 1996), pp. 257–354.
[CrossRef]

Barreiro, S.

A. Lezama, S. Barreiro, and A. M. Akulshin, “Electromagnetically induced absorption,” Phys. Rev. A 59, 4732–4735 (1999).
[CrossRef]

Crescimanno, M.

Delaney, M. J.

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, “On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards,” IEEE Trans. Instrum. Meas. 52, 822–831 (2003).
[CrossRef]

Fleischhauer, M.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
[CrossRef]

Hancox, C.

Harris, S. E.

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[CrossRef]

Hohensee, M.

Hollberg, L.

S. Knappe, J. Kitching, L. Hollberg, and R. Wynands, “Temperature dependence of coherent population trapping resonances,” Appl. Phys. B 74, 217–222 (2002).
[CrossRef]

Imamogdlu, A.

Imamoglu, A.

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
[CrossRef]

Janssen, D.

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, “On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards,” IEEE Trans. Instrum. Meas. 52, 822–831 (2003).
[CrossRef]

Kitching, J.

S. Knappe, J. Kitching, L. Hollberg, and R. Wynands, “Temperature dependence of coherent population trapping resonances,” Appl. Phys. B 74, 217–222 (2002).
[CrossRef]

Knappe, S.

S. Knappe, J. Kitching, L. Hollberg, and R. Wynands, “Temperature dependence of coherent population trapping resonances,” Appl. Phys. B 74, 217–222 (2002).
[CrossRef]

Kuga, T.

Levine, M. W.

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, “On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards,” IEEE Trans. Instrum. Meas. 52, 822–831 (2003).
[CrossRef]

Lezama, A.

A. Lezama, S. Barreiro, and A. M. Akulshin, “Electromagnetically induced absorption,” Phys. Rev. A 59, 4732–4735 (1999).
[CrossRef]

Lukin, M. D.

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
[CrossRef]

Masson, D. R.

D. R. Masson, “Schrödinger’s equation and continued fractions,” Int. J. Quantum Chem. 32, 699–712 (1987).
[CrossRef]

Matsko, A. B.

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, “Observation of a three-photon electromagnetically induced transparency in hot atomic vapor,” Phys. Rev. A 65, 043817 (2002).
[CrossRef]

Mukae, T.

Novikova, I.

Phillips, D. F.

Rostovtsev, Y. V.

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, “Observation of a three-photon electromagnetically induced transparency in hot atomic vapor,” Phys. Rev. A 65, 043817 (2002).
[CrossRef]

Schmidt, H.

Scully, M. O.

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, “Observation of a three-photon electromagnetically induced transparency in hot atomic vapor,” Phys. Rev. A 65, 043817 (2002).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, 1997).

Shirley, J. H.

J. H. Shirley, “Solution of the schrödinger equation with a hamiltonian periodic in time,” Phys. Rev. 138, B979–B987 (1965).
[CrossRef]

Taichenachev, A. V.

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “Cancellation of light shifts in an N-resonance clock,” Opt. Lett. 31, 622–624 (2006).
[CrossRef] [PubMed]

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “Comparison of 87Rb N-resonances for D1 and D2 transitions,” Opt. Lett. 31, 2353–2355 (2006).
[CrossRef] [PubMed]

S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, “Three-photon-absorption resonance for all-optical atomic clocks,” Phys. Rev. A 72, 011801 (2005).
[CrossRef]

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A 61, 011802 (1999).
[CrossRef]

Tan, S. M.

S. M. Tan, “A computational toolbox for quantum and atomic optics,” J. Opt. B: Quantum Semiclass. Opt. 1, 424–432 (1999).
[CrossRef]

Torii, Y.

Tumaikin, A. M.

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A 61, 011802 (1999).
[CrossRef]

Umeki, T.

Vanier, J.

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, “On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards,” IEEE Trans. Instrum. Meas. 52, 822–831 (2003).
[CrossRef]

Walsworth, R. L.

Wynands, R.

S. Knappe, J. Kitching, L. Hollberg, and R. Wynands, “Temperature dependence of coherent population trapping resonances,” Appl. Phys. B 74, 217–222 (2002).
[CrossRef]

Yamamoto, Y.

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

Ye, C. Y.

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, “Observation of a three-photon electromagnetically induced transparency in hot atomic vapor,” Phys. Rev. A 65, 043817 (2002).
[CrossRef]

Yelin, S. F.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
[CrossRef]

Yoshikawa, Y.

Yudin, V. I.

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “Comparison of 87Rb N-resonances for D1 and D2 transitions,” Opt. Lett. 31, 2353–2355 (2006).
[CrossRef] [PubMed]

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “Cancellation of light shifts in an N-resonance clock,” Opt. Lett. 31, 622–624 (2006).
[CrossRef] [PubMed]

S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, “Three-photon-absorption resonance for all-optical atomic clocks,” Phys. Rev. A 72, 011801 (2005).
[CrossRef]

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A 61, 011802 (1999).
[CrossRef]

Zibrov, A. S.

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “Cancellation of light shifts in an N-resonance clock,” Opt. Lett. 31, 622–624 (2006).
[CrossRef] [PubMed]

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “Comparison of 87Rb N-resonances for D1 and D2 transitions,” Opt. Lett. 31, 2353–2355 (2006).
[CrossRef] [PubMed]

S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, “Three-photon-absorption resonance for all-optical atomic clocks,” Phys. Rev. A 72, 011801 (2005).
[CrossRef]

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, “Observation of a three-photon electromagnetically induced transparency in hot atomic vapor,” Phys. Rev. A 65, 043817 (2002).
[CrossRef]

Zibrov, S.

S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, “Three-photon-absorption resonance for all-optical atomic clocks,” Phys. Rev. A 72, 011801 (2005).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, 1997).

Appl. Opt. (1)

Appl. Phys. B (1)

S. Knappe, J. Kitching, L. Hollberg, and R. Wynands, “Temperature dependence of coherent population trapping resonances,” Appl. Phys. B 74, 217–222 (2002).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, “On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards,” IEEE Trans. Instrum. Meas. 52, 822–831 (2003).
[CrossRef]

Int. J. Quantum Chem. (1)

D. R. Masson, “Schrödinger’s equation and continued fractions,” Int. J. Quantum Chem. 32, 699–712 (1987).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt. (1)

S. M. Tan, “A computational toolbox for quantum and atomic optics,” J. Opt. B: Quantum Semiclass. Opt. 1, 424–432 (1999).
[CrossRef]

Nature (London) (1)

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. (1)

J. H. Shirley, “Solution of the schrödinger equation with a hamiltonian periodic in time,” Phys. Rev. 138, B979–B987 (1965).
[CrossRef]

Phys. Rev. A (5)

A. Lezama, S. Barreiro, and A. M. Akulshin, “Electromagnetically induced absorption,” Phys. Rev. A 59, 4732–4735 (1999).
[CrossRef]

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A 61, 011802 (1999).
[CrossRef]

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, “Observation of a three-photon electromagnetically induced transparency in hot atomic vapor,” Phys. Rev. A 65, 043817 (2002).
[CrossRef]

S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, “Three-photon-absorption resonance for all-optical atomic clocks,” Phys. Rev. A 72, 011801 (2005).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

Phys. Today (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[CrossRef]

Other (2)

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, 1997).

E. Arimondo, “Coherent population trapping in laser spectroscopy,” in “Progress in Optics ,” vol. XXXV, E. Wolf, ed. (Elsevier, 1996), pp. 257–354.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Three-level Λ-system interacting with three-fields in an N-configuration scheme. (b) The interacting spectrum superimposed on the 87 Rb absorption spectrum.

Fig. 2
Fig. 2

Experimental setup. ECDL-External Cavity Diode Laser. PSBP-Polarization Spectroscopy using a Balanced Polarimeter. w-optical window (beam splitter). PM-fiber coupled Phase Modulator. m-mirror.ND-Natural Density filter. λ/4-a quarter waveplate. F-P-Fabry-Perot.

Fig. 3
Fig. 3

Measured normalized probe power versus modulation frequency deviation, δ, from 3417.345000 MHz for various C1L ratios. Inset: signal contrast versus C1L ratio.

Fig. 4
Fig. 4

Calculated ρ eg 2 imaginary part, oscillating at +ω RF versus δ. ω 1 and ω 2 one-photon detuning are Δ1 = –ω hfs /2 +δ and Δ2 = –ω hfs /2 – δ for ω hfs = 550Γ, Ω 1 2 + Ω 2 2 + Ω 3 2 = 0.2 Γ 2 , and Ω1 = Ω2. Inset: signal amplitude versus Ω 3 2 / Ω 1 2 ratio.

Fig. 5
Fig. 5

Measured normalized power spectra of each of the three interacting spectral components. The C1L ratio was set to obtain a maximum probe contrast at cell temperature of 58.5°C. Trace (a) refers to ω 3 ; Trace (b) refers to ω 1 ; Trace (c) refers to ω 2.

Equations (1)

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˜ = h ¯ ( Δ 1 0 Ω 1 * 2 0 Δ 2 Ω 2 * 2 + Ω 3 * 2 e + i ω R F t Ω 1 2 Ω 2 2 + Ω 3 2 e - i ω R F t 0 )

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