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.

© 2011 OSA

1. Introduction

Subnatural-width atomic resonances have stimulated great interest during the past few decades. Coherent Population Trapping (CPT) [1] and Electromagnetically Induced Transparency (EIT) [2, 3] are common examples for such resonant phenomena which occur when two coherent fields interact with a Λ configuration three-level atomic system. Furthermore, coupling a third field to the system enables to manipulate the resonance [4]. Several previous reports proposed and modeled systems where four-level atoms interact with three electromagnetic fields in an N configuration [57]. Electromagnetically Induced Absorption (EIA) resonance in two coupled and degenerated two-level systems which interact with two fields were described in [8, 9].

The N configuration can also be established in three-level Λ-systems such as Rubidium atoms. Zibrov et al. [10] described a system where two coherent fields interact with a medium consisting of an excited state and two ground states. The first field (probe) couples the excited state to the upper ground state, while the second (drive) is red-detuned by the frequency difference between the two ground states. As the drive is scanned, the probe exhibits a narrow resonant absorption profile with a contrast of up to 95% due to a three-photon process. A simplified scheme for inducing this three-photon absorption resonance by two fields originating from a modulated laser was demonstrated in [1114] for the potential application of atomic clocks.

In this paper we demonstrate large contrast EIA resonances obtained using a modification of the technique known as N-resonance [11]. In the present scheme, three separate co-propagating fields interact with a three-level Λ-system in an N configuration scheme. The D 2 transition of 87 Rb atoms serves as the Λ-system. It interacts with three spectral components in an N-type configuration as described schematically in Fig. 1(a). The probe, ω 3, couples the higher ground state |g 2〉 to the excited state |e〉 while ω 1 and ω 2 are far detuned from the |g 1〉 → |e〉 and |g 2〉 → |e〉 transition frequencies, respectively. The probe, ω 3 senses the resonance as the two other fields scan. By setting the one photon detuning values of ω 1 and ω 2 to be equal (zero two-photon Raman detuning), a two-photon transition which couples the ground states is obtained. The coupling repopulates |g 2〉 which is optically pumped by the probe and therefore increases the absorption of ω 3. The interacting spectrum is obtained by modulating a laser which emits at the |g 2〉 → |e〉 transition by half the hyperfine splitting frequency (fhfs) of 87 Rb. As shown in Fig. 1(b), the optical carrier, ω 3, serves as the probe while ω 1 and ω 2 are scanned by sweeping the modulation frequency near the two-photon Raman resonance. Under optimum conditions, the probe experiences a large absorption resonance with a contrast of up to 50%. The absorption enhancement may be thought of as a synchronous (intensity) optical pumping [15]. However, an analytical calculation shows that the experiments presented here can only be explained when the mutual coherence of the fields is taken into account. Hence, the process belongs to the family of EIA mechanisms.

 

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.

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2. The experimental setup

The experimental setup is described schematically in Fig. 2. A 780 nm External Cavity Diode Laser (ECDL) is set to the |F g = 2〉 → |F e = 2〉 transition, monitored by Polarization Spectroscopy using a Balanced Polarimeter (PSBP) [16] and coupled to a phase modulator. The RF signal feeding the modulator scans near 3.417 GHz (f hfs /2) generating the spectrum shown in Fig. 1(b). The carrier (at ω 3) to first side lobe (at ω 1 and ω 2) intensity ratio (C1L) is varied from a few percents to infinity by adjusting the modulator drive (DC bias and RF power). Second order side lobes are filtered by two backreflacting Fabry-Perot etalons; higher order side lobes are negligible. The spectrum is monitored by a Fabry-Perot spectrum analyzer and the total intensity of the three spectral lines is controlled by a natural density (ND) filter and kept constant at a moderately low value of 300 μW. The polarization is adjusted to be circular by a λ/4 plate. The Gaussian shaped beam is truncated by a 1 mm pinhole before it impinges on a cylindrical vapor cell with a diameter of 25 mm and a length of 30 mm which contains pure 87 Rb atoms and a buffer gas at a pressure of 20 torr. The cell temperature is stabilized to about 66°C. A large solenoid generates a magnetic field of 57 μT in a direction parallel to the propagation of the beam. The entire cell structure is surrounded by a μ-metal shield.

 

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.

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The output of the 87 Rb cell is filtered prior to detection by a cascade of two Fabry-Perot etalons which are slightly misaligned with respect to each other. The filters pass the carrier (probe) and rejects the first order side modes by a factor of 200.

3. Results and discussion

Measurements of probe intensities versus modulation frequency are presented in Fig. 3 for various C1L ratios. The output intensity is normalized so that the signal contrast (the ratio between resonance amplitude and its background) can be extracted. The resonance contrast versus C1L ratio is depicted in the inset of Fig. 3. The responses in Fig. 3 reveal a clear symmetric dip around the resonance frequency. For low C1L ratios, the weak probe is absorbed by the medium and therefore no additional increase in absorption is expected. For larger C1L ratios, the probe intensity increases and therefore the EIA resonance is enhanced. The resonance amplitude reaches a maximum value since the coupling efficiency is limited. The maximum value is related to the decay rates, the medium density and the relative intensities of the spectral components (proportional to the Rabi frequencies). The ratio between the spectral lines determines the relative significance of the two photon process and the optical pumping (due to ω 3) and therefore dictates the peak value of the EIA resonance. Figure 3 shows a maximum contrast of 47% at a C1L ratio of 50%. Increasing the C1L ratio above this level result in a monotonic decrease in signal contrast.

 

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.

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The three-level Λ-system described in Fig. 1(a) interacts with three field components and therefore the atom-photon interaction Hamiltonian formulated in the dipole approximation is time dependent. In a rotating frame, the secular approximation leads to a periodic time dependence with a single RF tone near ω hfs /2 = 2π · f hfs /2:

˜=h¯(Δ10Ω1*20Δ2Ω2*2+Ω3*2e+iωRFtΩ12Ω22+Ω32e-iωRFt0)
where the Rabi angular frequency Ωn = – 〈i|ε^ n · |j〉 · E n /h̄ is related to the |i〉 → |j〉 atomic transition which is induced by the n’th field component. Δn is the one-photon detuning of field component n and therefore Δ1, Δ2–ω hfs /2 while Δ3 ≃ 0. ω RF = Δ3 – Δ2 = ω hfs /2+δ where δ is the frequency deviation from ω hfs /2. The steady-state solution of a system described by the periodic Hamiltonian is obtained by solving the Schrödinger equation for the density matrix using the Flouquet theorem [17] implemented by the matrix continued fraction method [18, 19]. The steady-state solution has oscillating terms at multiples of ω RF. In the selected rotational transformation, the coherence term ρ eg2 oscillating at +ω RF is attributed to ω 3, denoted by ρeg2(+1). The imaginary part of ρeg2(+1) is therefore proportional to minus the absorption coefficient experienced by the probe. The calculated dependence of the first frequency component of ρ eg2 imaginary part on δ for various Ω32/Ω12 ratios is presented in Fig. 4. Similarly to the experiment, the sum over all squared Rabi frequencies which is proportional to the total intensity was kept constant at 0.2Γ2 while the excited state was assumed to decay to each of the ground states with the same probability, Γ/2.

 

Fig. 4 Calculated ρ eg2 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, Ω12+Ω22+Ω32=0.2Γ2, and Ω1 = Ω2. Inset: signal amplitude versus Ω32/Ω12 ratio.

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Figure 4 reveals a clear dip in the calculated transmission profile. As presented in the inset, the absorption increases with Ω32/Ω12 until it reaches a peak after which it decreases. This peak occurs when the two-photon coupling balances the optical pumping to the lower ground state due to the presence of the probe. However, the C1L ratio values in the measurement (Fig. 3) are larger than the corresponding calculated Ω32/Ω12 ratios. The difference is attributed to the complexity of the atomic structure of real Alkali atoms, especially of the D 2 transition, compared to the simplified three-level atom used in the calculations. The energetic manifold of 87 Rb in the experiment allows transitions other than the three-level Λ-system transitions. Moreover, Doppler broadened one-photon absorption processes mask the EIA effect at very low probe intensities. Similar effects are known to reduce the efficiency of CPT resonance [20]. Therefore the inset in Fig. 3 is shifted to larger C1L ratios compared to those in Fig. 4.

The EIA resonance which we described results from a population transfer between the ground states and hence also imprints a signature on the other two interacting fields. Figure 5 shows measured transmission spectra of each of the three interacting spectral components. This measurement used only one Fabry-Perot etalon at the cell output which was tuned to pass one field at a time. A clear peak and dip are observed in the ω 1 and ω 2 transmission profiles as shown in traces (b) and (c), respectively. Although the one-photon detunings of these frequency components are large, the atom absorbs a photon at ω 1 and stimulatingly emits one at ω 2 due to the two-photon process, consistent with predictions for the N configuration employing two fields in [10] and the model described here. This leads to an enhancement of the lower frequency component, ω 2, and to an absorption of ω 1.

 

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.

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4. Conclusions

In conclusion, we have presented experimentally and theoretically a high contrast EIA-type resonance in the transmission profile of a static probe beam. The underlying mechanism is a population transfer between the two ground states of a three-level Λ-system. Our calculations shows that the spectral constaletion provides a more efficient process compared to the one described by Zibrov et al. [1114] due to the lower one-photon detuning of the two fields inducing the transfer. Moreover the presented scheme naturally enables the utilization of a directly modulated diode as required for some future application such as small-scale atomic clocks.

By their nature EIA-type resonances exhibit larger contrasts than EIT-type resonances. Due to the one-photon Doppler broadened absorption processes in non-ideal Λ-systems, emitting or non-absorbing processes, like EIT, are masked while absorbing processes such as EIA are not. The measurements of the EIA profiles (Fig. 3) are hampered by the moderate resolution of the two Fabry-Perot etalons which increases the background signal and in turn reduces the observed contrast.

Finally, the setup can be easily modified so that the two photon population transfer is induced by two blue-detuned fields. This requires to tune the carrier, ω 3, to the |F g = 1〉 → |F e = 2〉 transition and exchanging the roles of ω 1 and ω 2.

Acknowledgments

This work was partially supported by the Technion Micro-Satellite Program. Ido Ben-Aroya acknowledges the Ramon fellowship of the Israeli Ministry of Science.

References and links

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]  

References

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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)

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