Abstract

We have characterized a novel photon-echo pulse sequence for a double-Λ-type energy level system where the input and rephasing transitions are different from the applied π pulses. We show that, despite having imperfect π-pulses associated with large coherent emission due to free induction decay (FID), the noise added in the echo mode is only 0.2±0.1 photons per shot, compared to 4×104 photons in the FID modes. Using this echo pulse sequence in the “rephased amplified spontaneous emission” (RASE) scheme [Phys. Rev. A 81, 012301 (2010)] will allow for generation of entangled photon pairs that are in different frequency, temporal, and potentially spatial modes to any bright driving fields. The coherence and efficiency properties of this sequence were characterized in a Pr3+:Y2SiO5 crystal.

© 2011 Optical Society of America

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  1. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature 414, 413 (2001).
    [CrossRef] [PubMed]
  2. P. M. Ledingham, W. R. Naylor, J. J. Longdell, S. E. Beavan, and M. J. Sellars, Phys. Rev. A 81, 012301 (2010).
    [CrossRef]
  3. I. D. Abella, N. A. Kurnit, and S. R. Hartmann, Phys. Rev. 141, 391 (1966).
    [CrossRef]
  4. J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 95, 63601 (2005).
    [CrossRef]
  5. E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 92, 77601 (2004).
    [CrossRef]
  6. M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, Nature 465, 1052 (2010).
    [CrossRef] [PubMed]
  7. R. W. Equall, R. L. Cone, and R. M. Macfarlane, Phys. Rev. B 52, 3963 (1995).
    [CrossRef]
  8. M. Nilsson, L. Rippe, S. Kröll, R. Klieber, and D. Suter, Phys. Rev. B 70, 214116 (2004).
    [CrossRef]
  9. T. Mossberg, A. Flusberg, R. Kachru, and S. Hartmann, Phys. Rev. Lett. 39, 1523 (1977).
    [CrossRef]
  10. G. J. Pryde, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 84, 1152 (2000).
    [CrossRef] [PubMed]
  11. E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 95, 30506 (2005).
    [CrossRef]
  12. The echo propagation is expected to be slightly different for the 4LE compared to the 2LE due to the difference in transition strengths; however, this accounts for just 4% less gain in the 4LE case (from ), which is similar in magnitude to the measurement uncertainty.
  13. Spontaneous emission is an incoherent process resulting from the population inversion and is, therefore, unavoidable, unlike the FID, which is a coherent process resulting from imprecise π pulses. The measured noise is consistent with an inversion optical depth of α34L=0.7, which is reasonable considering the low-quality of the π pulse and the original absorption of α25L=1.5.

2010 (2)

P. M. Ledingham, W. R. Naylor, J. J. Longdell, S. E. Beavan, and M. J. Sellars, Phys. Rev. A 81, 012301 (2010).
[CrossRef]

M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, Nature 465, 1052 (2010).
[CrossRef] [PubMed]

2005 (2)

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 95, 63601 (2005).
[CrossRef]

E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 95, 30506 (2005).
[CrossRef]

2004 (2)

E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 92, 77601 (2004).
[CrossRef]

M. Nilsson, L. Rippe, S. Kröll, R. Klieber, and D. Suter, Phys. Rev. B 70, 214116 (2004).
[CrossRef]

2001 (1)

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature 414, 413 (2001).
[CrossRef] [PubMed]

2000 (1)

G. J. Pryde, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 84, 1152 (2000).
[CrossRef] [PubMed]

1995 (1)

R. W. Equall, R. L. Cone, and R. M. Macfarlane, Phys. Rev. B 52, 3963 (1995).
[CrossRef]

1977 (1)

T. Mossberg, A. Flusberg, R. Kachru, and S. Hartmann, Phys. Rev. Lett. 39, 1523 (1977).
[CrossRef]

1966 (1)

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, Phys. Rev. 141, 391 (1966).
[CrossRef]

Abella, I. D.

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, Phys. Rev. 141, 391 (1966).
[CrossRef]

Beavan, S. E.

P. M. Ledingham, W. R. Naylor, J. J. Longdell, S. E. Beavan, and M. J. Sellars, Phys. Rev. A 81, 012301 (2010).
[CrossRef]

Cirac, J. I.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature 414, 413 (2001).
[CrossRef] [PubMed]

Cone, R. L.

R. W. Equall, R. L. Cone, and R. M. Macfarlane, Phys. Rev. B 52, 3963 (1995).
[CrossRef]

Duan, L.-M.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature 414, 413 (2001).
[CrossRef] [PubMed]

Equall, R. W.

R. W. Equall, R. L. Cone, and R. M. Macfarlane, Phys. Rev. B 52, 3963 (1995).
[CrossRef]

Flusberg, A.

T. Mossberg, A. Flusberg, R. Kachru, and S. Hartmann, Phys. Rev. Lett. 39, 1523 (1977).
[CrossRef]

Fraval, E.

E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 95, 30506 (2005).
[CrossRef]

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 95, 63601 (2005).
[CrossRef]

E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 92, 77601 (2004).
[CrossRef]

Hartmann, S.

T. Mossberg, A. Flusberg, R. Kachru, and S. Hartmann, Phys. Rev. Lett. 39, 1523 (1977).
[CrossRef]

Hartmann, S. R.

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, Phys. Rev. 141, 391 (1966).
[CrossRef]

Hedges, M. P.

M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, Nature 465, 1052 (2010).
[CrossRef] [PubMed]

Kachru, R.

T. Mossberg, A. Flusberg, R. Kachru, and S. Hartmann, Phys. Rev. Lett. 39, 1523 (1977).
[CrossRef]

Klieber, R.

M. Nilsson, L. Rippe, S. Kröll, R. Klieber, and D. Suter, Phys. Rev. B 70, 214116 (2004).
[CrossRef]

Kröll, S.

M. Nilsson, L. Rippe, S. Kröll, R. Klieber, and D. Suter, Phys. Rev. B 70, 214116 (2004).
[CrossRef]

Kurnit, N. A.

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, Phys. Rev. 141, 391 (1966).
[CrossRef]

Ledingham, P. M.

P. M. Ledingham, W. R. Naylor, J. J. Longdell, S. E. Beavan, and M. J. Sellars, Phys. Rev. A 81, 012301 (2010).
[CrossRef]

Li, Y.

M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, Nature 465, 1052 (2010).
[CrossRef] [PubMed]

Longdell, J. J.

M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, Nature 465, 1052 (2010).
[CrossRef] [PubMed]

P. M. Ledingham, W. R. Naylor, J. J. Longdell, S. E. Beavan, and M. J. Sellars, Phys. Rev. A 81, 012301 (2010).
[CrossRef]

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 95, 63601 (2005).
[CrossRef]

E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 95, 30506 (2005).
[CrossRef]

E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 92, 77601 (2004).
[CrossRef]

Lukin, M. D.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature 414, 413 (2001).
[CrossRef] [PubMed]

Macfarlane, R. M.

R. W. Equall, R. L. Cone, and R. M. Macfarlane, Phys. Rev. B 52, 3963 (1995).
[CrossRef]

Manson, N. B.

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 95, 63601 (2005).
[CrossRef]

G. J. Pryde, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 84, 1152 (2000).
[CrossRef] [PubMed]

Mossberg, T.

T. Mossberg, A. Flusberg, R. Kachru, and S. Hartmann, Phys. Rev. Lett. 39, 1523 (1977).
[CrossRef]

Naylor, W. R.

P. M. Ledingham, W. R. Naylor, J. J. Longdell, S. E. Beavan, and M. J. Sellars, Phys. Rev. A 81, 012301 (2010).
[CrossRef]

Nilsson, M.

M. Nilsson, L. Rippe, S. Kröll, R. Klieber, and D. Suter, Phys. Rev. B 70, 214116 (2004).
[CrossRef]

Pryde, G. J.

G. J. Pryde, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 84, 1152 (2000).
[CrossRef] [PubMed]

Rippe, L.

M. Nilsson, L. Rippe, S. Kröll, R. Klieber, and D. Suter, Phys. Rev. B 70, 214116 (2004).
[CrossRef]

Sellars, M. J.

M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, Nature 465, 1052 (2010).
[CrossRef] [PubMed]

P. M. Ledingham, W. R. Naylor, J. J. Longdell, S. E. Beavan, and M. J. Sellars, Phys. Rev. A 81, 012301 (2010).
[CrossRef]

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 95, 63601 (2005).
[CrossRef]

E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 95, 30506 (2005).
[CrossRef]

E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 92, 77601 (2004).
[CrossRef]

G. J. Pryde, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 84, 1152 (2000).
[CrossRef] [PubMed]

Suter, D.

M. Nilsson, L. Rippe, S. Kröll, R. Klieber, and D. Suter, Phys. Rev. B 70, 214116 (2004).
[CrossRef]

Zoller, P.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature 414, 413 (2001).
[CrossRef] [PubMed]

Nature (2)

M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, Nature 465, 1052 (2010).
[CrossRef] [PubMed]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature 414, 413 (2001).
[CrossRef] [PubMed]

Phys. Rev. (1)

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, Phys. Rev. 141, 391 (1966).
[CrossRef]

Phys. Rev. A (1)

P. M. Ledingham, W. R. Naylor, J. J. Longdell, S. E. Beavan, and M. J. Sellars, Phys. Rev. A 81, 012301 (2010).
[CrossRef]

Phys. Rev. B (2)

R. W. Equall, R. L. Cone, and R. M. Macfarlane, Phys. Rev. B 52, 3963 (1995).
[CrossRef]

M. Nilsson, L. Rippe, S. Kröll, R. Klieber, and D. Suter, Phys. Rev. B 70, 214116 (2004).
[CrossRef]

Phys. Rev. Lett. (5)

T. Mossberg, A. Flusberg, R. Kachru, and S. Hartmann, Phys. Rev. Lett. 39, 1523 (1977).
[CrossRef]

G. J. Pryde, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 84, 1152 (2000).
[CrossRef] [PubMed]

E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 95, 30506 (2005).
[CrossRef]

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 95, 63601 (2005).
[CrossRef]

E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 92, 77601 (2004).
[CrossRef]

Other (2)

The echo propagation is expected to be slightly different for the 4LE compared to the 2LE due to the difference in transition strengths; however, this accounts for just 4% less gain in the 4LE case (from ), which is similar in magnitude to the measurement uncertainty.

Spontaneous emission is an incoherent process resulting from the population inversion and is, therefore, unavoidable, unlike the FID, which is a coherent process resulting from imprecise π pulses. The measured noise is consistent with an inversion optical depth of α34L=0.7, which is reasonable considering the low-quality of the π pulse and the original absorption of α25L=1.5.

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Figures (4)

Fig. 1
Fig. 1

(a) Reduced energy level diagram for Pr 3 + : Y 2 SiO 5 . (b) Pulse sequence for the 4LE, with transition frequencies marked. The total delay time between input pulse and echo is 2 τ a + τ b . (c) Pulse sequence for the standard two-level echo used for comparison measurements of echo efficiency and decoherence.

Fig. 2
Fig. 2

Photon-echo amplitude with varying delay time. The x axis represents the time between input pulse and the echo; 2 τ a for the four-level sequence (here τ b = 0 ) and 2 τ for the two-level sequence. Amplitude FWHMs of the π pulses are 0.6 and 1.0 μs .

Fig. 3
Fig. 3

4LE amplitude as a function of τ b , the delay time between the two π pulses. The loss of coherence is predominantly due to inhomogeneity on the RF transition; however, the decay is not simply exponential, indicating a transition profile that is not purely Lorentzian. For these data, τ a = 15 μs .

Fig. 4
Fig. 4

Example amplitude spectrum obtained for the 4LE efficiency measurements. (a) The input pulse; peak power is 5 μW , or 0.3% of the π-pulse peak power. (b) Echo obtained after a total delay time ( 2 τ a ) of 30 μs ( τ b = 0 ). The x -axis is the frequency of the signal after mixing with a local oscillator beam. The frequency difference between input pulse and echo is 14.8 MHz .

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