Abstract

I theoretically study the behavior of strong pulses exciting emitters inside a cavity. The ensemble is supposed to be inhomogeneously broadened and the cavity matched finding application in quantum storage of optical or RF photons. My analysis is based on energy and pulse area conservation rules predicting important distortions for specific areas. It is well supported by numerical simulations. I propose a qualitative interpretation in terms of slow-light. The analogy with the free space situation is remarkable.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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  27. C. Greiner, B. Boggs, T. W. Mossberg, “Frustrated pulse-area quantization in accelerated superradiant atom-cavity systems,” Phys. Rev. A 67, 063811 (2003).
    [CrossRef]
  28. M. J. Collett, C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
    [CrossRef]
  29. C. W. Gardiner, M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
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    [CrossRef]
  32. B. Julsgaard, K. Mølmer, “Reflectivity and transmissivity of a cavity coupled to two-level systems: Coherence properties and the influence of phase decay,” Phys. Rev. A 85, 013844 (2012).
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  38. K. Ichimura, H. Goto, “Normal-mode coupling of rare-earth-metal ions in a crystal to a macroscopic optical cavity mode,” Phys. Rev. A 74, 033818 (2006).
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  39. H. Goto, S. Nakamura, K. Ichimura, “Experimental determination of intracavity losses of monolithic Fabry-Perot cavities made of Pr3+:Y2SiO5,” Opt. Express 18, 23763–23775 (2010).
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  40. M. Sabooni, Q. Li, L. Rippe, S. Kröll, “Three orders of magnitude cavity-linewidth narrowing by slow light in a rare-earth-ion-doped crystal cavity,” arXiv preprint arXiv:1304.4456 (2013).
  41. V. Damon, M. Bonarota, A. Louchet-Chauvet, T. Chanelière, J.-L. Le Gouët, “Revival of silenced echo and quantum memory for light,” New J. Phys. 13, 093031 (2011).
    [CrossRef]
  42. F. C. Spano, W. S. Warren, “Preparation of constant-bandwidth total inversion, independent of optical density, with phase-modulated laser pulses,” Phys. Rev. A 37, 1013–1016 (1988).
    [CrossRef] [PubMed]

2013

M. Sabooni, S. T. Kometa, A. Thuresson, S. Kröll, L. Rippe, “Cavity-enhanced storage-preparing for high-efficiency quantum memories,” New J. Phys. 15, 035025 (2013).
[CrossRef]

M. Afzelius, N. Sangouard, G. Johansson, M. U. Staudt, C. M. Wilson, “Proposal for a coherent quantum memory for propagating microwave photons,” New J. Phys. 15, 065008 (2013).
[CrossRef]

B. Julsgaard, C. Grezes, P. Bertet, K. Mølmer, “Quantum memory for microwave photons in an inhomogeneously broadened spin ensemble,” Phys. Rev. Lett. 110, 250503 (2013).
[CrossRef] [PubMed]

W. Gao, X.-D. Tan, M.-F. Wang, Y.-Z. Zheng, “Quantum memory with natural inhomogeneous broadening in an optical cavity,” Int. J. Theor. Phys. 52, 2092–2098 (2013).
[CrossRef]

S. A. Moiseev, “Off-resonant raman-echo quantum memory for inhomogeneously broadened atoms in a cavity,” Phys. Rev. A 88, 012304 (2013).
[CrossRef]

2012

B. Julsgaard, K. Mølmer, “Reflectivity and transmissivity of a cavity coupled to two-level systems: Coherence properties and the influence of phase decay,” Phys. Rev. A 85, 013844 (2012).
[CrossRef]

2011

V. Damon, M. Bonarota, A. Louchet-Chauvet, T. Chanelière, J.-L. Le Gouët, “Revival of silenced echo and quantum memory for light,” New J. Phys. 13, 093031 (2011).
[CrossRef]

R. Amsüss, C. Koller, T. Nöbauer, S. Putz, S. Rotter, K. Sandner, S. Schneider, M. Schramböck, G. Steinhauser, H. Ritsch, J. Schmiedmayer, J. Majer, “Cavity QED with magnetically coupled collective spin states,” Phys. Rev. Lett. 107, 060502 (2011).
[CrossRef] [PubMed]

P. Bushev, A. K. Feofanov, H. Rotzinger, I. Protopopov, J. H. Cole, C. M. Wilson, G. Fischer, A. Lukashenko, A. V. Ustinov, “Ultralow-power spectroscopy of a rare-earth spin ensemble using a superconducting resonator,” Phys. Rev. B 84, 060501 (2011).
[CrossRef]

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, P. Bertet, “Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[CrossRef] [PubMed]

2010

D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D. Awschalom, R. J. Schoelkopf, “High-cooperativity coupling of electron-spin ensembles to superconducting cavities,” Phys. Rev. Lett. 105, 140501 (2010).
[CrossRef]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J.-F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, D. Esteve, “Strong coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[CrossRef]

M. Afzelius, C. Simon, “Impedance-matched cavity quantum memory,” Phys. Rev. A 82, 022310 (2010).
[CrossRef]

S. A. Moiseev, S. N. Andrianov, F. F. Gubaidullin, “Efficient multimode quantum memory based on photon echo in an optimal QED cavity,” Phys. Rev. A 82, 022311 (2010).
[CrossRef]

J. Ruggiero, T. Chanelière, J.-L. Le Gouët, “Coherent response to optical excitation in a strongly absorbing rare-earth ion-doped crystal,” J. Opt. Soc. Am. B 27, 32–37 (2010).
[CrossRef]

H. Goto, S. Nakamura, K. Ichimura, “Experimental determination of intracavity losses of monolithic Fabry-Perot cavities made of Pr3+:Y2SiO5,” Opt. Express 18, 23763–23775 (2010).
[CrossRef] [PubMed]

2009

J. Ruggiero, J.-L. Le Gouët, C. Simon, T. Chanelière, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79, 053851 (2009).
[CrossRef]

2007

A. V. Gorshkov, A. André, M. D. Lukin, A. S. Sørensen, “Photon storage in λ-type optically dense atomic media. I. cavity model,” Phys. Rev. A 76, 033804 (2007).
[CrossRef]

2006

K. Ichimura, H. Goto, “Normal-mode coupling of rare-earth-metal ions in a crystal to a macroscopic optical cavity mode,” Phys. Rev. A 74, 033818 (2006).
[CrossRef]

2004

S. A. Moiseev, “Quantum memory for intense light fields in photon echo technique,” Izv. Ross. Akad. Nauk, Ser. Fiz. 68, 1260 (2004).

2003

C. Greiner, B. Boggs, T. W. Mossberg, “Frustrated pulse-area quantization in accelerated superradiant atom-cavity systems,” Phys. Rev. A 67, 063811 (2003).
[CrossRef]

2001

C. Greiner, T. Wang, T. Loftus, T. W. Mossberg, “Instability and pulse area quantization in accelerated superradiant atom-cavity systems,” Phys. Rev. Lett. 87, 253602 (2001).
[CrossRef] [PubMed]

1998

J. Eberly, “Area theorem rederived,” Opt. Express 2, 173–176 (1998).
[CrossRef] [PubMed]

L. Viola, S. Lloyd, “Dynamical suppression of decoherence in two-state quantum systems,” Phys. Rev. A 58, 2733–2744 (1998).
[CrossRef]

1997

V. A. Goryachev, S. M. Zakharov, “Dynamics of transmission of ultrashort light pulses by thin-film cavity structures,” Quantum Electron. 27, 245–248 (1997).
[CrossRef]

J. Van Wyk, E. Reynhardt, G. High, I. Kiflawi, “The dependences of ESR line widths and spin-spin relaxation times of single nitrogen defects on the concentration of nitrogen defects in diamond,” J. Phys. D Appl. Phys. 30, 1790 (1997).
[CrossRef]

1995

S. Zakharov, “Interaction of ultrashort light pulses with thin-film resonant structures,” Zh. Eksp. Teor. Fiz 108, 829–841 (1995).

1988

F. C. Spano, W. S. Warren, “Preparation of constant-bandwidth total inversion, independent of optical density, with phase-modulated laser pulses,” Phys. Rev. A 37, 1013–1016 (1988).
[CrossRef] [PubMed]

W. J. Kozlovsky, C. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped CW Nd: YAG laser using monolithic MgO: LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

1985

C. W. Gardiner, M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef] [PubMed]

1984

M. J. Collett, C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

1981

P. Drummond, “Optical bistability in a radially varying mode,” IEEE J. Quantum Electron. 17, 301–306 (1981).
[CrossRef]

1969

S. Stenholm, W. E. Lamb, “Semiclassical theory of a high-intensity laser,” Phys. Rev. 181, 618–635 (1969).
[CrossRef]

1967

S. L. McCall, E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

1964

F. Gires, P. Tournois, “Interfèromètre utilisable pour la compression d’impulsions lumineuses modulées en fréquence,” C. R. Acad. Sci. Paris 258, 6112–6115 (1964).

Abe, H.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, P. Bertet, “Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[CrossRef] [PubMed]

Afzelius, M.

M. Afzelius, N. Sangouard, G. Johansson, M. U. Staudt, C. M. Wilson, “Proposal for a coherent quantum memory for propagating microwave photons,” New J. Phys. 15, 065008 (2013).
[CrossRef]

M. Afzelius, C. Simon, “Impedance-matched cavity quantum memory,” Phys. Rev. A 82, 022310 (2010).
[CrossRef]

Allen, L.

L. Allen, J. Eberly, Optical Resonance and Two-Level Atoms (Courier Dover, 1987).

Amsüss, R.

R. Amsüss, C. Koller, T. Nöbauer, S. Putz, S. Rotter, K. Sandner, S. Schneider, M. Schramböck, G. Steinhauser, H. Ritsch, J. Schmiedmayer, J. Majer, “Cavity QED with magnetically coupled collective spin states,” Phys. Rev. Lett. 107, 060502 (2011).
[CrossRef] [PubMed]

André, A.

A. V. Gorshkov, A. André, M. D. Lukin, A. S. Sørensen, “Photon storage in λ-type optically dense atomic media. I. cavity model,” Phys. Rev. A 76, 033804 (2007).
[CrossRef]

Andrianov, S. N.

S. A. Moiseev, S. N. Andrianov, F. F. Gubaidullin, “Efficient multimode quantum memory based on photon echo in an optimal QED cavity,” Phys. Rev. A 82, 022311 (2010).
[CrossRef]

Auffeves, A.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, P. Bertet, “Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[CrossRef] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J.-F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, D. Esteve, “Strong coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[CrossRef]

Awschalom, D. D.

D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D. Awschalom, R. J. Schoelkopf, “High-cooperativity coupling of electron-spin ensembles to superconducting cavities,” Phys. Rev. Lett. 105, 140501 (2010).
[CrossRef]

Barthe, M. F.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J.-F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, D. Esteve, “Strong coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[CrossRef]

Bergonzo, P.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J.-F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, D. Esteve, “Strong coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[CrossRef]

Bertet, P.

B. Julsgaard, C. Grezes, P. Bertet, K. Mølmer, “Quantum memory for microwave photons in an inhomogeneously broadened spin ensemble,” Phys. Rev. Lett. 110, 250503 (2013).
[CrossRef] [PubMed]

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, P. Bertet, “Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[CrossRef] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J.-F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, D. Esteve, “Strong coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[CrossRef]

Boggs, B.

C. Greiner, B. Boggs, T. W. Mossberg, “Frustrated pulse-area quantization in accelerated superradiant atom-cavity systems,” Phys. Rev. A 67, 063811 (2003).
[CrossRef]

Bonarota, M.

V. Damon, M. Bonarota, A. Louchet-Chauvet, T. Chanelière, J.-L. Le Gouët, “Revival of silenced echo and quantum memory for light,” New J. Phys. 13, 093031 (2011).
[CrossRef]

Briggs, G. A. D.

D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D. Awschalom, R. J. Schoelkopf, “High-cooperativity coupling of electron-spin ensembles to superconducting cavities,” Phys. Rev. Lett. 105, 140501 (2010).
[CrossRef]

Buckley, B. B.

D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D. Awschalom, R. J. Schoelkopf, “High-cooperativity coupling of electron-spin ensembles to superconducting cavities,” Phys. Rev. Lett. 105, 140501 (2010).
[CrossRef]

Bushev, P.

P. Bushev, A. K. Feofanov, H. Rotzinger, I. Protopopov, J. H. Cole, C. M. Wilson, G. Fischer, A. Lukashenko, A. V. Ustinov, “Ultralow-power spectroscopy of a rare-earth spin ensemble using a superconducting resonator,” Phys. Rev. B 84, 060501 (2011).
[CrossRef]

Byer, R. L.

W. J. Kozlovsky, C. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped CW Nd: YAG laser using monolithic MgO: LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

Chanelière, T.

V. Damon, M. Bonarota, A. Louchet-Chauvet, T. Chanelière, J.-L. Le Gouët, “Revival of silenced echo and quantum memory for light,” New J. Phys. 13, 093031 (2011).
[CrossRef]

J. Ruggiero, T. Chanelière, J.-L. Le Gouët, “Coherent response to optical excitation in a strongly absorbing rare-earth ion-doped crystal,” J. Opt. Soc. Am. B 27, 32–37 (2010).
[CrossRef]

J. Ruggiero, J.-L. Le Gouët, C. Simon, T. Chanelière, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79, 053851 (2009).
[CrossRef]

Cole, J. H.

P. Bushev, A. K. Feofanov, H. Rotzinger, I. Protopopov, J. H. Cole, C. M. Wilson, G. Fischer, A. Lukashenko, A. V. Ustinov, “Ultralow-power spectroscopy of a rare-earth spin ensemble using a superconducting resonator,” Phys. Rev. B 84, 060501 (2011).
[CrossRef]

Collett, M. J.

C. W. Gardiner, M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef] [PubMed]

M. J. Collett, C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

Damon, V.

V. Damon, M. Bonarota, A. Louchet-Chauvet, T. Chanelière, J.-L. Le Gouët, “Revival of silenced echo and quantum memory for light,” New J. Phys. 13, 093031 (2011).
[CrossRef]

Dewes, A.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, P. Bertet, “Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[CrossRef] [PubMed]

DiCarlo, L.

D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D. Awschalom, R. J. Schoelkopf, “High-cooperativity coupling of electron-spin ensembles to superconducting cavities,” Phys. Rev. Lett. 105, 140501 (2010).
[CrossRef]

Diniz, I.

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M. Sabooni, S. T. Kometa, A. Thuresson, S. Kröll, L. Rippe, “Cavity-enhanced storage-preparing for high-efficiency quantum memories,” New J. Phys. 15, 035025 (2013).
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R. Amsüss, C. Koller, T. Nöbauer, S. Putz, S. Rotter, K. Sandner, S. Schneider, M. Schramböck, G. Steinhauser, H. Ritsch, J. Schmiedmayer, J. Majer, “Cavity QED with magnetically coupled collective spin states,” Phys. Rev. Lett. 107, 060502 (2011).
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M. Sabooni, S. T. Kometa, A. Thuresson, S. Kröll, L. Rippe, “Cavity-enhanced storage-preparing for high-efficiency quantum memories,” New J. Phys. 15, 035025 (2013).
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R. Amsüss, C. Koller, T. Nöbauer, S. Putz, S. Rotter, K. Sandner, S. Schneider, M. Schramböck, G. Steinhauser, H. Ritsch, J. Schmiedmayer, J. Majer, “Cavity QED with magnetically coupled collective spin states,” Phys. Rev. Lett. 107, 060502 (2011).
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Schoelkopf, R. J.

D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D. Awschalom, R. J. Schoelkopf, “High-cooperativity coupling of electron-spin ensembles to superconducting cavities,” Phys. Rev. Lett. 105, 140501 (2010).
[CrossRef]

Schramböck, M.

R. Amsüss, C. Koller, T. Nöbauer, S. Putz, S. Rotter, K. Sandner, S. Schneider, M. Schramböck, G. Steinhauser, H. Ritsch, J. Schmiedmayer, J. Majer, “Cavity QED with magnetically coupled collective spin states,” Phys. Rev. Lett. 107, 060502 (2011).
[CrossRef] [PubMed]

Schuster, D. I.

D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D. Awschalom, R. J. Schoelkopf, “High-cooperativity coupling of electron-spin ensembles to superconducting cavities,” Phys. Rev. Lett. 105, 140501 (2010).
[CrossRef]

Sears, A. P.

D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D. Awschalom, R. J. Schoelkopf, “High-cooperativity coupling of electron-spin ensembles to superconducting cavities,” Phys. Rev. Lett. 105, 140501 (2010).
[CrossRef]

Simon, C.

M. Afzelius, C. Simon, “Impedance-matched cavity quantum memory,” Phys. Rev. A 82, 022310 (2010).
[CrossRef]

J. Ruggiero, J.-L. Le Gouët, C. Simon, T. Chanelière, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79, 053851 (2009).
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Slichter, C. P.

C. P. Slichter, Principles of Magnetic Resonance (Springer, 1990), Vol. 1.
[CrossRef]

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A. V. Gorshkov, A. André, M. D. Lukin, A. S. Sørensen, “Photon storage in λ-type optically dense atomic media. I. cavity model,” Phys. Rev. A 76, 033804 (2007).
[CrossRef]

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F. C. Spano, W. S. Warren, “Preparation of constant-bandwidth total inversion, independent of optical density, with phase-modulated laser pulses,” Phys. Rev. A 37, 1013–1016 (1988).
[CrossRef] [PubMed]

Staudt, M. U.

M. Afzelius, N. Sangouard, G. Johansson, M. U. Staudt, C. M. Wilson, “Proposal for a coherent quantum memory for propagating microwave photons,” New J. Phys. 15, 065008 (2013).
[CrossRef]

Steinhauser, G.

R. Amsüss, C. Koller, T. Nöbauer, S. Putz, S. Rotter, K. Sandner, S. Schneider, M. Schramböck, G. Steinhauser, H. Ritsch, J. Schmiedmayer, J. Majer, “Cavity QED with magnetically coupled collective spin states,” Phys. Rev. Lett. 107, 060502 (2011).
[CrossRef] [PubMed]

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S. Stenholm, W. E. Lamb, “Semiclassical theory of a high-intensity laser,” Phys. Rev. 181, 618–635 (1969).
[CrossRef]

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Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, P. Bertet, “Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[CrossRef] [PubMed]

Tan, X.-D.

W. Gao, X.-D. Tan, M.-F. Wang, Y.-Z. Zheng, “Quantum memory with natural inhomogeneous broadening in an optical cavity,” Int. J. Theor. Phys. 52, 2092–2098 (2013).
[CrossRef]

Thuresson, A.

M. Sabooni, S. T. Kometa, A. Thuresson, S. Kröll, L. Rippe, “Cavity-enhanced storage-preparing for high-efficiency quantum memories,” New J. Phys. 15, 035025 (2013).
[CrossRef]

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Umeda, T.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, P. Bertet, “Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[CrossRef] [PubMed]

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P. Bushev, A. K. Feofanov, H. Rotzinger, I. Protopopov, J. H. Cole, C. M. Wilson, G. Fischer, A. Lukashenko, A. V. Ustinov, “Ultralow-power spectroscopy of a rare-earth spin ensemble using a superconducting resonator,” Phys. Rev. B 84, 060501 (2011).
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J. Van Wyk, E. Reynhardt, G. High, I. Kiflawi, “The dependences of ESR line widths and spin-spin relaxation times of single nitrogen defects on the concentration of nitrogen defects in diamond,” J. Phys. D Appl. Phys. 30, 1790 (1997).
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L. Viola, S. Lloyd, “Dynamical suppression of decoherence in two-state quantum systems,” Phys. Rev. A 58, 2733–2744 (1998).
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Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, P. Bertet, “Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[CrossRef] [PubMed]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J.-F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, D. Esteve, “Strong coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
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Wang, M.-F.

W. Gao, X.-D. Tan, M.-F. Wang, Y.-Z. Zheng, “Quantum memory with natural inhomogeneous broadening in an optical cavity,” Int. J. Theor. Phys. 52, 2092–2098 (2013).
[CrossRef]

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C. Greiner, T. Wang, T. Loftus, T. W. Mossberg, “Instability and pulse area quantization in accelerated superradiant atom-cavity systems,” Phys. Rev. Lett. 87, 253602 (2001).
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F. C. Spano, W. S. Warren, “Preparation of constant-bandwidth total inversion, independent of optical density, with phase-modulated laser pulses,” Phys. Rev. A 37, 1013–1016 (1988).
[CrossRef] [PubMed]

Wilson, C. M.

M. Afzelius, N. Sangouard, G. Johansson, M. U. Staudt, C. M. Wilson, “Proposal for a coherent quantum memory for propagating microwave photons,” New J. Phys. 15, 065008 (2013).
[CrossRef]

P. Bushev, A. K. Feofanov, H. Rotzinger, I. Protopopov, J. H. Cole, C. M. Wilson, G. Fischer, A. Lukashenko, A. V. Ustinov, “Ultralow-power spectroscopy of a rare-earth spin ensemble using a superconducting resonator,” Phys. Rev. B 84, 060501 (2011).
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Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J.-F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, D. Esteve, “Strong coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[CrossRef]

Wu, H.

D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D. Awschalom, R. J. Schoelkopf, “High-cooperativity coupling of electron-spin ensembles to superconducting cavities,” Phys. Rev. Lett. 105, 140501 (2010).
[CrossRef]

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S. Zakharov, “Interaction of ultrashort light pulses with thin-film resonant structures,” Zh. Eksp. Teor. Fiz 108, 829–841 (1995).

Zakharov, S. M.

V. A. Goryachev, S. M. Zakharov, “Dynamics of transmission of ultrashort light pulses by thin-film cavity structures,” Quantum Electron. 27, 245–248 (1997).
[CrossRef]

Zheng, D.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J.-F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, D. Esteve, “Strong coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[CrossRef]

Zheng, Y.-Z.

W. Gao, X.-D. Tan, M.-F. Wang, Y.-Z. Zheng, “Quantum memory with natural inhomogeneous broadening in an optical cavity,” Int. J. Theor. Phys. 52, 2092–2098 (2013).
[CrossRef]

C. R. Acad. Sci. Paris

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IEEE J. Quantum Electron.

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[CrossRef]

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[CrossRef]

Int. J. Theor. Phys.

W. Gao, X.-D. Tan, M.-F. Wang, Y.-Z. Zheng, “Quantum memory with natural inhomogeneous broadening in an optical cavity,” Int. J. Theor. Phys. 52, 2092–2098 (2013).
[CrossRef]

Izv. Ross. Akad. Nauk, Ser. Fiz.

S. A. Moiseev, “Quantum memory for intense light fields in photon echo technique,” Izv. Ross. Akad. Nauk, Ser. Fiz. 68, 1260 (2004).

J. Opt. Soc. Am. B

J. Phys. D Appl. Phys.

J. Van Wyk, E. Reynhardt, G. High, I. Kiflawi, “The dependences of ESR line widths and spin-spin relaxation times of single nitrogen defects on the concentration of nitrogen defects in diamond,” J. Phys. D Appl. Phys. 30, 1790 (1997).
[CrossRef]

New J. Phys.

M. Afzelius, N. Sangouard, G. Johansson, M. U. Staudt, C. M. Wilson, “Proposal for a coherent quantum memory for propagating microwave photons,” New J. Phys. 15, 065008 (2013).
[CrossRef]

M. Sabooni, S. T. Kometa, A. Thuresson, S. Kröll, L. Rippe, “Cavity-enhanced storage-preparing for high-efficiency quantum memories,” New J. Phys. 15, 035025 (2013).
[CrossRef]

V. Damon, M. Bonarota, A. Louchet-Chauvet, T. Chanelière, J.-L. Le Gouët, “Revival of silenced echo and quantum memory for light,” New J. Phys. 13, 093031 (2011).
[CrossRef]

Opt. Express

Phys. Rev.

S. Stenholm, W. E. Lamb, “Semiclassical theory of a high-intensity laser,” Phys. Rev. 181, 618–635 (1969).
[CrossRef]

Phys. Rev. A

C. Greiner, B. Boggs, T. W. Mossberg, “Frustrated pulse-area quantization in accelerated superradiant atom-cavity systems,” Phys. Rev. A 67, 063811 (2003).
[CrossRef]

M. J. Collett, C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

C. W. Gardiner, M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef] [PubMed]

A. V. Gorshkov, A. André, M. D. Lukin, A. S. Sørensen, “Photon storage in λ-type optically dense atomic media. I. cavity model,” Phys. Rev. A 76, 033804 (2007).
[CrossRef]

B. Julsgaard, K. Mølmer, “Reflectivity and transmissivity of a cavity coupled to two-level systems: Coherence properties and the influence of phase decay,” Phys. Rev. A 85, 013844 (2012).
[CrossRef]

L. Viola, S. Lloyd, “Dynamical suppression of decoherence in two-state quantum systems,” Phys. Rev. A 58, 2733–2744 (1998).
[CrossRef]

M. Afzelius, C. Simon, “Impedance-matched cavity quantum memory,” Phys. Rev. A 82, 022310 (2010).
[CrossRef]

S. A. Moiseev, S. N. Andrianov, F. F. Gubaidullin, “Efficient multimode quantum memory based on photon echo in an optimal QED cavity,” Phys. Rev. A 82, 022311 (2010).
[CrossRef]

J. Ruggiero, J.-L. Le Gouët, C. Simon, T. Chanelière, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79, 053851 (2009).
[CrossRef]

S. A. Moiseev, “Off-resonant raman-echo quantum memory for inhomogeneously broadened atoms in a cavity,” Phys. Rev. A 88, 012304 (2013).
[CrossRef]

F. C. Spano, W. S. Warren, “Preparation of constant-bandwidth total inversion, independent of optical density, with phase-modulated laser pulses,” Phys. Rev. A 37, 1013–1016 (1988).
[CrossRef] [PubMed]

K. Ichimura, H. Goto, “Normal-mode coupling of rare-earth-metal ions in a crystal to a macroscopic optical cavity mode,” Phys. Rev. A 74, 033818 (2006).
[CrossRef]

Phys. Rev. B

P. Bushev, A. K. Feofanov, H. Rotzinger, I. Protopopov, J. H. Cole, C. M. Wilson, G. Fischer, A. Lukashenko, A. V. Ustinov, “Ultralow-power spectroscopy of a rare-earth spin ensemble using a superconducting resonator,” Phys. Rev. B 84, 060501 (2011).
[CrossRef]

Phys. Rev. Lett.

Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, P. Bertet, “Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble,” Phys. Rev. Lett. 107, 220501 (2011).
[CrossRef] [PubMed]

D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D. Awschalom, R. J. Schoelkopf, “High-cooperativity coupling of electron-spin ensembles to superconducting cavities,” Phys. Rev. Lett. 105, 140501 (2010).
[CrossRef]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J.-F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, D. Esteve, “Strong coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[CrossRef]

R. Amsüss, C. Koller, T. Nöbauer, S. Putz, S. Rotter, K. Sandner, S. Schneider, M. Schramböck, G. Steinhauser, H. Ritsch, J. Schmiedmayer, J. Majer, “Cavity QED with magnetically coupled collective spin states,” Phys. Rev. Lett. 107, 060502 (2011).
[CrossRef] [PubMed]

B. Julsgaard, C. Grezes, P. Bertet, K. Mølmer, “Quantum memory for microwave photons in an inhomogeneously broadened spin ensemble,” Phys. Rev. Lett. 110, 250503 (2013).
[CrossRef] [PubMed]

C. Greiner, T. Wang, T. Loftus, T. W. Mossberg, “Instability and pulse area quantization in accelerated superradiant atom-cavity systems,” Phys. Rev. Lett. 87, 253602 (2001).
[CrossRef] [PubMed]

S. L. McCall, E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
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Quantum Electron.

V. A. Goryachev, S. M. Zakharov, “Dynamics of transmission of ultrashort light pulses by thin-film cavity structures,” Quantum Electron. 27, 245–248 (1997).
[CrossRef]

Zh. Eksp. Teor. Fiz

S. Zakharov, “Interaction of ultrashort light pulses with thin-film resonant structures,” Zh. Eksp. Teor. Fiz 108, 829–841 (1995).

Other

D. M. Pozar, Microwave Engineering, 3 (John Wiley, 2005).

C. P. Slichter, Principles of Magnetic Resonance (Springer, 1990), Vol. 1.
[CrossRef]

D. F. Walls, G. J. Milburn, Quantum Optics (Springer, 1995).

S. Haroche, J. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons, Oxford Graduate Texts (OUP Oxford, 2006).
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L. Allen, J. Eberly, Optical Resonance and Two-Level Atoms (Courier Dover, 1987).

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[CrossRef]

M. Sabooni, Q. Li, L. Rippe, S. Kröll, “Three orders of magnitude cavity-linewidth narrowing by slow light in a rare-earth-ion-doped crystal cavity,” arXiv preprint arXiv:1304.4456 (2013).

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Figures (4)

Fig. 1
Fig. 1

Active ring cavity uniformly filled with emitters. The entrance mirror is partially reflecting. The different fields are defined by their time-varying Rabi frequencies: Ωin, Ωout represent the incoming and the outgoing amplitudes on the entrance mirror and Ω the intracavity mode amplitude. The spatial dependence can be neglected when the round-trip absorption is small. The local interference because of a partial beam overlap is supposed to be negligibly within the cavity volume.

Fig. 2
Fig. 2

Outgoing Θout (top) and intracavity area Θ (bottom) as a function of the incoming area Θin calculated from the matched cavity area theorem (Eq. (10)). Squares correspond to the numerical simulation of the pulse temporal shapes that will be detailed later on (see 4.3). It serves as a validation of the numerically calculated area that can be compared to the analytic result of the area theorem.

Fig. 3
Fig. 3

Top: incoming gaussian pulses Ωin of varying area Θ in = 0.4 κ 2 π in black, Θ in = κ 2 π in red (π -pulse) and Θ in = κ π in blue (2π-pulse). The corresponding intracavity Ω (middle) and outgoing pulses Ωout (bottom).

Fig. 4
Fig. 4

Left: normalized outgoing pulse Ωout for Θ in = 0.4 κ 2 π, κ 2 π and κ π in black, red and blue respectively (as in Fig. 3). The normalised incoming pulse is plotted as a reference (dashed red). The long tail of the outgoing π-pulse (red) is prominent. Right: root mean square (rms) temporal widths of the calculated pulse (squares, a dashed line is used to guide the eye).

Equations (13)

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

t U Δ = Δ V Δ t V Δ = Δ U Δ + Ω W Δ t W Δ = Ω V Δ
t R Δ = i Δ R Δ + i Ω W Δ
1 𝒟 Ω t = κ 2 Ω + κ Ω in i α L Δ g ( Δ ) R Δ d Δ Ω out = κ Ω Ω in
r ( ω ) = κ 2 π α L 2 i ω / 𝒟 κ + 2 π α L + 2 i ω / 𝒟
α L = κ 2 π
κ 2 Θ κ Θ in = i α L t Δ g ( Δ ) R Δ ( t ) d Δ d t Θ out = κ Θ Θ in
R Δ ( t ) = i exp ( i Δ t ) t W Δ ( t ) Ω ( t ) exp ( i Δ t ) d t
W 0 ( t ) = cos ( t Ω d t )
κ 2 Θ κ Θ in = π α L sin ( Θ ) Θ out = κ Θ Θ in
Θ 2 κ Θ in = sin ( Θ ) Θ out = κ Θ Θ in
1 𝒟 Ω t = κ 2 Ω + κ Ω in i α L n ( U Δ n + i V Δ n ) d Δ
r W ( ω ) = κ + 4 π W α L 4 i π ω / 𝒟 κ 4 π W α L + 4 i π ω / 𝒟
r W ( 0 ) = 1 + W 1 W and T g = 1 Δ ω cav 4 ( 1 W ) 2

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