Abstract

The collective behavior of ensembles of atoms has been studied in-depth since the seminal paper of Dicke [Phys. Rev. 93, 99 (1954) [CrossRef]  ], where he demonstrated that a group of emitters in collective states is able to radiate with increased intensity and modified decay rates in particular directions, a phenomenon that he called superradiance. Here, we show that the fundamental setup of two atoms coupled to a single-mode cavity can distinctly exceed the free-space superradiant behavior, a phenomenon we call hyperradiance. The effect is accompanied by strong quantum fluctuations and surprisingly arises for atoms radiating out-of-phase, an alleged non-ideal condition where one expects subradiance. We are able to explain the onset of hyperradiance in a transparent way by a photon cascade taking place among manifolds of Dicke states with different photon numbers under particular out-of-phase coupling conditions. These theoretical results can be realized with current technology and should thus stimulate future experiments.

© 2017 Optical Society of America

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    [Crossref]
  2. N. E. Rehler and J. H. Eberly, “Superradiance,” Phys. Rev. A 3, 1735–1751 (1971).
    [Crossref]
  3. R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A 4, 302–313 (1971).
    [Crossref]
  4. R. Friedberg, S. Hartmann, and J. Manassah, “Frequency shifts in emission and absorption by resonant systems of two-level atoms,” Phys. Rep. 7, 101–179 (1973).
    [Crossref]
  5. G. S. Agarwal, Springer Tracts in Modern Physics: Quantum Optics (Springer, 1974), p. 55.
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    [Crossref]
  7. N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke superradiance in optically pumped HF gas,” Phys. Rev. Lett. 30, 309–312 (1973).
    [Crossref]
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  41. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade,” Nat. Phys. 4, 859–863 (2008).
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    [Crossref]
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    [Crossref]
  47. E. V. Goldstein and P. Meystre, “Dipole-dipole interaction in optical cavities,” Phys. Rev. A 56, 5135–5146 (1997).
    [Crossref]
  48. J. Johansson, P. Nation, and F. Nori, “Qutip: an open-source python framework for the dynamics of open quantum systems,” Comput. Phys. Commun. 183, 1760–1772 (2012).
    [Crossref]
  49. S. Fernández-Vidal, S. Zippilli, and G. Morigi, “Nonlinear optics with two trapped atoms,” Phys. Rev. A 76, 053829 (2007).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  54. Y. Tabuchi, S. Ishino, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, “Hybridizing ferromagnetic magnons and microwave photons in the quantum limit,” Phys. Rev. Lett. 113, 083603 (2014).
    [Crossref]
  55. L. V. Abdurakhimov, Y. M. Bunkov, and D. Konstantinov, “Normal-mode splitting in the coupled system of hybridized nuclear magnons and microwave photons,” Phys. Rev. Lett. 114, 226402 (2015).
    [Crossref]
  56. D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a milliHertz-linewidth laser,” Phys. Rev. Lett. 102, 163601 (2009).
    [Crossref]

2016 (4)

W. Guerin, M. O. Araújo, and R. Kaiser, “Subradiance in a large cloud of cold atoms,” Phys. Rev. Lett. 116, 083601 (2016).
[Crossref]

P. Longo, C. H. Keitel, and J. Evers, “Tailoring superradiance to design artificial quantum systems,” Sci. Rep. 6, 23628 (2016).
[Crossref]

A. A. Svidzinsky, F. Li, H. Li, X. Zhang, C. H. R. Ooi, and M. O. Scully, “Single-photon superradiance and radiation trapping by atomic shells,” Phys. Rev. A 93, 043830 (2016).
[Crossref]

A. Neuzner, M. Körber, O. Morin, S. Ritter, and G. Rempe, “Interference and dynamics of light from a distance-controlled atom pair in an optical cavity,” Nat. Photonics 10, 303–306 (2016).
[Crossref]

2015 (6)

R. Reimann, W. Alt, T. Kampschulte, T. Macha, L. Ratschbacher, N. Thau, S. Yoon, and D. Meschede, “Cavity-modified collective Rayleigh scattering of two atoms,” Phys. Rev. Lett. 114, 023601 (2015).
[Crossref]

B. Casabone, K. Friebe, B. Brandstätter, K. Schüppert, R. Blatt, and T. E. Northup, “Enhanced quantum interface with collective ion-cavity coupling,” Phys. Rev. Lett. 114, 023602 (2015).
[Crossref]

M. O. Scully, “Single photon subradiance: quantum control of spontaneous emission and ultrafast readout,” Phys. Rev. Lett. 115, 243602 (2015).
[Crossref]

D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Superbunching and nonclassicality as new hallmarks of superradiance,” Sci. Rep. 5, 17335 (2015).
[Crossref]

H. A. M. Leymann, A. Foerster, F. Jahnke, J. Wiersig, and C. Gies, “Sub- and superradiance in nanolasers,” Phys. Rev. Appl. 4, 044018 (2015).
[Crossref]

L. V. Abdurakhimov, Y. M. Bunkov, and D. Konstantinov, “Normal-mode splitting in the coupled system of hybridized nuclear magnons and microwave photons,” Phys. Rev. Lett. 114, 226402 (2015).
[Crossref]

2014 (4)

A. Rundquist, M. Bajcsy, A. Majumdar, T. Sarmiento, K. Fischer, K. G. Lagoudakis, S. Buckley, A. Y. Piggott, and J. Vučković, “Nonclassical higher-order photon correlations with a quantum dot strongly coupled to a photonic-crystal nanocavity,” Phys. Rev. A 90, 023846 (2014).
[Crossref]

J. A. Mlynek, A. A. Abdumalikov, C. Eichler, and A. Wallraff, “Observation of Dicke superradiance for two artificial atoms in a cavity with high decay rate,” Nat. Commun. 5, 5186 (2014).
[Crossref]

Y. Tabuchi, S. Ishino, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, “Hybridizing ferromagnetic magnons and microwave photons in the quantum limit,” Phys. Rev. Lett. 113, 083603 (2014).
[Crossref]

W. Feng, Y. Li, and S.-Y. Zhu, “Effect of atomic distribution on cooperative spontaneous emission,” Phys. Rev. A 89, 013816 (2014).
[Crossref]

2013 (4)

R. Röhlsberger, “Cooperative emission from nuclei: the collective lamb shift and electromagnetically induced transparency,” Fortschr. Phys. 61, 360–376 (2013).
[Crossref]

A. A. Svidzinsky, L. Yuan, and M. O. Scully, “Quantum amplification by superradiant emission of radiation,” Phys. Rev. X 3, 041001 (2013).
[Crossref]

T. Bienaimé, R. Bachelard, N. Piovella, and R. Kaiser, “Cooperativity in light scattering by cold atoms,” Fortschr. Phys. 61, 377–392 (2013).
[Crossref]

J. Miguel-Sánchez, A. Reinhard, E. Togan, T. Volz, A. Imamoglu, B. Besga, J. Reichel, and J. Estève, “Cavity quantum electrodynamics with charge-controlled quantum dots coupled to a fiber Fabry-Perot cavity,” New J. Phys. 15, 045002 (2013).
[Crossref]

2012 (3)

J. Johansson, P. Nation, and F. Nori, “Qutip: an open-source python framework for the dynamics of open quantum systems,” Comput. Phys. Commun. 183, 1760–1772 (2012).
[Crossref]

A. Stute, B. Casabone, P. Schindler, T. Monz, P. O. Schmidt, B. Brandstatter, T. E. Northup, and R. Blatt, “Tunable ion-photon entanglement in an optical cavity,” Nature 485, 482–485 (2012).
[Crossref]

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref]

2011 (2)

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Hänsel, M. Hennrich, and R. Blatt, “14-qubit entanglement: creation and coherence,” Phys. Rev. Lett. 106, 130506 (2011).
[Crossref]

R. Wiegner, J. von Zanthier, and G. S. Agarwal, “Quantum-interference-initiated superradiant and subradiant emission from entangled atoms,” Phys. Rev. A 84, 023805 (2011).
[Crossref]

2010 (3)

D. Meiser and M. J. Holland, “Steady-state superradiance with alkaline-earth-metal atoms,” Phys. Rev. A 81, 033847 (2010).
[Crossref]

D. Meiser and M. J. Holland, “Intensity fluctuations in steady-state superradiance,” Phys. Rev. A 81, 063827 (2010).
[Crossref]

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective lamb shift in single-photon superradiance,” Science 328, 1248–1251 (2010).
[Crossref]

2009 (6)

M. O. Scully and A. A. Svidzinsky, “The super of superradiance,” Science 325, 1510–1511 (2009).
[Crossref]

M. O. Scully, “Collective lamb shift in single photon Dicke superradiance,” Phys. Rev. Lett. 102, 143601 (2009).
[Crossref]

A. Maser, U. Schilling, T. Bastin, E. Solano, C. Thiel, and J. von Zanthier, “Generation of total angular momentum eigenstates in remote qubits,” Phys. Rev. A 79, 033833 (2009).
[Crossref]

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a milliHertz-linewidth laser,” Phys. Rev. Lett. 102, 163601 (2009).
[Crossref]

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[Crossref]

J. M. Fink, R. Bianchetti, M. Baur, M. Göppl, L. Steffen, S. Filipp, P. J. Leek, A. Blais, and A. Wallraff, “Dressed collective qubit states and the Tavis-Cummings model in circuit QED,” Phys. Rev. Lett. 103, 083601 (2009).
[Crossref]

2008 (2)

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade,” Nat. Phys. 4, 859–863 (2008).
[Crossref]

R. Blatt and D. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1015 (2008).
[Crossref]

2007 (3)

C. Thiel, J. von Zanthier, T. Bastin, E. Solano, and G. S. Agarwal, “Generation of symmetric Dicke states of remote qubits with linear optics,” Phys. Rev. Lett. 99, 193602 (2007).
[Crossref]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref]

S. Fernández-Vidal, S. Zippilli, and G. Morigi, “Nonlinear optics with two trapped atoms,” Phys. Rev. A 76, 053829 (2007).
[Crossref]

2004 (1)

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[Crossref]

1997 (1)

E. V. Goldstein and P. Meystre, “Dipole-dipole interaction in optical cavities,” Phys. Rev. A 56, 5135–5146 (1997).
[Crossref]

1996 (1)

R. G. DeVoe and R. G. Brewer, “Observation of superradiant and subradiant spontaneous emission of two trapped ions,” Phys. Rev. Lett. 76, 2049–2052 (1996).
[Crossref]

1992 (1)

R. J. Thompson, G. Rempe, and H. J. Kimble, “Observation of normal-mode splitting for an atom in an optical cavity,” Phys. Rev. Lett. 68, 1132–1135 (1992).
[Crossref]

1990 (1)

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, “Vacuum Rabi splitting as a feature of linear-dispersion theory: analysis and experimental observations,” Phys. Rev. Lett. 64, 2499–2502 (1990).
[Crossref]

1987 (1)

G. Nienhuis and F. Schuller, “Spontaneous emission and light scattering by atomic lattice models,” J. Phys. B 20, 23–36 (1987).
[Crossref]

1984 (2)

R. G. DeVoe and R. G. Brewer, “Laser-frequency division and stabilization,” Phys. Rev. A 30, 2827–2829 (1984).
[Crossref]

G. S. Agarwal, “Vacuum-field Rabi splittings in microwave absorption by Rydberg atoms in a cavity,” Phys. Rev. Lett. 53, 1732–1734 (1984).
[Crossref]

1982 (1)

M. Gross and S. Haroche, “Superradiance: an essay on the theory of collective spontaneous emission,” Phys. Rep. 93, 301–396 (1982).
[Crossref]

1977 (1)

Q. H. F. Vrehen, H. M. J. Hikspoors, and H. M. Gibbs, “Quantum beats in superfluorescence in atomic cesium,” Phys. Rev. Lett. 38, 764–767 (1977).
[Crossref]

1973 (2)

N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke superradiance in optically pumped HF gas,” Phys. Rev. Lett. 30, 309–312 (1973).
[Crossref]

R. Friedberg, S. Hartmann, and J. Manassah, “Frequency shifts in emission and absorption by resonant systems of two-level atoms,” Phys. Rep. 7, 101–179 (1973).
[Crossref]

1971 (2)

N. E. Rehler and J. H. Eberly, “Superradiance,” Phys. Rev. A 3, 1735–1751 (1971).
[Crossref]

R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A 4, 302–313 (1971).
[Crossref]

1968 (1)

M. Tavis and F. W. Cummings, “Exact solution for an n-molecule-radiation-field Hamiltonian,” Phys. Rev. 170, 379–384 (1968).
[Crossref]

1954 (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
[Crossref]

Abdumalikov, A. A.

J. A. Mlynek, A. A. Abdumalikov, C. Eichler, and A. Wallraff, “Observation of Dicke superradiance for two artificial atoms in a cavity with high decay rate,” Nat. Commun. 5, 5186 (2014).
[Crossref]

Abdurakhimov, L. V.

L. V. Abdurakhimov, Y. M. Bunkov, and D. Konstantinov, “Normal-mode splitting in the coupled system of hybridized nuclear magnons and microwave photons,” Phys. Rev. Lett. 114, 226402 (2015).
[Crossref]

Agarwal, G. S.

D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Superbunching and nonclassicality as new hallmarks of superradiance,” Sci. Rep. 5, 17335 (2015).
[Crossref]

R. Wiegner, J. von Zanthier, and G. S. Agarwal, “Quantum-interference-initiated superradiant and subradiant emission from entangled atoms,” Phys. Rev. A 84, 023805 (2011).
[Crossref]

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[Crossref]

C. Thiel, J. von Zanthier, T. Bastin, E. Solano, and G. S. Agarwal, “Generation of symmetric Dicke states of remote qubits with linear optics,” Phys. Rev. Lett. 99, 193602 (2007).
[Crossref]

G. S. Agarwal, “Vacuum-field Rabi splittings in microwave absorption by Rydberg atoms in a cavity,” Phys. Rev. Lett. 53, 1732–1734 (1984).
[Crossref]

G. S. Agarwal, Quantum Optics (Cambridge University, 2012).

G. S. Agarwal, Springer Tracts in Modern Physics: Quantum Optics (Springer, 1974), p. 55.

Alt, W.

R. Reimann, W. Alt, T. Kampschulte, T. Macha, L. Ratschbacher, N. Thau, S. Yoon, and D. Meschede, “Cavity-modified collective Rayleigh scattering of two atoms,” Phys. Rev. Lett. 114, 023601 (2015).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1.

Basic properties of the system. (a) Sketch of the system consisting of two atoms (A) that are coupled to a single-mode cavity (C) and driven by a coherent laser (L) with Rabi frequency η. Intracavity photons can leak through the mirrors by cavity decay (κ) and are registered by a detector (D). Another possible dissipative process is spontaneous emission (γ) by the atoms. The inset shows a magnified section of the arrangements of the atoms: one atom (depicted left) is fixed at an anti-node of the cavity field, while the other atom (right) can be scanned along the cavity axis causing a relative phase shift ϕz between the radiation of the atoms. (b) and (c) Energy levels and transitions of the system for (b) in-phase and (c) out-of-phase radiation of the atoms. In the case of two atoms, the state space consists of manifolds of four Dicke states with different intracavity photon numbers. For a fixed cavity state |n, these are unentangled two atom ground and two atom excited states |gg and |ee, respectively, as well as the maximally entangled symmetric and anti-symmetric Dicke states |±. For clarity, we draw neither the transitions due to cavity decay nor the detuning. (d) Energy levels and transitions of the corresponding system containing a single atom.

Fig. 2.
Fig. 2.

Radiance witness R for different regimes as a function of the interatomic phase ϕz and pumping rate η. The color encodes six different regimes of radiation, i.e., extremely subradiant (black), subradiant (blue), uncorrelated (light blue), enhanced (yellow), superradiant (orange), and hyperradiant (red). Dotted, dashed, and solid curves in the figures indicate the mean photon numbers aa2=0.01,0.1,1, respectively. (a) 3D plot and 2D surface map of the predominant hyperradiant area for γ=κ, g=10κ, and no detuning. Here, the superradiant and uncorrelated scattering area are very small and can hardly be seen. (b) and (c) Results for bad and intermediate cavity with γ=κ, no detuning, and (b) g=0.1κ or (c) g=κ. (d) and (e) Influence of the detuning on hyperradiance with γ=κ, g=10κ, and (d) δ=Δ=κ or (e) δ=Δ=10κ.

Fig. 3.
Fig. 3.

Results for different cavities. Vertical cuts of the radiance witness at η0.5κ as a function of the interatomic phase ϕz for different types of cavities: blue (dashed) for a bad cavity corresponding to Fig. 2(b); green (dot-dashed) for an intermediate cavity corresponding to Fig. 2(c); and black (bold) with highlighted hyperradiant area (R>1) for a good cavity corresponding to Fig. 2(a).

Fig. 4.
Fig. 4.

Comparison of in-phase and out-of-phase radiation. Both figures constitute a plot of R as a function of pumping rate η and atom-cavity coupling g, where g=0.1κ10κ reflects the transition from bad to good cavities. Results are shown for γ=κ with no detuning and (a) atoms radiating in-phase (ϕz=0) or (b) atoms radiating out-of-phase (ϕz=π). For clarification of the color code as well as dotted, dashed, and solid lines, see Fig. 2.

Fig. 5.
Fig. 5.

Comparison of classical and quantum-mechanical treatment. The ratio |a|2/aa comparing the classical intensity of the intracavity field with the quantum-mechanical mean photon number is shown as a function of the interatomic phase ϕz for g=10κ, γ=κ, and η=0.1κ.

Equations (3)

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

ddtρ=i[H0+HI+HL,ρ]+Lγρ+Lκρ,
Raa22aa12aa1,
a=ηgNG1g2(γ2+iΔ)(κ2+iδ)NH,