Abstract

We demonstrate that light quanta of well-defined characteristics can be generated in a coupled system of three two-level atoms. The quantum nature of light is controlled by the entanglement structure, discord, and monogamy of the system, which leads to sub- and superradiant behavior, as well as sub-Poissonian statistics, at lower temperatures. Two distinct phases with different entanglement characteristics are observed with uniform radiation in one case and the other displaying highly focused and anisotropic radiation in the far-field regime. At higher temperatures, radiance witness is found to exhibit sub- and superradiant behavior of radiation intensity in the absence of entanglement albeit with non-zero quantum discord. This establishes the physical manifestation of quantum discord. It is also observed that the radiation intensity can be a precise estimator of the inter-atomic distance of a coupled system of two-level atomic systems. Our investigation shows, for the first time, the three body correlation in the form of a ‘monogamy score’ controlling the sub- and superradiant nature of radiation intensity.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (5)

M. Padgett, E. Toninelli, T. Gregory, and P. A. Moreau, “Beating classical imaging limits with entangled photon,” Proc. SPIE 10934, 109341R (2019).
[Crossref]

M. Rezai, J. Wrachtrup, and I. Gerhardt, “Polarization-entangled photon pairs from a single molecule,” Optica 6(1), 34–40 (2019).
[Crossref]

Z. H. Xiang, J. Huwer, R. M. Stevenson, J. S. Szymanska, M. B. Ward, I. Farrer, D. A. Ritchie, and A. J. Shields, “Long-term transmission of entangled photons from a single quantum dot over deployed fiber,” Sci. Rep. 9(1), 4111 (2019).
[Crossref]

E. Suarez, D. Auwärter, T. J. Arruda, R. Bachelard, P. W. Courteille, C. Zimmermann, and S. Slama, “Photon-antibunching in the fluorescence of statistical ensembles of emitters at an optical nanofiber-tip,” New J. Phys. 21(3), 035009 (2019).
[Crossref]

Q. Bin, X. -Y. Lu, T.-S. Yin, Y. Li, and Y. Wu, “Collective radiance effects in the ultrastrong-coupling regime,” Phys. Rev. A 99(3), 033809 (2019).
[Crossref]

2018 (6)

X. Zhang, C. Xu, and Z. Ren, “High fidelity heralded single-photon source using cavity quantum electrodynamics,” Sci. Rep. 8(1), 3140 (2018) and references therein.
[Crossref]

D. Bhatti, R. Schneider, S. Oppel, and J. von Zanthier, “Directional Dicke Subradiance with Nonclassical and Classical Light Sources,” Phys. Rev. Lett. 120(11), 113603 (2018).
[Crossref]

F. Mivehvar, S. Ostermann, F. Piazza, and H. Ritsch, “Driven-Dissipative Supersolid in a Ring Cavity,” Phys. Rev. Lett. 120(12), 123601 (2018).
[Crossref]

R. Ma, W. Liu, Z. Qin, X. Su, X. Jia, J Zhang, and J. Gao, “Compact sub-kilohertz low-frequency quantum light source based on four-wave mixing in cesium vapor,” Opt. Lett. 43(6), 1243–1246 (2018).
[Crossref]

J. P. W. MacLean, J. M. Donohue, and K. J. Resch, “Ultrafast quantum interferometry with energy-time entangled photons,” Phys. Rev. A 97(6), 063826 (2018).
[Crossref]

G. Araneda, D. B. Higginbottom, L. Slodicka, Y. Colombe, and R. Blatt, “Interference of Single Photons Emitted by Entangled Atoms in Free Space,” Phys. Rev. Lett. 120(19), 193603 (2018) and references therein.
[Crossref]

2017 (5)

A. Zeilinger, “Light for the quantum. Entangled photons and their applications: a very personal perspective,” Phys. Scr. 92(7), 072501 (2017) and references therein.
[Crossref]

M.-O. Pleinert, J. Von Zanthier, and G. S. Agarwal, “Hyperradiance from collective behavior of coherently driven atoms,” Optica 4(7), 779–785 (2017).
[Crossref]

J. P. Xu, S. L. Chang, Y. P. Yang, S. Y. Zhu, and G. S. Agarwal, “Hyperradiance accompanied by nonclassicality,” Phys. Rev. A 96(1), 013839 (2017).
[Crossref]

I. Dimitrova, W. Lunden, J. Amato-Grill, N. Jepsen, Y. Yu, M. Messer, T. Rigaldo, G. Puentes, D. Weld, and W. Ketterle, “Observation of two-beam collective scattering phenomena in a Bose-Einstein condensate,” Phys. Rev. A 96(5), 051603 (2017).
[Crossref]

V. S. Bhaskara and P. K. Panigrahi, “Generalized concurrence and partial transpose for pure continuous variable systems of arbitrary degrees of freedom using Lagrange’s identity and wedge product,” Quantum Inf. Process. 16(5), 118 (2017) and references therein.
[Crossref]

2016 (3)

2015 (6)

J. M. Lukens, O. D. Odele, D. E. Leaird, and A. M. Weiner, “Electro-optic modulation for high-speed characterization of entangled photon pairs,” Opt. Lett. 40(22), 5331–5334 (2015).
[Crossref]

E. Prat, L. Florian, and S. Reiche, “Efficient generation of short and high-power x-ray free-electron-laser pulses based on superradiance with a transversely tilted beam,” Phys. Rev. Spec. Top. Accel. Beams 18(10), 100701 (2015).
[Crossref]

A. Goban, C. L. Hung, J. D. Hood, S. P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for Atoms Trapped along a Photonic Crystal Waveguide,” Phys. Rev. Lett. 115(6), 063601 (2015).
[Crossref]

S. Q. Tang, J. B. Yuan, L. M. Kuang, and X. W. Wang, “Quantum-discord triggered superradiance and subradiance in a system of two separated atoms,” Quantum Inf. Process. 14(8), 2883–2894 (2015).
[Crossref]

C. Mitra, “Spin chains: Long-distance relationship,” Nat. Phys. 11(3), 212–213 (2015).
[Crossref]

H. Singh, T. Chakraborty, P. K. Panigrahi, and C. Mitra, “Experimental estimation of discord in an antiferromagnetic Heisenberg compound $Cu(NO_3)_2.2.5H_2O$Cu(NO3)2.2.5H2O,” Quantum Inf. Process. 14(3), 951–961 (2015).
[Crossref]

2014 (1)

V. Vedral, “Quantum entanglement,” Nat. Phys. 10(4), 256–258 (2014) and references therein.
[Crossref]

2013 (1)

D. Das, H. Singh, T. Chakraborty, R. K. Gopal, and C. Mitra, “Experimental detection of quantum information sharing and its quantification in quantum spin systems,” New J. Phys. 15(1), 013047 (2013).
[Crossref]

2012 (1)

M. N. Bera, R. Prabhu, A. Sen(De), and U. Sen, “Characterization of tripartite quantum states with vanishing monogamy score,” Phys. Rev. A 86(1), 012319 (2012).
[Crossref]

2011 (2)

R. Wiegner, J. von-Zanthier, and G. S. Agarwal, “Quantum-interference-initiated superradiant and subradiant emission from entangled atoms,” Phys. Rev. A 84(2), 023805 (2011).
[Crossref]

A. M. Branczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express 19(1), 55–65 (2011).
[Crossref]

2010 (3)

M. Hunault, H. Takesue, O. Tadanaga, Y. Nishida, and M. Asobe, “Generation of time-bin entangled photon pairs by cascaded second-order nonlinearity in a single periodically poled $LiNbO_3$LiNbO3 waveguide,” Opt. Lett. 35(8), 1239–1241 (2010).
[Crossref]

S. Banerjee, V. Ravishankar, and R. Srikanth, “Dynamics of entanglement in Two-Qubit Open System Interacting with a Squeezed Thermal Bath via Dissipative interaction,” Ann. Phys. 325(4), 816–834 (2010).
[Crossref]

S. Banerjee, V. Ravishankar, and R. Srikanth, “Entanglement dynamics in two-qubit open system interacting with a squeezed thermal bath via quantum nondemolition interaction,” Eur. Phys. J. D 56(2), 277–290 (2010).
[Crossref]

2009 (2)

2008 (3)

D. D. B. Rao, P. K. Panigrahi, and C. Mitra, “Teleportation in the presence of common bath decoherence at the transmitting station,” Phys. Rev. A 78(2), 022336 (2008).
[Crossref]

D. Porras and J. I. Cirac, “Collective generation of quantum states of light by entangled atoms,” Phys. Rev. A 78(5), 053816 (2008).
[Crossref]

S. Luo, “Quantum discord for two-qubit systems,” Phys. Rev. A 77(4), 042303 (2008).
[Crossref]

2007 (1)

A. Kalachev, “Quantum storage on subradiant states in an extended atomic ensemble,” Phys. Rev. A 76(4), 043812 (2007).
[Crossref]

2006 (1)

A. Kalachev and S. Kroll, “Coherent control of collective spontaneous emission in an extended atomic ensemble and quantum storage,” Phys. Rev. A 74(2), 023814 (2006).
[Crossref]

2005 (1)

M. D. Eisaman, A. Andre, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature (London) 438(7069), 837–841 (2005).
[Crossref]

2004 (2)

2002 (1)

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65(3), 032314 (2002).
[Crossref]

2001 (4)

H. Ollivier and W. H. Zurek, “Quantum Discord: A Measure of the Quantumness of Correlations,” Phys. Rev. Lett. 88(1), 017901 (2001).
[Crossref]

L. Henderson and V Vedral, “Classical, quantum and total correlations,” J. Phys. A: Math. Gen. 34(35), 6899–6905 (2001).
[Crossref]

A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, “Photons yield to peer pressure,” Nature 412(6850), 887–890 (2001).
[Crossref]

G. Messin, J. P. Hermier, E. Giacobino, P. Desbiolles, and M. Dahan, “Bunching and antibunching in the fluorescence of semiconductor nanocrystals,” Opt. Lett. 26(23), 1891–1893 (2001).
[Crossref]

2000 (5)

R. Brouri, A. Beveratos, J. P. Poizat, and P. Grangier, “Photon antibunching in the fluorescence of individual color centers in diamond,” Opt. Lett. 25(17), 1294–1296 (2000).
[Crossref]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[Crossref]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum Cryptography with Entangled Photons,” Phys. Rev. Lett. 84(20), 4729–4732 (2000).
[Crossref]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum Cryptography Using Entangled Photons in Energy-Time Bell States,” Phys. Rev. Lett. 84(20), 4737–4740 (2000).
[Crossref]

V. Coffman, J. Kundu, and W. K. Wootters, “Distributed entanglement,” Phys. Rev. A 61(5), 052306 (2000).
[Crossref]

1998 (1)

W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80(10), 2245–2248 (1998).
[Crossref]

1991 (1)

R. Bonifacio, N. Piovella, and B. W. J. McNeil, “Superradiant evolution of radiation pulses in a free-electron laser,” Phys. Rev. A 44(6), R3441–R3444 (1991).
[Crossref]

1984 (1)

P. Sprangle and T. Coffey, “New sources of high-power coherent radiation,” Phys. Today 37(3), 44–51 (1984).
[Crossref]

1976 (1)

M. Gross, C. Fabre, P. Pillet, and S. Haroche, “Observation of Near-Infrared Dicke Superradiance on Cascading Transitions in Atomic Sodium,” Phys. Rev. Lett. 36(17), 1035–1038 (1976).
[Crossref]

1954 (1)

R. H. Dicke, “Coherence in Spontaneous Radiation Processes,” Phys. Rev. 93(1), 99–110 (1954).
[Crossref]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[Crossref]

Agarwal, G. S.

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A. Biswas and G. S. Agarwal, “Preparation of W, GHZ, and two-qutrit states using bimodal cavities,” J. Mod. Opt. 51(11), 1627–1636 (2004).
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J. P. Xu, S. L. Chang, Y. P. Yang, S. Y. Zhu, and G. S. Agarwal, “Hyperradiance accompanied by nonclassicality,” Phys. Rev. A 96(1), 013839 (2017).
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G. Araneda, D. B. Higginbottom, L. Slodicka, Y. Colombe, and R. Blatt, “Interference of Single Photons Emitted by Entangled Atoms in Free Space,” Phys. Rev. Lett. 120(19), 193603 (2018) and references therein.
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E. Suarez, D. Auwärter, T. J. Arruda, R. Bachelard, P. W. Courteille, C. Zimmermann, and S. Slama, “Photon-antibunching in the fluorescence of statistical ensembles of emitters at an optical nanofiber-tip,” New J. Phys. 21(3), 035009 (2019).
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J. P. W. MacLean, J. M. Donohue, and K. J. Resch, “Ultrafast quantum interferometry with energy-time entangled photons,” Phys. Rev. A 97(6), 063826 (2018).
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A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
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M. D. Eisaman, A. Andre, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature (London) 438(7069), 837–841 (2005).
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Fleischhauer, M.

M. D. Eisaman, A. Andre, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature (London) 438(7069), 837–841 (2005).
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E. Prat, L. Florian, and S. Reiche, “Efficient generation of short and high-power x-ray free-electron-laser pulses based on superradiance with a transversely tilted beam,” Phys. Rev. Spec. Top. Accel. Beams 18(10), 100701 (2015).
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Gerhardt, I.

Giacobino, E.

Gisin, N.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum Cryptography Using Entangled Photons in Energy-Time Bell States,” Phys. Rev. Lett. 84(20), 4737–4740 (2000).
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Goban, A.

A. Goban, C. L. Hung, J. D. Hood, S. P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for Atoms Trapped along a Photonic Crystal Waveguide,” Phys. Rev. Lett. 115(6), 063601 (2015).
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D. Das, H. Singh, T. Chakraborty, R. K. Gopal, and C. Mitra, “Experimental detection of quantum information sharing and its quantification in quantum spin systems,” New J. Phys. 15(1), 013047 (2013).
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M. Gross, C. Fabre, P. Pillet, and S. Haroche, “Observation of Near-Infrared Dicke Superradiance on Cascading Transitions in Atomic Sodium,” Phys. Rev. Lett. 36(17), 1035–1038 (1976).
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G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light, (Cambridge University Press, 2010).

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A. Goban, C. L. Hung, J. D. Hood, S. P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for Atoms Trapped along a Photonic Crystal Waveguide,” Phys. Rev. Lett. 115(6), 063601 (2015).
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Hung, C. L.

A. Goban, C. L. Hung, J. D. Hood, S. P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for Atoms Trapped along a Photonic Crystal Waveguide,” Phys. Rev. Lett. 115(6), 063601 (2015).
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Z. H. Xiang, J. Huwer, R. M. Stevenson, J. S. Szymanska, M. B. Ward, I. Farrer, D. A. Ritchie, and A. J. Shields, “Long-term transmission of entangled photons from a single quantum dot over deployed fiber,” Sci. Rep. 9(1), 4111 (2019).
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Jepsen, N.

I. Dimitrova, W. Lunden, J. Amato-Grill, N. Jepsen, Y. Yu, M. Messer, T. Rigaldo, G. Puentes, D. Weld, and W. Ketterle, “Observation of two-beam collective scattering phenomena in a Bose-Einstein condensate,” Phys. Rev. A 96(5), 051603 (2017).
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A. Goban, C. L. Hung, J. D. Hood, S. P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for Atoms Trapped along a Photonic Crystal Waveguide,” Phys. Rev. Lett. 115(6), 063601 (2015).
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A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
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V. Coffman, J. Kundu, and W. K. Wootters, “Distributed entanglement,” Phys. Rev. A 61(5), 052306 (2000).
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A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, “Photons yield to peer pressure,” Nature 412(6850), 887–890 (2001).
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Leuchs, G.

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Q. Bin, X. -Y. Lu, T.-S. Yin, Y. Li, and Y. Wu, “Collective radiance effects in the ultrastrong-coupling regime,” Phys. Rev. A 99(3), 033809 (2019).
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M. D. Eisaman, A. Andre, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature (London) 438(7069), 837–841 (2005).
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I. Dimitrova, W. Lunden, J. Amato-Grill, N. Jepsen, Y. Yu, M. Messer, T. Rigaldo, G. Puentes, D. Weld, and W. Ketterle, “Observation of two-beam collective scattering phenomena in a Bose-Einstein condensate,” Phys. Rev. A 96(5), 051603 (2017).
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M. D. Eisaman, A. Andre, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature (London) 438(7069), 837–841 (2005).
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McNeil, B. W. J.

R. Bonifacio, N. Piovella, and B. W. J. McNeil, “Superradiant evolution of radiation pulses in a free-electron laser,” Phys. Rev. A 44(6), R3441–R3444 (1991).
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Messer, M.

I. Dimitrova, W. Lunden, J. Amato-Grill, N. Jepsen, Y. Yu, M. Messer, T. Rigaldo, G. Puentes, D. Weld, and W. Ketterle, “Observation of two-beam collective scattering phenomena in a Bose-Einstein condensate,” Phys. Rev. A 96(5), 051603 (2017).
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H. Singh, T. Chakraborty, P. K. Panigrahi, and C. Mitra, “Experimental estimation of discord in an antiferromagnetic Heisenberg compound $Cu(NO_3)_2.2.5H_2O$Cu(NO3)2.2.5H2O,” Quantum Inf. Process. 14(3), 951–961 (2015).
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D. Das, H. Singh, T. Chakraborty, R. K. Gopal, and C. Mitra, “Experimental detection of quantum information sharing and its quantification in quantum spin systems,” New J. Phys. 15(1), 013047 (2013).
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D. D. B. Rao, P. K. Panigrahi, and C. Mitra, “Teleportation in the presence of common bath decoherence at the transmitting station,” Phys. Rev. A 78(2), 022336 (2008).
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F. Mivehvar, S. Ostermann, F. Piazza, and H. Ritsch, “Driven-Dissipative Supersolid in a Ring Cavity,” Phys. Rev. Lett. 120(12), 123601 (2018).
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M. Padgett, E. Toninelli, T. Gregory, and P. A. Moreau, “Beating classical imaging limits with entangled photon,” Proc. SPIE 10934, 109341R (2019).
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Muniz, J. A.

A. Goban, C. L. Hung, J. D. Hood, S. P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for Atoms Trapped along a Photonic Crystal Waveguide,” Phys. Rev. Lett. 115(6), 063601 (2015).
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Nishida, Y.

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D. Bhatti, R. Schneider, S. Oppel, and J. von Zanthier, “Directional Dicke Subradiance with Nonclassical and Classical Light Sources,” Phys. Rev. Lett. 120(11), 113603 (2018).
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Ostermann, S.

F. Mivehvar, S. Ostermann, F. Piazza, and H. Ritsch, “Driven-Dissipative Supersolid in a Ring Cavity,” Phys. Rev. Lett. 120(12), 123601 (2018).
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M. Padgett, E. Toninelli, T. Gregory, and P. A. Moreau, “Beating classical imaging limits with entangled photon,” Proc. SPIE 10934, 109341R (2019).
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A. Goban, C. L. Hung, J. D. Hood, S. P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for Atoms Trapped along a Photonic Crystal Waveguide,” Phys. Rev. Lett. 115(6), 063601 (2015).
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Panigrahi, P. K.

V. S. Bhaskara and P. K. Panigrahi, “Generalized concurrence and partial transpose for pure continuous variable systems of arbitrary degrees of freedom using Lagrange’s identity and wedge product,” Quantum Inf. Process. 16(5), 118 (2017) and references therein.
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H. Singh, T. Chakraborty, P. K. Panigrahi, and C. Mitra, “Experimental estimation of discord in an antiferromagnetic Heisenberg compound $Cu(NO_3)_2.2.5H_2O$Cu(NO3)2.2.5H2O,” Quantum Inf. Process. 14(3), 951–961 (2015).
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D. D. B. Rao, P. K. Panigrahi, and C. Mitra, “Teleportation in the presence of common bath decoherence at the transmitting station,” Phys. Rev. A 78(2), 022336 (2008).
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Peev, M.

Piazza, F.

F. Mivehvar, S. Ostermann, F. Piazza, and H. Ritsch, “Driven-Dissipative Supersolid in a Ring Cavity,” Phys. Rev. Lett. 120(12), 123601 (2018).
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M. Gross, C. Fabre, P. Pillet, and S. Haroche, “Observation of Near-Infrared Dicke Superradiance on Cascading Transitions in Atomic Sodium,” Phys. Rev. Lett. 36(17), 1035–1038 (1976).
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R. Bonifacio, N. Piovella, and B. W. J. McNeil, “Superradiant evolution of radiation pulses in a free-electron laser,” Phys. Rev. A 44(6), R3441–R3444 (1991).
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Poizat, J. P.

Poppe, A.

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D. Porras and J. I. Cirac, “Collective generation of quantum states of light by entangled atoms,” Phys. Rev. A 78(5), 053816 (2008).
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M. N. Bera, R. Prabhu, A. Sen(De), and U. Sen, “Characterization of tripartite quantum states with vanishing monogamy score,” Phys. Rev. A 86(1), 012319 (2012).
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E. Prat, L. Florian, and S. Reiche, “Efficient generation of short and high-power x-ray free-electron-laser pulses based on superradiance with a transversely tilted beam,” Phys. Rev. Spec. Top. Accel. Beams 18(10), 100701 (2015).
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I. Dimitrova, W. Lunden, J. Amato-Grill, N. Jepsen, Y. Yu, M. Messer, T. Rigaldo, G. Puentes, D. Weld, and W. Ketterle, “Observation of two-beam collective scattering phenomena in a Bose-Einstein condensate,” Phys. Rev. A 96(5), 051603 (2017).
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Rao, D. D. B.

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A. Goban, C. L. Hung, J. D. Hood, S. P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for Atoms Trapped along a Photonic Crystal Waveguide,” Phys. Rev. Lett. 115(6), 063601 (2015).
[Crossref]

Phys. Rev. Spec. Top. Accel. Beams (1)

E. Prat, L. Florian, and S. Reiche, “Efficient generation of short and high-power x-ray free-electron-laser pulses based on superradiance with a transversely tilted beam,” Phys. Rev. Spec. Top. Accel. Beams 18(10), 100701 (2015).
[Crossref]

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A. Zeilinger, “Light for the quantum. Entangled photons and their applications: a very personal perspective,” Phys. Scr. 92(7), 072501 (2017) and references therein.
[Crossref]

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[Crossref]

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M. Padgett, E. Toninelli, T. Gregory, and P. A. Moreau, “Beating classical imaging limits with entangled photon,” Proc. SPIE 10934, 109341R (2019).
[Crossref]

Quantum Inf. Process. (3)

V. S. Bhaskara and P. K. Panigrahi, “Generalized concurrence and partial transpose for pure continuous variable systems of arbitrary degrees of freedom using Lagrange’s identity and wedge product,” Quantum Inf. Process. 16(5), 118 (2017) and references therein.
[Crossref]

S. Q. Tang, J. B. Yuan, L. M. Kuang, and X. W. Wang, “Quantum-discord triggered superradiance and subradiance in a system of two separated atoms,” Quantum Inf. Process. 14(8), 2883–2894 (2015).
[Crossref]

H. Singh, T. Chakraborty, P. K. Panigrahi, and C. Mitra, “Experimental estimation of discord in an antiferromagnetic Heisenberg compound $Cu(NO_3)_2.2.5H_2O$Cu(NO3)2.2.5H2O,” Quantum Inf. Process. 14(3), 951–961 (2015).
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Z. H. Xiang, J. Huwer, R. M. Stevenson, J. S. Szymanska, M. B. Ward, I. Farrer, D. A. Ritchie, and A. J. Shields, “Long-term transmission of entangled photons from a single quantum dot over deployed fiber,” Sci. Rep. 9(1), 4111 (2019).
[Crossref]

X. Zhang, C. Xu, and Z. Ren, “High fidelity heralded single-photon source using cavity quantum electrodynamics,” Sci. Rep. 8(1), 3140 (2018) and references therein.
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Figures (5)

Fig. 1.
Fig. 1. The variation of radiation intensity as a function of $\frac {\omega }{\Omega }$ and observation angle is depicted for two different temperatures for (a) $k_BT=5\times 10^{-3}\hbar \Omega$ and (b) $k_BT=\hbar \Omega$. Panels $c$ and $d$ show the radiation intensity as a function of observation angle and ratio of emission wavelength and fixed inter-atomic spacing ($\frac {\lambda }{d}$) at ‘$\frac {\omega }{\Omega }=1$’ for (c) $k_BT=5\times 10^{-3}\hbar \Omega$ and (d) $k_BT=\hbar \Omega$, clearly showing the interference effect.
Fig. 2.
Fig. 2. Panels $a$ shows the variation of QCs as a function of temperature ($\times \frac {\hbar \Omega }{k_B}$) for $\frac {\omega }{\Omega }=1$. Panels $b$ shows the variation of QCs as function of $\frac {\omega }{\Omega }$ for $k_BT=5\times 10^{-3}\hbar \Omega$. Here $C$ stands for concurrence while $QD$ and $QC$ stand for quantum discord and quantum correlation, respectively.
Fig. 3.
Fig. 3. Panels $a$ and $b$ show intensity variation with respect to monogamy score ($\tau _{1:23}$) of negativity at $k_BT=5\times 10^{-3}\hbar \Omega$ for (a) $\frac {\lambda }{d}=2$ and (b) $\frac {\lambda }{d}=\frac {2}{3}$, showing the increase of intensity with increase in monogamy score.
Fig. 4.
Fig. 4. Panels $a$ and $b$ show photon-photon correlation for $\frac {\lambda }{d}=2$ as function of $\frac {\omega }{\Omega }$ and observation angle for (a) $k_BT=5\times 10^{-3}\hbar \Omega$ and (b) $k_BT=\hbar \Omega$. Panels $c$ and $d$ show photon-photon correlation for $\frac {\omega }{\Omega }=1$ as function of wavelength of emitted radiation and observation angle for (c) $k_BT=5\times 10^{-3}\hbar \Omega$ and (d) $k_BT=\hbar \Omega$, clearly indicating the sub and super-Poissonian statistics.
Fig. 5.
Fig. 5. The variation of radiance witness as a function of $\frac {\omega }{\Omega }$ and observation angle is depicted for two different temperatures for (a) $k_BT=5\times 10^{-3}\hbar \Omega$ and (b) $k_BT=\hbar \Omega$. Panels $c$ and $d$ show the radiance witness as a function of observation angle and ratio of emission wavelength and fixed inter-atomic spacing ($\frac {\lambda }{d}$) at ‘$\frac {\omega }{\Omega }=1$’ for (c) $k_BT=5\times 10^{-3}\hbar \Omega$ and (d) $k_BT=\hbar \Omega$, clearly showing the sub ($R<0$) and superradiance ($R>0$) effect.

Equations (26)

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H = i = 1 3 ω i S i z + i j = 1 3 Ω i j S i + S j .
ϵ 1 = 3 ω 2 ;   ϵ 2 = 2 Ω ω 2 ;   ϵ 3 = ω 2 ;   ϵ 4 = 2 Ω ω 2 ϵ 5 = 2 Ω + ω 2 ;   ϵ 6 = ω 2 ;   ϵ 7 = 2 Ω + ω 2 ;   ϵ 8 = 3 ω 2
| ψ 1 = | g 1 g 2 g 3 ;     | ψ 2 = 1 2 [ | e 1 g 2 g 3 2 | g 1 e 2 g 3 + | g 1 g 2 e 3 ] | ψ 3 = 1 2 [ | g 1 g 2 e 3 | e 1 g 2 g 3 ] ;     | ψ 4 = 1 2 [ | e 1 g 2 g 3 + 2 | g 1 e 2 g 3 + | g 1 g 2 e 3 ] | ψ 5 = 1 2 [ | e 1 e 2 g 3 2 | e 1 g 2 e 3 + | g 1 e 2 e 3 ] ;     | ψ 6 = 1 2 [ | g 1 e 2 e 3 | e 1 e 2 g 3 ] | ψ 7 = 1 2 [ | e 1 e 2 g 3 + 2 | e 1 g 2 e 3 + | g 1 e 2 e 3 ] ;     | ψ 8 = | e 1 e 2 e 3 .
ρ A B C = i = 1 8 | ψ i ψ i | exp ( β ϵ i ) Tr ( i = 1 8 | ψ i ψ i | exp ( β ϵ i ) ) .
ρ A B C ( T ) = 1 Z [ ρ 11 0 0 0 0 0 0 0 0 ρ 22 ρ 23 0 ρ 25 0 0 0 0 ρ 32 ρ 33 0 ρ 35 0 0 0 0 0 0 ρ 44 0 ρ 46 ρ 47 0 0 ρ 52 ρ 53 0 ρ 55 0 0 0 0 0 0 ρ 64 0 ρ 66 ρ 67 0 0 0 0 ρ 74 0 ρ 76 ρ 77 0 0 0 0 0 0 0 0 ρ 88 ]
Z = 2   cosh ( ω 2   k B T ) ( 1 + 8   cosh ( 2 Ω k B T ) + 2   cosh ( ω k B T ) ) .
ρ 11 = exp ( 3 ω 2 k B T ) ; ρ 22 = exp ( ω 2   k B T ) ( 1 + 2   cosh ( 2 Ω k B T ) ) ; ρ 23 = 2 2   exp ( ω 2   k B T ) sinh ( 2 Ω k B T ) ;   ρ 25 = exp ( ω 2 k B T ) ( 1 + 2   cosh ( 2 Ω k B T ) ) ; ρ 33 = 4   exp ( ω 2 k B T ) cosh ( 2 Ω k B T ) ;     ρ 35 = 2 2   exp ( ω 2   k B T ) sinh ( 2 Ω k B T ) ; ρ 44 = exp ( ω 2 k B T ) ( 1 + 2   cosh ( 2 Ω k B T ) ) ;     ρ 46 = 2 2   exp ( ω 2   k B T ) sinh ( 2 Ω k B T ) ; ρ 47 = exp ( ω 2 k B T ) ( 1 + 2   cosh ( 2 Ω k B T ) ) ;     ρ 55 = exp ( ω 2 k B T ) ( 1 + 2   cosh ( 2 Ω k B T ) ) ;   ρ 66 = 4   exp ( ω 2   k B T ) cosh ( 2 Ω k B T ) ;   ρ 67 = 2 2   exp ( ω 2   k B T ) sinh ( 2 Ω k B T ) ; ρ 77 = exp ( ω 2   k B T ) ( 1 + 2   cosh ( 2 Ω k B T ) ) ;   ρ 88 = exp ( 3 ω 2 k B T ) .
C = m a x { 0 , λ 1 λ 2 λ 3 λ 4 }
ρ ~ = σ y σ y ρ σ y σ y .
ρ X Y = [ a 0 0 f 0 b 1 z 0 0 z b 2 0 f 0 0 d ] .
Q D = 1 4 [ ( 1 c 1 c 2 c 3 ) log 2 ( 1 c 1 c 2 c 3 ) + ( 1 c 1 + c 2 + c 3 ) log 2 ( 1 c 1 + c 2 + c 3 ) + ( 1 + c 1 c 2 + c 3 ) log 2 ( 1 + c 1 c 2 + c 3 ) + ( 1 + c 1 + c 2 c 3 ) log 2 ( 1 + c 1 + c 2 c 3 )   ] [ ( 1 c ) 2 log 2 ( 1 c ) + ( 1 + c ) 2 log 2 ( 1 + c ) ] ,
N ( ρ T A ) = i = 1 | λ i |   ,
ρ = i j | i j | A i j .
ρ T A = i j | j i | A i j .
τ A : B C = N A : B C 2 N A B 2 N A C 2 .
E ^ ( + ) = e i k r r j n × ( n × p g e ) e i ϕ j S ^ j ,
E ^ ( + ) = j e i ϕ j S ^ j .
I ( r ) = E ^ ( ) E ^ ( + ) = i , j S ^ i + S ^ j e i ( ϕ i ϕ j ) , = i S ^ i + S ^ i + ( i j S ^ i + S ^ j + i j ( S ^ i + S ^ j S ^ i + S ^ j ) ) e i ( ϕ i ϕ j ) .
A ^ = Tr ( ρ ^ A ^ ) ,
ϕ j ( r ) ϕ j = k n . R j = j k d sin θ ,
I = E E + = A   ( B + C + D ) , with A = exp ( ω 2 k B T ) sech ( ω 2 k B T ) 2 [ 1 + 2   cosh ( ω k B T ) + 8   cosh ( 2 Ω k B T ) ] , B = 3   exp ( 2 ω k B T ) 2   exp ( ω k B T ) [ 2 + cos { 2   kd sin ( θ ) } ] , C = 4 ( 2 + cos { 2 kd sin ( θ ) } + exp ( ω k B T ) [ 4 + cos { 2   kd sin ( θ ) } ] ) cosh ( 2 Ω k B T ) ,     and D = 4   sin 2 { kd sin ( θ ) } 8 2 ( 1 + exp ( ω k B T ) ) cos { kd sin ( θ ) }   sinh ( 2 Ω k B T ) .
g ( 2 ) ( 0 ) = E E E + E + E E + E E + = E E E + E + E E + 2 .
E E E + E + = N 1   ( N 2 + N 3 ) , with N 1 = exp ( 2   k d sin ( θ ) + ω 2 Ω 2 k B T ) sech ( ω 2 k B T ) 2 [ 1 + 2   cosh ( ω k B T ) + 8   cosh ( 2 Ω k B T ) ] , N 2 = 4 2 ( 1 + exp ( 2 2 Ω k B T ) ) cos { kd sin ( θ ) } + 2   [ 2 + cos { 2   kd sin ( θ ) } ] ,         and N 3 = exp ( 2 2 Ω k B T ) [ 4 + 3   exp ( 2 ω k B T ) + 2   cos { 2   kd sin ( θ ) } ] + 4   exp ( 2 Ω k B T ) sin 2 { kd sin ( θ ) } .
g ( 2 ) ( 0 ) = N 1   ( N 2 + N 3 ) I 2 .
R = E E + N i = 1 N E E + i i = 1 N E E + i ,
R = E E + N N   E E + 1 N   E E + 1 .

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