Skip to main content
SpringerLink
Log in

Superradiant emission spectra of a two-qubit system in circuit quantum electrodynamics

  • Regular Article - Solid State and Materials
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

In this paper, we study the spontaneous emission spectra and the emission decay rates of a simplest atom system that exhibits sub- and superradiant properties: a system which consists of two artificial atoms (superconducting qubits) embedded in a one-dimensional open waveguide. The calculations are based on the method of the transition operator which was firstly introduced by R. H. Lehmberg to theoretically describe the spontaneous emission of two-level atoms in a free space. We obtain the explicit expressions for the photon radiation spectra and the emission decay rates for different initial two-qubit configurations with one and two excitations. For every initial state we calculate the radiation spectra and the emission decay rates for different effective distances between qubits. In every case, a decay rate is compared with a single qubit decay to show the superradiant or subradiant nature of a two-qubit decay with a given initial state.

Graphic Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data Availability Statement

The manuscript has associated data in a public repository arXiv: 2206.14481 [quant-ph]. This manuscript has associated data in a data repository. [Authors’ comment: This paper is theoretical and has no associated experimental data, and all numerical results are shown in the figures. Therefore, this manuscript has no associated data in a data repository.]

References

  1. D. Roy, C.M. Wilson, O. Firstenberg, Strongly interacting photons in one-dimensional continuum. Rev. Mod. Phys. 89, 021001 (2017)

    Article  MathSciNet  Google Scholar 

  2. J.M. Raimond, M. Brune, S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  3. S. Noda, M. Fujita, T. Asano, Spontaneous-emission control by photonic crystals and nanocavities. Nat. Photon. 1, 449 (2007)

    Article  ADS  Google Scholar 

  4. A. Blais, A.L. Grimsmo, S.M. Girvin, A. Wallraff, Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 (2021)

    Article  MathSciNet  ADS  Google Scholar 

  5. G. Wendin, Quantum information processing with superconducting circuits: a review. Rep. Prog. Phys. 80, 106001 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  6. X. Gu, A.F. Kockum, A. Miranowicz, Y.X. Liu, F. Nori, Microwave photonics with superconducting quantum circuits. Phys. Rep. 718–719, 1 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  7. A. Wallraff, D.I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S.M. Girvin, R.J. Schoelkopf, Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature (London) 431, 162 (2004)

    Article  ADS  Google Scholar 

  8. P. Forn-Diaz, L. Lamata, E. Rico, J. Kono, E. Solano, Ultrastrong coupling regimes of light-matter interaction. Rev. Mod. Phys. 91, 025005 (2019)

    Article  ADS  Google Scholar 

  9. R.H. Lehmberg, Radiation from an N-Atom system. I. General formalism. Phys. Rev. A 2, 883 (1970)

    Article  ADS  Google Scholar 

  10. R.H. Lehmberg, Radiation from an N-atom system. II. Spontaneous emission from a pair of atoms. Phys. Rev. A 2, 889 (1970)

    Article  ADS  Google Scholar 

  11. Z. Ficek, B.C. Sanders, Quantum beats in two-atom resonance fluorescence. Phys. Rev. A 41, 359 (1990)

    Article  ADS  Google Scholar 

  12. T.G. Rudolph, Z. Ficek, B.J. Dalton, Two-atom resonance fluorescence in running- and standing-wave laser fields. Phys. Rev A 52, 636 (1995)

    Article  ADS  Google Scholar 

  13. Z. Ficek, R. Tanas, Entangled states and collective non-classical effects in two-atom systems. Phys. Rep. 372, 369 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  14. G. Lenz, P. Meystre, Resonance fluorescence from two identical atoms in a standing-wave field. Phys. Rev. A 48, 3365 (1993)

    Article  ADS  Google Scholar 

  15. R.H. Dicke, Coherence in spontaneous radiation processes. Phys. Rev. 93, 99 (1954)

    Article  ADS  Google Scholar 

  16. M. Gross, S. Haroche, Superradiance: an essay on the theory of collective spontaneous emission. Phys. Rep. 93, 301 (1982)

    Article  ADS  Google Scholar 

  17. K. Cong, Q. Zhang, Y. Wang, G.T. Noe II., A. Belyanin, J. Kono, Dicke superradiance in solids. J. Opt. Soc. Am. B 33, C80 (2016)

    Article  Google Scholar 

  18. E.M. Purcell, Spontaneous emission probabilities at radio frequencies. Phys. Rev. 69, 681 (1946)

  19. A. Albrecht, L. Henriet, A. Asenjo-Garcia, P.B. Dieterle, O. Painter, D.E. Chang, Subradiant states of quantum bits coupled to a one-dimensional waveguide. N. J. Phys. 21, 025003 (2019)

    Article  MathSciNet  Google Scholar 

  20. Y.-X. Zhang, K. Molmer, Theory of subradiant states of a one-dimensional two-level atom chain. Phys. Rev. Lett. 122, 203605 (2019)

    Article  ADS  Google Scholar 

  21. Y.S. Greenberg, A.A. Shtygashev, A.G. Moiseev, Spontaneous decay of artificial atoms in a three-qubit system. Eur. Phys. J. B 94, 221 (2021)

    Article  ADS  Google Scholar 

  22. J.D. Brehm, A.N. Poddubny, A. Stehli, T. Wolz, H. Rotzinger, Waveguide bandgap engineering with an array of superconducting qubits. npj Quantum Mater. 6, 10 (2021)

    Article  ADS  Google Scholar 

  23. M. Mirhosseini, E. Kim, Xu. Zhang, A. Sipahigil, P.B. Dieterle, A.J. Keller, A. Asenjo-Garcia, D.E. Chang, O. Painter, Cavity quantum electrodynamics with atom-like mirrors. Nature (London) 569, 692 (2019)

    Article  ADS  Google Scholar 

  24. J.Q. You, F. Nori, Superconducting circuits and quantum information. Phys. Today 58, 42 (2005)

    Article  Google Scholar 

  25. S.N. Shevchenko, Mesoscopic physics meets quantum engineering (World Scientific, Singapore, 2019)

    Book  Google Scholar 

  26. G. Ordonez, S. Kim, Complex collective states in a one-dimensional two-atom system. Phys. Rev. A 70, 032702 (2004)

    Article  ADS  Google Scholar 

  27. K. Lalumiere, B.C. Sanders, A.F. van Loo, A. Fedorov, A. Wallraff, A. Blais, Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms. Phys. Rev. A 88, 043806 (2013)

    Article  ADS  Google Scholar 

  28. A.F. van Loo, A. Fedorov, K. Lalumiere, B.C. Sanders, A. Blais, A. Wallraff, Photon-mediated interactions between distant artificial atoms. Science 342, 1494 (2013)

    Article  ADS  Google Scholar 

  29. M. Delanty, S. Rebic, J. Twamley, Superradiance and phase multistability in circuit quantum electrodynamics. N. J. Phys. 13, 053032 (2011)

    Article  Google Scholar 

  30. N. Lambert, Y. Matsuzaki, K. Kakuyanagi, N. Ishida, S. Saito, F. Nori, Superradiance with an ensemble of superconducting flux qubits. Phys. Rev. B 94, 224510 (2016)

    Article  ADS  Google Scholar 

  31. F.L. Kien, S.D. Gupta, K.P. Nayak, K. Hakuta, Nanofiber-mediated radiative transfer between two distant atom. Phys. Rev. A 72, 063815 (2005)

    Article  ADS  Google Scholar 

  32. A.A. Makarov, V.S. Letokhov, Spontaneous decay in a system of two spatially separated atoms (one-dimensional case). J. Exper. Theor. Phys. 97, 688 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. R.H. Lehmberg, Transition operators in radiative damping theory. Phys. Rev. 181, 32 (1969)

  35. A. Gonzalez-Tudela, D. Porras, Mesoscopic entanglement induced by spontaneous emission in solid-state quantum optics. Phys. Rev. Lett. 110, 080502 (2013)

    Article  ADS  Google Scholar 

  36. C.M. Caves, Quantum limits on noise in linear amplifiers. Phys. Rev. D 26, 1817 (1982)

    Article  ADS  Google Scholar 

  37. C. Eichler, D. Bozyigit, A. Wallraff, Characterizing quantum microwave radiation and its entanglement with superconducting qubits using linear detectors. Phys. Rev. A 86, 032106 (2012)

  38. B. Kannan, D.L. Campbell, F. Vasconcelos, R. Winik, D.K. Kim, M. Kjaergaard, P. Krantz, A. Melville, B.M. Niedzielski, J.L. Yoder, T.P. Orlando, S. Gustavsson, W.D. Oliver, Generating spatially entangled itinerant photons with waveguide quantum electrodynamics. Sci. Adv. 6, eabb8780 (2020)

  39. M.O. Scully, A.A. Svidzinsky, The super of superradiance. Science 325, 1510 (2009)

    Article  Google Scholar 

Download references

Acknowledgements

The work is supported by the Ministry of Science and Higher Education of Russian Federation under the project FSUN-2020-0004 and by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”.

Author information

Authors and Affiliations

  1. Novosibirsk State Technical University, Novosibirsk, Russia

    Ya. S. Greenberg & O. A. Chuikin

Authors
  1. Ya. S. Greenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. A. Chuikin
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

YSG wrote the manuscript and contributed to its theoretical interpretation. OAC performed analytical calculations and computer simulations. All authors discussed the results and commented on the manuscript. The authors declare that they have no competing interests.

Corresponding author

Correspondence to Ya. S. Greenberg.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Greenberg, Y.S., Chuikin, O.A. Superradiant emission spectra of a two-qubit system in circuit quantum electrodynamics. Eur. Phys. J. B 95, 151 (2022). https://doi.org/10.1140/epjb/s10051-022-00418-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-022-00418-6

Search

Navigation