Skip to main content
Log in

Frequency–modulated qubits in a dissipative cavity: entanglement dynamics and protection

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We address the problem of preserving entanglement in open quantum systems specifically two-qubit system via devising a new strategy in which a structured environment and modulation mechanism cooperatively benefit the whole system. The model is quite general and encompasses any two arbitrary qubits whether the same or different with various modulation parameters. Hence, we consider two more plausible scenarios once with similar qubits and once again with dissimilar qubits. For the special case when the system possesses two similar qubits, we investigate the dynamics of entanglement in the presence (resonance) and absence of detuning (non-resonance) for both weak and strong coupling regimes. It is revealed that there are optimal modulation parameters and detuning for which the maximal protection and generation of entanglement are achieved. Finally, we consider a more general scenario for which the qubits can have different transition frequencies. It is observed that with the optimal choices of the detuning parameters as well as the modulation parameters one shall attain a nearly perfect protection.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data Availability

The authors declare that all data supporting the findings of this study are available within the article and its supplementary information files.

References

  1. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009). https://doi.org/10.1103/RevModPhys.81.865

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition, 10th edn. Cambridge University Press, New York (2011)

    MATH  Google Scholar 

  3. Mattle, K., Weinfurter, H., Kwiat, P.G., Zeilinger, A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, 4656–4659 (1996). https://doi.org/10.1103/PhysRevLett.76.4656

    Article  ADS  Google Scholar 

  4. Hu, C.Y., Rarity, J.G.: Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity. Phys. Rev. B 83, 115303 (2011). https://doi.org/10.1103/PhysRevB.83.115303

    Article  ADS  Google Scholar 

  5. Egger, D., et al.: Entanglement generation in superconducting qubits using holonomic operations. Phys. Rev. Appl. 11, 014017 (2019). https://doi.org/10.1103/PhysRevApplied.11.014017

    Article  ADS  Google Scholar 

  6. Cirac, J.I., Zoller, P.: Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995). https://doi.org/10.1103/PhysRevLett.74.4091

    Article  ADS  Google Scholar 

  7. Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Great Clarendon Street (2002)

    MATH  Google Scholar 

  8. Nourmandipour, A., Tavassoly, M.K., Rafiee, M.: Dynamics and protection of entanglement in \(n\)-qubit systems within Markovian and non-Markovian environments. Phys. Rev. A 93, 022327 (2016). https://doi.org/10.1103/PhysRevA.93.022327

    Article  ADS  Google Scholar 

  9. Maniscalco, S., Francica, F., Zaffino, R.L., Lo Gullo, N., Plastina, F.: Protecting entanglement via the quantum Zeno effect. Phys. Rev. Lett. 100, 090503 (2008). https://doi.org/10.1103/PhysRevLett.100.090503

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Nourmandipour, A., Tavassoly, M.K., Bolorizadeh, M.A.: Quantum Zeno and anti-Zeno effects on the entanglement dynamics of qubits dissipating into a common and non-Markovian environment. J. Opt. Soc. Am. B 33, 1723–1730 (2016)

    Article  ADS  Google Scholar 

  11. Gholipour, H., Mortezapour, A., Nosrati, F., Franco, R.L.: Quantumness and memory of one qubit in a dissipative cavity under classical control. Ann. Phys. 414, 168073 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mortezapour, A., Nourmandipour, A., Gholipour, H.: The effect of classical driving field on the spectrum of a qubit and entanglement swapping inside dissipative cavities. Quantum Inf. Process. 19, 136 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Nourmandipour, A., Vafafard, A., Mortezapour, A., Franzosi, R.: Entanglement protection of classically driven qubits in a lossy cavity. Sci. Rep. 11, 16259 (2021). https://doi.org/10.1038/s41598-021-95623-1

    Article  ADS  Google Scholar 

  14. Mortezapour, A., Abedi, M., Mahmoudi, M., Khajehpour, M.R.H.: The effect of a coupling field on the entanglement dynamics of a three-level atom. J. Phys. B: At. Mol. Opt. Phys. 44, 085501 (2011). https://doi.org/10.1088/0953-4075/44/8/085501

    Article  ADS  Google Scholar 

  15. Roffe, J.: Quantum error correction: an introductory guide. Contemp. Phys. 60, 226–245 (2019). https://doi.org/10.1080/00107514.2019.1667078

    Article  ADS  Google Scholar 

  16. Kim, Y.-S., Lee, J.-C., Kwon, O., Kim, Y.-H.: Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nat. Phys. 8, 117 (2012)

    Article  Google Scholar 

  17. Rafiee, M., Nourmandipour, A., Mancini, S.: Optimal feedback control of two-qubit entanglement in dissipative environments. Phys. Rev. A 94, 012310 (2016). https://doi.org/10.1103/PhysRevA.94.012310

    Article  ADS  Google Scholar 

  18. Rafiee, M., Nourmandipour, A., Mancini, S.: Universal feedback control of two-qubit entanglement. Phys. Rev. A 96, 012340 (2017). https://doi.org/10.1103/PhysRevA.96.012340

    Article  ADS  Google Scholar 

  19. Nosrati, F., Mortezapour, A., Lo Franco, R.: Validating and controlling quantum enhancement against noise by the motion of a qubit. Phys. Rev. A 101, 012331 (2020). https://doi.org/10.1103/PhysRevA.101.012331

    Article  ADS  Google Scholar 

  20. Golkar, S., Tavassoly, M.K., Nourmandipour, A.: Entanglement dynamics of moving qubits in a common environment. J. Opt. Soc. Am. B 37, 400–411 (2020)

    Article  ADS  Google Scholar 

  21. Mortezapour, A., Naeimi, G., Lo Franco, R.: Coherence and entanglement dynamics of vibrating qubits. Opt. Commun. 424, 26–31 (2018)

    Article  ADS  Google Scholar 

  22. Mortezapour, A., Borji, M.A., Franco, R.L.: Protecting entanglement by adjusting the velocities of moving qubits inside non-Markovian environments. Laser Phys. Lett. 14, 055201 (2017). https://doi.org/10.1088/1612-202x/aa63c5

    Article  ADS  Google Scholar 

  23. Mortezapour, A., Borji, M.A., Park, D., Franco, R.L.: Non-Markovianity and coherence of a moving qubit inside a leaky cavity. Open. Syst. Inf. Dyn. 24, 1740006 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  24. Golkar, S., Tavassoly, M.K., Nourmandipour, A.: Qubit movement-assisted entanglement swapping. Chin. Phys. B 29, 050304 (2020). https://doi.org/10.1088/1674-1056/ab7da3

    Article  ADS  Google Scholar 

  25. Radhakrishnan, C., Chen, P.-W., Jambulingam, S., Byrnes, T., Ali, M.M.: Time dynamics of quantumcoherence and monogamy in a non-Markovian environment. Sci. Rep. 9, 2363 (2019). https://doi.org/10.1038/s41598-019-39027-2

    Article  ADS  Google Scholar 

  26. Nourmandipour, A., Tavassoly, M.K., Mancini, S.: The entangling power of a glocal dissipative map. Quantum Inf. Comput. 16, 0969 (2016)

    MathSciNet  Google Scholar 

  27. Rafiee, M., Nourmandipour, A., Mancini, S.: Enforcing dissipative entanglement by feedback. Phys. Lett. A 384, 126748 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  28. Beaudoin, F., da Silva, M.P., Dutton, Z., Blais, A.: First-order sidebands in circuit qed using qubit frequency modulation. Phys. Rev. A 86, 022305 (2012). https://doi.org/10.1103/PhysRevA.86.022305

    Article  ADS  Google Scholar 

  29. Janowicz, M.: Non-Markovian decay of an atom coupled to a reservoir: Modification by frequency modulation. Phys. Rev. A 61, 025802 (2000). https://doi.org/10.1103/PhysRevA.61.025802

    Article  ADS  Google Scholar 

  30. Ficek, Z., Seke, J., Soldatov, A.V., Adam, G.: Fluorescence spectrum of a two-level atom driven by a multiple modulated field. Phys. Rev. A 64, 013813 (2001). https://doi.org/10.1103/PhysRevA.64.013813

    Article  ADS  Google Scholar 

  31. Silveri, M.P., Tuorila, J.A., Thuneberg, E.V., Paraoanu, G.S.: Quantum systems under frequency modulation. Rep. Prog. Phys. 80, 056002 (2017). https://doi.org/10.1088/1361-6633/aa5170

    Article  ADS  Google Scholar 

  32. Nakamura, Y., Pashkin, Y.A., Tsai, J.S.: Rabi oscillations in a Josephson-junction charge two-level system. Phys. Rev. Lett. 87, 246601 (2001). https://doi.org/10.1103/PhysRevLett.87.246601

    Article  ADS  Google Scholar 

  33. Mortezapour, A., Franco, R.L.: Protecting quantum resources via frequency modulation of qubits in leaky cavities. Sci. Rep. 8, 14304 (2018)

    Article  ADS  Google Scholar 

  34. Forozesh, M., Mortezapour, A., Nourmandipour, A.: Controlling qubit-photon entanglement, entanglement swapping and entropic uncertainty via frequency modulation. Eur. Phys. J. Plus 136, 778 (2021)

    Article  Google Scholar 

  35. Ali, M.M., Chen, P.-W., Goan, H.-S.: Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir. Phys. Rev. A 82, 022103 (2010). https://doi.org/10.1103/PhysRevA.82.022103

    Article  ADS  Google Scholar 

  36. Chen, P.-W., Ali, M., Chen, S.-H.: Enhanced quantum nonlocality induced by the memory of a thermal-squeezed environment. J. Phys. A: Math. Theor. 49, 395302 (2016). https://doi.org/10.1088/1751-8113/49/39/395302

    Article  MathSciNet  MATH  Google Scholar 

  37. Kastoryano, M.J., Reiter, F., Sørensen, A.S.: Dissipative preparation of entanglement in optical cavities. Phys. Rev. Lett. 106, 090502 (2010). https://doi.org/10.1103/PhysRevLett.106.090502

    Article  Google Scholar 

  38. Li, D.-X., Shao, X.-Q., Wu, J.-H., Yi, X.X.: Engineering steady-state entanglement via dissipation and quantum Zeno dynamics in an optical cavity. Opt. Lett. 42, 3904 (2017). https://doi.org/10.1364/OL.42.003904

    Article  ADS  Google Scholar 

  39. Salah, R., Ahmed, M., Abdel-Aty, M., Eleuch, H., Obada, A.-S.: Entanglement control of two-level atoms in dissipative cavities. Appl. Sci. 10, 3904 (2020). https://doi.org/10.3390/app10041510

    Article  Google Scholar 

  40. Wang, J. et al.: Protecting entanglement of two V-type atoms in dissipative cavity by dipole-dipole interaction. arXiv preprint arXiv:2212.04650v1 (2022)

  41. Fei, S.-M., Jing, N.: Equivalence of quantum states under local unitary transformations. Phys. Lett. A 342, 77–81 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. Nourmandipour, A., Tavassoly, M.: Dynamics and protecting of entanglement in two-level systems interacting with a dissipative cavity: the Gardiner-Collett approach. J. Phys. B: At. Mol. Opt. Phys. 48, 165502 (2015). https://doi.org/10.1088/0953-4075/48/16/165502/pdf

    Article  ADS  Google Scholar 

  43. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998). https://doi.org/10.1103/PhysRevLett.80.2245

    Article  ADS  MATH  Google Scholar 

  44. Silveri, M.P., Tuorila, J.A., Thuneberg, E.V., Paraoanu, G.S.: Quantum systems under frequency modulation. Rep. Prog. Phys. 80, 056002 (2017)

    Article  ADS  Google Scholar 

  45. Nakamura, Y., Pashkin, Y.A., Tsai, J.S.: Rabi oscillations in a Josephson-junction charge two-level system. Phys. Rev. Lett. 87, 246601 (2001)

    Article  ADS  Google Scholar 

  46. Oliver, W.D., et al.: Mach-Zehnder interferometry in a strongly driven superconducting qubit. Science 310, 1653–1657 (2005)

    Article  ADS  Google Scholar 

  47. Tuorila, J., et al.: Stark effect and generalized Bloch-Biegert shift in a strongly driven two-level system. Phys. Rev. Lett. 105, 257003 (2010)

    Article  ADS  Google Scholar 

  48. Tuorila, J., et al.: Motional averaging in a superconducting qubit. Nat. Comm. 4, 1420 (2013)

    Article  ADS  Google Scholar 

  49. Trabesinger, A.: Quantum computing: towards reality. Nature 543, S1 (2017)

    Article  ADS  Google Scholar 

  50. Preskill, J.: Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018). https://doi.org/10.22331/q-2018-08-06-79

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ali Mortezapour.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Alireza Nourmandipour and Ali Mortezapour have contributed equally to this work.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) 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

Nourmandipour, A., Mortezapour, A. Frequency–modulated qubits in a dissipative cavity: entanglement dynamics and protection. Quantum Inf Process 22, 254 (2023). https://doi.org/10.1007/s11128-023-03992-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-03992-5

Keywords

Navigation