Skip to main content
SpringerLink
Log in

Generation of Nonmaximally Entangled States between BECs with Quantum Optimal Control Methods

  • QUANTUM INFORMATICS: COMPUTING
  • Published:
Russian Microelectronics Aims and scope Submit manuscript

Abstract

In the last decade, different theoretical methods for entanglement generation between distant BEC qubits (macroscopic cold atomic ensembles) were proposed. However, experimental realization of such states is still challenging beside some special cases. The most theoretically investigated entangled states between macroscopic BECs are nonmaximally entangled states obtained with \(SzSz\) entangling Hamiltonian. With the use of such states, the protocols for quantum teleportation, remote state preporation and many others were developed for macroscopic qubits on the basis of BECs. Here we show that it is possible to obtain such states with the use of the bosonic analog of \(XY\) Hamiltonian and the methods of quantum optimal control. We compare performance of this scheme in the meaning of fidelity and entanglement for different drift and control Hamiltonians. We use the well-established QuTip open python library for all calculations.

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.

REFERENCES

  1. Galland, C., Sangouard, N., Piro, N., Gisin, N., and Kippenberg, T.J., Heralded single-phonon preparation, storage, and readout in cavity optomechanics, Phys. Rev. Lett., 2014, vol. 112, no. 14, p. 143602. https://doi.org/10.1103/physrevlett.112.143602

    Article  Google Scholar 

  2. Safavi-Naeini, A.H., Hill, J.T., Meenehan, S., Chan, J., Gröblacher, S., and Painter, O., Two-dimensional phononic-photonic band gap optomechanical crystal cavity, Phys. Rev. Lett., 2014, vol. 112, no. 15, p. 153603. https://doi.org/10.1103/physrevlett.112.153603

    Article  Google Scholar 

  3. Duan, L.-M., Sørensen, A., Cirac, J.I., and Zoller, P., Squeezing and Entanglement of Atomic Beams, Phys. Rev. Lett., 2000, vol. 85, no. 19, pp. 3991–3994. https://doi.org/10.1103/physrevlett.85.3991

    Article  Google Scholar 

  4. Pu, H. and Meystre, P., Creating macroscopic atomic Einstein–Podolsky–Rosen states from Bose–Einstein condensates, Phys. Rev. Lett., 2000, vol. 85, no. 19, pp. 3987–3990. https://doi.org/10.1103/physrevlett.85.3987

    Article  Google Scholar 

  5. Pyrkov, A.N. and Byrnes, T., Entanglement generation in quantum networks of Bose–Einstein condensates, New J. Phys., 2013, vol. 15, no. 9, p. 093019. https://doi.org/10.1088/1367-2630/15/9/093019

    Article  MathSciNet  Google Scholar 

  6. Kitagawa, M. and Ueda, M., Squeezed spin states, Phys. Rev. A, 1993, vol. 47, no. 6, p. 5138. https://doi.org/10.1103/PhysRevA.47.5138

    Article  Google Scholar 

  7. Lücke, B., Scherer, M., Kruse, J., Pezze, L., Deuretzbacher, F., Hyllus, P., Topic, O., Peise, J., Ertmer, W., Arlt, J., Santos, L., Smerzi, A., and Klempt, C., Twin matter waves for interferometry beyond the classical limit, Science, 2011, vol. 334, no. 6057, pp. 773–776. https://doi.org/10.1126/science.1208798

    Article  Google Scholar 

  8. Baumgarten, C., Braun, B., Capiluppi, M., Ciullo, G., Dalpiaz, P.F., Kolster, H., Lenisa, P., Marukyan, H., Nass, A., Reggiani, D., Stancari, M., and Steffens, E., First measurement of the hydrogen spin-exchange collision cross-section in the low temperature region, Eur. Phys. J. D, 2008, vol. 48, no. 3, pp. 343–350. https://doi.org/10.1140/epjd/e2008-00124-1

    Article  Google Scholar 

  9. Byrnes, T., Fractality and macroscopic entanglement in two-component Bose–Einstein condensates, Phys. Rev. A, 2013, vol. 88, no. 2, p. 023609.

    Article  Google Scholar 

  10. Rosseau, D., Ha, Q., and Byrnes, T., Entanglement generation between two spinor Bose–Einstein condensates with cavity QED, Phys. Rev. A, 2014, vol. 90, no. 5, p. 052315. https://doi.org/10.1103/PhysRevA.90.052315

    Article  Google Scholar 

  11. Kurkjian, H., Pawlowski, K., Sinatra, A., and Treutlein, P., Spin squeezing and Einstein–Podolsky–Rosen entanglement of two bimodal condensates in state-dependent potentials, Phys. Rev. A, 2013, vol. 88, no. 4, p. 043605. https://doi.org/10.1103/PhysRevA.88.043605

    Article  Google Scholar 

  12. Pettersson, O. and Byrnes, T., Light-mediated non-Gaussian entanglement of atomic ensembles, Phys. Rev. A, 2017, vol. 95, no. 4, p. 043817. https://doi.org/10.1103/PhysRevA.95.043817

    Article  Google Scholar 

  13. Idlas, S., Domenzain, L., Spreeuw, R., and Byrnes, T., Entanglement generation between spinor Bose–Einstein condensates using Rydberg excitations, Phys. Rev. A, 2016, vol. 93, no. 2, p. 022319. https://doi.org/10.1103/PhysRevA.93.022319

    Article  Google Scholar 

  14. Julsgaard, B., Kozhekin, A., and Polzik, E.S., Experimental long-lived entanglement of two macroscopic objects, Nature, 2001, vol. 413, no. 6854, pp. 400–403. https://doi.org/10.1038/35096524

    Article  Google Scholar 

  15. Krauter, H., Salart, D., Muschik, C.A., Petersen, J.M., Shen, H., Fernholz, T., and Polzik, E.S., Deterministic quantum teleportation between distant atomic objects, Nat. Phys., 2013, vol. 9, no. 7, pp. 400–404. https://doi.org/10.1038/nphys2631

    Article  Google Scholar 

  16. Sørensen, A., Duan, L.M., Cirac, J.I., and Zoller, P., Many-particle entanglement with Bose–Einstein condensates, Nature, 2001, vol. 409, no. 6816, pp. 63–66. https://doi.org/10.1038/35051038

    Article  Google Scholar 

  17. Strobel, H., Muessel, W., Linnemann, D., Zibold, T., Hume, D.B., Pezzè, L., Smerzi, A., and Oberthaler, M.K., Fisher information and entanglement of non-Gaussian spin states, Science, 2014, vol. 345, no. 6195, pp. 424–427. https://doi.org/10.1126/science.1250147

    Article  Google Scholar 

  18. Kunkel, P., Prüfer, M., Strobel, H., Linnemann, D., Frölian, A., Gasenzer, T., Gärttner, M., and Oberthaler, M.K., Spatially distributed multipartite entanglement enables EPR steering of atomic clouds, Science, 2018, vol. 360, no. 6387, pp. 413–416. https://doi.org/10.1126/science.aao2254

    Article  MathSciNet  Google Scholar 

  19. Lange, K., Peise, J., Lücke, B., Kruse, I., Vitagliano, G., Apellaniz, I., Kleinmann, M., Tóth, G., and Klempt, C., Entanglement between two spatially separated atomic modes, Science, 2018, vol. 360, no. 6387, pp. 416–418. https://doi.org/10.1126/science.aao2035

    Article  MathSciNet  Google Scholar 

  20. Fadel, M., Zibold, T., Décamps, B., and Treutlein, P., Spatial entanglement patterns and Einstein–Podolsky–Rosen steering in Bose–Einstein condensates, Science, 2018, vol. 360, no. 6387, pp. 409–413. https://doi.org/10.1126/science.aao1850

    Article  MathSciNet  Google Scholar 

  21. Tura, J., Augusiak, R., Sainz, A.B., Vértesi, T., Lewenstein, M., and Acín, A., Detecting nonlocality in many-body quantum states, Science, 2014, vol. 344, no. 6189, pp. 1256–1258. https://doi.org/10.1126/science.1247715

    Article  Google Scholar 

  22. Schmied, R., Bancal, J.-D., Allard, B., Fadel, M., Scarani, V., Treutlein, P., and Sangouard, N., Bell correlations in a Bose–Einstein condensate, Science, 2016, vol. 352, no. 6284, pp. 441–444. https://doi.org/10.1126/science.aad8665

    Article  MathSciNet  Google Scholar 

  23. Engelsen, N.J., Krishnakumar, R., Hosten, O., and Kasevich, M.A., Bell correlations in spin-squeezed states of 500 000 atoms, Phys. Rev. Lett., 2017, vol. 118, p. 140401. https://doi.org/10.1103/PhysRevLett.118.140401

    Article  Google Scholar 

  24. Colciaghi, P., Li, Yi., Treutlein, Ph., and Zibold, T., Einstein–Podolsky–Rosen experiment with two Bose–Einstein condensates, Phys. Rev. X, 2023, vol. 13, no. 2, p. 021031. https://doi.org/10.1103/physrevx.13.021031

    Article  Google Scholar 

  25. Byrnes, T., Rosseau, D., Khosla, M., Pyrkov, A., Thomasen, A., Mukai, T., Koyama, Sh., Abdelrahman, A., and Ilo-Okeke, E., Macroscopic quantum information processing using spin coherent states, Opt. Commun., 2015, vol. 337, pp. 102–109. https://doi.org/10.1016/j.optcom.2014.08.017

    Article  Google Scholar 

  26. Pyrkov, A.N. and Byrnes, T., Quantum teleportation of spin coherent states: beyond continuous variables teleportation, New J. Phys., 2014, vol. 16, no. 7, p. 073038.

    Article  Google Scholar 

  27. Pyrkov, A.N. and Byrnes, T., Full-Bloch-sphere teleportation of spinor Bose−Einstein condensates and spin ensembles, Phys. Rev. A, 2014, vol. 90, no. 6, p. 062336. https://doi.org/10.1103/PhysRevA.90.062336

    Article  Google Scholar 

  28. Chaudhary, M., Fadel, M., Ilo-Okeke, E.O., Pyrkov, A.N., Ivannikov, V., and Byrnes, T., Remote state preparation of two-component Bose–Einstein condensates, Phys. Rev. A, 2021, vol. 103, p. 062417. https://doi.org/10.1103/PhysRevA.103.062417

    Article  MathSciNet  Google Scholar 

  29. Dupont, N., Chatelain, G., Gabardos, L., Arnal, M., Billy, J., Peaudecerf, B., Sugny, D., and Guéry-Odelin, D., Quantum state control of a Bose–Einstein condensate in an optical lattice, PRX Quantum, 2021, vol. 2, no. 4, p. 040303. https://doi.org/10.1103/prxquantum.2.040303

    Article  Google Scholar 

  30. Kitzinger, J., Chaudhary, M., Kondappan, M., Ivannikov, V., and Byrnes, T., Two-axis two-spin squeezed states, Phys. Rev. Res., 2020, vol. 2, p. 033504. https://doi.org/10.1103/PhysRevResearch.2.033504

    Article  Google Scholar 

  31. Li, Yu., Treutlein, P., Reichel, J., and Sinatra, A., Spin squeezing in a bimodal condensate: spatial dynamics and particle losses, Eur. Phys. J. B, 2009, vol. 68, no. 3, pp. 365–381. https://doi.org/10.1140/epjb/e2008-00472-6

    Article  Google Scholar 

  32. Treutlein, P., Steinmetz, T., Colombe, Yv., Lev, B., Hommelhoff, P., Reichel, J., Greiner, M., Mandel, O., Widera, A., Rom, T., et al., Quantum information processing in optical lattices and magnetic microtraps, Fortschritte Phys.: Prog. Phys., 2006, vol. 54, nos. 8–10, pp. 702–718. https://doi.org/10.1002/prop.200610325

    Article  Google Scholar 

  33. Lloyd, S., Almost any quantum logic gate is universal, Phys. Rev. Lett., 1995, vol. 75, no. 2, pp. 346–349. https://doi.org/10.1103/PhysRevLett.75.346

    Article  Google Scholar 

  34. Braunstein, S.L. and van Loock, P., Quantum information with continuous variables, Rev. Mod. Phys., 2005, vol. 77, no. 2, p. 513. https://doi.org/10.1103/RevModPhys.77.513

    Article  MathSciNet  Google Scholar 

  35. Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrüggen, T., and Glaser, S.J., Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms, J. Magn. Reson., 2005, vol. 172, no. 2, pp. 296–305. https://doi.org/10.1016/j.jmr.2004.11.004

    Article  Google Scholar 

  36. Johansson, J.R., Nation, P.D., and Nori, F., QuTiP: An open-source Python framework for the dynamics of open quantum systems, Comput. Phys. Commun., 2012, vol. 183, no. 8, pp. 1760–1772. https://doi.org/10.1016/j.cpc.2012.02.021

    Article  Google Scholar 

Download references

Funding

This work is supported by Russian Science Foundation (grant no. 23-21-00507).

Author information

Authors and Affiliations

  1. Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry, Russian Academy of Sciences, 142432, Chernogolovka, Moscow oblast, Russia

    I. D. Lazarev & A. N. Pyrkov

Authors
  1. I. D. Lazarev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. N. Pyrkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. N. Pyrkov.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lazarev, I.D., Pyrkov, A.N. Generation of Nonmaximally Entangled States between BECs with Quantum Optimal Control Methods. Russ Microelectron 52 (Suppl 1), S403–S411 (2023). https://doi.org/10.1134/S1063739723600553

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063739723600553

Keywords:

Search

Navigation