The Synthetic Hilbert Space of Laser-Driven Free-Electrons

Guy Braiman, Ori Reinhardt, Chen Mechel, Omer Levi, and Ido Kaminer

Department of Electrical and Computer Engineering and Solid State Institute, Technion - Israel Institute of Technology, 32000 Haifa, Israel

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


Recent advances in laser interactions with coherent free electrons have enabled to shape the electron's quantum state. Each electron becomes a superposition of energy levels on an infinite quantized ladder, shown to contain up to thousands of energy levels. We propose to utilize the quantum nature of such laser-driven free electrons as a "synthetic Hilbert space" in which we construct and control qudits (quantum digits). The question that motivates our work is what qudit states can be accessed using electron-laser interactions, and whether it is possible to implement any arbitrary quantum gate. We find how to encode and manipulate free-electron qudit states, focusing on dimensions which are powers of 2, where the qudit represents multiple qubits implemented on the same single electron – algebraically separated, but physically joined. As an example, we prove the possibility to fully control a 4-dimenisonal qudit, and reveal the steps required for full control over any arbitrary dimension. Our work enriches the range of applications of free electrons in microscopy and spectroscopy, offering a new platform for continuous-variable quantum information.

Various platforms for quantum information processing are being studied nowadays. In this work we propose a new platform for continuous-variable quantum information – free electrons. We propose to utilize the energy levels on the quantized ladder of a single laser-driven free electron as a “synthetic Hilbert space” in which we can construct and control qudits (quantum digits).

► BibTeX data

► References

[1] Nielsen, M. A. and Chuang, I., Quantum computation and quantum information (2002).

[2] Cirac, J. I. and Zoller, P., Physical review letters, 74 4091 (1995).

[3] Loss, D. and DiVincenzo, D. P., Physical Review A, 57 120 (1998).

[4] Knill, E., Laflamme, R. and Milburn, G. J., Nature, 409 46 (2001).

[5] Devoret, M. H. and Schoelkopf, R. J., Science, 339 1169 (2013).

[6] Takui, T., Berliner, L. and Hanson, G., Electron spin resonance (ESR) based quantum computing, Springer New York (2016).

[7] P. W. Shor, Proceedings 35th Annual Symposium on Foundations of Computer Science, Santa Fe NM USA, 124-134 (1994).

[8] Saffman, M., Walker, T. G. and Mølmer, K., Reviews of modern physics, 82 2313 (2010).

[9] Reinhardt, O., Mechel, C., Lynch, M. H. and Kaminer, I., Annalen der Physik, 533 2000254 (2020).

[10] Tsarev, M. V., Ryabov, A. and Baum, P., Physical Review Research, 3 043033 (2021).

[11] Wernsdorfer, W. and Ruben, M. Advanced Materials, 31 1806687 (2019).

[12] Sawant, R., Blackmore, J. A., Gregory, P. D., Mur-Petit, J., Jaksch, D., Aldegunde, J., ... and Cornish, S. L., New Journal of Physics, 22 013027 (2020).

[13] Lu, H. H., Hu, Z., Alshaykh, M. S., Moore, A. J., Wang, Y., Imany, P., ... and Kais, S., Advanced Quantum Technologies, 3 1900074 (2020).

[14] J. Brendel, N. Gisin, W. Tittel and H. Zbinden., ‏Physical Review Letters, 82 2594 (1999).

[15] I. Marcikic, H. De Riedmatten, W. Tittel, H. Zbinden, M. Legré and N. Gisin, Physical Review Letters, 93 180502 (2004).

[16] Babazadeh, A., Erhard, M., Wang, F., Malik, M., Nouroozi, R., Krenn, M. and Zeilinger, A., Physical review letters, 119 180510 (2017).

[17] Kok, P., Munro, W. J., Nemoto, K., Ralph, T. C., Dowling, J. P. and Milburn, G. J., Reviews of Modern Physics, 79 135 (2007).

[18] O'brien, J. L., Science, 318 1567 (2007).

[19] O'brien, J. L., Furusawa, A. and Vučković, J., Nature Photonics, 3 687 (2009).

[20] Aspuru-Guzik, A. and Walther, P., Nature physics, 8 285 (2012).

[21] Lloyd, S. and Braunstein, S. L., Quantum Information with Continuous Variables, Springer Dordrecht (1999).

[22] Gottesman, D., Kitaev, A. and Preskill, J., Phys. Rev. A, 64 12310 (2001).

[23] Walschaers, M., PRX Quantum, 2 30204 (2021).

[24] Arrazola, J. M. et al., Nature, 591 54 (2021).

[25] Ruimy, R., Gorlach, A., Mechel, C., Rivera, N. and Kaminer, I., Physical Review Letters, 126 233403 (2021).

[26] Zhao, Z., Sun, X. Q. and Fan, S., Phys. Rev. Lett., 126 233402 (2021).

[27] Mechel, C., Kurman, Y., Karnieli, A., Rivera, N., Arie, A. and Kaminer, I., Optica, 8 70 (2021).

[28] Kruit, P., Krielaart, M., van Staaden, Y. and Loginov, S., Creating contrast in electron microscopy using the quantum Zeno effect, EBSN (2019).

[29] Zewail, A. H., Science ,328 187 (2010).

[30] Barwick, B., Flannigan, D. J. and Zewail, A. H., Nature, 462 902 (2009).

[31] Echternkamp, K. E., Feist, A., Schäfer, S. and Ropers, C., Nature Physics, 12 1000 (2016).

[32] Morimoto, Y. and Baum, P., Nature Physics, 14 252 (2018).

[33] Priebe, K. E., Rathje, C., Yalunin, S. V., Hohage, T., Feist, A., Schäfer, S. and Ropers, C., Nature Photonics, 11 793 (2017).

[34] Kozák, M., Schönenberger, N. and Hommelhoff, P., Physical review letters, 120 103203 (2018).

[35] Feist, A., Echternkamp, K. E., Schauss, J., Yalunin, S. V., Schäfer, S. and Ropers, C., Nature, 521 200 (2015).

[36] Reinhardt, O. and Kaminer, I., ACS Photonics, 7 2859 (2020).

[37] Vanacore, G. M., et al., Nature communications, 9 2694 (2018).

[38] García de Abajo, F. J., Asenjo-Garcia, A. and Kociak, M., Nano letters, 10 1859 (2010).

[39] Park, S. T., Lin, M., and Zewail, A. H., New Journal of Physics, 12 123028 (2010).

[40] García de Abajo F. J., Barwick, B. and Carbone, F., Physical Review B, 94 041404 (2016).

[41] Wang, K., Dahan, R., Shentcis, M., Kauffmann, Y., Hayun, A. B., Reinhardt, O., ... and Kaminer, I., Nature, 582 50 (2020)‏.

[42] Kfir, O. et al., Nature, 582 46 (2020).

[43] Jones, J. A. and Mosca, M., The Journal of chemical physics, 109 1648 (1998).

[44] Vatan, Farrokh and Colin Williams., Physical Review A, 69 032315 (2004).

[45] Feist, A., et al., Ultramicroscopy, 176 63 (2017).

[46] Losquin, A. and Lummen, T. T., Frontiers of Physics, 12 127301 (2017).

[47] Yalunin, S. V., Feist, A. and Ropers, C., Physical Review Research, 3 032036 (2021).

[48] Dahan, R., et al., Nature Physics, 16 1123 (2020).

[49] Piazza, L. Lummen, T., Quinonez, E., Murooka, Y., Reed, B. W., Barwick, B. and Carbone, F., Nature communications, 6 6407 (2015).

[50] Kruit, P., et al., Ultramicroscopy, 164 31 (2016).

[51] Juffmann, T., Koppell, S. A., Klopfer, B. B., Ophus, C., Glaeser, R. M. and Kasevich, M. A., Scientific reports, 7 1699 (2017).

[52] Okamoto, H., Latychevskaia, T. and Fink, H. W., Applied physics letters, 88 164103 (2006).

[53] Kfir, O., Physical review letters, 123 103602 (2019).

[54] Imany, P., Jaramillo-Villegas, J. A., Alshaykh, M. S., Lukens, J. M., Odele, O. D., Moore, A. J., ... and Weiner, A. M., npj Quantum Information, 5 1 (2019).

[55] Lu, H. H., Weiner, A. M., Lougovski, P. and Lukens, J. M., IEEE Photonics Technology Letters, 31 1858 (2019).

[56] Kues, M., Reimer, C., Roztocki, P., Cortés, L. R., Sciara, S., Wetzel, B., ... and Moss, D. J., Nature, 546 622 (2017).

[57] Low, P. J., White, B. M., Cox, A. A., Day, M. L. and Senko, C., Physical Review Research, 2 033128 (2020).

[58] Bremner, M. J., Bacon, D. and Nielsen, M. A., Physical Review A, 71 052312 (2005).

[59] Rungta, P., Munro, W. J., Nemoto, K., Deuar, P., Milburn, G. J. and Caves, C. M., Directions in Quantum Optics, Springer Berlin Heidelberg, 149-164 (2001).

[60] Pirandola, S., Mancini, S., Braunstein, S. L. and Vitali, D., Physical Review A, 77 032309 (2008).

[61] Marques, B., Matoso, A. A., Pimenta, W. M., Gutiérrez-Esparza, A. J., Santos, M. F. and Pádua, S., Scientific reports, 5 16049 (2015).

[62] Gedik, Z., Silva, I. A., Çakmak, B., Karpat, G., Vidoto, E. L. G., Soares-Pinto, D. D. O., ... and Fanchini, F. F., Scientific reports, 5 14671 (2015).

[63] Kiktenko, E. O., Fedorov, A. K., Strakhov, A. A. and Man'Ko, V. I., Physics Letters A, 379 1409 (2015).

[64] Bliokh, K. Y., Bliokh, Y. P., Savel’Ev, S. and Nori, F., Physical Review Letters, 99 190404 (2007).

[65] Cai, W., Reinhardt, O., Kaminer, I. and de Abajo, F. J. G., Physical Review B, 98 045424 (2018).

[66] Vanacore, G. M., et al., Nature materials, 18 573 (2019).

[67] Verbeeck, J., Tian, H. and Schattschneider, P., Nature, 467 301 (2010).

[68] Uchida, M. and Tonomura, A., Nature, 464 737 (2010).

[69] McMorran, B. J., Agrawal, A., Anderson, I. M., Herzing, A. A., Lezec, H. J., McClelland, J. J. and Unguris, J., Science, 331 192 (2011).

[70] Larocque, H., Kaminer, I., Grillo, V., Leuchs, G., Padgett, M. J., Boyd, R. W., Segev M. and Karimi, E., Contemporary Physics, 59 126 (2018).

[71] Wang, J., Yang, J., Fazal, I. M., Ahmed, N., Yan, Y., Huang, H., Ren, Y., Yue, Y., Dolinar, S., Tur, M. and Willner, A. E., Nature photonics, 6 488 (2012).

[72] Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C. and Woerdman, J. P., Physical review A, 45 8185 (1992).

[73] Gibson, G., Courtial, J., Padgett, M. J., Vasnetsov, M., Pas’ko, V., Barnett, S. M. and Franke-Arnold, S., Optics express, 12 5448 (2004).

[74] Perumangatt, C., Lal, N., Anwar, A., Reddy, S. G. and Singh, R. P., Physics Letters A, 22 1858 (2017).

Cited by

[1] Gefen Baranes, Shiran Even-Haim, Ron Ruimy, Alexey Gorlach, Raphael Dahan, Asaf A. Diringer, Shay Hacohen-Gourgy, and Ido Kaminer, "Free-electron interactions with photonic GKP states: Universal control and quantum error correction", Physical Review Research 5 4, 043271 (2023).

[2] Ron Ruimy and Ido Kaminer, 2023 IEEE 36th International Vacuum Nanoelectronics Conference (IVNC) 142 (2023) ISBN:979-8-3503-0143-4.

The above citations are from Crossref's cited-by service (last updated successfully 2024-04-15 13:22:06) and SAO/NASA ADS (last updated successfully 2024-04-15 13:22:07). The list may be incomplete as not all publishers provide suitable and complete citation data.