Visualizing the emission of a single photon with frequency and time resolved spectroscopy

Aleksei Sharafiev1, Mathieu L. Juan2, Oscar Gargiulo1, Maximilian Zanner3, Stephanie Wögerer3, Juan José García-Ripoll4, and Gerhard Kirchmair1,3

1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstrasse 21a, 6020 Innsbruck, Austria
2Institut quantique and Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, J1K 2R1, Canada
3Institute for Experimental Physics, University of Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
4Instituto de Fisica Fundamental IFF-CSIC, 28006 Madrid, Spain

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

Abstract

At the dawn of Quantum Physics, Wigner and Weisskopf obtained a full analytical description (a $\textit{photon portrait}$) of the emission of a single photon by a two-level system, using the basis of frequency modes (Weisskopf and Wigner, "Zeitschrift für Physik", 63, 1930). A direct experimental reconstruction of this portrait demands an accurate measurement of a time resolved fluorescence spectrum, with high sensitivity to the off-resonant frequencies and ultrafast dynamics describing the photon creation. In this work we demonstrate such an experimental technique in a superconducting waveguide Quantum Electrodynamics (wQED) platform, using single transmon qubit and two coupled transmon qubits as quantum emitters. In both scenarios, the photon portraits agree quantitatively with the predictions of the input-output theory and qualitatively with Wigner-Weisskopf theory. We believe that our technique allows not only for interesting visualization of fundamental principles, but may serve as a tool, e.g. to realize multi-dimensional spectroscopy in waveguide Quantum Electrodynamics.

We report on a direct measurement of a single photon "wave function" (electrical field amplitude distribution) in frequency and time domains. The "wavefunction" has been measured directly (without any post-processing) taking advantage of superconducting quantum circuits platform for the first time. We demonstrate the technique on a rather simple example of a two-level system emitting a single excitation into a waveguide – the situation with well known analytical description. This technique can be readily applied, for instance, to study near field radiation from an artificial atom or to realize a multi-dimensional spectroscopy of an artificial matter.

► BibTeX data

► References

[1] V. Weisskopf and E. Wigner. Berechnung der natürlichen Linienbreite auf Grund der Diracschen Lichttheorie. Zeitschrift für Physik, 63 (1): 54–73, January 1930. ISSN 0044-3328. 10.1007/​BF01336768.
https:/​/​doi.org/​10.1007/​BF01336768

[2] Marlan O. Scully and M. Suhail Zubairy. Quantum optics. Cambridge University Press, September 1997. 10.1017/​CBO9780511813993.
https:/​/​doi.org/​10.1017/​CBO9780511813993

[3] J. E. Sipe. Photon wave functions. Physical Review A, 52 (3): 1875–1883, September 1995. 10.1103/​PhysRevA.52.1875.
https:/​/​doi.org/​10.1103/​PhysRevA.52.1875

[4] Iwo Bialynicki-Birula. On the wave function of the photon. Acta Physica Polonica A, 86 (1-2): 97–111, August 1994. 10.12693/​APHYSPOLA.86.97.
https:/​/​doi.org/​10.12693/​APHYSPOLA.86.97

[5] Iwo Bialynicki-Birula. Progress in Optics, volume XXXVI, chapter Photon wave function, pages 245–294. Elsevier, Amsterdam, 1996. 10.1016/​S0079-6638(08)70316-0.
https:/​/​doi.org/​10.1016/​S0079-6638(08)70316-0

[6] Jeff S. Lundeen, Brandon Sutherland, Aabid Patel, Corey Stewart, and Charles Bamber. Direct measurement of the quantum wavefunction. Nature, 474 (7350): 188–191, June 2011. ISSN 1476-4687. 10.1038/​nature10120.
https:/​/​doi.org/​10.1038/​nature10120

[7] Alex O. C. Davis, Valérian Thiel, Michał Karpiński, and Brian J. Smith. Measuring the Single-Photon Temporal-Spectral Wave Function. Physical Review Letters, 121 (8): 083602, August 2018. 10.1103/​PhysRevLett.121.083602.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.083602

[8] T. D. Newton and E. P. Wigner. Localized States for Elementary Systems. Reviews of Modern Physics, 21 (3): 400–406, July 1949. 10.1103/​RevModPhys.21.400.
https:/​/​doi.org/​10.1103/​RevModPhys.21.400

[9] Srikanth J. Srinivasan, Neereja M. Sundaresan, Darius Sadri, Yanbing Liu, Jay M. Gambetta, Terri Yu, S. M. Girvin, and Andrew A. Houck. Time-reversal symmetrization of spontaneous emission for quantum state transfer. Physical Review A, 89 (3): 033857, March 2014. 10.1103/​PhysRevA.89.033857.
https:/​/​doi.org/​10.1103/​PhysRevA.89.033857

[10] M. Pechal, L. Huthmacher, C. Eichler, S. Zeytinoğlu, A. A. Abdumalikov, S. Berger, A. Wallraff, and S. Filipp. Microwave-Controlled Generation of Shaped Single Photons in Circuit Quantum Electrodynamics. Physical Review X, 4 (4): 041010, October 2014. 10.1103/​PhysRevX.4.041010.
https:/​/​doi.org/​10.1103/​PhysRevX.4.041010

[11] P. Forn-Díaz, J. J. García-Ripoll, B. Peropadre, M. A. Yurtalan, J.-L. Orgiazzi, R. Belyansky, C. M. Wilson, and A. Lupascu. Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime. Nature Physics, 13 (1): 39–43, October 2016. ISSN 1745-2473, 1745-2481. 10.1038/​nphys3905.
https:/​/​doi.org/​10.1038/​nphys3905

[12] N. K. Langford, R. Sagastizabal, M. Kounalakis, C. Dickel, A. Bruno, F. Luthi, D. J. Thoen, A. Endo, and L. DiCarlo. Experimentally simulating the dynamics of quantum light and matter at deep-strong coupling. Nature Communications, 8 (1): 1715, November 2017. ISSN 2041-1723. 10.1038/​s41467-017-01061-x.
https:/​/​doi.org/​10.1038/​s41467-017-01061-x

[13] Jochen Braumüller, Michael Marthaler, Andre Schneider, Alexander Stehli, Hannes Rotzinger, Martin Weides, and Alexey V. Ustinov. Analog quantum simulation of the Rabi model in the ultra-strong coupling regime. Nature Communications, 8 (1): 779, October 2017. ISSN 2041-1723. 10.1038/​s41467-017-00894-w.
https:/​/​doi.org/​10.1038/​s41467-017-00894-w

[14] Yanbing Liu and Andrew A. Houck. Quantum electrodynamics near a photonic bandgap. Nature Physics, 13 (1): 48–52, January 2017. ISSN 1745-2481. 10.1038/​nphys3834.
https:/​/​doi.org/​10.1038/​nphys3834

[15] Nicholas T. Bronn, Yanbing Liu, Jared B. Hertzberg, Antonio D. Córcoles, Andrew A. Houck, Jay M. Gambetta, and Jerry M. Chow. Broadband filters for abatement of spontaneous emission in circuit quantum electrodynamics. Applied Physics Letters, 107 (17): 172601, October 2015. ISSN 0003-6951. 10.1063/​1.4934867.
https:/​/​doi.org/​10.1063/​1.4934867

[16] I.-C. Hoi, A. F. Kockum, L. Tornberg, A. Pourkabirian, G. Johansson, P. Delsing, and C. M. Wilson. Probing the quantum vacuum with an artificial atom in front of a mirror. Nature Physics, 11 (12): 1045–1049, 2015. ISSN 1745-2481. 10.1038/​nphys3484.
https:/​/​doi.org/​10.1038/​nphys3484

[17] J. A. Mlynek, A. A. Abdumalikov, C. Eichler, and A. Wallraff. Observation of Dicke superradiance for two artificial atoms in a cavity with high decay rate. Nature Communications, 5: 5186, November 2014. ISSN 2041-1723. 10.1038/​ncomms6186.
https:/​/​doi.org/​10.1038/​ncomms6186

[18] Mohammad Mirhosseini, Eunjong Kim, Xueyue Zhang, Alp Sipahigil, Paul B. Dieterle, Andrew J. Keller, Ana Asenjo-Garcia, Darrick E. Chang, and Oskar Painter. Cavity quantum electrodynamics with atom-like mirrors. Nature, 569 (7758): 692–697, May 2019. ISSN 1476-4687. 10.1038/​s41586-019-1196-1.
https:/​/​doi.org/​10.1038/​s41586-019-1196-1

[19] G. Wendin. Quantum information processing with superconducting circuits: a review. Reports on Progress in Physics, 80 (10): 106001, September 2017. ISSN 0034-4885. 10.1088/​1361-6633/​aa7e1a.
https:/​/​doi.org/​10.1088/​1361-6633/​aa7e1a

[20] Carlton M. Caves. Quantum limits on noise in linear amplifiers. Physical Review D, 26 (8): 1817–1839, October 1982. 10.1103/​PhysRevD.26.1817.
https:/​/​doi.org/​10.1103/​PhysRevD.26.1817

[21] N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret. Phase-preserving amplification near the quantum limit with a Josephson ring modulator. Nature, 465 (7294): 64–68, May 2010. ISSN 1476-4687. 10.1038/​nature09035.
https:/​/​doi.org/​10.1038/​nature09035

[22] M. Dalmonte, S. I. Mirzaei, P. R. Muppalla, D. Marcos, P. Zoller, and G. Kirchmair. Realizing dipolar spin models with arrays of superconducting qubits. Physical Review B, 92 (17): 174507, November 2015. 10.1103/​PhysRevB.92.174507.
https:/​/​doi.org/​10.1103/​PhysRevB.92.174507

[23] Kevin Lalumière, Barry C. Sanders, A. F. van Loo, A. Fedorov, A. Wallraff, and A. Blais. Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms. Physical Review A, 88 (4): 043806, October 2013. 10.1103/​PhysRevA.88.043806.
https:/​/​doi.org/​10.1103/​PhysRevA.88.043806

[24] A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. Generating single microwave photons in a circuit. Nature, 449 (7160): 328–331, September 2007. ISSN 1476-4687. 10.1038/​nature06126.
https:/​/​doi.org/​10.1038/​nature06126

[25] A. A. Abdumalikov, O. V. Astafiev, Yu. A. Pashkin, Y. Nakamura, and J. S. Tsai. Dynamics of Coherent and Incoherent Emission from an Artificial Atom in a 1d Space. Physical Review Letters, 107 (4): 043604, July 2011. 10.1103/​PhysRevLett.107.043604.
https:/​/​doi.org/​10.1103/​PhysRevLett.107.043604

[26] C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff. Experimental State Tomography of Itinerant Single Microwave Photons. Physical Review Letters, 106 (22): 220503, June 2011. 10.1103/​PhysRevLett.106.220503.
https:/​/​doi.org/​10.1103/​PhysRevLett.106.220503

[27] F. Mallet, M. A. Castellanos-Beltran, H. S. Ku, S. Glancy, E. Knill, K. D. Irwin, G. C. Hilton, L. R. Vale, and K. W. Lehnert. Quantum State Tomography of an Itinerant Squeezed Microwave Field. Physical Review Letters, 106 (22): 220502, June 2011. 10.1103/​PhysRevLett.106.220502.
https:/​/​doi.org/​10.1103/​PhysRevLett.106.220502

[28] Tomás Ramos and Juan José García-Ripoll. Multiphoton scattering tomography with coherent states. Phys. Rev. Lett., 119: 153601, Oct 2017. 10.1103/​PhysRevLett.119.153601.
https:/​/​doi.org/​10.1103/​PhysRevLett.119.153601

[29] Peter C. Chen. An Introduction to Coherent Multidimensional Spectroscopy. Applied Spectroscopy, 70 (12): 1937–1951, December 2016. ISSN 0003-7028. 10.1177/​0003702816669730.
https:/​/​doi.org/​10.1177/​0003702816669730

[30] A. Lukashenko and A. V. Ustinov. Improved powder filters for qubit measurements. Review of Scientific Instruments, 79 (1): 014701, January 2008. ISSN 0034-6748. 10.1063/​1.2827515.
https:/​/​doi.org/​10.1063/​1.2827515

[31] Florent Lecocq, Ioan M Pop, Zhihui Peng, Iulian Matei, Thierry Crozes, Thierry Fournier, Cécile Naud, Wiebke Guichard, and Olivier Buisson. Junction fabrication by shadow evaporation without a suspended bridge. Nanotechnology, 22 (31): 315302, August 2011. ISSN 0957-4484, 1361-6528. 10.1088/​0957-4484/​22/​31/​315302.
https:/​/​doi.org/​10.1088/​0957-4484/​22/​31/​315302

[32] J.R. Johansson, P.D. Nation, and Franco Nori. Qutip: An open-source python framework for the dynamics of open quantum systems. Computer Physics Communications, 183 (8): 1760–1772, 2012. ISSN 0010-4655. https:/​/​doi.org/​10.1016/​j.cpc.2012.02.021.
https:/​/​doi.org/​10.1016/​j.cpc.2012.02.021

[33] J.R. Johansson, P.D. Nation, and Franco Nori. Qutip 2: A python framework for the dynamics of open quantum systems. Computer Physics Communications, 184 (4): 1234–1240, 2013. ISSN 0010-4655. https:/​/​doi.org/​10.1016/​j.cpc.2012.11.019.
https:/​/​doi.org/​10.1016/​j.cpc.2012.11.019

Cited by

On Crossref's cited-by service no data on citing works was found (last attempt 2021-06-16 03:41:29). On SAO/NASA ADS no data on citing works was found (last attempt 2021-06-16 03:41:29).