Kerr nonlinearity in a superconducting Josephson metamaterial

Krupko, Yu.; Nguyen, V. D.; Weißl, T.; Dumur, É.; Puertas, J.; Dassonneville, R.; Naud, C.; Hekking, F. W. J.; Basko, D. M.; Buisson, O.; Roch, N.; Hasch-Guichard, W.

doi:10.1103/PhysRevB.98.094516

Title: Kerr nonlinearity in a superconducting Josephson metamaterial

Journal Article · 18 September 2018 · Physical Review B

DOI: https://doi.org/10.1103/PhysRevB.98.094516 · OSTI ID:1485126

Krupko, Yu. ^[1]; Nguyen, V. D. ^[2]; Weißl, T. ^[3]; Dumur, É. ^[4]; Puertas, J. ^[1]; Dassonneville, R. ^[1]; Naud, C. ^[1]; Hekking, F. W. J. ^[2]; Basko, D. M. ^[2]; Buisson, O. ^[1]; Roch, N. ^[1]; Hasch-Guichard, W. ^[1]

Univ. Grenoble Alpes, Grenoble (France)
Univ. Grenoble Alpes and CNRS, Grenoble (France)
Univ. Grenoble Alpes, Grenoble (France); Royal Institute of Technology (KTH), Stockholm (Sweden)
Univ. Grenoble Alpes, Grenoble (France); Argonne National Lab. (ANL), Argonne, IL (United States)

Here, we present a detailed experimental and theoretical analysis of the dispersion and nonlinear Kerr frequency shifts of plasma modes in a one-dimensional Josephson junction chain containing 500 superconducting quantum interfence devices in the regime of weak nonlinearity. The measured low-power dispersion curve agrees perfectly with the theoretical model if we take into account the Kerr renormalization of the bare frequencies and the long-range nature of the island charge screening by a remote ground plane. We measured the self- and cross-Kerr shifts for the frequencies of the eight lowest modes in the chain. We compare the measured Kerr coefficients with theory and find good agreement.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: European Research Council (ERC); USDOE

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1485126

Journal Information:: Physical Review B, Vol. 98, Issue 9; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (52)

Amplification and squeezing of quantum noise with a tunable Josephson metamaterial Castellanos-Beltran, M. A.; Irwin, K. D.; Hilton, G. C. Nature Physics, Vol. 4, Issue 12 https://doi.org/10.1038/nphys1090	journal	October 2008
Stabilizing spin coherence through environmental entanglement in strongly dissipative quantum systems Bera, Soumya; Florens, Serge; Baranger, Harold U. Physical Review B, Vol. 89, Issue 12 https://doi.org/10.1103/PhysRevB.89.121108	journal	March 2014
Junction fabrication by shadow evaporation without a suspended bridge Lecocq, Florent; Pop, Ioan M.; Peng, Zhihui Nanotechnology, Vol. 22, Issue 31 https://doi.org/10.1088/0957-4484/22/31/315302	journal	July 2011
Invited Review Article: The Josephson bifurcation amplifier Vijay, R.; Devoret, M. H.; Siddiqi, I. Review of Scientific Instruments, Vol. 80, Issue 11 https://doi.org/10.1063/1.3224703	journal	November 2009
Plasmonic and metamaterial cloaking: physical mechanisms and potentials Alù, Andrea; Engheta, Nader Journal of Optics A: Pure and Applied Optics, Vol. 10, Issue 9 https://doi.org/10.1088/1464-4258/10/9/093002	journal	August 2008
Traveling wave parametric amplifier with Josephson junctions using minimal resonator phase matching White, T. C.; Mutus, J. Y.; Hoi, I. -C. Applied Physics Letters, Vol. 106, Issue 24 https://doi.org/10.1063/1.4922348	journal	June 2015
Length-Scale Dependence of the Superconductor-to-Insulator Quantum Phase Transition in One Dimension Chow, Edmond; Delsing, Per; Haviland, David B. Physical Review Letters, Vol. 81, Issue 1 https://doi.org/10.1103/PhysRevLett.81.204	journal	July 1998
Quantum phase slips in Josephson junction rings Rastelli, G.; Pop, I. M.; Hekking, F. W. J. Physical Review B, Vol. 87, Issue 17 https://doi.org/10.1103/PhysRevB.87.174513	journal	May 2013
Planar negative refractive index media using periodically L-C loaded transmission lines Eleftheriades, G. V.; Iyer, A. K.; Kremer, P. C. IEEE Transactions on Microwave Theory and Techniques, Vol. 50, Issue 12 https://doi.org/10.1109/TMTT.2002.805197	journal	December 2002
Onset of superconductivity in ultrathin granular metal films Jaeger, H. M.; Haviland, D. B.; Orr, B. G. Physical Review B, Vol. 40, Issue 1 https://doi.org/10.1103/PhysRevB.40.182	journal	July 1989
Energetic and spectral properties of triple photon downconversion in a phase-matched KTiOPO_4 crystal Dot, Audrey; Borne, Adrien; Boulanger, Benoît Optics Letters, Vol. 37, Issue 12 https://doi.org/10.1364/OL.37.002334	journal	January 2012
Spatial and temporal distribution of phase slips in Josephson junction chains Ergül, Adem; Weißl, Thomas; Johansson, Jan Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-11670-7	journal	September 2017
Generation of non-classical photon states in superconducting quantum metamaterials Mukhin, S. I.; Fistul, M. V. Superconductor Science and Technology, Vol. 26, Issue 8 https://doi.org/10.1088/0953-2048/26/8/084003	journal	June 2013
Quantum phase transitions and vortex dynamics in superconducting networks Fazio, R. Physics Reports, Vol. 355, Issue 4 https://doi.org/10.1016/S0370-1573(01)00022-9	journal	December 2001
Phase-charge duality in Josephson junction circuits: Role of inertia and effect of microwave irradiation Guichard, W.; Hekking, F. W. J. Physical Review B, Vol. 81, Issue 6 https://doi.org/10.1103/PhysRevB.81.064508	journal	February 2010
A near-quantum-limited Josephson traveling-wave parametric amplifier Macklin, C.; O'Brien, K.; Hover, D. Science, Vol. 350, Issue 6258 https://doi.org/10.1126/science.aaa8525	journal	September 2015
Josephson-junction-embedded transmission-line resonators: From Kerr medium to in-line transmon Bourassa, J.; Beaudoin, F.; Gambetta, Jay M. Physical Review A, Vol. 86, Issue 1 https://doi.org/10.1103/PhysRevA.86.013814	journal	July 2012
Measurement of the effect of quantum phase slips in a Josephson junction chain Pop, I. M.; Protopopov, I.; Lecocq, F. Nature Physics, Vol. 6, Issue 8 https://doi.org/10.1038/nphys1697	journal	June 2010
Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light Le Hur, Karyn; Henriet, Loïc; Petrescu, Alexandru Comptes Rendus Physique, Vol. 17, Issue 8 https://doi.org/10.1016/j.crhy.2016.05.003	journal	October 2016
Kerr coefficients of plasma resonances in Josephson junction chains Weißl, T.; Küng, B.; Dumur, E. Physical Review B, Vol. 92, Issue 10 https://doi.org/10.1103/PhysRevB.92.104508	journal	September 2015
Quantum fluctuations in chains of Josephson junctions Bradley, R. M.; Doniach, S. Physical Review B, Vol. 30, Issue 3 https://doi.org/10.1103/PhysRevB.30.1138	journal	August 1984
One-dimensional Josephson junction arrays: Lifting the Coulomb blockade by depinning Vogt, Nicolas; Schäfer, Roland; Rotzinger, Hannes Physical Review B, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevB.92.045435	journal	July 2015
Microwave Characterization of Josephson Junction Arrays: Implementing a Low Loss Superinductance Masluk, Nicholas A.; Pop, Ioan M.; Kamal, Archana Physical Review Letters, Vol. 109, Issue 13 https://doi.org/10.1103/PhysRevLett.109.137002	journal	September 2012
Inelastic Microwave Photon Scattering off a Quantum Impurity in a Josephson-Junction Array Goldstein, Moshe; Devoret, Michel H.; Houzet, Manuel Physical Review Letters, Vol. 110, Issue 1 https://doi.org/10.1103/PhysRevLett.110.017002	journal	January 2013
The physics and applications of superconducting metamaterials Anlage, Steven M. Journal of Optics, Vol. 13, Issue 2 https://doi.org/10.1088/2040-8978/13/2/024001	journal	November 2010
Tunable microwave impedance matching to a high impedance source using a Josephson metamaterial Altimiras, Carles; Parlavecchio, Olivier; Joyez, Philippe Applied Physics Letters, Vol. 103, Issue 21 https://doi.org/10.1063/1.4832074	journal	November 2013
Evidence for Macroscopic Quantum Tunneling in One-Dimensional Superconductors Giordano, N. Physical Review Letters, Vol. 61, Issue 18 https://doi.org/10.1103/PhysRevLett.61.2137	journal	October 1988
Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles Pop, Ioan M.; Geerlings, Kurtis; Catelani, Gianluigi Nature, Vol. 508, Issue 7496 https://doi.org/10.1038/nature13017	journal	April 2014
A low‐noise series‐array Josephson junction parametric amplifier Yurke, B.; Roukes, M. L.; Movshovich, R. Applied Physics Letters, Vol. 69, Issue 20 https://doi.org/10.1063/1.116845	journal	November 1996
Strongly Interacting Photons in a Nonlinear Cavity Imamoḡlu, A.; Schmidt, H.; Woods, G. Physical Review Letters, Vol. 79, Issue 8 https://doi.org/10.1103/PhysRevLett.79.1467	journal	August 1997
Progress in superconducting metamaterials Jung, Philipp; Ustinov, Alexey V.; Anlage, Steven M. Superconductor Science and Technology, Vol. 27, Issue 7 https://doi.org/10.1088/0953-2048/27/7/073001	journal	May 2014
Propagating plasma mode in thin superconducting filaments Mooij, J. E.; Schön, Gerd Physical Review Letters, Vol. 55, Issue 1 https://doi.org/10.1103/PhysRevLett.55.114	journal	July 1985
Superconducting metamaterials and qubits Plourde, B. L. T.; Wang, Haozhi; Rouxinol, Francisco SPIE Sensing Technology + Applications, SPIE Proceedings https://doi.org/10.1117/12.2180012	conference	May 2015
Black-Box Superconducting Circuit Quantization Nigg, Simon E.; Paik, Hanhee; Vlastakis, Brian Physical Review Letters, Vol. 108, Issue 24 https://doi.org/10.1103/PhysRevLett.108.240502	journal	June 2012
Emission Pattern of High-Energy Pions: A New Probe for the Early Phase of Heavy-Ion Collisions Wagner, A.; Müntz, C.; Oeschler, H. Physical Review Letters, Vol. 85, Issue 1 https://doi.org/10.1103/PhysRevLett.85.18	journal	July 2000
Bistability in a mesoscopic Josephson junction array resonator Muppalla, P. R.; Gargiulo, O.; Mirzaei, S. I. Physical Review B, Vol. 97, Issue 2 https://doi.org/10.1103/PhysRevB.97.024518	journal	January 2018
Microwave photonics with superconducting quantum circuits Gu, Xiu; Kockum, Anton Frisk; Miranowicz, Adam Physics Reports, Vol. 718-719 https://doi.org/10.1016/j.physrep.2017.10.002	journal	November 2017
On-chip quantum simulation with superconducting circuits Houck, Andrew A.; Türeci, Hakan E.; Koch, Jens Nature Physics, Vol. 8, Issue 4 https://doi.org/10.1038/nphys2251	journal	April 2012
Josephson Metamaterial with a Widely Tunable Positive or Negative Kerr Constant Zhang, Wenyuan; Huang, W.; Gershenson, M. E. Physical Review Applied, Vol. 8, Issue 5 https://doi.org/10.1103/PhysRevApplied.8.051001	journal	November 2017
Amplification and squeezing of quantum noise with a tunable Josephson metamaterial Castellanos-Beltran, M. A.; Irwin, K. D.; Hilton, G. C. arXiv https://doi.org/10.48550/arxiv.0806.0659	text	January 2008
Measurement of the effect of quantum phase-slips in a Josephson Junction chain Pop, I. M.; Protopopov, I.; Lecocq, F. arXiv https://doi.org/10.48550/arxiv.0912.2417	text	January 2009
Quantum phase-slips in Josephson junction rings Rastelli, G.; Pop, I. M.; Hekking, F. W. J. arXiv https://doi.org/10.48550/arxiv.1201.0539	text	January 2012
Josephson junction-embedded transmission-line resonators: from Kerr medium to in-line transmon Bourassa, J.; Beaudoin, F.; Gambetta, Jay M. arXiv https://doi.org/10.48550/arxiv.1204.2237	text	January 2012
Generation of non-classical photon states in superconducting quantum metamaterials Mukhin, S. I.; Fistul, M. V. arXiv https://doi.org/10.48550/arxiv.1302.5558	text	January 2013
Stabilizing Spin Coherence Through Environmental Entanglement in Strongly Dissipative Quantum Systems Bera, Soumya; Florens, Serge; Baranger, Harold U. arXiv https://doi.org/10.48550/arxiv.1307.5681	text	January 2013
Progress in Superconducting Metamaterials Jung, Philipp; Ustinov, Alexey V.; Anlage, Steven M. arXiv https://doi.org/10.48550/arxiv.1403.6514	text	January 2014
Tunable microwave impedance matching to a high impedance source using a Josephson metamaterial Altimiras, Carles; Parlavecchio, Olivier; Joyez, Philippe arXiv https://doi.org/10.48550/arxiv.1404.1792	text	January 2014
Bloch band dynamics of a Josephson junction in an inductive environment Weißl, T.; Rastelli, G.; Matei, I. arXiv https://doi.org/10.48550/arxiv.1407.7728	text	January 2014
Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light Hur, Karyn Le; Henriet, Loïc; Petrescu, Alexandru arXiv https://doi.org/10.48550/arxiv.1505.00167	text	January 2015
Bistability in a Mesoscopic Josephson Junction Array Resonator Muppalla, P. R.; Gargiulo, O.; Mirzaei, S. I. arXiv https://doi.org/10.48550/arxiv.1706.04172	text	January 2017
Microwave photonics with superconducting quantum circuits Gu, Xiu; Kockum, Anton Frisk; Miranowicz, Adam arXiv https://doi.org/10.48550/arxiv.1707.02046	text	January 2017
The Emission Pattern of High-Energy Pions: A New Probe for the Early Phase of Heavy Ion Collisions Wagner, A.; Muentz, C.; Oeschler, H. arXiv https://doi.org/10.48550/arxiv.nucl-ex/0005004	text	January 2000

Cited By (7)

A general characterization method for nonlinearities in superconducting circuits Weißl, T.; Jolin, S. W.; Borgani, R. New Journal of Physics, Vol. 21, Issue 5 https://doi.org/10.1088/1367-2630/ab175a	journal	May 2019
Understanding the Saturation Power of Josephson Parametric Amplifiers Made from SQUID Arrays Planat, Luca; Dassonneville, Rémy; Martínez, Javier Puertas Physical Review Applied, Vol. 11, Issue 3 https://doi.org/10.1103/physrevapplied.11.034014	journal	March 2019
Josephson Array-Mode Parametric Amplifier Sivak, V. V.; Shankar, S.; Liu, G. Physical Review Applied, Vol. 13, Issue 2 https://doi.org/10.1103/physrevapplied.13.024014	journal	February 2020
Nondegenerate Parametric Amplifiers Based on Dispersion-Engineered Josephson-Junction Arrays Winkel, Patrick; Takmakov, Ivan; Rieger, Dennis Physical Review Applied, Vol. 13, Issue 2 https://doi.org/10.1103/physrevapplied.13.024015	journal	February 2020
Internally resonant wave energy exchange in weakly nonlinear lattices and metamaterials Fronk, Matthew D.; Leamy, Michael J. Physical Review E, Vol. 100, Issue 3 https://doi.org/10.1103/physreve.100.032213	journal	September 2019
Understanding the saturation power of Josephson Parametric Amplifiers made from SQUIDs arrays Planat, Luca; Dassonneville, Remy; Martinez, Javier Puertas arXiv https://doi.org/10.48550/arxiv.1809.08476	text	January 2018
Josephson Array Mode Parametric Amplifier Sivak, V. V.; Shankar, S.; Liu, G. arXiv https://doi.org/10.48550/arxiv.1909.08005	text	January 2019