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Nondegenerate Parametric Resonance in a Tunable Superconducting Cavity

Waltraut Wustmann1,2 and Vitaly Shumeiko1

  • 1Chalmers University of Technology, S-41296 Göteborg, Sweden
  • 2Laboratory for Physical Sciences, College Park, Maryland 20740, USA

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Phys. Rev. Applied 8, 024018 – Published 21 August, 2017

DOI: https://doi.org/10.1103/PhysRevApplied.8.024018

Abstract

We develop a theory for nondegenerate parametric resonance in a tunable superconducting cavity. We focus on nonlinear effects that are caused by nonlinear Josephson elements connected to the cavity. We analyze parametric amplification in a strong nonlinear regime at the parametric-instability threshold, and we calculate maximum gain values. Above the threshold, in the parametric-oscillator regime, the cavity linear response diverges at the oscillator frequency at all pump strengths. We show that this divergence is related to the continuous degeneracy of the free oscillator state with respect to the phase. Applying on-resonance input lifts the degeneracy and removes the divergence. We also investigate quantum noise squeezing. It is shown that in the strong amplification regime, the noise undergoes four-mode squeezing, and that, in this regime, the output signal-to-noise ratio can significantly exceed the input value. We also analyze the intermode frequency conversion and identify the parameters at which full conversion is achieved.

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References (45)

  1. T. Yamamoto, K. Inomata, M. Watanabe, K. Matsuba, T. Miyazaki, W. D. Oliver, Y. Nakamura, and J. S. Tsai, Flux-driven Josephson parametric amplifier, Appl. Phys. Lett. 93, 042510 (2008).
  2. M. A. Castellanos-Beltran and K. W. Lehnert, Widely tunable parametric amplifier based on a superconducting quantum interference device array resonator, Appl. Phys. Lett. 91, 083509 (2007).
  3. M. A. Castellanos-Beltran, K. D. Irwin, G. C. Hilton, L. R. Vale, and K. W. Lehnert, Amplification and squeezing of quantum noise with a tunable Josephson metamaterial, Nat. Phys. 4, 929 (2008).
  4. 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 (London) 465, 64 (2010).
  5. J. Mutus et al., Design and characterization of a lumped element single-ended superconducting microwave parametric amplifier with on-chip flux bias line, Appl. Phys. Lett. 103, 122602 (2013).
  6. X. Zhou, V. Schmitt, P. Bertet, D. Vion, W. Wustmann, V. Shumeiko, and D. Esteve, High-gain weakly nonlinear flux-modulated Josephson parametric amplifier using a SQUID array, Phys. Rev. B 89, 214517 (2014).
  7. M. Hatridge, R. Vijay, D. H. Slichter, J. Clarke, and I. Siddiqi, Dispersive magnetometry with a quantum limited SQUID parametric amplifier, Phys. Rev. B 83, 134501 (2011).
  8. C. Macklin, K. O. Brien, D. Hover, M. E. Schwartz, V. Bolkhovsky, X. Zhang, W. D. Oliver, and I. Siddiqi, A near-quantum-limited Josephson traveling-wave parametric amplifier, Science 350, 307 (2015).
  9. M. Simoen, C. W. S. Chang, P. Krantz, J. Bylander, W. Wustmann, V. Shumeiko, P. Delsing, and C. M. Wilson, Characterization of a multimode coplanar waveguide parametric amplifier, J. Appl. Phys. 118, 154501 (2015).
  10. R. Vijay, D. H. Slichter, and I. Siddiqi, Observation of Quantum Jumps in a Superconducting Artificial Atom, Phys. Rev. Lett. 106, 110502 (2011).
  11. K. W. Murch, S. J. Weber, C. Macklin, and I. Siddiqi, Observing single quantum trajectories of a superconducting quantum bit, Nature (London) 502, 211 (2013).
  12. Z. R. Lin, K. Inomata, W. D. Oliver, K. Koshino, Y. Nakamura, J. S. Tsai, and T. Yamamoto, Single-shot readout of a superconducting flux qubit with a flux-driven Josephson parametric amplifier, Appl. Phys. Lett. 103, 132602 (2013).
  13. D. Riste, M. Dukalski, C. A. Watson, G. de Lange, M. J. Tiggelman, Y. M. Blanter, K. W. Lehnert, R. N. Schouten, and L. DiCarlo, Deterministic entanglement of superconducting qubits by parity measurement and feedback, Nature (London) 502, 350 (2013).
  14. P. Krantz, A. Bengtsson, M. Simoen, S. Gustavsson, V. Shumeiko, W. D. Oliver, C. M. Wilson, P. Delsing, and J. Bylander, Single-shot read-out of a superconducting qubit using a Josephson parametric oscillator, Nat. Commun. 7, 11417 (2016).
  15. C. Eichler, D. Bozyigit, C. Lang, M. Baur, L. Steffen, J. M. Fink, S. Filipp, and A. Wallraff, Observation of Two-Mode Squeezing in the Microwave Frequency Domain, Phys. Rev. Lett. 107, 113601 (2011).
  16. K. W. Murch, S. J. Weber, K. M. Beck, E. Ginossar, and I. Siddiqi, Reduction of the radiative decay of atomic coherence in squeezed vacuum, Nature (London) 499, 62 (2013).
  17. D. M. Toyli, A. W. Eddins, S. Boutin, S. Puri, D. Hover, V. Bolkhovsky, W. D. Oliver, A. Blais, and I. Siddiqi, Resonance Fluorescence from an Artificial Atom in Squeezed Vacuum, Phys. Rev. X 6, 031004 (2016).
  18. N. Bergeal, F. Schackert, L. Frunzio, and M. H. Devoret, Two-Mode Correlation of Microwave Quantum Noise Generated by Parametric Down-Conversion, Phys. Rev. Lett. 108, 123902 (2012).
  19. E. Flurin, N. Roch, F. Mallet, M. H. Devoret, and B. Huard, Generating Entangled Microwave Radiation over Two Transmission Lines, Phys. Rev. Lett. 109, 183901 (2012).
  20. N. Roch, E. Flurin, F. Nguyen, P. Morfin, P. Campagne-Ibarcq, M. H. Devoret, and B. Huard, Widely Tunable, Nondegenerate Three-Wave Mixing Microwave Device Operating near the Quantum Limit, Phys. Rev. Lett. 108, 147701 (2012).
  21. C. Eichler, C. Lang, J. M. Fink, J. Govenius, S. Filipp, and A. Wallraff, Observation of Entanglement Between Itinerant Microwave Photons and a Superconducting Qubit, Phys. Rev. Lett. 109, 240501 (2012).
  22. E. P. Menzel, R. Di Candia, F. Deppe, P. Eder, L. Zhong, M. Ihmig, M. Haeberlein, A. Baust, E. Hoffmann, D. Ballester, K. Inomata, T. Yamamoto, Y. Nakamura, E. Solano, A. Marx, and R. Gross, Path Entanglement of Continuous-Variable Quantum Microwaves, Phys. Rev. Lett. 109, 250502 (2012).
  23. E. Zakka-Bajjani, F. Nguyen, M. Lee, L. R. Vale, R. W. Simmonds, and J. Aumentado, Quantum superposition of a single microwave photon in two different “colour” states, Nat. Phys. 7, 599 (2011).
  24. B. Abdo, K. Sliwa, F. Schackert, N. Bergeal, M. Hatridge, L. Frunzio, A. D. Stone, and M. Devoret, Full Coherent Frequency Conversion between Two Propagating Microwave Modes, Phys. Rev. Lett. 110, 173902 (2013).
  25. W. Wustmann and V. Shumeiko, Parametric resonance in tunable superconducting cavities, Phys. Rev. B 87, 184501 (2013).
  26. M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, Tuning the field in a microwave resonator faster than the photon lifetime, Appl. Phys. Lett. 92, 203501 (2008).
  27. M. Wallquist, V. S. Shumeiko, and G. Wendin, Selective coupling of superconducting charge qubits mediated by a tunable stripline cavity, Phys. Rev. B 74, 224506 (2006).
  28. C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature (London) 479, 376 (2011).
  29. R. Graham and H. Haken, The quantum-fluctuations of the optical parametric oscillator, Z. Phys. 210, 276 (1968).
  30. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 2008).
  31. C. M. Caves, Quantum limits on noise in linear amplifiers, Phys. Rev. D 26, 1817 (1982).
  32. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 2006).
  33. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82, 1155 (2010).
  34. C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, Noise characteristics of a non-degenerate optical parametric oscillator—Application to quantum noise reduction, J. Phys. (Paris) 50, 1209 (1989).
  35. G. Björk and Y. Yamamoto, Generation and amplification of number states by nondegenerate parametric oscillators with idler-measurement feedback, Phys. Rev. A 37, 125 (1988).
  36. M. D. Reid and P. D. Drummond, Correlations in nondegenerate parametric oscillation: Squeezing in the presence of phase diffusion, Phys. Rev. A 40, 4493 (1989).
  37. A. S. Villar, M. Martinelli, and P. Nussenzveig, Testing the entanglement of intense beams produced by a non-degenerate optical parametric oscillator, Opt. Commun. 242, 551 (2004).
  38. C. Navarrete-Benlloch, A. Romanelli, E. Roldán, and G. J. de Valcárcel, Noncritical quadrature squeezing in two-transverse-mode optical parametric oscillators, Phys. Rev. A 81, 043829 (2010).
  39. S. L. Braunstein, Squeezing as an irreducible resource, Phys. Rev. A 71, 055801 (2005).
  40. G. Patera, N. Treps, C. Fabre, and G. J. de Valcarcel, Quantum theory of synchronously pumped type I optical parametric oscillators: Characterization of the squeezed supermodes, Eur. Phys. J. D 56, 123 (2010).
  41. M. J. Collett and C. W. Gardiner, Squeezing of intracavity and traveling-wave light fields, produced in parametric amplification, Phys. Rev. A 30, 1386 (1984).
  42. B. Yurke, in Quantum Squeezing, edited by P. D. Drummond and Z. Fizek (Springer, Berlin, 2004).
  43. P. D. Drummond, in Quantum Squeezing, edited by P. D. Drummond and Z. Fizek (Springer, Berlin, 2004).
  44. M. J. Collett, Exact density-matrix calculations for simple open systems, Phys. Rev. A 38, 2233 (1988).
  45. A. M. Perelomov, Generalized coherent states and some of their applications, Sov. Phys. Usp. 20, 703 (1977).

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Phys. Rev. Applied 8, 024018– Published 21 August, 2017
  • Received 19 April 2017

© 2017 American Physical Society

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