Abstract

Two-photon loss mechanisms often accompany a Kerr nonlinearity. The kinetic inductance exhibited by superconducting transmission lines provides an example of a Kerr-like nonlinearity that is accompanied by a nonlinear resistance of the two-photon absorptive type. Such nonlinear dissipation can degrade the performance of amplifiers and mixers employing a Kerr-like nonlinearity as the gain or mixing medium. As an aid for parametric-amplifier design, the authors provide a quantum analysis of a cavity parametric amplifier employing a Kerr nonlinearity that is accompanied by a two-photon absorptive loss. Because of their usefulness in diagnostics, we obtain expressions for the pump amplitude within the cavity, the reflection coefficient for the pump amplitude reflected off of the cavity, the parametric gain, and the intermodulation gain. Expressions by which the degree of squeezing can be computed are also presented. Although the focus here is on providing aids for the design of kinetic-inductance parametric amplifiers, much of what is presented is directly applicable to analogous optical and mechanical amplifiers.

© 2006 IEEE

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  4. B. Yurke, L. R. Corruccini, P. G. Kaminsky, L. W. Rupp, A. D. Smith, A. H. Silver, R. W. Simon, E. A. Whittaker, "Observation of parametric amplification and deamplification in a Josephson parametric amplifier," Phys. Rev. A, Gen. Phys. 39, 2519-2533 (1989).
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  29. H. Ezaki, "Photon number squeezing due to two-photon absorption in internal and external fields of a microcavity," J. Phys. Soc. Jpn. 68, 1562-1566 (1999).
  30. M. Kitamura, T. Tokihiro, "Squeezed states of light in a cavity with a local two-photon absorber," J. Opt., B Quantum Semiclass. Opt. 1, 546-556 (1999).
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  34. B. Yurke, "Squeezed-coherent-state generation via four-wave mixers and detection via homodyne detectors," Phys. Rev. A, Gen. Phys. 32, 300-310 (1985).
  35. E. Buks, B. Yurke, "Dephasing due to intermode coupling in superconducting stripline resonators," Phys. Rev. A, Gen. Phys. 73, 023 815 (2006).

Appl. Phys. Lett. (3)

B. Abdo, E. Segev, O. Shtempluck, E. Buks, "Intermodulation gain in nonlinear NbN superconducting microwave resonators," Appl. Phys. Lett. 88, 022508 1-022508 3 (2006).

A. Villeneuve, C. C. Yang, G. I. Stegeman, C.-H. Lin, H.-H. Lin, "Nonlinear refractive-index and two photon-absorption near half the band gap in AlGaAs," Appl. Phys. Lett. 62, 2465-2467 (1993).

R. Almog, S. Zaitsev, O. Shtempluck, E. Buks, "High intermodulation gain in a micromechanical duffing resonator," Appl. Phys. Lett. 88, 213 509 (2006).

Chin. Phys. Lett. (1)

G. X. Li, J. S. Peng, P. Zhou, "Squeezing of field in the system of a Kerr medium embedded in a nondegenerate two-photon absorption cavity," Chin. Phys. Lett. 12, 79-82 (1995).

IEEE J. Quantum Electron. (1)

J. R. Tucker, "Quantum limited detection in tunnel junction mixers," IEEE J. Quantum Electron. QE-15, 1234-1258 (1979).

IEEE Trans. Appl. Superconduc. (1)

B. Abdo, E. Segev, O. Shtempluck, E. Buks, "Observation of bifurcations and hysteresis in nonlinear NbN superconducting microwave resonators," IEEE Trans. Appl. Superconduc. (2005) Digital Object Identifier: 10.1109/TASC.2006.881823.

IEEE Trans. Magn. (1)

L. S. Kuzmin, K. K. Likharev, V. V. Migulin, A. B. Zorin, "Quantum noise in Josephson-junction parametric amplifiers," IEEE Trans. Magn. MAG-19, 618-621 (1983).

J. Appl. Phys. (1)

T. Dahm, D. J. Scalapino, "Theory of intermodulation in a superconducting microstrip resonator," J. Appl. Phys. 81, 2002-2009 (1997).

J. Opt. Soc. Amer. B, Opt. Phys. (1)

S.-T. Ho, X. Zhang, M. K. Udo, "Single-beam squeezed-state generation in semiconductor waveguides with $\chi^{(3)}$ nonlinearity at below half-band gap," J. Opt. Soc. Amer. B, Opt. Phys. 12, 1537-1549 (1995).

J. Opt., B Quantum Semiclass. Opt. (2)

A. G. White, P. K. Lam, D. E. McClelland, H.-A. Bachor, J. Munro, "Kerr noise reduction and squeezing," J. Opt., B Quantum Semiclass. Opt. 2, 553-561 (2000).

M. Kitamura, T. Tokihiro, "Squeezed states of light in a cavity with a local two-photon absorber," J. Opt., B Quantum Semiclass. Opt. 1, 546-556 (1999).

J. Phys. Soc. Jpn. (1)

H. Ezaki, "Photon number squeezing due to two-photon absorption in internal and external fields of a microcavity," J. Phys. Soc. Jpn. 68, 1562-1566 (1999).

Opt. Commun. (3)

N. Tornau, A. Bach, "Quantum statistics of two-photon absorption," Opt. Commun. 11, 46-49 (1974).

G. S. Agarwal, G. P. Hildred, "Time development of squeezing in two photon absorption," Opt. Commun. 58, 287-289 (1986).

C. C. Gerrry, E. E. Hach, III"Enhanced squeezing from a Kerr medium combined with two-photon absorption," Opt. Commun. 100, 211-214 (1993).

Phys. Rev. A, Gen. Phys. (10)

L. Gilles, B. M. Garraway, P. L. Knight, "Generation of nonclassical light by dissipative two-photon processes," Phys. Rev. A, Gen. Phys. 49, 2785-2799 (1994).

B. Yurke, J. S. Denker, "Quantum network theory," Phys. Rev. A, Gen. Phys. 29, 1419-1437 (1984).

C. W. Gardiner, M. J. Collett, "Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation," Phys. Rev. A, Gen. Phys. 31, 3761-3774 (1985).

J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, K. Wodkiewich, "Treatment of the spectrum of squeezing based on the modes of the Universe. I. Theory and a physical picture," Phys. Rev. A, Gen. Phys. 41, 369-380 (1990).

N. Imoto, H. A. Haus, Y. Yamamoto, "Quantum nondemolition measurement of the photon number via the optical Kerr effect," Phys. Rev. A, Gen. Phys. 32, 2287-2292 (1985).

L. Gilles, P. L. Knight, "Two-photon absorption and nonclassical states of light," Phys. Rev. A, Gen. Phys. 48, 1582-1593 (1993).

B. Yurke, D. S. Greywall, A. N. Pargellis, P. A. Busch, "Theory of amplifier-noise evasion in an oscillator employing a nonlinear resonator," Phys. Rev. A, Gen. Phys. 51, 4211-4229 (1995).

B. Yurke, "Squeezed-coherent-state generation via four-wave mixers and detection via homodyne detectors," Phys. Rev. A, Gen. Phys. 32, 300-310 (1985).

E. Buks, B. Yurke, "Dephasing due to intermode coupling in superconducting stripline resonators," Phys. Rev. A, Gen. Phys. 73, 023 815 (2006).

B. Yurke, L. R. Corruccini, P. G. Kaminsky, L. W. Rupp, A. D. Smith, A. H. Silver, R. W. Simon, E. A. Whittaker, "Observation of parametric amplification and deamplification in a Josephson parametric amplifier," Phys. Rev. A, Gen. Phys. 39, 2519-2533 (1989).

Phys. Rev. B, Condens. Matter (1)

B. Abdo, E. Segev, O. Shtempluck, E. Buks, "Nonlinear dynamics in the resonance lineshape of NbN superconducting resonators," Phys. Rev. B, Condens. Matter 73, 134 513 (2006) arXiv:cond-mat/0601146.

Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. (1)

E. Buks, B. Yurke, "Mass detection with nonlinear nanomechanical resonator," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 74, 046 619 (2006).

Phys. Rev. Lett. (2)

A. M. Fox, J. J. Baumberg, M. Dabbicco, B. Huttner, J. F. Ryan, "Squeezed light generation in semiconductors," Phys. Rev. Lett. 74, 1728-1731 (1995).

R. Movshovich, B. Yurke, P. G. Kaminsky, A. D. Smith, A. H. Silver, R. W. Simon, M. V. Schneider, "Observation of zero-point noise squeezing via a Josephson-parametric amplifier," Phys. Rev. Lett. 65, 1419-1422 (1990).

Rev. Mod. Phys. (1)

J. R. Tucker, M. J. Feldman, "Quantum detection at millimeter wavelengths," Rev. Mod. Phys. 57, 1055-1113 (1985).

Other (5)

B. Abdo, E. Segev, O. Shtempluck, E. Buks, Nonlinear Coupling in Nb/NbN Superconducting Microwave Resonators (2005) arXiv:cond-mat/0501236.

S. Zaitsev, R. Almog, O. Shtempluck, E. Buks, Nonlinear Damping in Nanomechanical Beam Oscillator (2005) arXiv:cond-mat/053130v1.

R. Almog, S. Zaitsev, O. Shtempluck, E. Buks, Noise Squeezing in a Nanomechanical Duffing Resonator (2006) arXiv:cond-mat/0607055.

A. H. Nayfeh, D. T. Mook, Nonlinear Oscillations (Wiley, 1979).

L. D. Landau, Mechanics (Pergamon, 1976).

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