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Quantum Microwave Parametric Interferometer

F. Kronowetter, F. Fesquet, M. Renger, K. Honasoge, Y. Nojiri, K. Inomata, Y. Nakamura, A. Marx, R. Gross, and K.G. Fedorov
Phys. Rev. Applied 20, 024049 – Published 21 August 2023
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  • INTRODUCTION
  • EXPERIMENT
  • RESULTS AND DISCUSSION
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Classical interferometers are indispensable tools for the precise determination of various physical quantities. Their accuracy is bound by the standard quantum limit. This limit can be overcome by using quantum states or nonlinear quantum elements. Here, we present the experimental study of a nonlinear Josephson interferometer operating in the microwave regime. Our quantum microwave parametric interferometer (QUMPI) is based on superconducting flux-driven Josephson parametric amplifiers combined with linear microwave elements. We perform a systematic analysis of the implemented QUMPI. We find that its interferometric power exceeds the shot-noise limit and observe sub-Poissonian photon statistics in the output modes. Furthermore, we identify a low-gain operation regime of the QUMPI that is essential for optimal quantum measurements in quantum illumination protocols.

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    • Received 6 April 2023
    • Revised 28 July 2023
    • Accepted 3 August 2023

    DOI:https://doi.org/10.1103/PhysRevApplied.20.024049

    © 2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Nonlinear opticsOptoelectronicsQuantum metrologySuperconducting quantum optics
    1. Physical Systems
    Josephson junctionsOptical parametric oscillators & amplifiers
    1. Techniques
    Microwave techniquesOptical interferometry
    Quantum Information, Science & TechnologyAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

    Authors & Affiliations

    F. Kronowetter1,2,3,*, F. Fesquet1,2, M. Renger1,2, K. Honasoge1,2, Y. Nojiri1,2, K. Inomata4,5, Y. Nakamura4,6, A. Marx1, R. Gross1,2,7, and K.G. Fedorov1,2,†

    • 1Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Garching 85748, Germany
    • 2School of Natural Sciences, Technische Universität München, Garching 85748, Germany
    • 3Rohde & Schwarz GmbH & Co. KG, Munich 81671, Germany
    • 4RIKEN Center for Quantum Computing (RQC), Wako, Saitama 351-0198, Japan
    • 5National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8563, Japan
    • 6Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
    • 7Munich Center for Quantum Science and Technology (MCQST), Munich 80799, Germany

    • *fabian.kronowetter@wmi.badw.de
    • †kirill.fedorov@wmi.badw.de

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    Vol. 20, Iss. 2 — August 2023

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    Images

    • Figure 1
      Figure 1

      (a) General scheme of the QUMPI. (b) Details of the experimental setup consisting of a 180∘ hybrid ring (HR), which splits and symmetrically superimposes two incoming signals from ports In1 and In2, two JPAs for phase-sensitive amplification, and a second 180∘ HR, which completes the nonlinear interferometer. Output two-mode signals are detected with a heterodyne microwave receiver, followed by analog-to-digital (ADC) conversion, and digitally processed to extract statistical signal moments. The latter enable a full state tomography. (c) A circulator separates the incoming and outgoing signals for each JPA.

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    • Figure 2
      Figure 2

      Planck spectroscopy of the interferometer in the linear regime for output channel powers (b) P1 at Out1 and (c) P2 at Out2. Orange points correspond to thermal-state injection at In1 and vacuum at In2, and purple points correspond to the inverted case of thermal-state injection at In2 and vacuum state at In1, as depicted schematically in the quadrature planes in (a). The temperature dependence of P1 (P2) for orange (purple) data points yields the photon-number calibration for the interferometer and verifies its functionality. The corresponding error bars are smaller than the symbol size. The solid red lines represent fits based on Planck’s law.

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    • Figure 3
      Figure 3

      Interferometer measurements with coherent signals applied to In1 and In2. The corresponding displacement amplitudes are |α1|=|α2|=0.83(5), and the displacement angle θ1 is fixed to 0.64π, while θ2 varies from 0 to 2π. Both JPAs are operated as squeezers with the average gain G¯1,2=7.73dB and squeezing angle γ1 varying from 0 to 2π, while γ2=0. Top row shows the experimentally reconstructed photon numbers (a) N1 and (b) N2 at ports Out1 and Out2, respectively, as a function of θ2 and γ1. (c) Interferometric power P of the QUMPI illustrating the two-mode state probe capabilities.

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    • Figure 4
      Figure 4

      Second-order correlation analysis of the QUMPI. Single-mode second-order correlation functions, g1(2)(0) and g2(2)(0), at the interferometer ports (a) Out1 and (b) Out2. (c) Second-order cross-correlation function, gC(2)(0), between ports Out1 and Out2. The experimental parameters are identical to those in Fig. 3.

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    • Figure 5
      Figure 5

      Intensity cross-correlations, gC(2)(0), of the interferometer output fields for variable displacement amplitudes of coherent input signals. (a) Model predictions as a function of the number of coherent photons |α1|2 and |α2|2 (θ1=θ2=0.81π) entering the circuit at In1 and In2, respectively. (b) Experimental results for gC(2)(0) (orange crosses with standard deviation shown in shaded orange) as a function of the symmetrically varied displacement amplitudes. The blue line depicts the theoretical prediction. The black dashed line illustrates the classical limit of gC(2)(0)=1. (c) Analogy between Wigner functions of single-mode (theory) and two-mode [experiment; green cross from (b)] displaced squeezed states exhibiting g(2)(0)<1 (gC(2)(0)<1).

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    • Figure 6
      Figure 6

      Schematic of the measurement setup. The output signals are amplified and filtered in subsequent steps, down-converted, and digitized. An arbitrary waveform generator (AWG) creates a pulse sequence for the individual rf sources and the FPGA, which is required for the reference-state reconstruction [29].

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    • Figure 7
      Figure 7

      Scheme of the theoretical model of the interferometer circuit. The incoming modes a^1 and a^2 sequentially undergo various transformations, as indicated by the vertical dashed lines. The final states are reconstructed after operation L^3.

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    • Figure 8
      Figure 8

      Interferometer calibration. The squashed variances σs,i2 and amplified variances σa,i2 (i=1,2) of the reconstructed Wigner functions W(qi,pi) of the output fields in (a) Out1 and (b) Out2 are used to define a balancing parameter B, which enables optimization of (c) JPA pump powers PP1 and PP2 (at the JPA ports) and (d) a relative JPA amplification orientation Δγ=|γ1−γ2|.

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