Widely Tunable, Nondegenerate Three-Wave Mixing Microwave Device Operating near the Quantum Limit

We present the first experimental realization of a widely frequency tunable, nondegenerate three-wave mixing device for quantum signals at gigahertz frequency. It is based on a new superconducting building block consisting of a ring of four Josephson junctions shunted by a cross of four linear inductances. The phase configuration of the ring remains unique over a wide range of magnetic fluxes threading the loop. It is thus possible to vary the inductance of the ring with flux while retaining a strong, dissipation-free, and noiseless nonlinearity. The device has been operated in amplifier mode, and its noise performance has been evaluated by using the noise spectrum emitted by a voltage-biased tunnel junction at finite frequency as a test signal. The unprecedented accuracy with which the crossover between zero-point fluctuations and shot noise has been measured provides an upper bound for the noise and dissipation intrinsic to the device.

Figure 1

(a) Device schematic: four linear inductances $L$ cross-link a ring of four Josephson junctions. Each subloop is biased by a magnetic flux ${\phi }_{\mathrm{ext}}{\varphi }_0$. For $L<L_J^0/4$, the current through the inductances is zero, and the external flux phase biases the junctions to ${\phi }_{\mathrm{ext}}$. (b) The device is embedded at the intersection of four transmission lines and couples to spatial modes $X$, $Y$, and $Z$ represented as arrows. (c) Optical microscope image of the ring modulator. The meanders in the center of the ring implement the four linear inductances from (a). The stripes on the meanders are due to the fabrication process based on shadow evaporation. (d) Simplified schematic of the setup used to characterize three-wave mixing operation. The idler resonator ($X$) is excited through a 180° hybrid coupler, while the signal resonator ($Y$) is single-ended. The noise emitted by the voltage-biased tunnel junction in its normal state is amplified through the signal port.

Figure 2

(a) Dots: Measured resonance frequency ${\omega }_Y$ of the signal cavity as a function of flux applied to the ring modulator without the pump. Solid line: Fit of ${\omega }_Y$ using Eq. (2) with ${\omega }_Y^0/2\pi =8.82\mathrm{GHz}$, $L=49\mathrm{pH}$, and $E_J={\varphi }_0\times 1.9\mu \mathrm{A}$ and including the known stray inductance around the loop $4L_S=200\mathrm{pH}$ (see Ref. 9). (b) Reflection gain measured on the signal port as a function of frequency for various values of the flux indicated by the color lines in (a). Pump parameters are optimized for each curve. The numbers on top represent the 1 dB compression point (maximum input power) expressed in input photon rate per dynamical bandwidth for six different working frequencies coded by color.

Figure 3

Reflection gain of the phase-preserving Josephson amplifier observed on the signal $Y$ (a) and the idler $X$ (b) modes. The color bar indicates the pump power referred to the output of the generator. The pump frequency is ${\omega }_Z/2\pi =14.071\mathrm{GHz}$, and the flux is set to ${\phi }_{\mathrm{ext}}/2\pi \approx 0.3125$.

Figure 4

(a) Power spectral density as a function of frequency measured at the output of signal out for three settings: pump off and $V=0$, pump on and $V=0$, or $V=100\mu \mathrm{V}$. The colored area represents the averaging range used in the right panel. (b) Average power spectral density over a 2 MHz bandwidth around the center frequency of the amplifier as a function of bias voltage $V$. The solid line shows what is expected by using Eq. (5) and fitting an overall gain $G_{\mathrm{sys}}=94.6\mathrm{dB}$ and an extra noise $N_{\mathrm{add}}$ of 2.8 quanta coming from both the unavoidable quantum noise of the idler port (0.5 quanta) and the unwanted losses between the tunnel junction and the amplifier (2.3 quanta). The gain $G_{\mathrm{sys}}$ allows us to express this power spectral density in units of photon number or quantum.