Research ArticlePHYSICS

Microwave quantum illumination using a digital receiver

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Science Advances  08 May 2020:
Vol. 6, no. 19, eabb0451
DOI: 10.1126/sciadv.abb0451

Figures

  • Fig. 1 Implementation of microwave QI.

    (A) Schematic representation of microwave QI. A quantum source generates and emits stationary entangled microwave fields in two separate paths. The signal mode âS is used to interrogate the presence (i = 1) or absence (i = 0) of a room-temperature object with total roundtrip reflectivity η. The returned mode âS,idet is measured together with the unperturbed idler mode âI. (B) Circuit diagram of the experimental setup. A superconducting Josephson parametric converter (JPC) is used to entangle signal and idler modes at frequencies ωS and ωI by applying a suitable parametric pump tone at the sum frequency ωp = ωS + ωI at ∼ 7 mK. A coherent microwave tone or a classically correlated noise source is used to generate benchmark signals at room temperature that are sent into the dilution refrigerator and reflected from the JPC ports. The outputs of the JPC or the reflected classical signals are amplified, down converted, and digitized simultaneously and independently for both channels. The signal mode passes through a measurement line that contains a room-temperature switch that is used to select between a digitally controllable attenuator η and a free-space link realized with two antennas and a movable reflective object. Here, we consider η as the total signal loss between the two room temperature switches used in our measurement chain. For the system noise and gain calibration, we use two latching microwave switches at cold temperatures, which are used to select between the JPC outputs and a temperature T variable 50-ohm load (black squares). In both panels above, the final detection step corresponds to a two-channel quadrature measurement, followed by digital postprocessing.

  • Fig. 2 Entanglement and QI.

    (A) The measured entanglement parameter Δ for the output of the JPC (blue) and classically correlated noise (orange) as a function of the inferred signal photon number NS at the output of the JPC and the pump power Pp at the input of the JPC. (B) Comparison of the measured single-mode signal-to-noise ratio (SNR) of QI (solid blue), symmetric classically correlated illumination (CI, solid orange), coherent-state illumination with homodyne (solid green) and heterodyne detection (solid yellow), and the inferred SNR of calibrated QI (dashed blue) and CI (dashed orange) as a function of the signal photon number NS for a perfectly reflective object and a 5-μs measurement time. The dots are measured and inferred data points, and the solid and dashed lines are the theory prediction. For both (A) and (B), the error bars indicate the 95% confidence interval based on three sets of measurements, each with 380,000 two-channel quadrature pairs for QI/CI, and 192,000 quadrature pairs for coherent-state illumination.

  • Fig. 3 Low-reflectivity quantum correlated noise radar.

    The inferred SNR of calibrated QI (blue) and symmetric CI (orange), and the measured coherent-state illumination with digital heterodyne detection (yellow) as a function of (A) the total signal loss η and (B) object distance from the transmitting and receiving antennas for free-space illumination. The error bars are calculated similar to Fig. 2. For both (A) and (B), the signal photon number is NS = 0.5. The shaded regions are the theoretical uncertainties extracted by fitting the experimental data. The SNR of the coherent state with homodyne detection is not presented in this figure since the expected advantage at the chosen NS is smaller than systematic errors in this measurement.

  • Fig. 4 Schematic representation of the JPC.

    The Josephson parametric amplifier (JPC) contains a Josephson ring modulator (JRM) consisting of four Josephson junctions, and four large Josephson junctions inside the ring act as a shunt inductance for the JRM (41). Two microwave resonators are coupled to the JRM forming idler and signal resonators with resonance frequencies ωI and ωS, respectively. These resonators are capacitively coupled to the input and output ports. To use the JPC in the three-wave mixing condition, the device is biased using an external magnetic field and pumped at frequency ωp = ωI + ωS. Two broadband 180° hybrids are used to feed-in and feed-out the pump, idler, and signal. In this configuration, the second port of the signal is terminated using a 50-ohm cold termination.

  • Fig. 5 System noise calibration.

    Calibration of signal (A) and idler (B) output channels. The measured noise density in units of quanta, Si = Ni/(ħωiBRGi) − nadd, i, is shown as a function of the temperature T of the 50-ohm load. The error bars indicate the SD obtained from three measurements with 576,000 quadrature pairs each. The solid lines are fits to Eq. 5 in units of quanta, which yields the system gain and noise with the standard errors (95% confidence interval) as stated in section Results.

  • Fig. 6 Full measurement setup.

    The outputs of the JPC are amplified in different stages before being down converted to 20 MHz using two local oscillators (LO1 and LO2). After the down-conversion, the signals are filtered and amplified once more and then digitized using an analog-to-digital converter (ADC). Classically CI is performed by using correlated white noise generated by an arbitrary waveform (noise) generator. For coherent-state illumination, we generate a coherent tone and send it to the refrigerator. The signal is reflected from the unpumped JPC and passes through the measurement chain.

  • Fig. 7 Schematic of the postprocessing.

    (A) The recorded data from the ADC is chopped in M shorter arrays. We apply digital FFT at idler (ωI) and signal frequencies (ωS) after analog down conversion on each array individually to infer the measurement statistics of the signal and idler mode quadratures X̂idet and P̂idet with i = S, I. The measurement results are then used to calculate the covariances of the signal and idler modes aˆidet=(Xˆidet+iPˆidet)/2. (B) The digital phase-conjugate receiver used to infer the SNR of QI and CI. The M copies of the signal and idler modes, generated in postprocessing, are sent one by one to the digital phase-conjugate receiver. A 50:50 beam splitter mixes the phase-conjugated signal mode âS,iPC returned from the target region, with the locally detected idler mode âIdet. The beam splitter’s outputs are detected, yielding classical outcomes equivalent to the quantum measurements k=1MN̂i,±(k) (includes all M copies), and the difference of these outputs, equivalent to the quantum measurement of N̂i, is used as the input to a threshold detector whose output is the target absence or presence decision.

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