Microwave Quantum Illumination

Quantum illumination is a quantum-optical sensing technique in which an entangled source is exploited to improve the detection of a low-reflectivity object that is immersed in a bright thermal background. Here, we describe and analyze a system for applying this technique at microwave frequencies, a more appropriate spectral region for target detection than the optical, due to the naturally occurring bright thermal background in the microwave regime. We use an electro-optomechanical converter to entangle microwave signal and optical idler fields, with the former being sent to probe the target region and the latter being retained at the source. The microwave radiation collected from the target region is then phase conjugated and upconverted into an optical field that is combined with the retained idler in a joint-detection quantum measurement. The error probability of this microwave quantum-illumination system, or quantum radar, is shown to be superior to that of any classical microwave radar of equal transmitted energy.

Figure 1

(a) Schematic of the EOM converter in which driven microwave and optical cavities are coupled by a mechanical resonator. (b) Microwave-optical QI using EOM converters. The transmitter’s EOM converter entangles microwave and optical fields. The receiver’s EOM converter transforms the returning microwave field to the optical domain while performing a phase-conjugate operation.

Figure 2

Performance of our microwave-optical source versus the cooperativity parameters ${\mathrm{\Gamma }}_w$ and ${\mathrm{\Gamma }}_o$. We show the behavior of the entanglement metric $\mathcal{E}$ (abstract units) in panel (a), the normalized logarithmic negativity $E_N/{\overline{n}}_w$ (ebits per microwave photon) in panel (b), the normalized coherent information $I(o⟩w)/{\overline{n}}_w$ (qubits per microwave photon) in panel (c), and the normalized quantum discord $D(w|o)/{\overline{n}}_w$ (discordant bits per microwave photon) in panel (d). In all panels, we assume experimentally achievable parameters [29, 31]: a 10-ng-mass mechanical resonator with ${\omega }_M/2\pi =10\mathrm{MHz}$ and $Q=30\times 10^3$; a microwave cavity with ${\omega }_w/2\pi =10\mathrm{GHz}$ and ${\kappa }_w=0.2{\omega }_M$; and a 1-mm-long optical cavity with ${\kappa }_o=0.1{\omega }_M$ driven by a 1064-nm-wavelength laser. The opto-mechanical and electro-mechanical coupling rates are $g_{\mathrm{o}}/2\pi =115.512\mathrm{Hz}$ and $g_w/2\pi =0.327\mathrm{Hz}$, and the entire EOM converter is held at temperature $T_{\mathrm{EOM}}=30\mathrm{mK}$. In each panel, the boundary between stable and unstable operation was obtained from the Routh-Hurwitz criterion [32].

Figure 3

$P_{\mathrm{QI}}^{(M)}$ and $P_{\mathrm{coh}}^{(M)}$ versus the time-bandwidth product, $M$, assuming $\eta =0.07$, ${\mathrm{\Gamma }}_w=5181.95$ and ${\mathrm{\Gamma }}_o=668.43$ (implying ${\overline{n}}_w=0.739$ and ${\overline{n}}_o=0.681$), and room temperature $T_B=293\mathrm{K}$ (implying ${\overline{n}}_B=610\gg {\overline{n}}_B^{\text{thresh}}=0.069$).

Figure 4

QI-advantage figure of merit, $\mathcal{F}$, versus ${\mathrm{\Gamma }}_w$ and ${\mathrm{\Gamma }}_o$. For $\mathcal{F}>1$, the QI system has lower error probability than any classical-state system, i.e., classical transmitter (CT), of the same transmitted energy. See Fig. 2 for the other parameter values.