Entanglement-enhanced lidars for simultaneous range and velocity measurements

Lidar is a well-known optical technology for measuring a target's range and radial velocity. We describe two lidar systems that use entanglement between transmitted signals and retained idlers to obtain significant quantum enhancements in simultaneous measurements of these parameters. The first entanglement-enhanced lidar circumvents the Arthurs-Kelly uncertainty relation for simultaneous measurements of range and radial velocity from the detection of a single photon returned from the target. This performance presumes there is no extraneous (background) light, but is robust to the round-trip loss incurred by the signal photons. The second entanglement-enhanced lidar—which requires a lossless, noiseless environment—realizes Heisenberg-limited accuracies for both its range and radial-velocity measurements, i.e., their root-mean-square estimation errors are both proportional to $1/M$ when $M$ signal photons are transmitted. These two lidars derive their entanglement-based enhancements from the use of a unitary transformation that takes a signal-idler photon pair with frequencies ${\omega }_S$ and ${\omega }_I$ and converts it to a signal-idler photon pair whose frequencies are $({\omega }_S+{\omega }_I)/2$ and $({\omega }_S-{\omega }_I)/2$. Insight into how this transformation provides its benefits is provided through an analogy to continuous-variable superdense coding.

Figure 1

(a) Lidar sensing of target range and radial velocity. $\eta$ is the round-trip transmissivity, i.e., the fraction of the lidar's transmitted signal photons that return to the lidar's receiver. (b) Equivalent quantum-channel representation.

Figure 2

(a) Entangled-state and (b) product-state representations of the single-photon target-return lidar.

Figure 3

Schematic for simultaneous time-delay and Doppler-shift measurements with HL rms accuracies ($M=3$).

Figure 4

Notional scheme for approximating the biphoton transform ${\widehat{B}}_{SI}$. SPDC: Single-photon-sensitive spontaneous parametric downconverter with extended phase matching. SFG: Single-photon-sensitive sum-frequency generator. DFG: Single-photon-sensitive difference-frequency generator.