How to Project onto an Arbitrary Single-Photon Wavepacket

Abstract

The time-frequency degree of freedom of the electromagnetic field is the final frontier for singlephoton measurements. The temporal and spectral distribution a measurement retrodicts (that is, the state it projects onto) is determined by the detector's intrinsic resonance structure. In this paper, we construct ideal and more realistic positive operator-valued measures (POVMs) that project onto arbitrary single-photon wavepackets with high efficiency and low noise. We discuss applications to super-resolved measurements and quantum communication. In doing so we will give a fully quantum description of the entire photo detection process, give prescriptions for (in principle) performing single-shot Heisenberg-limited time-frequency measurements of single photons, and discuss fundamental limits and trade-offs inherent to single-photon detection.

Heisenberg picture of photodetection

“…That should allow us to formulate the POVM (projecting onto a specific temporal state of the photon) that describes our detector, as in Ref. [13].…”

“…For just this purpose-finding fundamental limits on photodetectors-a third type of theory has been developed in recent years. Here the aim is to develop fully quantum-mechanical and sufficiently realistic models that include all stages of the photodetection process, including the crucial amplification process [6][7][8][9][10][11][12][13]. The point of this paper is to continue this recent work and present a quantum description of the processes involved in the detection of a single photon, especially the connection between the photoabsorption and amplification processes.…”