Optimal imaging by measuring photon-number

Abstract

Transition-edge sensors (TES’s) are are extremely sensitive calorimeters able to measure energies of the order of a few electronvolts. They are now well-known in the quantum technology community because of their superb combination of high-efficiency— higher than 95% for photons in the near infrared range [1]—essentially zero dark counts, and photon-number resolution. One of the main challenges when working with TES’s is to extract the photon-number information from the continuous output signal of the detectors. The usual procedure is to accumulate signals over some time—typically ~2 GB per minuite—and then use post-processing techniques to obtain photon-number resolution from the recorded signals [2]\n\nHere we introduce an FPGA circuit that analyses TES signals in real-time—recording only specific characteristics such as signal area, height, and length—allowing near realtime photon-number resolution and reducing the memory requirements by orders-of-magnitude. Using this new capability, we are able to optimise the number-resolution of the detector to the range we are interested in for each new experiment. In a preliminary study, we calibrated the TES with a weakly-pulsed 820 nm diode laser, and using just the area data from the FPGA were able to discriminate up to 15 photons. We are able to accurately discriminate an n=2 photon Fock state with parts-per-billion precision, dropping to parts-per-hundred precision at n=15 [3].\n\nIt is well known that there are physical limits to the precision with which an image can be formed. There are ways in which this limit can be circumvented, for example using super-resolution techniques that exploit the physical structure of the object, or object illumination with entangled states of light. However, in many applications—for example when the object is very far away—we cannot directly interact with the object, or illuminate it with entangled light: the quantum state of the light field is all that is accessible to the observer. Given a finite size imaging system in the far field—i.e., systems with a finite effective numerical aperture—we show the best way to extract the spatial characteristics of the light source.\n\nWe implement a general imaging method by measuring the complex degree of coherence using linear optics and our photon-number-resolving detectors. In the absence of collective or entanglement-assisted measurements, our method is optimal over a large range of practically relevant values of the complex degree of coherence [4]. We measure the size and position of a small distant source of pseudo-thermal light, and show that our method outperforms the traditional imaging method by an order of magnitude in precision. Additionally, we show that a lack of photon-number resolution in the detectors has only a modest detrimental effect on measurement precision, further highlighting the practicality of this method as a way to gain significant imaging improvements in a wide range of imaging applications.\n\nReferences\n[1] A. E. Lita, A. J. Miller, and S. W. Nam, Optics Express 16, 3032 (2008).\n[2] G. Brida, et al., New Journal of Physics 14, 085001, (2012).\n[3] L. Assis, et al., preprint (2020)\n[4] L. A. Howard, et al., Physical Review Letters 123, 143604 (2019).