Resolution of Quantum Imaging with Undetected Photons

Abstract

Quantum imaging with undetected photons is a recently introduced technique that goes significantly beyond what was previously possible. In this technique, images are formed without detecting the light that interacted with the object that is imaged. Given this unique advantage over the existing imaging schemes, it is now of utmost importance to understand its resolution limits, in particular what governs the maximal achievable spatial resolution. We show both theoretically and experimentally that the momentum correlation between the detected and undetected photons governs the spatial resolution — a stronger correlation results in a higher resolution. In our experiment, the momentum correlation plays the dominating role in determining the resolution compared to the effect of diffraction. We find that the resolution is determined by the wavelength of the undetected light rather than the wavelength of the detected light. Our results thus show that it is in principle possible to obtain resolution characterized by a wavelength much shorter than the detected wavelength.

Fundamental resolution limit of quantum imaging with undetected photons

“…Although the presented analysis focuses on QIUP based on position correlations, the same fundamental diffraction limit applies to the setup based on momentum correlations since the change of the optical elements cannot affect the limited range of transverse momenta of propagated photons. The difference between the achievable resolution in the two schemes based on position correlations and momentum correlations occurs only within the paraxial regime (thick crystals), where the minimum resolvable distance for the latter is d min ∝ λ I /σ P , with σ P as the transverse width of the pump [7,20]. However, in the non-paraxial limit, the imaging resolution of both cases will be restricted by the limited range of transverse momenta that can be generated by a photon-pair source.…”

“…Considering that the path of the idler photons are aligned, see Eq. (20), and signal photons of both sources interfere q S,A = q S,B = q S , then the state of the system can be written as…”

“…Consequently, it is of great interest to investigate twocolor quantum imaging configurations to determine the exact role of both wavelengths in the resolution. Although several works have discussed the resolution of quantum imaging [7,13,[17][18][19][20][21][22], they have treated this question only within the paraxial regime. This fits very well with most experiments relying on commercially available nonlinear crystals.…”

Quantum Sensing with Extreme Light

“…This allows analytically calculating the limits of some properties of an interferometer. [155,164] Effects such as misalignment of the optical system diminish the quality of the interferometer output. One cause is the variation of phase shifts within the idler distribution p(k i ; k s ).…”

Subdiffraction Quantum Imaging with Undetected Photons

“…We use the term "far-field" in contrast to "near-field", where nearfield interactions can involve evanescent modes and are usually only effective within wavelength-range distances [13]. Hence, resolution of far-field QIUP will be constrained by the diffraction limit [4,[14][15][16]. For the case where the probing wavelength λ I is larger than the detection wavelength λ S , object's information is transferred by propagating idler fields and consequently the transverse spatial resolution in this information is constrained by the idler diffraction limit [14].…”