We present quantum theory of superresolving imaging of discrete subwavelength structures. We demonstrate that the standard quantum limit of superresolution for imaging of such structures is much higher than for continuous objects.
We present the quantum theory of superresolution for discrete subwavelength structures. It allows to formulate, in particular, the standard quantum limit of superresolution achieved for illumination of the structure by light in coherent state. Our theory is based on discrete prolate spheroidal sequences and functions which are the proper basis set of the problem. We demonstrate that the superresolution factor is much higher for discrete structures than for continuous objects for the same signal-to-noise ratio. This result is a clear illustration of the crucial role of a priori information in superresolution problems.
We propose a novel, to the best of our knowledge, approach to superresolution optical imaging by combining quantum optics and near-field optics. Our concept involves the utilization of single-photon quantum emitters to generate a standalone evanescent wave. We demonstrate that the quantum interference effects of single-photon emitters, in conjunction with their near-field, result in a higher resolution of subwavelength structures than systems that are only quantum enhanced or only near-field enhanced. We believe that nano-sized emitters could be employed to accomplish the goals of this research, taking into account the current progress in nanophotonics and quantum optics technology.
We numerically investigate the role of quantum fluctuations in superresolution of optical objects. First, we confirm that when quantum fluctuations are not taken into account, one can easily improve the resolution by one order of magnitude beyond the diffraction limit. Then we investigate the standard quantum limit of superresolution which is achieved for illumination of an object by a light wave in a coherent state. We demonstrate that this limit can be beyond the diffraction limit. Finally, we show that further improvement of superresolution beyond the standard quantum limit is possible using the object illumination by a multimode squeezed light.
Here we relate two methods of subdiffraction imaging: bandwidth extrapolation for spatially bounded sources and quantum-metrology-inspired methods under assumptions about source structure. We present a quantum estimation theoretical approach in which the source is modeled in terms of unknown parameters corresponding to the Fourier components, whose impact on resolution is very intuitive. Using this method, we find that imaging spatially bounded sources faces an unavoidable fundamental resolution limit, but that in the small-source limit, certain measurement approaches can significantly improve the sensitivity over conventional methods.
We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First, we show that the problem of estimating the separation between two pointlike sources is equivalent to the estimation of the loss parameters of two lossy bosonic channels, i.e., the transmissivities of two beam splitters. Using this representation, we establish the ultimate precision bound for resolving two pointlike sources in an arbitrary quantum state, with a simple formula for the specific case of two thermal sources. We find that the precision bound scales with the number of collected photons according to the standard quantum limit. Then, we determine the sources whose separation can be estimated optimally, finding that quantum-correlated sources (entangled or discordant) can be superresolved at the sub-Rayleigh scale. Our results apply to a variety of imaging setups, from astronomical observation to microscopy, exploiting quantum detection as well as source engineering.