We show that it is possible to estimate the shape of an object by measuring only the fluctuations of a probing field, allowing us to expose the object to a minimal light intensity. This scheme, based on noise measurements through homodyne detection, is useful in the regime where the number of photons is low enough that direct detection with a photodiode is difficult but high enough such that photon counting is not an option. We generate a few-photon state of multi-spatial-mode vacuum-squeezed twin beams using four-wave mixing and direct one of these twin fields through a binary intensity mask whose shape is to be imaged. Exploiting either the classical fluctuations in a single beam or quantum correlations between the twin beams, we demonstrate that under some conditions quantum correlations can provide an enhancement in sensitivity when estimating the shape of the object.
We show that it is possible to estimate the shape of an object by measuring only the fluctuations of a probing field, allowing us to expose the object to a minimal light intensity. This scheme, based on noise measurements through homodyne detection, is useful in the regime where the number of photons is low enough that direct detection with a photodiode is difficult but high enough such that photon counting is not an option. We generate a few-photon state of multi-spatial-mode vacuum-squeezed twin beams using four-wave mixing and direct one of these twin fields through a binary intensity mask whose shape is to be imaged. Exploiting either the classical fluctuations in a single beam or quantum correlations between the twin beams, we demonstrate that under some conditions quantum correlations can provide an enhancement in sensitivity when estimating the shape of the object.
Four-wave-mixing in hot atomic vapor is a versatile tool for spatially multimode squeezed light generation. We experimentally investigate a scheme that exploits multispatial quantum correlations between twin squeezed vacuum beams in order to resolve the shape of a mask partially obstructing one of the beams. Specifically, this is accomplished using twin homodyne detection with matched local oscillators that are dynamically shaped using a spatial light modulator (SLM). We demonstrate that detecting both of the twin beams allows for enhanced spatial resolution of the obstructing mask compared to using a single multispatial mode classical state of light.
Abstract In this review we present the potentialities and the achievements of the use of non-classical photon-number correlations in twin-beam states for many applications, ranging from imaging to metrology. Photon-number correlations in the quantum regime are easily produced and are rather robust against unavoidable experimental losses, and noise in some cases, if compared to the entanglement, where losing one photon can completely compromise the state and its exploitable advantages. Here, we will focus on quantum enhanced protocols in which only phase-insensitive intensity measurements (photon-number counting) are performed, which allow probing the transmission/absorption properties of a system, leading, for example, to innovative target detection schemes in a strong background. In this framework, one of the advantages is that the sources experimentally available emit a wide number of pair-wise correlated modes, which can be intercepted and exploited separately, for example by many pixels of a camera, providing a parallelism, essential in several applications, such as wide-field sub-shot-noise imaging and quantum enhanced ghost imaging. Finally, non-classical correlation enables new possibilities in quantum radiometry, e.g. the possibility of absolute calibration of a spatial resolving detector from the on-off single-photon regime to the linear regime in the same setup.
We present a workbench for the study of real-time quantum imaging by measuring the frame-by-frame quantum noise reduction of multi-spatial-mode twin beams generated by four wave mixing in Rb vapor. Exploiting the multiple spatial modes of this squeezed light source, we utilize spatial light modulators to selectively pass macropixels of quantum correlated modes from each of the twin beams to a high quantum efficiency balanced detector. In low-light-level imaging applications, the ability to measure the quantum correlations between individual spatial modes and macropixels of spatial modes with a single pixel camera will facilitate compressive quantum imaging with sensitivity below the photon shot noise limit.
Imaging is the estimation of the spatial distribution of a physical object by measuring the optical radiation it emits, or by making use of an optical wave that interacts with the object, via reflection or transmission, for example, before being measured by a detector. The resolution of an imaging system is limited by the inability to localize the optical field at points of the object. Under otherwise ideal conditions, resolution is limited by diffraction. The sensitivity of an imaging system is limited by the uncertainty in the measurement. Under ideal conditions, this is determined by photon noise, which depends on the statistical fluctuations of the light. In conventional imaging systems, an extended detector, such as a CCD camera or an array detector, measures the spatial distribution of the optical intensity, which is proportional to the photon flux density. In interferometric systems, the spatial distribution of the optical field is inferred from measurements of the optical intensity. With the emergence of coherence theory, imaging systems based on measurements of the second-order coherence function at pairs of points in the detection plane were developed. An example is the imaging of an incoherent object based on the van Cittert-Zernike theorem. Imaging systems based on measurement of intensity correlation, or the photon coincidence rate, at pairs of points, were developed in the 1960s. A classic example of the photon-correlation imaging of an object emitting thermal light is stellar imaging using a Hanbury-Brown-Twiss intensity-correlation interferometer. More recently, two-photon light, which may be generated via spontaneous parametric downconversion in a second-order nonlinear optical crystal, has been used for imaging. This type of two-photon (or biphoton) imaging, which has come to be called quantum imaging, is also based on the measurement of photon coincidence by the use of photon-counting array detectors or by scanning two photon-counting detectors at pairs of points. To compare the resolution and sensitivity of imaging systems based on the aforementioned types of measurements, it is necessary to derive expressions for the measured quantities in terms of the object distribution. The point-spread functions based on such expressions can be used to assess the resolution. One measure of the sensitivity of the imaging process is the signal-to-noise ratio (SNR) of the measured variables. The statistical nature of the light source must be known in order to determine the SNR. The purpose of this chapter is to compare the resolution and sensitivity of photon-correlation imaging systems that make use of thermal light and two-photon light. We will henceforth refer to these two imaging modalities as classical and quantum photon-correlation imaging, or simply classical and quantum imaging, respectively. Clearly, light in other quantum states can also be used for imaging.
Two beams of light can be quantum mechanically entangled through correlations of their phase and intensity fluctuations. For a pair of spatially extended image-carrying light fields, the concept of entanglement can be applied not only to the entire images but also to their smaller details. We used a spatially multimode amplifier based on four-wave mixing in a hot vapor to produce twin images that exhibit localized entanglement. The images can be bright fields that display position-dependent quantum noise reduction in their intensity difference or vacuum twin beams that are strongly entangled when projected onto a large range of different spatial modes. The high degree of spatial entanglement demonstrates that the system is an ideal source for parallel continuous-variable quantum information protocols.
The first part of our work is devoted to identify regimes suitable for weak image detection. Moreover, we investigate a method of data analysis that identifies the centre of symmetry of the signal-idler images with a sub-pixel precision. In the second part of our work we study an imaging scheme, where a weakly absorbing object is posed in the far-field of the signal beam and the image is retrieved by subtracting pixel by pixel the signal idler intensities. We show that imaging with spatially correlated twin beams provides a substantial enhancement of the signal-to-noise ratio with respect to classical imaging in a domain of parameters accessible to experimental implementations.