Jeffrey H. Shapiro

Ghost imaging: from quantum to classical to computational

Ghost-imaging experiments correlate the outputs from two photodetectors: an high-spatial-resolution (scanning pinhole or CCD array) detector that measures an field that has not interacted with the object to be imaged, and a bucketn (single-pixel) detector that collects a field that has interacted with the object. Wen give a comprehensive review of ghost imaging—within a unified Gaussian-staten framework—presenting detailed analyses of its resolution, field of view,n image contrast, and signal-to-noise ratio behavior. We consider three classes ofn illumination: thermal-state (classical), biphoton-state (quantum), andn classical-state phase-sensitive light. The first two have been employed in a varietyn of ghost-imaging demonstrations. The third is the classical Gaussian state thatn produces ghost images that most closely mimic those obtained from biphotonn illumination. The insights we develop lead naturally to a new, single-beam approachn to ghost imaging, called computational ghost imaging, in which only the bucketn detector is required. We provide quantitative results while simultaneouslyn emphasizing the underlying physics of ghost imaging. The key to developing the lattern understanding lies in the coherence behavior of a pair of Gaussian-state light beamsn with either phase-insensitive or phase-sensitive cross correlation.

The physics of ghost imaging

Ghost images are obtained by correlating the output of a single-pixel (bucket) photodetector—which collects light that has been transmitted through or reflected from an object—with the output from a high spatial-resolution scanning photodetector or photodetector array whose illumination has not interacted with that object. The term “ghost image” is apt because neither detector’s output alone can yield an image: the bucket detector has no spatial resolution, while the high spatial-resolution detector has not viewed the object. The first ghost imaging experiment relied on the entangled signal and idler outputs from a spontaneous parametric downconverter, and hence the image was interpreted as a quantum phenomenon. Subsequent theory and experiments showed, however, that classical correlations can be used to form ghost images. For example, ghost images can be formed with pseudothermal light, for which quantum mechanics is not required to characterize its photodetection statistics. This paper presents an overview of the physics of ghost imaging. It clarifies and unites two disparate interpretations of pseudothermal ghost imaging—two-photon interference and classical intensity-fluctuation correlations—that had previously been thought to be conflicting. It also reviews recent work on ghost imaging in reflection, ghost imaging through atmospheric turbulence, computational ghost imaging, and two-color ghost imaging.

Phase-conjugate optical coherence tomography

We demonstrate a new type of optical coherence tomography using only classical resources to achieve results that are typically associated with quantum-enhancedmetrology: factor-of-two axial resolution enhancement and even-order dispersion cancellation.

The Quantum Theory of Optical Communications

Communication theory applied to lightwave channels is ordinarily carried out using the semiclassical theory of photodetection. Recent development of nonclassical light sources-whose photodetection statistics require the use of quantum theory-plus increasing interest in optics-based approaches to quantum information processing necessitates a thorough understanding of the similarities and distinctions between the semiclassical and quantum theories of optical communications. This paper is addressed to that need, focusing, for convenience, on the free-space communication channel using Gaussian states of light. The quantum version of the Huygens-Fresnel diffraction integral is reviewed, along with the semiclassical and quantum theories of direct, homodyne, and heterodyne detection. Maximally entangled Gaussian state light is used, in conjunction with quantum photodetection theory, to explain the nonclassical effects seen in Hong-Ou-Mandel interferometry and violation of the Clauser-Horne-Shimony-Holt form of Bells inequality. The classical information capacities of several bosonic channels are reviewed, and shown to exceed what can be achieved using conventional optical receivers.

Semiclassical versus quantum behavior in fourth-order interference

A theoretical construct is presented for fourth-order interference between the signal and the idler beams of a parametric downconverter. Previous quantum treatments of fourth-order interference have employed correlated single-photon wave packets. The introduced approach, however, relies on Gaussian-state field correlations, which were previously used to characterize quadrature-noise squeezing produced by an optical parametric amplifier and nonclassical twin-beam generation in an optical parametric oscillator. Three principal benefits accrue from the correlation-function formalism. First, the quantum theory of fourth-order interference is unified with that for the other nonclassical effects of χ(2) interactions, i.e., squeezing and twin-beam production. Second, the semiclassical photodetection limit on Gaussian-state fourth-order interference is established; a purely quantum effect can be claimed at fringe visibilities substantially below the 50% level. Finally, both photon-coincidence counting (within the low-photon-flux regime) and intensity interferometry (in the high-photon-flux limit) are easily analyzed within a common framework.

Optical coherence tomography with phase-sensitive light

A new configuration for optical coherence tomography is proposed that utilizes a phase-conjugate amplifier in conjunction with a Michelson interferometer to detect interference between two classical light fields with a non-zero phase-sensitive cross correlation. This imaging configuration - which we call phase-conjugate optical coherence tomography (PC-OCT) - shares the same factor-of-two axial resolution improvement and cancellation of even-order dispersion terms that are the key features of quantum optical coherence tomography, but without the necessity for non-classical signal and reference beams. Under appropriate conditions, PC-OCT can achieve a signal-to-noise ratio that is comparable to that of conventional optical coherence tomography.

Gaussian-state theory of two-photon imaging

Biphoton states of signal and idler fields--obtained from spontaneous parametric downconversion (SPDC) in the low-brightness, low-flux regime--have been utilized in several quantum imaging configurations to exceed the resolution performance of conventional imagers that employ coherent-state or thermal light. Recent work--using the full Gaussian-state description of SPDC--has shown that the same resolution performance seen in quantum optical coherence tomography and the same imaging characteristics found in quantum ghost imaging can be realized by classical-state imagers that make use of phase-sensitive cross correlations. This paper extends the Gaussian-state analysis to two additional biphoton-state quantum imaging scenarios: far field diffraction-pattern imaging; and broadband thin-lens imaging. It is shown that the spatial resolution behavior in both cases is controlled by the nonzero phase-sensitive cross correlation between the signal and idler fields. Thus, the same resolution can be achieved in these two configurations with classical-state signal and idler fields possessing a nonzero phase-sensitive cross correlation.