Spontaneous parametric downconversion produces entangled signal and idler fields that are in a zero-mean jointly Gaussian state whose postselected, low-brightness, low-flux limit is a biphoton. This paper applies Gaussian-state analysis to two 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. In other words, the image formation process in these two scenarios is intrinsically classical coherence propagation.Spontaneous parametric downconversion produces entangled signal and idler fields that are in a zero-mean jointly Gaussian state whose postselected, low-brightness, low-flux limit is a biphoton. This paper applies Gaussian-state analysis to two 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. In other words, the image formation process in these two scenarios is intrinsically classical coherence propagation.

arXiv:0804.2653Physical Review AAug 27, 200812 citations

Unified theory of ghost imaging with Gaussian-state light

Baris I. Erkmen, Jeffrey H. Shapiro

The theory of ghost imaging is developed in a Gaussian-state framework that both encompasses prior work---on thermal-state and biphoton-state imagers---and provides a complete understanding of the boundary between classical and quantum behavior in such systems. The core of this analysis is the expression derived for the photocurrent-correlation image obtained using a general Gaussian-state source. This image is expressed in terms of the phase-insensitive and phase-sensitive cross correlations between the two detected fields, plus a background. Because any pair of cross correlations is obtainable with classical Gaussian states, the image does not carry a quantum signature per se. However, if the image characteristics of classical and nonclassical Gaussian-state sources with identical autocorrelation functions are compared, the nonclassical source provides resolution improvement in its near field and field-of-view improvement in its far field.The theory of ghost imaging is developed in a Gaussian-state framework that both encompasses prior work---on thermal-state and biphoton-state imagers---and provides a complete understanding of the boundary between classical and quantum behavior in such systems. The core of this analysis is the expression derived for the photocurrent-correlation image obtained using a general Gaussian-state source. This image is expressed in terms of the phase-insensitive and phase-sensitive cross correlations between the two detected fields, plus a background. Because any pair of cross correlations is obtainable with classical Gaussian states, the image does not carry a quantum signature per se. However, if the image characteristics of classical and nonclassical Gaussian-state sources with identical autocorrelation functions are compared, the nonclassical source provides resolution improvement in its near field and field-of-view improvement in its far field.

arXiv:0712.3554Physical Review AApr 7, 2008181 citations

Biphoton Pulse Shaping

Joseph M. Lukens, Andrew M. Weiner

Springer series in optical sciences/SPringer series in optical sciencesJan 1, 20152 citations

Quality of spatial entanglement propagation

Matthew C. Reichert, Xiaohang Sun, Jason W. Fleischer

We explore, both experimentally and theoretically, the propagation dynamics of spatially entangled photon pairs (biphotons). Characterization of entanglement is done via the Schmidt number, which is a universal measurement of the degree of entanglement directly related to the nonseparability of the state into its subsystems. We develop expressions for the terms of the Schmidt number that depend on the amplitude and phase of the commonly used double-Gaussian approximation for the biphoton wave function, and demonstrate migration of entanglement between amplitude and phase upon propagation. We then extend this analysis to incorporate both phase curvature in the pump beam and higher spatial frequency content of more realistic non-Gaussian wave functions. Specifically, we generalize the classical beam quality parameter ${M}^{2}$ to the biphotons, allowing the description of more information-rich beams and more complex dynamics. Agreement is found with experimental measurements using direct imaging and Fourier optics.We explore, both experimentally and theoretically, the propagation dynamics of spatially entangled photon pairs (biphotons). Characterization of entanglement is done via the Schmidt number, which is a universal measurement of the degree of entanglement directly related to the nonseparability of the state into its subsystems. We develop expressions for the terms of the Schmidt number that depend on the amplitude and phase of the commonly used double-Gaussian approximation for the biphoton wave function, and demonstrate migration of entanglement between amplitude and phase upon propagation. We then extend this analysis to incorporate both phase curvature in the pump beam and higher spatial frequency content of more realistic non-Gaussian wave functions. Specifically, we generalize the classical beam quality parameter ${M}^{2}$ to the biphotons, allowing the description of more information-rich beams and more complex dynamics. Agreement is found with experimental measurements using direct imaging and Fourier optics.

arXiv:1611.07967Physical Review AJun 22, 201735 citations

{M}^{2}

to the biphotons, allowing the description of more information-rich beams and more complex dynamics. Agreement is found with experimental measurements using direct imaging and Fourier optics.