Abstract
Partially coherent optical beams present phenomena that may not appear in perfectly coherent beams. In this regard, spontaneous parametric downconversion is an intriguing physical process, since the optical properties of the pump laser beam are transferred to the quantum properties of the down-converted photon pairs. Here, the authors study the transfer of twist phase, a novel property of the so-called twisted Gaussian Schell model beams, from a pump beam to down-converted photons. The authors show that a non-zero twist phase can lead to highly entangled yet highly mixed states. The correlations that appear in near/far-field intensity measurements, in the two-photon covariance matrix as well as in orbital angular momentum modes, are explored. The authors derive expressions for the purity of the two-photon state and relate it to the transverse spatial coherence of the pump beam. Their main results utilize a Wigner function formalism that can be applied to a number of scenarios involving partially coherent downconversion sources and contribute to the recent interest in spatially correlated photon pairs produced in mixed states, with possible applications in quantum communication and imaging.
Highlights
Spontaneous parametric downconversion (SPDC) is a non-linear optical process that has served as a robust and versatile source of entangled photons and, as such, has played a crucial role in improving our understanding of quantum optics, fundamental quantum mechanics, and quantum information
We have investigated the use of twisted Gaussian Schell model beams to produce pairs of spatially correlated photons from spontaneous parametric downconversion
Our study is conducted using a general Wigner function approach to partially coherent spontaneous parametric down conversion, where the spatially correlated photons can be produced by a source with partial coherence that arises from either the transverse properties of the pump beam, the coherence of possible downconversion events, or both
Summary
Spontaneous parametric downconversion (SPDC) is a non-linear optical process that has served as a robust and versatile source of entangled photons and, as such, has played a crucial role in improving our understanding of quantum optics, fundamental quantum mechanics, and quantum information. 39–41, the authors studied the intensity correlations of photon pairs produced from SPDC with a pump beam with partial transverse spatial coherence. It was shown that a more general class of pump beam, known as the twisted GSM (TGSM),[33,34] can lead to an increase in entanglement as incoherence increases, thanks to a non-zero twist phase.[45]. This motivates a more thorough investigation into spatial correlations and entanglement in the case of a partially coherent twophoton source. Our results show how these parameters can be manipulated to control the entanglement and engineer the correlations of the two-photon state
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