Abstract
We experimentally study the properties of coherent mode decomposition for the intensity correlation function of quasi-thermal light. We use the technique of spatial mode selection developed for studying the transverse entanglement of photon pairs, and show that it can be extended to characterize classical spatial correlations. Our results demonstrate the existence of a unique, for a given thermal source, basis of coherent modes, correlated in a way much resembling the Schmidt modes of spatially entangled photons.
Highlights
Entanglement in spatial degrees of freedom of quantum light, such as pairs of photons generated in spontaneous parametric down-conversion (SPDC), is currently an object of active research
As stated by Law and Eberly in their seminal work [1], a unique basis of coherent modes {|uk, |vk } exist, such that a spatial state of biphoton pairs |Ψ12 = dx1dx2Ψ(x1,√x2)a†(x1)a†(x2) |vac can be decomposed as |Ψ = k λk |uk |vk, with these, so-called, Schmidt modes being eigenvectors of reduced single-particle density matrices and λk - corresponding eigenvalues
Technical limitations of the SLM used do not allow to use it for amplitude modulation, which is necessary for perfect transformations of Hermite-Gaussian modes
Summary
Entanglement in spatial degrees of freedom of quantum light, such as pairs of photons generated in spontaneous parametric down-conversion (SPDC), is currently an object of active research These studies are motivated by applications in quantum information science, where infinite-dimensional Hilbert space of spatial states of photons offers attractive capabilities for high-dimensional quantum state engineering. A remarkable feature of this decomposition is its single-sum form, implying perfect one-to-one correlations between Schmidt modes These correlations were studied in several recent works [2,3,4], and number of significant terms in the decomposition is routinely used as an entanglement quantifier [1, 5,6,7,8,9,10,11,12].
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