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European Quantum Electronics Conference (EQEC)

Manipulating the temporal correlations of two-photon states through the spatial degree of freedom

Alexander Büse, Nora Tischler, L. G. Helt, Mathieu L. Juan, Michael J. Steel, Gabriel Molina‐Terriza

Published Jun 21, 2015• 0 citations
OpenAlex

Abstract

Here we report our efforts in the characterization and engineering of spatio-temporally [1] entangled photon states. We use photon pairs obtained from spontaneous parametric down-conversion (SPDC) and present a novel way to reconstruct the complex spectral wavefunction from information obtained in a two-dimensional Hong-Ou-Mandel experiment [2]. This represents a novel and straightforward way to access otherwise hidden information in the wavefunction. Furthermore, the choice of the detection mode gives us some control over the spatio-temporal structure of the wavefunction.

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Here we report our efforts in the characterization and engineering of spatio-temporally [1] entangled photon states. We use photon pairs obtained from spontaneous parametric down-conversion (SPDC) and present a novel way to reconstruct the complex spectral wavefunction from information obtained in a two-dimensional Hong-Ou-Mandel experiment [2]. This represents a novel and straightforward way to access otherwise hidden information in the wavefunction. Furthermore, the choice of the detection mode gives us some control over the spatio-temporal structure of the wavefunction.
Spontaneous parametric down-conversion (SPDC) is a widely used source for photonic entanglement. Years of focused research have led to a solid understanding of the process, but a cohesive analytical description of the paraxial biphoton state has yet to be achieved. We derive a general expression for the spatio-temporal biphoton state that applies universally across common experimental settings and correctly describes the nonseparability of spatial and spectral modes. We formulate a criterion on how to decrease the coupling of the spatial from the spectral degree of freedom by taking into account the Gouy phase of interacting beams. This work provides new insights into the role of the Gouy phase in SPDC, and also into the preparation of engineered entangled states for multidimensional quantum information processing.
Spontaneous parametric down-conversion (SPDC) is the most widely-used source of high-dimensional entangled two-photon states, and the entanglement in the spatial degree of freedom is considered best suited for harnessing high-dimensional advantages. Although the Schmidt basis provides a natural choice for state characterisation of entangled two-photon states in any degree of freedom, there is currently no technique that can measure the Schmidt basis of an entangled two-photon field. The existing techniques can only reconstruct the Schmidt spectrum when the Schmidt basis is known a priori. In contrast, we present a technique that measures the complete set of spatial Schmidt modes without any prior knowledge. Using this technique, we report measurement of states with over 3000 Schmidt modes -- highest reported yet -- with up to 98%\%% fidelity. We expect our work to significantly advance the harnessing of high-dimensional advantages in SPDC-based systems.
In most configurations aimed at generating entangled photons based on spontaneous parametric down conversion (SPDC), the generated pairs of photons are required to be entangled in only one degree of freedom. Any distinguishing information coming from the other degrees of freedom that characterize the photon should be suppressed to avoid correlations with the degree of freedom of interest. However, this suppression is not always possible. Here, we show how the frequency information available affects the purity of the two-photon state in space, revealing a correlation between the frequency and the space degrees of freedom. This correlation should be taken into account to calculate the total amount of entanglement between the photons.
Correlations in light can be used for a variety of applications in metrology and imaging. Several schemes in quantum imaging rely on multi-photon absorption. Therefore a detailed knowledge of the temporal and spatial correlations of the photons used is desired. This paper investigates the correlations of space-momentum entangled biphotons generated from type II parametric down conversion. The type II generation allows for individual manipulation in each path to control the spatial modes involved in the subsequent biphoton beam creation utilizing a Hong-Ou-Mandel interference.
The entangled photon pairs (biphotons) produced from parametric down-conversion (PDC) in a χ(2)crystal are the key element for several quantum information and communication schemes. Recent theoretical investigations [1–2] have revealed the peculiar structure of the biphotonic correlation characterizing the entanglement of twin beams in the space-time domain. The biphotonic correlation in type I PDC is characterized in the near field by a X-shaped geometry, which turns out to be non-factorable in space and time, offering thus the relevant possibility of manipulating the temporal bandwidth of biphoton entanglement by acting on their spatial degrees of freedom. The name “X-entanglement” was coined to describe this geometry [1]. An other key feature which emerged is the extreme spatial and temporal localization of the biphotonic correlation, on the micrometer and femtosecond range, respectively.