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Physica Scripta

Two-photon spectral amplitude of entangled states resolved in separable Schmidt modes

Alessio Avella, G. Brida, Maria V. Chekhova, Marco Gramegna, Alexander P. Shurupov, Marco Genovese

Published Oct 1, 2015• 2 citations
Publisher

Abstract

The ability to access high dimensionality in Hilbert spaces represents a demanding key-stone for state-of-the-art quantum information. The manipulation of entangled states in continuous variables, wavevector as well frequency, represents a powerful resource in this sense. The number of dimensions of the Hilbert space that can be used in practical information protocols can be determined by the number of Schmidt modes that it is possible to address one by one. In the case of wavevector variables, the Schmidt modes can be losslessly selected using single-mode fibre and a spatial light modulator, but no similar procedure exists for the frequency space. The aim of this work is to present a technique to engineer the spectral properties of biphoton light, emitted via ultrafast spontaneous parametric down conversion, in such a way that the two-photon spectral amplitude (TPSA) contains several non-overlapping Schmidt modes, each of which can be filtered losslessly in frequency variables. Such TPSA manipulation is operated by a fine balancing of parameters like the pump frequency, the shaping of pump pulse spectrum, the dispersion dependence of spontaneous parametric down-conversion crystals as well as their length. Measurements have been performed exploiting the group velocity dispersion induced by the passage of optical fields through dispersive media, operating a frequency-to-time two-dimensional Fourier transform of the TPSA. Exploiting this kind of measurement we experimentally demonstrate the ability to control the Schmidt modes structure in TPSA through the pump spectrum manipulation.

DOI
10.1088/0031-8949/2015/t165/014005

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The ability to access high dimensionality in Hilbert spaces represents a demanding key-stone for state-of-the-art quantum information. The manipulation of entangled states in continuous variables, wavevector as well frequency, represents a powerful resource in this sense. The number of dimensions of the Hilbert space that can be used in practical information protocols can be determined by the number of Schmidt modes that it is possible to address one by one. In the case of wavevector variables, the Schmidt modes can be losslessly selected using single-mode fibre and a spatial light modulator, but no similar procedure exists for the frequency space. The aim of this work is to present a technique to engineer the spectral properties of biphoton light, emitted via ultrafast spontaneous parametric down conversion, in such a way that the two-photon spectral amplitude (TPSA) contains several non-overlapping Schmidt modes, each of which can be filtered losslessly in frequency variables. Such TPSA manipulation is operated by a fine balancing of parameters like the pump frequency, the shaping of pump pulse spectrum, the dispersion dependence of spontaneous parametric down-conversion crystals as well as their length. Measurements have been performed exploiting the group velocity dispersion induced by the passage of optical fields through dispersive media, operating a frequency-to-time two-dimensional Fourier transform of the TPSA. Exploiting this kind of measurement we experimentally demonstrate the ability to control the Schmidt modes structure in TPSA through the pump spectrum manipulation.
Two-photon states entangled in continuous variables such as wave vector or frequency represent a powerful resource for quantum-information protocols in higher-dimensional Hilbert spaces. At the same time, there is a problem of addressing separately the corresponding Schmidt modes. We propose a method of engineering two-photon spectral amplitude in such a way that it contains several nonoverlapping Schmidt modes, each of which can be filtered losslessly. The method is based on spontaneous parametric down-conversion (SPDC) pumped by radiation with a comblike spectrum. There are many ways of producing such a spectrum; here we consider the simplest one, namely, passing the pump beam through a Fabry-Perot interferometer. For the two-photon spectral amplitude (TPSA) to consist of nonoverlapping Schmidt modes, the crystal dispersion dependence, the length of the crystal, the Fabry-Perot free spectral range, and its finesse should satisfy certain conditions. We experimentally demonstrate the control of TPSA through these parameters. We also discuss a possibility to realize a similar situation using cavity-based SPDC.
We present an experimental implementation of spectral properties engineering on biphoton light, emitted via ultrafast type II spontaneous parametric down conversion (SPDC), based on the shaping of the pump pulse spectrum and propagation of the emitted correlated photons through dispersive media. Spectral properties of a biphoton state are fully characterized by the two-photon spectral amplitude (TPSA). Exploiting the group velocity dispersion (GVD) induced by the passage of optical fields through dispersive media, an energy to time two dimensional Fourier transform of the TPSA is operated: this returns a technique to reconstruct TPSA by means of a temporal measurement among the delay between the laser pulse emission (trigger) and the detection times of the two correlated photons. Exploiting this kind of measurement it is possible to deeply resolve the interference pattern in the shape of TPSA. In this research we report on the conditions under which subtle structure on TPSA spectra can be deliberately engineered via modulation of the pump beam spectrum.
Here we investigate the all-optical control of spectral correlations in spontaneous parametric down-conversion. We show that when photon pairs are projected onto high-order spatial modes, the spatial structure of the pump field defines the phase-matching function of the nonlinear interaction. Thus, by structuring the pump field in both space and spectrum, the biphoton spectral correlations are fully controlled. Considering a standard periodically-poled crystal as the nonlinear medium, we show that the Gouy phase matching method proposed here can generate both spectrally uncorrelated and high-dimensional spectrally entangled photon pairs, similarly to what is achieved with aperiodically-poled crystals. Furthermore, we show that our method can generate a wider class of quantum states if the pump field is a spatiotemporal wavepacket, that is, if its spatial and spectral structures are correlated.