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arXiv:2007.12014 · Physical Review A

Engineering multipartite coupling in doubly pumped parametric down-conversion processes

A. Gatti, E. Brambilla, Ottavia Jedrkiewicz

Published Apr 26, 2021• 1 citation
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Abstract

We investigate the quantum state generated by optical parametric down-conversion in a ${\ensuremath{\chi}}^{(2)}$ medium driven by two noncollinear light modes. The analysis shows the emergence of multimode, namely, three- or four-mode, entangled states in a subset of the spatiotemporal modes generated by the process. These appear as bright spots against the background fluorescence, providing an interesting analogy with the phenomenology recently observed in two-dimensional nonlinear photonic crystals. We study two realistic setups. (1) Noncritical phase matching in a periodically poled lithium tantalate slab, characterized by a three-mode entangled state. (2) A type I setup in a beta-barium borate crystal, where the spatial walk-off between the two pumps can be exploited to make a transition to a four-mode entangled state. In both cases, we show that the properties of the state can be controlled by modulating the relative intensity of two pump waves, making the device a versatile tool for quantum state engineering.

DOI
10.1103/physreva.103.043720

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We investigate the quantum state generated by optical parametric down-conversion in a \ensuremathχ(2){\ensuremath{\chi}}^{(2)}\ensuremathχ(2) medium driven by two noncollinear light modes. The analysis shows the emergence of multimode, namely, three- or four-mode, entangled states in a subset of the spatiotemporal modes generated by the process. These appear as bright spots against the background fluorescence, providing an interesting analogy with the phenomenology recently observed in two-dimensional nonlinear photonic crystals. We study two realistic setups. (1) Noncritical phase matching in a periodically poled lithium tantalate slab, characterized by a three-mode entangled state. (2) A type I setup in a beta-barium borate crystal, where the spatial walk-off between the two pumps can be exploited to make a transition to a four-mode entangled state. In both cases, we show that the properties of the state can be controlled by modulating the relative intensity of two pump waves, making the device a versatile tool for quantum state engineering.
We experimentally investigate the parametric down-conversion process in a nonlinear bulk crystal, driven by two non-collinear pump modes. The experiment shows the emergence of bright hot-spots in modes shared by the two pumps, similar to the phenomenology recently observed in 2D nonlinear photonic crystals. By exploiting the spatial walk-off between the two extraordinary pump modes, we have been able to recreate a peculiar resonance condition, reported by a local enhancement of the parametric gain, which corresponds to a transition from a three-mode to a four-mode coupling. From a quantum point of view, this opens the way to the generation of multimode entangled states of light, such as tripartite or quadripartite states, in simple bulk nonlinear sources.
We present a parametric down-conversion (PDC) process in a nonlinear ß-barium borate (BBO) crystal, driven by two non-collinear pump beams, obtained from a Mach-Zehnder type interferometer. We show the possibility to reproduce in a bulk crystal a phenomenology analogue to that previously observed in a PDC process inside a χ 2 2D nonlinear photonic crystal (NPC) [1] , [2] . Each pump mode generates a family of cones of parametric radiation collinear with its direction. The intersection zones define an ensemble of modes shared by the two pumps, indistinguishably populated by the photons generated by pump 1 or by pump 2. As in [1] , in the high-gain regime these two possibilities sum up coherently, leading to a local increase of the parametric gain. Indeed we observe an unusual far-field distribution of the down-converted light, in the form of three bright branches of hot-spots against a more diffuse background [3] .
We study the quantum state of twin photons generated by parametric down-conversion in a two-dimensional nonlinear photonic crystal, driven by a dual pump beam. The interplay between the grating of the ${\ensuremath{\chi}}^{(2)}$ nonlinear response and the transverse spatial modulation of the pump opens a rich scenario of possibilities for controlling the quantum state. We focus on a spatial resonance condition between the pump and the nonlinear grating, where a quadripartite entangled state is generated in proper light modes. The device is shown to implement the mixing of a pair of independent two-mode squeezed states onto four separate spatial modes, without the need of any external beam-splitter. Remarkably, both the squeezing parameters and the mixing coefficients can be reconfigured by modulating the relative phase and intensity of the two pumps, enabling thus the generation of a variety of quantum states in a single device.
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.
Continuous-variable multipartite entanglement is a key resource for quantum technologies. This paper considers the multipartite entanglement generated in separated spatial modes of the same light beam by three different parametric sources: a standard ${\ensuremath{\chi}}^{(2)}$ medium pumped by two pumps, a single-pump nonlinear photonic crystal, and a doubly pumped nonlinear photonic crystal. These sources have in common the coexistence of several concurrent nonlinear processes in the same medium, which allows the generation of nonstandard three- and four-mode couplings. We test the genuine nature of the multipartite entangled states thereby generated in a common framework, using criteria based both on proper bounds for the variances of nonlocal observables and on the positive partial transpose criterion. The relative simplicity of these states allows a (hopefully) useful comparison of the different inseparability tests.
The two-photon state generated by spontaneous parametric down-conversion (SPDC) exhibit spatial entanglement embedded in the corresponding mode function. The control of the spatial characteristics of the generated two-photon state is an issue of paramount importance. For example, the spatial entanglement of the two down converted photons forms the basis of quantum imaging, and entanglement in orbital angular momentum has opened a new scenario for implementing multidimensional Hilbert spaces. We put forward several techniques to engineer the spatial structure of entangled two-photon states generated in SPDC. The first strategy we consider for spatial control of the quantum state makes use of the direct manipulation of the pump beam. This technique makes feasible to prepare arbitrary engineered entangled states in any d-dimensional Hilbert space. The second strategy is based on the proper preparation of the down-converting crystal itself, namely quantum state manipulation by quasi-phase-matching (QPM) engineering. We use properly designed transversely varying QPM gratings in nonlinear crystals.