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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Engineering a multimode coupling in doubly pumped parametric down-conversion: hot-spots and gain enhancement

Ottavia Jedrkiewicz, Erica Invernizzi, E. Brambilla, A. Gatti

Published Jun 21, 2021• 0 citations
Publisher

Abstract

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] .

DOI
10.1109/cleo/europe-eqec52157.2021.9542396

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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 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 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.
Uniaxial anisotropy in nonlinear birefringent crystals limits the efficiency of nonlinear optical interactions and breaks the spatial symmetry of light generated in the parametric down-conversion (PDC) process. Therefore, this effect is usually undesirable and must be compensated for. However, high gain may be used to overcome the destructive role of anisotropy in order to generate bright two-mode correlated twin-beams. In this work, we provide a rigorous theoretical description of the spatial properties of bright squeezed light in the presence of strong anisotropy. We investigate a single crystal and a system of two crystals with an air gap (corresponding to a nonlinear SU(1,1) interferometer) and demonstrate the generation of bright correlated twin-beams in such configurations at high gain due to anisotropy. We explore the mode structure of the generated light and show how anisotropy, together with crystal spacing, can be used for radiation shaping.
Photon-based quantum information schemes have increased the need for light sources that produce individual photons, with many such schemes relying on optical parametric down-conversion (PDC). Practical realizations of this technology require that the PDC light be collected into a single spatial mode defined by an optical fibre. We present two possible models to describe single-mode fibres coupling with PDC light fields in a non-collinear configuration, that lead to two different results. These approaches include factors such as crystal length and walk-off, non-collinear phase-matching and transverse pump field distribution. We propose an experimental test to distinguish between the two. The goal is to help clarify open issues, such as how to extend the theory beyond the simplest experimental arrangements and, more importantly, to suggest ways to improve the collection efficiency.
Optimizing the brightness of a spontaneous parametric down-conversion (SPDC) source is an important task for many quantum information applications. We investigate the optimal focusing conditions to maximize the number of photons produced in an SPDC process and coupled with single-mode fibers. We provide a general expression for the two-photon wave function, generalizing previous known results, by considering collinear and noncollinear emission. We present analytical expressions for our results in the thin-crystal limit and clarify the relation between different focusing conditions already existing in the literature. Differently from what was previously reported, we show that the optimal ratio between the pump waist and the generated photons waist depends on the emission angle: It is 1/21/\sqrt{2}1/2​ for collinear degenerate emission and approaches 1/21/21/2 for larger collection angles. The role of spectral filters is also analyzed. We support and enrich our discussion with numerical simulations, performed for type-I SPDC in a $\ensuremath{\beta}$ barium borate crystal. For this type of emission, we also investigate the role of the transverse walk-off outside the thin-crystal regime.