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arXiv:2007.12429 · Optics Express

Hot-spots and gain enhancement in a doubly pumped parametric down-conversion process

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

Published Oct 9, 2020• 4 citations
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Abstract

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.

DOI
10.1364/oe.403668

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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 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.
nonlinear grating. A peculiar feature of this resonant configuration is that the two pumps simultaneously generate photon pairs over an entire branch of modes, via quasi-phase matching with both fundamental vectors of the reciprocal lattice of the nonlinearity. The parametric gain of these modes depends thus coherently on the sum of the two pump amplitudes and can be controlled by varying their relative intensities and phases. We find that a significant enhancement of the source conversion efficiency, comparable to that of one-dimensionally poled crystals, can be achieved by a dual symmetric pump. We also show how the four-mode coupling arising among shared modes at resonance can be tailored by changing the dual pump parameters.
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.
In this paper we study photon pairs generated in a nonlinear cavity composed of a nonlinear crystal surrounded by mirrors, by the process of spotaneous parametric downconversion. We analyze two different regimes: singly-resonant cavities where the signal and idler modes are resonant and doubly-resonant cavities where the pump mode is also resonant. We present analytic expressions for the joint spectral amplitude in these two cases and study the reduction in emission bandwidth as the cavity coefficient finesse is increased. We also study the enhancement of the source brightness from the presence of the cavity.
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.