#
Experimental Investigation of Quantum Decay via Integrated Photonics^{ †}

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Results

## 3. Discussion

## 4. Materials and Methods

#### Waveguide Fabrication

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Nakazato, H.; Namiki, M.; Pascazio, S. Temporal behavior of quantum mechanical systems. Int. J. Mod. Phys. B
**1996**, 10, 247. [Google Scholar] [CrossRef] - Wilkinson, S.R.; Bharucha, C.F.; Fischer, M.C.; Madison, K.W.; Morrow, P.R.; Niu, Q.; Sundaram, B.; Raizen, M.G. Experimental evidence for non-exponential decay in quantum tunnelling. Nature
**1997**, 387, 575–577. [Google Scholar] [CrossRef] - Biagioni, P.; Della Valle, G.; Ornigotti, M.; Finazzi, M.; Duo, L.; Laporta, P.; Longhi, S. Experimental demonstration of the optical Zeno effect by scanning tunneling optical microscopy. Opt. Express
**2008**, 16, 3762–3767. [Google Scholar] [CrossRef] [PubMed] - Longhi, S. Quantum-optical analogies using photonic structures. Laser Photonics Rev.
**2009**, 3, 243–261. [Google Scholar] [CrossRef] - Szameit, A.; Nolte, S. Discrete optics in femtosecond-laser-written photonic structures. J. Phys. B
**2010**, 43, 163001. [Google Scholar] [CrossRef] - Chiodo, N.; Della Valle, G.; Osellame, R.; Longhi, S.; Cerullo, G.; Ramponi, R.; Laporta, P.; Morgner, U. Imaging of Bloch oscillations in erbium-doped curved waveguide arrays. Opt. Lett.
**2006**, 31, 1651–1653. [Google Scholar] [CrossRef] [PubMed] - Corrielli, G.; Crespi, A.; Della Valle, G.; Longhi, S.; Osellame, R. Fractional Bloch oscillations in photonic lattices. Nat. Commun.
**2014**, 4, 1555. [Google Scholar] [CrossRef] [PubMed] - Martin, L.; Di Giuseppe, G.; Perez-Leija, A.; Keil, R.; Dreisow, F.; Heinrich, M.; Nolte, S.; Szameit, A.; Abouraddy, A.F.; Christodoulides, D.N.; Saleh, B.E. Anderson localization in optical waveguide arrays with off-diagonal coupling disorder. Opt. Express
**2011**, 19, 13636–13646. [Google Scholar] [CrossRef] - Osellame, R.; Cerullo, G.; Ramponi, R. (Eds.) Femtosecond Laser Micromachining: Photonic and Microfluidic Devices in Transparent Materials; Springer: Berlin/Heidelberg, Germany, 2012; ISBN 978-3-642-23365-4. [Google Scholar]
- Crespi, A.; Longhi, S.; Osellame, R. Photonic realization of the quantum Rabi model. Phys. Rev. Lett.
**2012**, 108, 163601. [Google Scholar] [CrossRef] - Crespi, A.; Pepe, F.V.; Facchi, P.; Sciarrino, F.; Mataloni, P.; Nakazato, H.; Pascazio, S.; Osellame, R. Experimental investigation of quantum decay at short, intermediate and long times via integrated photonics. Phys. Rev. Lett.
**2019**, 122, 130401. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**(

**a**) Typical temporal evolution of the survival probability $p\left(t\right)$ of a discrete quantum state coupled to a continuum, where different regimes can be observed at short, intermediate and late evolution times. (

**b**) The system is a linear array of optical waveguides, coupled by evanescent-field interaction, excited with coherent light. The first waveguide represents the discrete state and is coupled to the remaining part of the array, which acts as a continuum of states. The temporal evolution of the system is mapped into the longitudinal propagation coordinate t. See the text for details.

**Figure 2.**Coherent light from a He:Ne laser is injected in the array. To characterize the light distribution in the photonic structure, scattered light is imaged from above using a movable microscope-assembly that scans automatically the full length of the glass chip (

**a**). Panel (

**b**) reports an example of acquired intensity distribution from a waveguide array. The original image is monochrome and corresponds to a physical region of about 88 mm × 640 $\mathsf{\mu}$m; here it is reshaped for better readability and shown in false colors. A horizontal section yields the time evolution of a given state (waveguide). A vertical section gives the probability distribution within the photonic modes at a given time. Laser light is coupled in the array from the left in the topmost waveguide; the intensity of the first line in the picture thus corresponds to the survival probability of the initial state.

**Figure 3.**(

**a**) Experimental survival probability in a weakly coupled system (${\kappa}_{0}<\kappa $). The measured points (black dots) are encircled by a gray area indicating the experimental uncertainty. (

**b**) Experimental survival probability in a system with stronger coupling (${\kappa}_{0}\sim \kappa $); the red dashed line is a fitted $C{t}^{-3}$ asymptotic trend.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Crespi, A.; Pepe, F.V.; Facchi, P.; Sciarrino, F.; Mataloni, P.; Nakazato, H.; Pascazio, S.; Osellame, R.
Experimental Investigation of Quantum Decay via Integrated Photonics. *Proceedings* **2019**, *12*, 9.
https://doi.org/10.3390/proceedings2019012009

**AMA Style**

Crespi A, Pepe FV, Facchi P, Sciarrino F, Mataloni P, Nakazato H, Pascazio S, Osellame R.
Experimental Investigation of Quantum Decay via Integrated Photonics. *Proceedings*. 2019; 12(1):9.
https://doi.org/10.3390/proceedings2019012009

**Chicago/Turabian Style**

Crespi, Andrea, Francesco V. Pepe, Paolo Facchi, Fabio Sciarrino, Paolo Mataloni, Hiromichi Nakazato, Saveri Pascazio, and Roberto Osellame.
2019. "Experimental Investigation of Quantum Decay via Integrated Photonics" *Proceedings* 12, no. 1: 9.
https://doi.org/10.3390/proceedings2019012009