A quantum walk in an ordered medium exhibits ballistic propagation. A related process is the driven quantum walk, in which the number of walkers varies along the propagation. In this work, we show that a driven quantum walk of biphoton states in an array of nonlinear waveguides does not propagate ballistically, but instead presents two transport regimes: superballistic and superdiffusive. We also study the effects of off-diagonal and diagonal disorder. In addition to the observation of Anderson localization, both types of disorder lead to the disappearance of the superballistic regime.
A quantum walk in an ordered medium exhibits ballistic propagation. A related process is the driven quantum walk, in which the number of walkers varies along the propagation. In this work, we show that a driven quantum walk of biphoton states in an array of nonlinear waveguides does not propagate ballistically, but instead presents two transport regimes: superballistic and superdiffusive. We also study the effects of off-diagonal and diagonal disorder. In addition to the observation of Anderson localization, both types of disorder lead to the disappearance of the superballistic regime.
Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so-called ballistic behavior, which is generally expected for the spreading in a quantum process. We have experimentally investigated the superdiffusive behavior of a quantum walk, whose dynamics can be related to energy transport phenomena, with a resolution which is high enough to clearly distinguish between different disorder regimes. By our experimental setup, the region between ballistic and diffusive spreading can be effectively scanned by suitably setting few degrees of freedom and without applying any decoherence to the quantum walk evolution.
In an array of nonlinear waveguides, quantum states can be generated from classical states through spontaneous parametric down-conversion of photons. This work simulates and analyzes the effect of disorder on light propagation and its quantum correlations, implementing disorder in three system parameters: coupling, injection amplitude, and injection phase. It is determined that when light is injected into only one waveguide, disorder in the coupling increases localization and reduces dispersion. Moreover, in this case, propagation tends to remain ballistic, a characteristic feature of waveguide arrays. Conversely, disorder in the injection amplitude and phase tends to delocalize the wave function, with the latter having a more pronounced effect. Finally, it is observed that quantum correlations, obtained from the correlation matrix, are robust in the presence of disorder, particularly the null elements.
We report on our latest findings on photonic Quantum Walks (QW) of entangled particles in several quantum transport regimes as for instance in photonic Bloch lattices or disordered lattices. Furthermore, the discrete fractional Fourier transform of quantum states is presented in the context of QWs. The propagation of a classical single walker on a random graph is an important field in statistics and can be applied on many domains in nature reaching from a foraging animals over Brownian molecular motion towards the evolution of lead changes in competitive team sports. Its quantum mechanical counterpart, the Quantum Walk (QW), features genuine quantum objects to walk on a random graph and hence, leading to non-classical quantum interference, in particular when considering two or more walkers. Their great potential lies i.a. in their ability to exponentially speed up a multitude of algorithms, as for instance the data bank search algorithm from L. Grover. In this regard, photonic lattices of evanescently coupled waveguides represent an ideal platform to study QW dynamics, since they feature advantages in stability, robustness and miniaturization. Our waveguide lattices were fabricated by means the direct laser inscription technique. In doing so, three dimensional waveguide geometries are realizable, enabling the implementation of various QW graphs. Along these lines, we study QWs of entangled photon pairs in disordered lattices. There we observe Anderson co-localization, meaning that neither the individual photons nor the pair localizes, rather their distance does. It turns out that both photons tend to bunch as they will be found together in the same lattice site, implying that their original correlation remains while performing a QW in a disordered lattice. Further, we investigate QWs of non-local two-photon EPR-states in Bloch-lattices. The experimental results reveal the strong dependence of the correlation output statistics (bosonic-, anyonicor fermionic-like) on the input states' symmetry. Finally, the discrete fractional Fourier transform of quantum states is realized through a discrete QW lattice. The results demonstrate the enormous potential of waveguide lattices in the field of quantum photonics and give rise to further investigations like the Fourier suppression law.
Quantum entanglement became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demonstrated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. Spontaneous parametric down-conversion (SPDC) in nonlinear crystals provides an efficient source for entangled photon pairs, so-called biphotons. However, SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional arrays can be simulated through classical optical beam propagation in a two-dimensional photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-like inequality.
∗ both authors contributed equally Quantum entanglement, the non-separability of a multipartite wave function, became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demon-strated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. With the discovery of spontaneous parametric down-conversion (SPDC) in nonlinear crystals, an efficient source for entangled photon pairs, so-called biphotons, be-came available. It has recently been shown that SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional spatial dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional (1D) arrays can be simulated through classical optical beam propagation in a two-dimensional (2D) photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-type inequality. PACS numbers: 42.50.-p, 42.82.Et, 42.65.Lm