Anderson localization of entangled photons in an integrated quantum walk

Abstract

Waves fail to propagate in random media. First predicted for quantum particles in the presence of a disordered potential, Anderson localization has been observed also in classical acoustics, electromagnetism and optics. Here, for the first time, we report the observation of Anderson localization of pairs of entangled photons in a two-particle discrete quantum walk affected by position dependent disorder. A quantum walk on a disordered lattice is realized by an integrated array of interferometers fabricated in glass by femtosecond laser writing. A novel technique is used to introduce a controlled phase shift into each unit mesh of the network. Polarization entanglement is exploited to simulate the different symmetries of the two-walker system. We are thus able to experimentally investigate the genuine effect of (bosonic and fermionic) statistics in the absence of interaction between the particles. We will show how different types of randomness and the symmetry of the wave-function affect the localization of the entangled walkers.In 1958 P.W. Anderson [1] predicted that the wavefunction of a quantum particle can be localized in the presence of a static disordered potential. As a consequence of this mechanism it is expected that particle and energy transport through a disordered medium should be strongly suppressed and that an initially localized wave packet should not spread out with time. After more than fifty years from its discovery Anderson localization is still widely studied and it has pervaded many different areas of physics ranging from condensed matter and cold atomic physics to wave dynamics and quantum chaos [2]. This phenomenon emerges quite generically in the behavior of waves in complex media, and it has been experimentally observed in a variety of different systems: BoseEinsten condensates [3,4] Anderson localization is a single-particle process which arises from the destructive interference among different scattering paths. Nevertheless, even in the absence of a direct interaction between particles, pure quantum correlations [13] are expected to influence in a non-trivial way the underlying localization dynamics [14][15][16][17]. By taking advantage of the perfect phase stability provided by miniaturized integrated waveguide circuits [18], we experimentally simulate a quantum walk of a two-photon polarization-entangled state in a disordered medium. We are thus able, through a mapping derived in Ref. [14], to test the localization of a pair of non interacting particles obeying bosonic/fermionic statistics [19].A quantum walk (QW) [20] is an extension of the classical random walk, where the walker goes back and forth along a line and the direction at each step depends on the result of a fair coin flip. At the quantum level, interference and superposition phenomena lead to a non-classical behavior of the walker giving rise to new interesting effects, which can be harnessed to exponentially speed up search algorithms [21] and to realize universal quantum computation [22]. Besides, QWs have also been pr...

Large scale quantum walks by means of optical fiber cavities

“…Quantum walks, both discrete and continuous, have been realised using cold atoms [17,18], single optically trapped atoms [19], trapped ions [20][21][22], and photons. Optical systems have been used to implement quantum walks using bulk optics [23,24], photonic chips [25][26][27][28], fiber optics [29], and hybrid bulkfiber optic approaches [30][31][32].…”

“…A promising route for control within our all-fiber apparatus is strainoptic modulation [39]. The flexibility of the integrated fiber platform is in contrast to photonic chip approaches, which are limited in geometry and have not yet achieved reconfigurability in large waveguide arrays [28,31].A future direction for this work, which we are now investigating, is studying the quantum interference of multiple single photons by connecting the input to a heralded single-photon source. This approach can enable the exploration of quantum walks with multiple walkers, and more generally, the study of time-encoded boson sampling [40] and related Gaussian sampling problems [41].…”

Progress in ultrafast laser processing and future prospects

“…A 3D multipath interferometer constructed with femtosecond laser-inscribed optical waveguides has demonstrated tunable quantum interference at the chip scale and is thus capable of quantumenhanced phase measurements [91]. Several functional quantum photonic circuits have been built in glass chips, on which quantum information processing such as photonic boson sampling and Anderson localization (i.e., trapping of scattered fields in a disordered material) has been successfully demonstrated [92,93]. Conventional quantum circuits for quantum information processing are constructed with bulk optics that include a large amount of discrete elements on optical tables, which suffer from a large footprint size with poor stability.…”

Generation and manipulation of entangled photons on silicon chips

“…The use of waveguides provides increased phase stability and enables the integration of larger numbers of quantum gates in a limited area. With the use of waveguides, several quantum tasks have been implemented, from basic quantum optic experiments [1,4,5] to sophisticated quantum information processing such as Shor's algorithm [6], quantum walks [7,8], and boson sampling [9][10][11][12][13][14]. In the future, it is expected that such quantum functional circuits will be integrated on chip with other devices such as photon sources [15,16], functional circuits [17,18], buffers [19], and detectors [20][21][22][23], so that we can realize all optical quantum processors, as shown in Figure 1 [19].…”