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Physical Review A

Quantum random walks and wave-packet reshaping at the single-photon level

P. H. Souto Ribeiro, Stephen Patrick Walborn, Cesar Raitz, L. Davidovich, Nicim Zagury

Published Jul 15, 2008• 21 citations
Publisher

Abstract

We realize an experimental implementation of one step of a quantum random walk at the single-photon level. After a single step, it is already possible to observe the difference between the quantum and classical random walk. The single photon is obtained using twin photons from parametric down-conversion, in which the detection of one photon of the idler prepares a single-photon state of the signal. We used two different experimental setups, one based on an interferometer and a second using a birefringent crystal. The physical process behind these effects is the spatial reshaping of the single-photon wave packet, which is the spatial analog of the time reshaping observed in tunneling experiments.

DOI
10.1103/physreva.78.012326

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We realize an experimental implementation of one step of a quantum random walk at the single-photon level. After a single step, it is already possible to observe the difference between the quantum and classical random walk. The single photon is obtained using twin photons from parametric down-conversion, in which the detection of one photon of the idler prepares a single-photon state of the signal. We used two different experimental setups, one based on an interferometer and a second using a birefringent crystal. The physical process behind these effects is the spatial reshaping of the single-photon wave packet, which is the spatial analog of the time reshaping observed in tunneling experiments.
Quantum walks are the quantum mechanical analog to classical random walks. However, due to the wavelike nature of quantum particles, they reveal drastically different dynamics compared to their classical counterpart. These unique properties make quantum walks a new promising platform for quantum algorithms and a powerful tool to understand complex transport phenomena. This thesis presents three experiments specifically designed to send photons on a quantum walk. The experiments are based on a fiber network spreading the photonic wave packets over discrete time bins. With these Quantum Walks in Time we simulate the propagation of quantum particles in various different environments, revealing diverse dynamics such as a fast ballistic spread and an Anderson-like localization effect. Furthermore we use our concept to implement the first quantum walk on a two-dimensional lattice. The underlying topology allows for investigations of the intriguing dynamics of two strongly interacting quantum particles, which reveals unique effects such as the creation of bound states.
We experimentally demonstrate temporal shaping of a heralded single-photon wave packet, prepared by conditional measurement of the idler photon of the entangled photon pair in the process of spontaneous parametric down-conversion. The heralded single-photon wave packet for the signal photon, after being tailored with the help of chirp broadening and interference effects, was observed directly by measuring the time-correlated single-photon-counting histogram. We also demonstrate remote control of the temporal shaping effect by spectral filtering of the idler photon.
Quantum random walks have attracted special interest because they could lead to new quantum algorithms. Photons can carry orbital angular momentum (OAM) thereby offering a practical realization of a high-dimensional quantum information carrier. By employing OAM of photons, we experimentally realized the one-dimensional discrete-time quantum random walk. Three steps of a one-dimensional quantum random walk were implemented in our protocol showing the obvious difference between quantum and classical random walks.
We report the experimental observation of quantum holographic imaging of one-dimensional object with entangled photon pairs, generated in a spontaneous parametric down-conversion process. The signal photons play both roles of “object wave” and “reference wave” in holography but are recorded by a point detector providing only encoding information, while the idler photons travel freely and are locally manipulated with spatial resolution. The holographic image is formed by the two-photon correlation measurement, although both the signal and idler beams are incoherent. Three types of quantum holography schemes are analyzed according to the detection regime of the signal photons.
We put forward a versatile and highly scalable experimental setup for the realization of discrete two-dimensional quantum random walks with a single-qubit coin and tunable degree of decoherence. The proposed scheme makes use of a small number of simple optical components arranged in a multipath Mach-Zehnder-like configuration, where a weak coherent state is injected. Environmental effects (decoherence) are generated by a spatial light modulator, which introduces pure dephasing in the transverse spatial plane perpendicular to the direction of propagation of the light beam. By controlling the characteristics of this dephasing, one can explore a great variety of scenarios of quantum random walks: pure quantum evolution (ballistic spread), fast fluctuating environment leading to a diffusive classical random walk, and static disorder resulting in the observation of Anderson localization.