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arXiv:1009.0415 · Physical Review Letters

Bloch Oscillations of Path-Entangled Photons

Yaron Bromberg, Yoav Lahini, Yaron R. Silberberg

Published Dec 22, 2010• 71 citations
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Abstract

We show that when photons in N-particle path-entangled |N,0)+|0,N) or N00N states undergo Bloch oscillations, they exhibit a periodic transition between spatially bunched and antibunched states. The period of the bunching-antibunching oscillation is N times faster than the period of the oscillation of the photon density, manifesting the unique coherence properties of N00N states. The transition occurs even when the photons are well separated in space.

DOI
10.1103/physrevlett.105.263604

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We show that when photons in N-particle path-entangled |N,0)+|0,N) or N00N states undergo Bloch oscillations, they exhibit a periodic transition between spatially bunched and antibunched states. The period of the bunching-antibunching oscillation is N times faster than the period of the oscillation of the photon density, manifesting the unique coherence properties of N00N states. The transition occurs even when the photons are well separated in space.
Bloch oscillations of quantum particles manifest themselves as periodic spreading and relocalization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit this phenomenon is deeply rooted into the very foundations of quantum mechanics, all experimental observations so far have only contemplated dynamics of one and two particles initially prepared in separable local states. Evidently, a more general description of genuinely quantum Bloch oscillations will be achieved on excitation of a Bloch oscillator by nonlocal states. Here we report the observation of Bloch oscillations of two-particle N00N states, and discuss the nonlocality on the ground of Bell-like inequalities. The time evolution of two-photon N00N states in Bloch oscillators, whether symmetric, antisymmetric or partially symmetric, reveals transitions from particle antibunching to bunching. Consequently, the initial states can be tailored to produce spatial correlations akin to those of bosons, fermions and anyons, presenting potential applications in photonic quantum simulation.
We demonstrate that single-photon as well as biphoton revivals are possible in a new class of dynamic optical systems---the so-called Glauber-Fock oscillator lattices. In these arrays, both Bloch-like oscillations and dynamic delocalization can occur which can be described in closed form. The bunching and antibunching response of path-entangled photons can be pre-engineered in such coupled optical arrangements, and the emulation of fermionic behavior in this family of lattices is also considered. We elucidate these effects via pertinent examples.
We demonstrate that perfect transfer of path-entangled photons as well as of single-photon states is possible in a certain class of spin inspired optical systems---the so-called Jx{J}_{x}Jx​ photonic lattices. In these fully integrable optical arrangements, perfect cyclic transitions from correlated states to totally anticorrelated states can naturally occur. Moreover we show that the bunching and antibunching response of path-entangled photons can be preengineered at will in such coupled optical arrangements. We elucidate these effects via pertinent examples.
A quantum theory of optical Bloch oscillations and Zener tunneling (ZT) in arrays of coupled waveguides is theoretically presented, and the particlelike behavior of photons undergoing ZT is highlighted. In singly-periodic arrays excited by a photon-number-state input beam, each photon behaves as a classical particle which independently undergoes a coin-toss ZT event with a probability described by classical Zener theory. In binary arrays, excitation with two tilted beams enables us to observe the Hong-Ou-Mandel interference for two photons undergoing Bloch-Zener oscillations.
Being bosons, photons like to group together, with the behavior of photon bunching described as an attribute of classical light. At the other extreme, photons emitted by a single emitter are expected to antibunch, trickling out of the emitter one at a time. Although bunching and antibunching are well established behaviors of classical and nonclassical light, respectively, the transition between the two has not been observed. It is expected that as the number of emitters is increased, a smooth transition should occur. Using a high-quality cavity into which they can place a variable number of atoms, Hennrich et al. show that they can probe the transition systematically as the number of emitters (atoms in the cavity) is gradually increased. They observe that the antibunching behavior disappears when the average number of atoms in the cavity is one, and they are able to explain the experimental data well if the emitters are assumed to form an independent ensemble. — ISO