Quantum, Nonlocal Aberration Cancellation

Abstract

Phase distortions, or aberrations, can negatively influence the performance of an optical imaging system. Through the use of position-momentum entangled photons, we nonlocally correct for aberrations in one photon's optical path by intentionally introducing the complementary aberrations in the optical path of the other photon. In particular, we demonstrate the simultaneous nonlocal cancellation of aberrations that are of both even and odd order in the photons' transverse degrees of freedom. We also demonstrate a potential application of this technique by nonlocally cancelling the effect of defocus in a quantum imaging experiment and thereby recover the original spatial resolution.Entangled photons display strong correlations in conjugate continuous variables and are therefore of interest not only for the foundations of quantum physics [1-9], but are also routinely used for quantum information processing [10-12] and quantum imaging [13][14][15][16]. Group velocity dispersion (GVD) [17] and wavefront aberrations [18] can negatively influence the correlations and entanglement of continuous variables.In this Letter, we show that through the use of position-momentum entangled photon pairs aberrations experienced by one photon can in a sense be undone by tailoring the wavefront structure of the other photon without ever bringing the two photons back together. In this sense, we demonstrate nonlocal aberration cancellation.The mitigation of GVD has been proposed and demonstrated both in a local scheme based on indistinguishability [19,20] and in a nonlocal manner that relied on frequency correlations of the light [9,21,22]. The simultaneous [23,24] and non-simultaneous [25] cancellation of even-and odd-order terms in the dispersion relation have also been demonstrated in a local manner. Because frequency correlations do not necessarily have to be of quantum origin, even classical dispersion cancellation techniques have been realized [26][27][28][29]. As the spatial analog to dispersion [30], aberrations caused by transverse momentum-dependent phase shifts can be canceled in a conceptually similar manner. Only local aberration cancellation has been performed experimentally [31,32], except for the nonlocal compensation of pure phase objects revealed through polarization correlations [33].We complement these studies by demonstrating both even-and odd-order nonlocal aberration cancellation simultaneously with entangled photon pairs. Because the observation of position-momentum entanglement is strongly influenced by the propagation of the photons [34,35], aberrations in the path of one photon affect the observed entanglement significantly. In particular, quadratic aberrations that act as defocus lead to a form of entanglement migration [35]. These deleterious effects can be cancelled by acting on the state of the second photon with an appropriately chosen aberration. In contrast to Ref.[35], we perform higher-order as well as quadratic aberration cancellation and enhance the quality of quantum imaging in the presence of aberr...