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...

Spatial Mode Correction of Single Photons Using Machine Learning

“…Hitherto, these limitations have been alleviated through conventional schemes that use adaptive optics, quantum correlations, and nonlinear optics. [ 30,33–35 ] However, an efficient and fast protocol to overcome undesirable turbulence effects, at the single‐photon level, has not yet been experimentally demonstrated.…”

Nonlocal dispersion cancellation for three or more photons

“…Quantum key distribution based on nonlocal dispersion cancellation between pairs of photons has already been proposed [24][25][26][27], and it may be possible to extend these techniques to larger numbers of photons in a network configuration. Dispersion cancellation has also been proposed as a means of increasing the imaging quality in biomedical applications [31][32][33][34] and for quantum clock synchronization [28][29][30].…”

“…Nonlocal dispersion cancellation can also be employed for clock synchronization in a protocol that is resistant to pulse distortions caused in transit [28][29][30]. Biomedical imaging applications have also made use of nonlocal dispersion cancellation to improve the quality of the images [31][32][33][34]. We expect that the extension of nonlocal dispersion cancellation to higher numbers of photons will also have potential applications, especially for quantum networks with three or more nodes.…”

Interference-contrast optical activity: a new technique for probing the chirality of anisotropic samples and more

“…Let us suppose now that PR 1 and PR 2 are modulated between their σ = 0 and σ = 90°settings such that the (average) intensity of the final field becomes OR , 0), regardless of the linear birefringence (β and δ) of S. If S is not sufficiently thin and well matched with the surrounding medium to satisfy jajDz & 1 but is nevertheless sufficiently flat that jD(aDz)j & 1, the desired image can be obtained for a choice of relative phase equivalent to c = (αΔz + π)mod(2π) (assuming that tDz & 1). If neither jajDz & 1 nor jD(aDz)j & 1 is satisfied, appropriate compensations might be made by deforming the phase fronts of the sampling and/or reference fields using adaptive optics [33,34].…”

“…The final term on the right-hand side of equation 3.7vanishes for many samples of interest (including all of the samples considered in §4), in which case equation (3.7) reduces further still to C GOR j). If ja s Dz s À aDzj & 1 is not satisfied, appropriate compensations might be made by deforming the phase fronts of the sampling and/or reference fields using adaptive optics [33,34].…”