Noise-resistant phase imaging with intensity correlation.

Interferometric methods form the basis of highly sensitive measurement techniques from astronomy to bioimaging. Interferometry typically requires high stability between the measured and reference beams. The presence of rapid phase fluctuations washes out interference fringes, making phase profile recovery impossible. This challenge can be addressed by shortening the measurement time. However, such an approach reduces photon-counting rates, precluding applications in low-intensity imaging. We introduce a phase imaging technique which is immune to time-dependent phase fluctuations. Our technique, relying on intensity correlation instead of direct intensity measurements, allows one to obtain high interference visibility for arbitrarily long acquisition times. We prove the optimality of our method using the Cramér-Rao bound in the extreme case when no more than two photons are detected within the time window of phase stability. Our technique will broaden prospects in phase measurements, including emerging applications such as in infrared and x-ray imaging and quantum and matter-wave interferometry.

One-Photon Measurement of Two-Photon Entanglement.

Measuring entanglement is an essential step in a wide range of applied and foundational quantum experiments. When a two-particle quantum state is not pure, standard methods to measure the entanglement require detection of both particles. We realize a conceptually new method for verifying and measuring entanglement in a class of two-part (bipartite) mixed states. Contrary to the approaches known to date, in our experiment we verify and measure entanglement in mixed quantum bipartite states by detecting only one subsystem, the other remains undetected. Only one copy of the mixed or pure state is used but that state is in a superposition of having been created in two identical sources. We show that information shared in entangled systems can be accessed through single-particle interference patterns. Our experiment enables entanglement characterization even when one of the subsystems cannot be detected, for example, when suitable detectors are not available.

Resolution limit in quantum imaging with undetected photons using position correlations.

Quantum imaging with undetected photons (QIUP) is a unique method of image acquisition where the photons illuminating the object are not detected. This method relies on quantum interference and spatial correlations between the twin photons to form an image. Here we present a detailed study of the resolution limits of position correlation enabled QIUP. We establish a quantitative relation between the spatial resolution and the twin-photon position correlation. Furthermore, we also quantitatively establish the roles that the wavelength of the undetected illumination field and the wavelength of the detected field play in the resolution. Like ghost imaging and unlike conventional imaging, the resolution limit imposed by the spatial correlation between the twin photons in QIUP cannot be further improved by conventional optical techniques.

Position correlation enabled quantum imaging with undetected photons.

Quantum imaging with undetected photons (QIUP) is a unique imaging technique that does not require the detection of the light used for illuminating the object. This technique requires a correlated pair of photons. In the existing implementations of QIUP, the imaging is enabled by the momentum correlation between the twin photons. We investigate the complementary scenario in which the imaging is instead enabled by the position correlation between the two photons. We present a general theory and show that the properties of the images obtained in these two cases are significantly distinct.

Erratum: Entanglement by Path Identity [Phys. Rev. Lett. 118, 080401 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.118.080401.

Entanglement by Path Identity.

Quantum entanglement is one of the most prominent features of quantum mechanics and forms the basis of quantum information technologies. Here we present a novel method for the creation of quantum entanglement in multipartite and high-dimensional systems. The two ingredients are (i) superposition of photon pairs with different origins and (ii) aligning photons such that their paths are identical. We explain the experimentally feasible creation of various classes of multiphoton entanglement encoded in polarization as well as in high-dimensional Hilbert spaces-starting only from nonentangled photon pairs. For two photons, arbitrary high-dimensional entanglement can be created. The idea of generating entanglement by path identity could also apply to quantum entities other than photons. We discovered the technique by analyzing the output of a computer algorithm. This shows that computer designed quantum experiments can be inspirations for new techniques.

Quantifying the momentum correlation between two light beams by detecting one.

We report a measurement of the transverse momentum correlation between two photons by detecting only one of them. Our method uses two identical sources in an arrangement in which the phenomenon of induced coherence without induced emission is observed. In this way, we produce an interference pattern in the superposition of one beam from each source. We quantify the transverse momentum correlation by analyzing the visibility of this pattern. Our approach might be useful for the characterization of correlated photon pair sources and may lead to an experimental measure of continuous variable entanglement, which relies on the detection of only one of two entangled particles.

Propagation of electromagnetic beams of any state of spatial coherence and polarization through multilayered stratified media.

We present a theory of propagation of a partially coherent and partially polarized electromagnetic beam through a multilayered stratified medium. The analysis shows that spatial coherence and polarization properties of the beam change, in general, on propagation through such a medium. We illustrate the results by an example.

Change in spatial coherence of light on refraction and on reflection.

A theory of refraction and reflection of partially coherent electromagnetic beams has been recently developed. In this paper, we apply it to study the change in spatial coherence caused by refraction and by reflection more fully. By considering a Gaussian Schell-model beam, we show that the change is, in general, dependent on the angle of incidence.

Negative refraction of a partially coherent electromagnetic beam.

A theory of usual (positive) refraction of partially coherent electromagnetic beams has been developed recently. In this Letter, we discuss the theory of negative refraction of a partially coherent electromagnetic beam. We show that negative refraction can produce change in spatial coherence of such a beam.

Concept of purity in the theory of optical polarization.

It was shown some time ago that the space-time and the space-frequency degrees of polarization of a stochastic electromagnetic beam are not equivalent to each other. It is not possible, in general, to obtain a formal relationship between them. In this Letter, we discuss certain conditions under which they are directly related. These conditions lead to the concept of polarization-purity. If an optical beam obeys these conditions, its space-frequency degree of polarization has the same value at all frequencies present in the spectrum, and the value is equal to the space-time degree of polarization.

Spectral changes of stochastic beams scattered on a deterministic medium.

It is well known that scattering of a polychromatic plane wave by a random medium, i.e., by a medium whose refractive index varies randomly with position, may produce frequency shifts of spectral lines. It has been a common perception that a random medium is required for generation of such spectral shifts by scattering. In this Letter we show that such a phenomenon occurs even when the refractive index of the medium is a deterministic function of position. We also show that this phenomenon may be used to obtain information about the structure of a deterministic medium.

Statistical similarity and cross-spectral purity of stationary stochastic fields.

In practical situations, one often generates a beam by superposition of two or more light beams. The beam generated by superposition displays, in general, different spectral properties than do the original beams. However, there are some optical beams, called cross-spectrally pure beams, which can generate a light beam of identical spectral distribution on superposition. The relationship between cross-spectral purity and spatial coherence has been the subject of investigations for some time. Recently, a concept of so-called statistical similarity has been introduced which provides a new way to elucidate complete spatial coherence. In this Letter, we discuss some implications of statistical similarity of an optical field on its cross-spectral purity.

Implications of complete coherence in the space-frequency domain.

It was shown not long ago that complete spatial coherence of light at a pair of points in the space-time domain may be interpreted as a manifestation of so-called "statistical similarity" between the fluctuating field at the two points. In this Letter, we consider complete spatial coherence at a pair of points in the space-frequency domain and derive a condition that the field at those points must obey. We illustrate the usefulness of the condition by an example.

Relationship between complete coherence in the space-time and in the space-frequency domains.

We present some new results relating to properties of completely coherent optical fields. Our analysis elucidates the relationship between the theories of such fields in the space-time and in the space-frequency domains. We also show that the concept of cross-spectral purity, introduced by L. Mandel many years ago, plays an important role in clarifying this relationship.

The influence of the degree of cross-polarization on the Hanbury Brown-Twiss effect.

We show, by an example, that the knowledge of the degree of coherence and of the degree of polarization of a light beam incident on two photo detectors is not adequate to predict correlations in the fluctuations of the currents generated in the detectors (the Hanbury Brown-Twiss effect). The knowledge of the so-called degree of cross-polarization, introduced not long ago, is also needed.

Polarization properties of stochastic light beams in the space-time and space-frequency domains.

Although the theories of polarization in the space-time and space-frequency domains are somewhat analogous, they have been developed independently, and there is no obvious connection between them. We investigate how they are related.

Beam condition for scattering on random media.

Properties of random media are frequently investigated by studying their interactions with stochastic electromagnetic fields. However, a stochastic beam does not necessarily retain its beamlike form on scattering, and the theory of stochastic electromagnetic fields that are not beamlike is rather complicated. In this paper a necessary and sufficient condition is derived for a beam to retain its beamlike form after it is scattered on a stochastic medium. We illustrate the result by an example.

Determination of correlation functions of scattering potentials of stochastic media from scattering experiments.

The classic "Ewald-sphere construction" for determining the structure of crystalline objects from x-ray and neutron diffraction experiments is generalized to determine the correlation functions of scattering potentials of stationary random media from scattering experiments.

Cross-spectral density matrices of polarized light beams.

We show that there is no unique form of the cross-spectral density matrix of completely polarized light beams. We present three kinds of such matrices, each of which represents a beam that is completely polarized at every point. Some of the beams do not imitate monochromatic beams, in contrast to the usual assumption made in polarization optics.