We measured individual trajectories of fluorescently labeled telomeres in the nucleus of eukaryotic cells in the time range of 10 À2 -10 4 sec by combining a few acquisition methods. At short times the motion is subdiffusive with hr 2 i $ t and it changes to normal diffusion at longer times. The short times diffusion may be explained by the reptation model and the transient diffusion is consistent with a model of telomeres that are subject to a local binding mechanism with a wide but finite distribution of waiting times. These findings have important biological implications with respect to the genome organization in the nucleus. DOI: 10.1103/PhysRevLett.103.018102 PACS numbers: 87.16.Zg, 05.40.Jc, 87.15.Vv The nucleus of the eukaryotic cell contains tens of thousands of genes ($23 000 in human) organized as chromosomal DNA. This crowded environment contains packed genetic material, RNA transcripts, protein factors, and a variety of nuclear bodies. The genetic information (DNA) can be either replicated to form daughter cells, or transcribed to RNA molecules leading to protein translation. These processes depend on the ability of protein factors to locate and interact with specific DNA sequence within this packed nucleus [1], as well as on the organization and structure of chromatin in the nucleus [2]. Telomeres are the end caps of the linear eukaryotic chromosomes. They play an important role in maintaining chromosome organization and integrity throughout the cell cycle. The telomeres are protected by a number of protein factors that are collectively referred to as shelterin and can bind to either the nuclear envelope, nuclear matrix, or heterochromatin, depending on the cell species [3]. Therefore, studying the dynamics of telomeres can shed light on chromosome dynamics, the role of telomeres in genome organization, and the coordination of physical structures and biological processes in the nucleus [4].Chromosomes occupy specific nuclear volumes referred to as chromosome territories [5], and their motion is highly constrained. The diffusion of telomeres was previously studied on a limited time scale of either minutes [6] or 1-200 sec [7] and exhibited mainly normal constrained diffusion with a heterogeneous diffusion coefficient of 2-6 Â 10 À4 m 2 =s. This is significantly lower than the diffusion of small molecules such as dextran in the nucleus (10-100 m 2 =s), which reflects the dense nature of the nucleus. The dynamics of other nuclear bodies as well as messenger RNAs were also measured [8][9][10] and anomalous diffusion was found for specific DNA loci [11].In this study, we examined the diffusion properties of telomeres in the nucleus in a broad time range of almost 6 orders of magnitude (10 À2 -10 4 sec ). Such a broad time range was employed by combining two different imaging setups on the same microscope. We find that the diffusion is anomalous at short times of $10 À2 -10 3 sec . It changes to normal diffusion at longer time intervals and the diffusion constants are found to have a wide distribution...

A quantum polarized light microscope using entangled NOON states with N=2 and N=3 is shown to provide phase supersensitivity beyond the standard quantum limit. We constructed such a microscope and imaged birefringent objects at a very low light level of 50 photons per pixel, where shot noise seriously hampers classical imaging. The NOON light source is formed by combining a coherent state with parametric down-converted light. We were able to show improved phase images with sensitivity close to the Heisenberg limit.

The principles of quantum optics have yielded a plethora of ideas to surpass the classical limitations of sensitivity and resolution in optical microscopy. While some ideas have been applied in proof-of-principle experiments, imaging a biological sample has remained challenging mainly due to the inherently weak signal measured and the fragility of quantum states of light. In principle, however, these quantum protocols can add new information without sacrificing the classical information and can therefore enhance the capabilities of existing super-resolution techniques. Image scanning microscopy (ISM), a recent addition to the family of super-resolution methods, generates a robust resolution enhancement without sacrificing the signal level. Here we introduce quantum image scanning microscopy (Q-ISM): combining ISM with the measurement of quantum photon correlation allows increasing the resolution of ISM up to two-fold, four times beyond the diffraction limit. We introduce the Q-ISM principle and obtain super-resolved optical images of a biological sample stained with fluorescent quantum dots using photon antibunching, a quantum effect, as a resolution enhancing contrast mechanism. Main TextThe diffraction limit, as formulated by Abbe, sets the attainable resolution in far-field optical microscopy to about half of the visible wavelength 1 , hindering its applicability in life science studies at very small scales. Over the past two decades, several super-resolution methods have successfully overcome the diffraction limit, including emission depletion microscopy, localization microscopy and structured illumination microscopy 2-6 . The continuous and rapid improvement in detector technology has enabled two more recent developments in the field of super-resolution microscopy, which are the center of this work: quantum super-resolution microscopy and image scanning microscopy (ISM). As for the first, a surge of interest in super-resolution imaging based on quantum optics concepts 7-13 , inspired and facilitated by the progress in high temporal resolution imagers, resulted in a few successful proof-of-principle demonstrations 7,8,14 . The second, ISM, relies on a small array of fast detector and offers a two-fold enhancement of resolution 15,16 . Since ISM is compatible with a standard confocal microscope architecture it has already been integrated into commercial products.While all super-resolution modalities violate at least one of the basic assumptions of the Abbe theory, many rely on breaking more than one. For instance, stimulated emission depletion (STED) and saturated structured illumination microscopy (SSIM) breach both the assumption of a linear response of a fluorophore to the excitation light and that of a uniform illumination field 17,18 . In contrast, the few demonstrations of quantum super-resolution microscopy 7,8,14 relied solely on violating the implicit assumption, underlying Abbe's derivation, that light behaves as waves rather than particles. ISM, as well, depends on violating a single assumption, a u...

We have performed experimental quantum state tomography of NOON states with up to four photons. The measured states are generated by mixing a classical coherent state with spontaneous parametric down-conversion. We show that this method produces states which exhibit a high fidelity with ideal NOON states. The fidelity is limited by the overlap of the two-photon down-conversion state with any two photons originating from the coherent state, for which we introduce and measure a figure of merit. A second limitation on the fidelity set by the total setup transmission is discussed. We also apply the same tomography procedure for characterizing correlated photon hole states.

Despite advances in low-light-level detection, single-photon methods such as photon correlation have rarely been used in the context of imaging. The few demonstrations, for example of subdiffraction-limited imaging utilizing quantum statistics of photons, have remained in the realm of proof-of-principle demonstrations. This is primarily due to a combination of low values of fill factors, quantum efficiencies, frame rates and signal-to-noise characteristic of most available single-photon sensitive imaging detectors. Here we describe an imaging device based on a fibre bundle coupled to single-photon avalanche detectors that combines a large fill factor, a high quantum efficiency, a low noise and scalable architecture. Our device enables localization-based super-resolution microscopy in a non-sparse non-stationary scene, utilizing information on the number of active emitters, as gathered from non-classical photon statistics.

Entangled coherent states are shown to emerge, with high fidelity, when mixing coherent and squeezed vacuum states of light on a beam-splitter. These maximally entangled states, where photons bunch at the exit of a beam-splitter, are measured experimentally by Fock-state projections. Entanglement is examined theoretically using a Bell-type nonlocality test and compared with ideal entangled coherent states. We experimentally show nearly perfect similarity with entangled coherent states for an optimal ratio of coherent and squeezed vacuum light. In our scheme, entangled coherent states are generated deterministically with small amplitudes, which could be beneficial, for example, in deterministic distribution of entanglement over long distances.

The retrieval of phases from intensity measurements is a key process in many fields in science, from optical microscopy to x-ray crystallography. Here we study phase retrieval of a one-dimensional multi-phase object that is illuminated by quantum states of light. We generalize the iterative Gerchberg-Saxton algorithm to photon correlation measurements on the output plane, rather than the standard intensity measurements. We report a numerical comparison of classical and quantum phase retrieval of a small one-dimensional object of discrete phases from its far-field diffraction. While the classical algorithm was ambiguous and often converged to wrong solutions, quantum light produced a unique reconstruction with smaller errors and faster convergence. We attribute these improvements to a larger Hilbert space that constrains the algorithm.

Quantum lithography achieves phase superresolution using fragile, experimentally challenging entangled states of light. We propose a scalable scheme for creating features narrower than classically achievable with reduced use of quantum resources and, consequently, enhanced resistance to loss. The scheme is an implementation of interferometric lithography using a mixture of a spontaneous parametric down-converted entangled state with intense classical coherent light. We measure coincidences of up to four photons mimicking multiphoton absorption. The results show a narrowing of the interference fringes of up to 30% with respect to the best analogous classical scheme using only 10% of the nonclassical light required for creating NOON states.