In the last years several theoretical papers discussed if time can be an emergent propertiy deriving from quantum correlations. Here, to provide an insight into how this phenomenon can occur, we present an experiment that illustrates Page and Wootters' mechanism of "static" time, and Gambini et al. subsequent refinements. A static, entangled state between a clock system and the rest of the universe is perceived as evolving by internal observers that test the correlations between the two subsystems. We implement this mechanism using an entangled state of the polarization of two photons, one of which is used as a clock to gauge the evolution of the second: an "internal" observer that becomes correlated with the clock photon sees the other system evolve, while an "external" observer that only observes global properties of the two photons can prove it is static."Quid est ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare velim, nescio." [1] The "problem of time" [2][3][4][5][6] in essence stems from the fact that a canonical quantization of general relativity yields the Wheeler-De Witt equation [7,8] predicting a static state of the universe, contrary to obvious everyday evidence. A solution was proposed by Page and Wootters [9, 10]: thanks to quantum entanglement, a static system may describe an evolving "universe" from the point of view of the internal observers. Energy-entanglement between a "clock" system and the rest of the universe can yield a stationary state for an (hypothetical) external observer that is able to test the entanglement vs. abstract coordinate time. The same state will be, instead, evolving for internal observers that test the correlations between the clock and the rest [9][10][11][12][13][14]. Thus, time would be an emergent property of subsystems of the universe deriving from their entangled nature: an extremely elegant but controversial idea [2,15]. Here we want to demystify it by showing experimentally that it can be naturally embedded into (small) subsystems of the universe, where Page and Wootters' mechanism (and Gambini et al. subsequent refinements [12,16]) can be easily studied. We show how a static, entangled state of two photons can be seen as evolving by an observer that uses one of the two photons as a clock to gauge the time-evolution of the other photon. However, an external observer can show that the global entangled state does not evolve.Even though it revolutionizes our ideas on time, Page and Wootters' (PaW) mechanism is quite simple [9-11]: they provide a static entangled state |Ψ whose subsystems evolve according to the Schrödinger equation for an observer that uses one of the subsystems as a clock system C to gauge the time evolution of the rest R. While the division into subsystems is largely arbitrary, the PaW model assumes the possibility of neglecting interaction among them writing the Hamiltonian of the global system as H = H c ⊗ 1 1 r + 1 1 c ⊗ H r , where H c , H r are the local terms associated with C and R, respectively and Uc(t) = e −iHct/ are the ...

We experimentally demonstrate quantum enhanced resolution in confocal fluorescence microscopy exploiting the nonclassical photon statistics of single nitrogen-vacancy color centers in diamond. By developing a general model of superresolution based on the direct sampling of the kth-order autocorrelation function of the photoluminescence signal, we show the possibility to resolve, in principle, arbitrarily close emitting centers. DOI: 10.1103/PhysRevLett.113.143602 PACS numbers: 42.50.-p, 42.30.Va, 42.50.Ar, 42.50.St In the last decade, measurement techniques enhanced by using peculiar properties of quantum light [1,2] have been successfully demonstrated in several remarkable real application scenarios, for example, interferometric measurements aimed to reveal gravitational waves and the quantum gravity effect [3,4], biological particle tracking [5], phase contrast microscopy [6], and imaging [7,8]. Very recently, a novel technique to beat the diffraction limit in microscopy that relies on the antibunching behavior of photons emitted by single fluophores has been proposed [9], and realized in wide field microscopy [10] by using an EMCCD camera.The maximum obtainable imaging resolution in classical far-field fluorescence microscopy, according to the Abbe diffraction limit, is R ≃ 0.61λ=NA, where λ is the wavelength of the light and NA is the numerical aperture of the objective. This restricts the current capability of precisely measuring the position of very small objects such as single photon emitters (color centers, quantum dots, etc.) [11][12][13][14][15][16][17][18][19], limiting their potential exploitation in the frame quantum technology [20,21]. In general, the research of methods to obtain a microscopy resolution below the diffraction limit is a topic of the utmost interest [22][23][24][25][26][27][28][29] that could provide dramatic improvement in the observation of several systems spanning from quantum dots [30] to living cells [31][32][33][34]. As a notable example, in several entanglement-related experiments using strongly coupled single photon emitters it is of the utmost importance to measure their positions with the highest spatial resolution [35]. In principle, this limitation can be overcome by recently developed microscopy techniques such as stimulated emission depletion (STED) and ground state depletion (GSD) [36,37]. Nevertheless, even if they have been demonstrated effectively able to provide superresolved imaging in many specific applications, among which are color centers in diamond [38], they are characterized by rather specific experimental requirements (dual laser excitation system, availability of luminescence quenching mechanisms by stimulated emission, nontrivial shaping of the quenching beam, high power). Furthermore, these techniques are not suitable in applications in which the fluorescence is not optically induced [39,40], so that new methods are required for those applications.Inspired by the works in [9], in this Letter we develop a comprehensive theory of superresolution ima...

The fabrication of luminescent defects in single-crystal diamond upon Sn implantation and annealing is reported. The relevant spectral features of the optical centers (emission peaks at 593.5, 620.3, 630.7, and 646.7 nm) are attributed to Sn-related defects through the correlation of their photoluminescence (PL) intensity with the implantation fluence. Single Sn-related defects were identified and characterized through the acquisition of their second-order autocorrelation emission functions, by means of Hanbury-Brown and Twiss interferometry. The investigation of their single-photon emission regime as a function of excitation laser power revealed that Sn-related defects are based on three-level systems with a 6 ns radiative decay lifetime. In a fraction of the studied centers, the observation of a blinking PL emission is indicative of the existence of a dark state. Furthermore, absorption dependence on the polarization of the excitation radiation with ∼45% contrast was measured. This work shed light on the existence of a new optical center associated with a group-IV impurity in diamond, with similar photophysical properties to the already well-known Si–V and Ge–V emitters, thus, providing results of interest from both the fundamental and applicative points of view.

We show that the wave packet of a biphoton generated via spontaneous parametric down conversion is strongly anisotropic. Its anisotropic features manifest themselves very clearly in comparison of measurements performed in two different schemes: when the detector scanning plane is perpendicular or parallel to the plane containing the crystal optical axis and the laser axis. The first of these two schemes is traditional whereas the second one gives rise to such unexpected new results as anomalously strong narrowing of the biphoton wave packet measured in the coincidence scheme and very high degree of entanglement. The results are predicted theoretically and confirmed experimentally.

A novel operational method for estimating the efficiency of quantum state tomography protocols is suggested. It is based on a priori estimation of the quality of an arbitrary protocol by means of universal asymptotic fidelity distribution and condition number, which takes minimal value for better protocol. We prove the adequacy of the method both with numerical modeling and through the experimental realization of several practically important protocols of quantum state tomography.

We discuss the concept of polarization states of four-dimensional quantum systems based on the frequency nondegenerate biphoton field. Several quantum tomography protocols were developed and implemented for the measurement of an arbitrary state of ququart. A simple method that does not rely on the interferometric technique is used to generate and measure the sequence of states that can be used for quantum communication purposes.

The novel experimental realization of four-level optical quantum systems (ququarts) is presented. We exploit the polarization properties of the frequency non-degenerate biphoton field to obtain such systems. A simple method that does not rely on interferometer is used to generate and measure the sequence of states that can be used in quantum key distribution (QKD) protocol. PACS numbers: 42.50.-p, 42.50.Dv, 03.67.-a I. Introduction. Recently multi-dimensional (D>2) quantum systems or qudits attracted much attention in context of quantum information and communication. It is partly caused by fundamental aspects of quantum theory since the usage of qudits allows one to violate Bell-type inequalities longer than with two dimensional systems (for the references see the review [1]). Much interest in qudits also comes from the application point, especially from the applied quantum key distribution (QKD). Multilevel systems are proved to be more robust against noise in the transmission channel, although measurement and preparation procedures of such systems seems to be much more technically complicated than in the case of qubits. Different aspects of the security of qudit-based protocols have been analyzed [2, 3]. Lately a proof-of-principle realization of a QKD protocol with entangled qutrits (D = 3) [4] and with qudits [5] have been demonstrated. For the last years several elegant experiments have been performed where different kinds of optical qu-dits were introduced [5, 6, 7, 8, 9, 10, 11, 12]. Recently an experiment that ensured the full control over a polarization qutrit state was demonstrated [12, 13]. However polarization qutrits do not seem to serve as a practical candidate for the multilevel QKD, since it is impossible to achieve a demanded state using only SU2 transformations that are done with linear optical elements. Meantime transformations done by these elements are needed for practical realization of QKD protocols. In this Letter we present the results of the experimental preparation, transformation, and measurement carried out with polarization based ququarts or quantum systems with dimensionality D = 4. II. Polarization ququarts and their properties. If one considers the two-photon field, generated via spontaneous parametric down-conversion (SPDC) process, then the pure polarization state can be written as a superpo-sition of four basic components:

We show that the wave packet of a biphoton generated via spontaneous parametric down-conversion is strongly anisotropic. Its anisotropic features manifest themselves very clearly in comparison with measurements performed in two different schemes: When the detector scanning plane is perpendicular or parallel to the plane containing the crystal optical axis and the laser axis. The first of these two schemes is traditional whereas the second one gives rise to such unexpected results, such as anomalously strong narrowing of the biphoton wave packet measured in the coincidence scheme and very high degree of entanglement. The results are predicted theoretically and confirmed experimentally.