The violation of the Cauchy-Schwarz and Bell inequalities ranks among the major evidence of the genuinely quantum nature of an emitter. The conventional theoretical approaches associate operators with spectral lines to study correlations between photons from real-state transitions. Instead, we use a formalism that studies directly correlations between the physical reality---the photons---with no prejudice as to their origin. This allows us to extend photon correlations to all frequencies in all the possible windows of detection and to reveal landscapes of two-photon correlations that delineate regions of quantum emission, i.e., where classical inequalities are violated. We show that quantum correlations are rooted in the joint emission of two photons involving virtual states of the emitter instead of, as previously assumed, cascaded transitions between real states. As a result, correlations can be optimized in a process akin to distillation by keeping only the emission which is quantum and filtering out that which is not.
The violation of the Cauchy-Schwarz and Bell inequalities ranks among the major evidence of the genuinely quantum nature of an emitter. The conventional theoretical approaches associate operators with spectral lines to study correlations between photons from real-state transitions. Instead, we use a formalism that studies directly correlations between the physical reality---the photons---with no prejudice as to their origin. This allows us to extend photon correlations to all frequencies in all the possible windows of detection and to reveal landscapes of two-photon correlations that delineate regions of quantum emission, i.e., where classical inequalities are violated. We show that quantum correlations are rooted in the joint emission of two photons involving virtual states of the emitter instead of, as previously assumed, cascaded transitions between real states. As a result, correlations can be optimized in a process akin to distillation by keeping only the emission which is quantum and filtering out that which is not.
The violation of the Cauchy-Schwarz and Bell inequalities ranks among the major evidences of the genuinely quantum nature of an emitter. We show that by dispensing from the usual approximation of mode correlations and studying directly correlations between the physical reality -the photons- these violations can be optimized. This is achieved by extending the concept of photon correlations to all frequencies in all the possible windows of detections, with no prejudice to the supposed origin of the photons. We identify the regions of quantum emission as rooted in collective de-excitation involving virtual states instead of, as previously assumed, cascaded transitions between real states.
Two-color second-order correlations of the light scattered near-resonantly by a quantum dot were measured by means of spectrally filtered coincidence detection. The effects of filter frequency and bandwidth were studied under monochromatic laser excitation, and a complete two-photon spectrum was reconstructed. The two-photon spectrum exhibits a rich structure associated with both real and virtual two-photon transitions down the ``dressed states'' ladder. Photon pairs generated via virtual transitions are found to violate the Cauchy-Schwarz inequality by a factor of 60. Our experiments are well described by the theoretical expressions obtained by del Valle et al. [Phys. Rev. Lett. 109, 183601 (2012)] via time- and normally-ordered correlation functions.
A review is given of correlation experiments in optics which explicitly distinguish between the predictions of classical and quantum theory. In particular, the Cauchy-Schwarz and Bell's inequalities and the phenomena of photon antibunching and squeezing are discussed. The violation of classical inequalities is shown to be associated with the nonexistence of a positive Glauber-Sudarshan P function. An example is given of a dissipative system where a violation of Bell's inequality occurs.
Self-assembled semiconductor quantum dots have attracted considerable interest recently, ranging from fundamental studies of quantum optics to advanced applications in the field of quantum information science. With their atom-like properties, quantum dot based nanophotonic devices may also substantially contribute to the development of quantum computers. This work presents experimental progress towards the understanding of light-matter interactions that occur beyond well-understood monochromatic resonant light scattering processes in semiconductor quantum dots. First, we report measurements of resonance fluorescence under bichromatic laser excitation. With the inclusion of a second laser, both first-order and second-order correlation functions are substantially altered. Under these conditions, the scattered light exhibits a rich spectrum containing many spectral features that lead to a range of nonlinear multiphoton dynamics. These observations are discussed and compared with a theoretical model. Second, we investigated the light scattered by a quantum dot in the presence of spectral filtering. By scanning the tunable filters placed in front of each detector of a Hanbury-Brown and Twiss setup and recording coincidence measurements, a \\two-photon spectrum" has been experimentally reconstructed for the first time. The two-photon spectrum contains a wealth of information about the cascaded emission involved in the scattering process, such as transitions occurring via virtual intermediate states. Our measurements also reveal that the scattered frequency-filtered light from a quantum dot violates the Cauchy-Schwarz inequality. Finally, Franson-interferometry has been performed using spectrally filtered light from quantum dot resonance fluorescence. Visibilities exceeding the classical limit were demonstrated by using a pair of folded Mach-Zehnder interferometers, paving the way for producing single time-energy entangled photon pairs that could violate Bell's inequalities.
Abstract. We apply our recently developed theory of frequency-filtered and time-resolved N-photon correlations [1] to study the two-photon spectra of a variety of systems of increasing complexity: single mode emitters with two limiting statistics (one harmonic oscillator or a two-level system) and the various combinations that arise from their coupling. We consider both the linear and nonlinear regimes under incoherent excitation. We find that even the simplest systems display a rich dynamics of emission, not accessible by simple single photon spectroscopy. In the strong coupling regime, novel two-photon emission processes involving virtual states are revealed. Furthermore, two general results are unraveled by two-photon correlations with narrow linewidth detectors: i) filtering induced bunching and ii) breakdown of the semi-classical theory. We show how to overcome this shortcoming in a fully-quantized picture. PACS numbers: 42.50.Ar,42.50.Lc,05.10.Gg,42.25.Kb,42.79.Pw ar X iv
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation. In particular, within the framework of a standard Bell experiment, i.e., a Bell inequality test that is directly performed on a single copy of a quantum state r, we have derived two algorithms to determine, respectively, a lower bound and an upper bound on the strength of correlations that r can offer for any given Bell inequality. Both of these algorithms make use convex optimization techniques in the form of a semidefinite program. By examples, we show that these algorithms can often be used in tandem, in conjunction with convexity arguments, to determine if a quantum state can offer nonclassical correlations and hence violates a given Bell inequality. On the other hand, since a standard Bell experiment typically involves measurements over many copies of the quantum systems, we have also investigated the possibility of enhancing the strength of nonclassical correlation by, instead, performing collective measurements on multiple copies of the quantum systems. Our findings show that even without postselection, such joint measurements may also lead to stronger nonclassical correlations, and hence a better Bell inequality violation. Meanwhile, previous studies have indicated that entangled state admitting locally causal models may still lead to observable nonclassical correlations if, prior to a standard Bell experiment, the state is subjected to some appropriate local preprocessing. This phenomenon of hidden nonlocality was discovered more than a decade ago, but to date, it is still not known if all entangled states can demonstrate nonclassical correlations through these more sophisticated Bell experiments. A key result in this thesis then consists of showing that for all bipartite entangled states, observable nonclassical correlations, in the form of a Bell-CHSH inequality violation, can indeed be derived if we allow both local preprocessing and the usage of shared ancillary state which by itself does not violate the Bell-CHSH inequality. This establishes a kind of equivalence between bipartite entanglement and states that cannot be simulated by classical correlations. In summary, for a standard Bell experiment where no local preprocessing on a quantum state r is allowed, we have provided two algorithms that can be used in tandem to determine if r can be simulated by a locally causal theory, whereas in the scenario where local preprocessing is allowed, we have demonstrated that bipartite entangled states are precisely those which cannot always be simulated classically.