We discuss quantum and classical aspects of two-photon interference in light transmission through disordered media. We show that disorder is the main factor that suppresses the interference, whatever the quantum state of the incident light. Secondarily, the two-photon interference is affected by the quantum nature of light (i.e., the well-defined number of photons in the two-photon entangled and Fock states as compared to the coherent state). And finally, entanglement is a resource that allows to prepare two-photon states with special symmetries with respect to the interchange of the photons and, in particular, the states with bosonic and fermionic symmetries. The two-photon interference is more robust for the latter states and its sign can be inverted for the fermionic state.
We consider the propagation of several entangled photons through an elastically scattering medium and study statistical properties of their speckle patterns. We find the spatial correlations of multiphoton speckles and their sensitivity to changes of system parameters. Our analysis covers both the directed-wave regime, where rays propagate almost ballistically while experiencing small-angle diffusion, and the real-space diffusive regime. We demonstrate that long-range correlations of the speckle patterns dominate experimental signatures for large-aperture photon detectors. We also show that sp…
We calculate the statistical distribution P_2(I_2) of the speckle pattern produced by a photon pair current I_2 transmitted through a random medium, and compare with the single-photon speckle distribution P_1(I_1). We show that the purity Tr rho^2 of a two-photon density matrix rho can be directly extracted from the first two moments of P_1 and P_2. A one-to-one relationship is derived between P_1 and P_2 if the photon pair is in an M-dimensional entangled pure state. For M>>1 the single-photon speckle disappears, while the two-photon speckle acquires an exponential distribution. The exponenti…
Topological insulators combine insulating properties in the bulk with scattering-free transport along edges, supporting dissipationless unidirectional energy and information flow even in the presence of defects and disorder. The feasibility of engineering quantum Hamiltonians with photonic tools, combined with the availability of entangled photons, raises the intriguing possibility of employing topologically protected entangled states in optical quantum computing and information processing. However, while two-photon states built as a product of two topologically protected single-photon states …
We report the experimental realization and the characterization of polarization and momentum hyperentangled two photon states, generated by a new parametric source of correlated photon pairs. By adoption of these states an "all versus nothing" test of quantum mechanics was performed. The two photon hyperentangled states are expected to find at an increasing rate a widespread application in state engineering and quantum information. PACS: 03.65.Ud, 03.67.Mn, 42.65. Lm
While the theoretical studies in waveguide quantum electrodynamics predominate with single-photon and two-photon Fock state (photon number states) input, the experiments are primarily carried out using a faint coherent light. We create a theoretical toolbox to compare and contrast linear and nonlinear light scattering by a two-level or a three-level emitter embedded in an open waveguide carrying Fock state or coherent state inputs. We identify rules to compare light transport properties, the Kerr, and cross-Kerr nonlinearities of the medium for the two types of inputs. A generalized descriptio…
We introduce an all-versus-nothing proof of impossibility of Einstein-Podolsky-Rosen's local elements of reality for two photons entangled both in polarization and path degrees of freedom, which leads to a Bell's inequality where the classical bound is 8 and the quantum prediction is 16. A simple estimation of the detection efficiency required to close the detection loophole using this proof gives eta > 0.69. This efficiency is lower than that required for previous proposals.
Using entropic inequalities for Shannon entropies new inequalities for some classical polynomials are obtained. To this end, photon distribution functions for one-, two- and multi-mode squeezed states in terms of Hermite, Laguerre, Legendre polynomials and Gauss' hypergeometric functions are used. The dependence between the violation of the quadrature uncertainty relation, the sign and the existence of the distribution function of such states is considered.
We report on the effects of quantum interference induced by transmission of an arbitrary number of optical quantum states through a multiple scattering medium. We identify the role of quantum interference on the photon correlations and the degree of continuous variable entanglement between two output modes. It is shown that the effect of quantum interference survives averaging over all ensembles of disorder and manifests itself as increased photon correlations giving rise to photon anti-bunching. Finally, the existence of continuous variable entanglement correlations in a volume speckle patter…
We develop and exploit a source of two-photon four-dimensional entanglement to report the first two-particle all-versus-nothing test of local realism with a linear optics setup, but without resorting to a non-contextuality ssumption. Our experimental results are in well agreement with quantum mechanics while in extreme contradiction with local realism. Potential applications of our experiment are briefly discussed.
In our work, we compare three teleportation protocols: the original protocol, the photon subtraction protocol, and the protocol with a cubic phase gate. We evaluate the fidelity of each protocol using the example of teleportation of the squeezed state and the Schrodinger's cat state. We show that, under equal conditions, the teleportation scheme with a cubic phase gate achieves significantly higher fidelity than the other protocols considered.
We study the physics of four-photon states generated in spontaneous parametric down-conversion with a pulsed pump field. In the limit where the coherence time of the photons t_c is much shorter than the duration of the pump pulse Delta t, the four photons can be described as two independent pairs. In the opposite limit, the four photons are in a four-particle entangled state. Any intermediate case can be characterized by a single parameter chi, which is a function of t_c/Delta t. We present a direct measurement of chi through a simple experimental setup. The full theoretical analysis is also p…
It is shown that the Greenberger-Horne-Zeilinger theorem can be generalized to the case with only two entangled particles. The reasoning makes use of two photons which are maximally entangled both in polarization and in spatial degrees of freedom. In contrast to Cabello's argument of "all versus nothing" nonlocality with four photons [Phys. Rev. Lett. 87, 010403 (2001)], our proposal to test the theorem can be implemented with linear optics and thus is well within the reach of current experimental technology.
We devise an approach to characterizing the intricate interplay between classical and quantum interference of two-photon states in a network, which comprises multiple time-bin modes. By controlling the phases of delocalized single photons, we manipulate the global mode structure, resulting in distinct two-photon interference phenomena for time-bin resolved (local) and time-bucket (global) coincidence detection. This coherent control over the photons' mode structure allows for synthesizing two-photon interference patterns, where local measurements yield standard Hong-Ou-Mandel dips while the gl…
We investigate two different kinds of quantum trajectories for a nonlinear photon resonator subject to two-photon pumping, a configuration recently studied for the generation of photonic Schroedinger cat states. In the absence of feedback control and in the strong-driving limit, the steady-state density matrix is a statistical mixture of two states with equal weight. While along a single photon-counting trajectory the systems intermittently switches between an odd and an even cat state, we show that upon homodyne detection the situation is different. Indeed, homodyne quantum trajectories revea…
We image with cameras entangled photon light transmitted through a random medium. Near-field and far-field spatial quantum correlations show that entangled photon pairs (bi-photons) generated by spontaneous optical parametric down-conversion exhibit speckle pattern. In contrast, no information from the random medium can be extracted using incoherent light issued from one photon of the pair. Although these measurements require several hours to record thousands of image pairs, our method is instantaneous for the recording of one pair of twin images and involve all the photons of the images.
The creation of specified quantum states is important for most, if not all, applications in quantum computation and communication. The quality of the state preparation is therefore an essential ingredient in any assessment of a quantum-state gun. We show that the fidelity, under the standard definitions is not sufficient to assess quantum sources, and we propose a new measure of suitability that necessarily depends on the application for the source. We consider the performance of single-photon guns in the context of quantum key distribution (QKD) and linear optical quantum computation. Single-…
We consider a coupled-cavity array (CCA), where one cavity interacts with a two-level atom under the rotating-wave approximation. We investigate the excitation transport dynamics across the array, which arises in the atom's emission process into the CCA vacuum. Due to the known formation of atom-photon bound states, partial field localization and atomic population trapping in general take place. We study the functional dependance on the coupling strength of these two phenomena and show that the threshold values beyond which they become significant are different. As the coupling strength grows …
We compare effects of decoherence and detection inefficiency on entangled coherent states (ECSs) and entangled photon pairs (EPPs), both of which are known to be particularly useful for quantum information processing (QIP). When decoherence effects caused by photon losses are heavy, the ECSs outperform the EPPs as quantum channels for teleportation both in fidelities and in success probabilities. On the other hand, when inefficient detectors are used, the teleportation scheme using the ECSs suffers undetected errors that result in the degradation of fidelity, while this is not the case for the…
Lloyd [1] proved that a large performance gain accrues from use of entanglement in single-photon target detection within a lossy, noisy environment when compared to what can be achieved with unentangled single-photon states. We show that the performance of Lloyd's "quantum illumination" system is, at best, equal to that of a coherent-state transmitter, and may be substantially worse. Nevertheless, as shown in [2], quantum illumination may offer a significant performance gain when operation is not limited to the single-photon regime.
When a laser beam passes through a rotating ground glass (RGG), the scattered light exhibits thermal statistics. This is extensively used in speckle imaging. This scattering process has not been addressed in photon picture and is especially relevant if non-classical light is scattered by the RGG. We develop the photon picture for the scattering process using the Bose statistics for distributing $N$ photons in $M$ pixels. We obtain analytical form for the P-distribution of the output field in terms of the P-distribution of the input field. In particular we obtain a general relation for the $n$-…
We discuss theoretically the concept of spatial resolution in near-field scanning optical microscopy (NSOM) in light of a recent work [Opt. Express 17 (2009) 19969] which reported on the achievement of active tips made of a single ultrasmall fluorescent nanodiamond grafted onto the apex of a substrate tip and on their validation in NSOM imaging. Since fluorescent nanodiamonds tend to decrease steadily in size, we assimilate a nanodiamond-based tip to a point-like single photon source and compare its ultimate resolution with that offered by standard metal-coated aperture NSOM tips. We demonstra…
We develop a theoretical analysis of four-wave mixing used to generate photon pairs useful for quantum information processing. The analysis applies to a single mode microstructured fibre pumped by an ultra-short coherent pulse in the normal dispersion region. Given the values of the optical propagation constant inside the fibre, we can estimate the created number of photon pairs per pulse, their central wavelength and their respective bandwidth. We use the experimental results from a picosecond source of correlated photon pairs using a micro-structured fibre to validate the model. The fibre is…
We investigate two-photon quantum interference in an opaque scattering medium that intrinsically supports $10^6$ transmission channels. By adaptive spatial phase-modulation of the incident wavefronts, the photons are directed at targeted speckle spots or output channels. From $10^3$ experimentally available coupled channels, we select two channels and enhance their transmission, to realize the equivalent of a fully programmable $2\times2$ beam splitter. By sending pairs of single photons from a parametric down-conversion source through the opaque scattering medium, we observe two-photon quantu…
Classical versus non-classical photon states for detecting vacuum non-linearity
Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿罗森多夫赫尔姆霍兹中心）；The Extreme Light Infrastructure ERIC, ELI Beamlines Facility（极端光基础设施欧洲研究联盟，ELI光束线设施）；Institut für Theoretische Physik, Technische Universität Dresden（德累斯顿工业大学理论物理研究所）
Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon number distribution of a linear optical interferometric network, which is fed with single-photon Fock state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other than the Fock states) to a linear optical network and suitable output detection strategies are also of similar computational complexity as boson sampling. We consider the states that differ from the Fo…
Indistinguishable quantum emitters confined to length scales smaller than the wavelength of the light become superradiant. Compared to uncorrelated and distinguishable emitters, superradiance results in qualitative modifications of optical signals such as photon coincidences. However, recent experiments revealed that similar signatures can also be obtained in situations where emitters are too far separated to be superradiant if correlations between emitters are induced by the wave function collapse during an emission-angle-selective photon detection event. Here, we compare two sources for coop…
Based on modern quantum measurement theory, we use Zurek's "triple model" to study, from the viewpoint of quantum information theory, the wave and particle nature of a photon in a symmetric Mach-Zehnder interferometer. In the process of quantum measurement, the state of both the system and the detector is not an entangled state but a correlated state. We find that the information gain about the photon is related to the correlations (including classical and quantum correlations) between the photon and the detector. We also derive the relationship between the information gain and the fringe visi…
We consider the problem of obtaining maximally entangled photon states at distance in the presence of loss. We compare the efficiency of two different schemes in establishing $N$ shared ebits: i) $N$ single ebit states with the qubit encoded on polarization; ii) a single continuous variable entangled state (emode) assisted by optimal local operation and classical communication (LOCC) protocol in order to obtain a $2^N$-dimensional maximally entangled state, with qubits encoded on the photon number.
In practical quantum cryptography, the source sometimes produces multi-photon pulses, thus enabling the eavesdropper Eve to perform the powerful photon-number-splitting (PNS) attack. Recently, it was shown by Curty and Lutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not always the optimal attack when two photons are present: if errors are present in the correlations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Eve gains a larger amount of information using another attack based on a 2->3 cloning machine. In this work, we extend this analysis to all distances…
We propose a flexible numerical framework for extracting the energy spectra and photon transfer dynamics of a unit kagome cell with disordered cavity-cavity couplings under realistic experimental conditions. A projected-entangled pair state (PEPS) ansatz to the many-photon wavefunction allows to gain a detailed understanding of the effects of undesirable disorder in fabricating well-controlled and scalable photonic quantum simulators. The correlation functions associated with the propagation of two-photon excitations reveal intriguing interference patterns peculiar to the kagome geometry and p…
Photon statistics of superbunching pseudothermal light
Key Laboratory of Multifunctional Materials and Structures, Ministry of Education & International Center for Dielectric Research, School of Electronic Science and Engineering, Xi’an Jiaotong University（多功能材料与结构教育部重点实验室、国际介电研究中心，西安交通大学电子科学与工程学院）；The Key Laboratory of Weak Light Nonlinear Photonics (Nankai University, Tianjin 300457), Ministry of Education, China（弱光非线性光子学教育部重点实验室（南开大学））；MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Department of Applied Physics, Xi’an Jiaotong University（凝聚态物质非平衡合成与调制教育部重点实验室，西安交通大学应用物理系）
A theoretical comparison of the electronic excitation and ionisation behaviour of molecular hydrogen oriented either parallel or perpendicular to a linear polarised laser pulse is performed. The investigation is based on a non-perturbative treatment that solves the full time-dependent Schrödinger equation of both correlated electrons within the fixed-nuclei approximation and the dipole. Results are shown for two different laser pulse lengths and intensities as well as for a large variety of photon frequencies starting in the 1- and reaching into the 6-photon regime. In order to investigate the…
In this article we make a comparison between the behavior of entanglement and quantum degree of polarization for a special class of states of the radiation field, namely the Bell-type diagonal mixed states. For the three-photon mixed states we have plotted the concurrence and the Chernoff quantum degree of polarization in terms of the parameter, which defines the state. We find the the entanglement and the quantum degree of polarization are incomparable measures.
We study the experimental realisation of quantum teleportation as performed by Bouwmeester {\em et al}. [Nature {\bf 390}, 575 (1997)] and the adjustments to it suggested by Braunstein and Kimble [Nature {\bf 394}, 841 (1998)]. These suggestions include the employment of a detector cascade and a relative slow-down of one of the two down-converters. We show that coincidences between photon-pairs from parametric down-conversion automatically probe the non-Poissonian structure of these sources. Furthermore, we find that detector cascading is of limited use, and that modifying the relative strengt…
