Synthesis and analysis of entangled photonic qubits in spatial-parity space

We present the novel embodiment of a photonic qubit that makes use of one continuous spatial degree of freedom of a single photon and relies on the parity of the photon's transverse spatial distribution. Using optical spontaneous parametric down-conversion to produce photon pairs, we demonstrate the controlled generation of entangled-photon states in this new space. Specifically, two Bell states, and a continuum of their superpositions, are generated by simple manipulation of a classical parameter, the optical-pump spatial parity, and not by manipulation of the entangled photons themselves. An interferometric device, isomorphic in action to a polarizing beam splitter, projects the spatial-parity states onto an even-odd basis. This new physical realization of photonic qubits could be used as a foundation for future experiments in quantum information processing.     

六光子超纠缠态制备方案

自发参量下转换对应于一种非线性光学过程, 实验上作为一种标准方法, 人们利用自发参量下转换源产生纠缠光子对. 本文考虑由自发参量下转换源产生三对纠缠光子的情况. 通过使用由几组偏振光 束分束器、分束器和半波片等线性光学器件组成的量子线路演化三对光子, 给出了一个高效制备 包含偏振纠缠和空间纠缠的六光子超纠缠态方案. 因为方案中包含了参量下转换源产生三对纠缠光子 的所有可能情况, 所以本方案有很高的效率. 基于弱非线性介质构建了一个量子非破坏性测量装置, 用于区分光子在两指定的空间模中的两种分布情况. 特别地, 方案中可以通过合理约束在量子非破坏性测量过程中引入的非线性强度来达到实际实验所限定的数量级, 因此, 该方案易于在实验上实现.     

Scalable scheme for entangling multiple ququarts using linear optical elements

We report a scalable linear optical scheme for generating entangled states of multiple ququarts in which the individual single-ququart state is prepared with the biphoton polarization state of frequency-nondegenerate spontaneous parametric down-conversion. The output state is calculated with the full consideration of the higher order effect (double-pair events) of spontaneous parametric down-conversion. Scalability to multiple-ququart entanglement is demonstrated with examples: linear optical entanglement of three and four individual biphoton ququarts.     

One-photon and two-photon double-slit interference in spontaneous and stimulated parametric down-conversions

We theoretically discuss two-photon double-slit interference for spontaneous and stimulated parametric down-conversions and compare it with one-photon case. We show that two-photon sub-wavelength interference can exist in a general interaction of spontaneous parametric down-conversion (SPDC) for both type I and type II crystals. In low gain SPDC, interference effect can be attributed to the previous study based on two-photon entangled state. But the important fact is that the sub-wavelength interference will not be washed out even if in very high gain SPDC, revealing the macroscopic nature. We propose an alternative scheme to observe sub-wavelength interference with a joint-intensity measurement, which occurs for a type I crystal in the high gain case. The theoretical analysis shows that the effect originates from classical thermal correlation. However, we also formulate the one-photon and two-photon double-slit interference in the stimulated process, and show amplified interference patterns.     

Polarization entangled photons at x-ray energies

We show that polarization entangled photons at x-ray energies can be generated via spontaneous parametric down-conversion. Each of the four Bell states can be generated by choosing the angle of incidence and polarization of the pumping beam.     

Conditional-phase switch at the single-photon level

We present an experimental realization of a two-photon conditional phase switch, related to the " c-phis;" gate of quantum computation. This gate relies on quantum interference between photon pairs and generates entanglement between two optical modes through the process of spontaneous parametric down-conversion (SPDC). The interference effect serves to enhance the effective nonlinearity by many orders of magnitude, so it is significant at the quantum (single-photon) level. By adjusting the relative optical phase between the classical pump for SPDC and the pair of input modes, one can impress a large phase shift on one beam which depends on the presence or absence of a single photon in a control mode.     

On the Development of Controllable Sources of Single-Photon States with an Orbital Angular Momentum on the Basis of Spontaneous Parametric Down-Conversion of Light

Methods for beam shaping with nonzero orbital angular momentum are studied using diffraction optical elements with the purpose of developing a source of single-photon states based on spontaneous parametric down-conversion of light in the LiNbO₃ crystal in the cavity resonator. The probability of the coincidence of the number of photocounts in detecting signal and idle fields under pumping by a beam with the orbital angular momentum is simulated.     

Fourth-order image formation by spontaneous parametric down-conversion: The effect of anisotropy

We analyze the transfer of angular spectrum and fourth-order image formation in two-photon states generated by spontaneous parametric down-conversion in both type I and type II phase matchings. We show how the image transfer from the pump beam to the two-photon field is affected by the anisotropy of the nonlinear crystal and by the coupling between frequency and wave vector. We also show how the distortion produced by the anisotropy can be compensated by the frequency bandwidth in type II phase matching.     

Theory for quantum state of photon pairs generated from spontaneous parametric down-conversion nonlinear process

A theory is presented for the quantum state of photon pairs generated from spontaneous parametric down-conversion nonlinear process. In this theory, the influence of the final sizes of nonlinear optical crystals on optical eigenmodes is explicitly taken into consideration. It was found that these photon pairs are not in entangled quantum states. Polarization correlations between the signal beam and the idler beam are explained. It is also shown that the two photons generated from SPDC are not spatially separated, therefore the polarization correlation between the signal and idler beams is not an evidence for quantum non-locality. The text was submitted by the authors in English.     

Multimode Hong-Ou-mandel interference

We consider multimode two-photon interference at a beam splitter by photons created by spontaneous parametric down-conversion. The resulting interference pattern is shown to depend upon the transverse spatial symmetry of the pump beam. In an experiment, we employ the first-order Hermite-Gaussian modes in order to show that, by manipulating the pump beam, one can control the resulting two-photon interference behavior. We expect these results to play an important role in the engineering of quantum states of light for use in quantum information processing and quantum imaging.     

Reconstruction of the polarization states of a biphoton field

A method for reconstructing an arbitrary quantum state of an optical system in Hilbert space with dimension d = 4 is discussed. Such states can be realized using a collinear frequency-nondegenerate regime of generating spontaneous parametric down-conversion. The method has been tested for a number of polarization states of a biphoton field. The high accuracy of the reconstruction of the states (above 99%) indicates that the procedures proposed for reconstructing the quantum state of the system are adequate.     

Entangled optical vortex links

Optical vortices are lines of phase singularity which percolate through all optical fields. We report the entanglement of linked optical vortex loops in the light produced by spontaneous parametric down-conversion. As measured by using a Bell inequality, this entanglement between topological features extends over macroscopic and finite volumes. The entanglement of photons in complex three-dimensional topological states suggests the possibility of entanglement of similar features in other quantum systems describable by complex scalar functions, such as superconductors, superfluids, and Bose-Einstein condensates.     

Quantum Zeno effect in two coupled nonlinear optical processes

Consecutive nonlinear optical interactions consisting of two coupled parametric processes, namely, the nondegenerate spontaneous parametric down-conversion and up-conversion, are analyzed. The vacuum state of the input light is considered to be an unstable state decaying into a reservoir of down-converted modes, with one of the modes generated being continuously measured using the up-conversion process. Mean photon numbers at interacting frequencies are studied. Special attention is paid to the case where the nonlinear coupling coefficient for the up-conversion process is much larger than that for the nondegenerate spontaneous parametric down-conversion. It is shown that in this case the result of such consecutive interactions can be interpreted from the viewpoint of the quantum Zeno effect.     

Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides

We analyze the process of photon-pair generation with simultaneous quantum walks in a quadratic nonlinear waveguide array. We demonstrate that the spontaneous parametric down-conversion in the array allows for creating quantum states with strongly pronounced spatial correlations, which are qualitatively different from those possible in bulk crystals or through quantum walks in linear waveguide arrays. Most importantly, the photon correlations can be controlled entirely classically by varying the spatial profile of the pump beam or the phase-matching conditions.     

Realization of Three-Qubit Controlled-Phase Gate Operation with Atoms in Cavity QED System

We propose a scheme for realization of three-qubit controlled-phase gate via passing two three-level atoms through a high-Q optical cavity in a cavity QED system. In the presented protocol, the two stable ground states of the atoms act as the two controlling qubits and the zero- and one-photon Fock states of the cavity-field form the target qubit, and no auxiliary state or any measurement is required. The numerical simulation shows that the gate fidelities remain at a high level under the influence of the atomic spontaneous emission, the decay of the cavity mode and deviation of the coupling strength. The experimental feasibility of our proposal is also discussed.     

Experimental violation of Bell's inequality in spatial-parity space

We report the first experimental violation of Bell's inequality in the spatial domain using the Einstein-Podolsky-Rosen state. Two-photon states generated via optical spontaneous parametric down-conversion are shown to be entangled in the parity of their one-dimensional transverse spatial profile. Superpositions of Bell states are prepared by manipulation of the optical pump's transverse spatial parity-a classical parameter. The Bell-operator measurements are made possible by devising simple optical arrangements that perform rotations in the one-dimensional spatial-parity space of each photon of an entangled pair and projective measurements onto a basis of even-odd functions. A Bell-operator value of 2.389+/-0.016 is recorded, a violation of the inequality by more than 24 standard deviations.     

Practical implementation of multilevel quantum cryptography

The physical principles of a quantum key distribution protocol using four-level optical systems are discussed. Quantum information is encoded into polarization states created by frequency-nondegenerate spontaneous parametric down-conversion in collinear geometry. In the scheme under analysis, the required nonorthogonal states are generated in a single nonlinear crystal. All states in the selected basis are measured deterministically. The results of initial experiments on transformation of the basis polarization states of a four-level optical system are discussed.     

Polarization tomography of a narrow-band biphoton field

Narrow-band orthogonally polarized collinear frequency-degenerate biphotons are generated in the process of the spontaneous parametric down-conversion of light in a nonlinear BBO crystal placed in an optical resonator. Quantum polarization tomography and polarization transformation of the generated biphoton states are performed. The results from our experiment agree well with theoretical calculations.     

Total teleportation of zero- and one-photon entangled states in running waves

Inspired by a recent paper [2002 {\it J. Opt. B {\bf 4 316] we present an alternative scheme to teleport an entanglement of zero- and one-photon states of a running-wave field. The scheme employs only linear optical elements plus single-photon sources and detectors.     

Total teleportation of zero- and one-photon entangled states in running waves

Inspired by a recent paper [2002 J. Opt. B 4 316] we present an alternative scheme to teleport an entanglement of zero- and one-photon states of a running-wave field. The scheme employs only linear optical elements plus single-photon sources and detectors.