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Spin defects in atomically thin two-dimensional (2D) materials such as hexagonal boron nitride (hBN) attract significant attention for their potential quantum applications. The layered host materials not only facilitate seamless integration with optoelectronic devices but also enable the formation of heterostructures with on-demand functionality. Furthermore, their atomic thickness renders them particularly suitable for sensing applications. However, the short coherence times of the spin defects in hBN limit them in quantum applications that require extended coherence time. One primary reason is that both boron and nitrogen atoms have non-zero nuclear spins. Here, we present another 2D material germanium disulfide ($\beta$-GeS$_2$) characterized by a wide bandgap and potential nuclear-spin-free lattice. This makes it as a promising host material for spin defects that possess long-coherence time. Our findings reveal the presence of more than two distinct types of spin defects in single-crystal $\beta$-GeS$_2$. Coherent control of one type defect has been successfully demonstrated at both 5 K and room temperature, and the coherence time $T_2$ can achieve tens of microseconds, 100-folds of that of negatively charged boron vacancy (V$_{\text{B}}^-$) in hBN, satisfying the minimal threshold required for metropolitan quantum networks--one of the important applications of spins. We entatively assign the observed optical signals come from substitution defects. Together with previous theoretical prediction, we believe the coherence time can be further improved with optimized lattice quality, indicating $\beta$-GeS$_2$ as a promising host material for long-coherence-time spins., Comment: 8 pages, 5 figures

Narrow optical resonances of atoms or molecules have immense significance in various precision measurements, such as testing fundamental physics and the generation of primary frequency standards. In these studies, accurate transition centers derived from fitting the measured spectra are demanded, which critically rely on the knowledge of spectral line profiles. Here, we propose a new mechanism of Fano-like resonance induced by distant discrete levels %in atoms or molecules and experimentally verify it with Doppler-free spectroscopy of vibration-rotational transitions of CO$_2$. The observed spectrum has an asymmetric profile and its amplitude increases quadratically with the probe laser power. Our results facilitate a broad range of topics based on narrow transitions. %, such as optical clocks, determination of fundamental physical constants, and quantum memory., Comment: 6 pages, 4 figures

Optically addressable spin defects in wide-bandage semiconductors as promising systems for quantum information and sensing applications have attracted more and more attention recently. Spin defects in two-dimensional materials are supposed to have unique superiority in quantum sensing since their atomatic thickness. Here, we demonstrate that the negatively boron charged vacancy (V$ _\text{B}^{-} $) with good spin properties in hexagonal boron nitride can be generated by ion implantation. We carry out optically detected magnetic resonance measurements at room temperature to characterize the spin properties of V$ _\text{B}^{-} $ defects, showing zero-filed splitting of $ \sim $ 3.47 GHz. We compare the photoluminescence intensity and spin properties of V$ _\text{B}^{-} $ defects generated by different implantation parameters, such as fluence, energy and ion species. With proper parameters, we can create V$ _\text{B}^{-} $ defects successfully with high probability. Our results provide a simple and practicable method to create spin defects in hBN, which is of great significance for integrated hBN-based devices.

Hexagonal boron nitride (hBN) has recently been demonstrated to contain optically polarized and detected electron spins that can be utilized for implementing qubits and quantum sensors in nanolayered-devices. Understanding the coherent dynamics of microwave driven spins in hBN is of crucial importance for advancing these emerging new technologies. Here, we demonstrate and study the Rabi oscillation and related dynamical phenomena of the negatively charged boron vacancy ($\rm V_B^-$) spins in hBN. We report on different dynamics of the $\rm V_B^-$ spins at weak and strong magnetic fields. In the former case the defect behaves like a single electron spin system, while in the latter case it behaves like a multi-spin system exhibiting the multiple-frequency dynamical oscillation like clear beat in Ramsey fringes. We also carry out theoretical simulations for the spin dynamics of $\rm V_B^-$ and reveal that the nuclear spins can be driven via the strong electric-nuclear coupling existing in $\rm V_B^-$ center, which can be modulated by the magnetic field and microwave field., Comment: 9 pages, 5 figures

Two-dimensional hexagonal boron nitride (hBN) has attracted large attentions as platforms for realizations for integrated nanophotonics and collective effort has been focused on the spin defect centers. Here, the temperature dependence of the resonance spectrum in the range of 5-600 K is investigated. The zero-field splitting (ZFS) parameter D is found to decrease monotonicly with increasing temperature and can be described by Varshni empirical equation perfectly, while E almost does not change. We systematically study the differences among different hBN nanopowders and provide an evidence of edge effects on ODMR of VB- defects. Considering the proportional relation between D and reciprocal of lattice volume, the thermal expansion might be the dominant reason for energy-level shifts. We also demonstrate that the VB- defects still exist stably at least at 600 K. Moreover, we propose a scheme for detecting laser intensity using the VB- defects in hBN nanopowders, which is based on the obvious dependence of its D value on laser intensity. Our results are helpful to gain insight into the spin properties of VB- and for the realizations of miniaturized, integrated thermal sensor.

During the last ten years, the studies on non-Markovian open system dynamics has become increasingly popular and having contributions from diverse set of research communities. This interest has arisen due to fundamental problematics how to define and quantify memory effects in the quantum domain, how to exploit and develop applications based on them, and also due to the question what are the ultimate limits for controlling open system dynamics. We give here a simple theoretical introduction to the basic approaches to define and quantify quantum non-Markovianity -- also highlighting their connections and differences. In addition to the importance of the development for open quantum systems studies, we also discuss the implications of the progress for other fields including, e.g., formal studies of stochastic processes and quantum information science, and conclude with possible future directions the recent developments open., Comment: 7 pages. Perspective Article on the theory of quantifying non-Markovianity

Recent developments in practical quantum engineering and control techniques have allowed significant developments for experimental studies of open quantum systems and decoherence engineering. Indeed, it has become possible to test experimentally various theoretical, mathematical, and physical concepts related to non-Markovian quantum dynamics. This includes experimental characterization and quantification of non-Markovian memory effects and proof-of-principle demonstrations how to use them for certain quantum communication and information tasks. We describe here recent experimental advances for open system studies, focussing in particular to non-Markovian dynamics including the applications of memory effects, and discuss the possibilities for ultimate control of decoherence and open system dynamics., Comment: 7 pages. Perspective Article on the experiments of non-Markovian quantum dynamics

Recently, the tensor network states (TNS) methods have proven to be very powerful tools to investigate the strongly correlated many-particle physics in one and two dimensions. The implementation of TNS methods depends heavily on the operations of tensors, including contraction, permutation, reshaping tensors, SVD and son on. Unfortunately, the most popular computer languages for scientific computation, such as Fortran and C/C++ do not have a standard library for such operations, and therefore make the coding of TNS very tedious. We develop a Fortran2003 package that includes all kinds of basic tensor operations designed for TNS. It is user-friendly and flexible for different forms of TNS, and therefore greatly simplifies the coding work for the TNS methods.

We introduce a scheme for remote entanglement generation for the photon polarization. The technique is based on transferring the initial frequency correlations to specific polarization-frequency correlations by local dephasing and their subsequent removal by frequency up-conversion. On fundamental level, our theoretical results show how to create and transfer entanglement, to particles which never interact, by means of local operations. This possibility stems from the multi-path interference and its control in frequency space. For applications, the developed techniques and results allow for the remote generation of entanglement with distant parties without Bell state measurements and opens the perspective to probe frequency-frequency entanglement by measuring the polarization state of the photons., Comment: 8 pages

Non-reciprocal devices, such as circulators and isolators, are indispensable components in classical and quantum information processing in an integrated photonic circuit. Aside from those applications, the non-reciprocal phase shift is of fundamental interest for exploring exotic topological photonics, such as the realization of chiral edge states and topological protection. However, incorporating low optical-loss magnetic materials into a photonic chip is technically challenging. In this study, we experimentally demonstrate non-magnetic non-reciprocity using optomechanical interactions in a whispering-gallery microresonator, as proposed by Hafezi and Rabl. Optomechanically induced non-reciprocal transparency and amplification are observed, and a non-reciprocal phase shift of up to 40 degrees is demonstrated in this study. The results of this study represent an important step towards integrated all-optical controllable isolators and circulators, as well as non-reciprocal phase shifters., Comment: 5 pages, 4 Figures

Establishing a quantum interface between different physical systems is of special importance for developing the practical versatile quantum networks. Entanglement between low- and high-lying atomic spin waves is essential for building up Rydberg-based quantum information engineering, otherwhile be more helpful to study the dynamics behavior of entanglement under external pertur- bations. Here, we report on the successful storage of a single photon as a high-lying atomic spin wave in quantum regime. Via storing a K-vector entanglement between single photon and lowly lying spin wave, we thereby experimentally realize the entanglement between low- and high-lying atomic spin waves in two separated atomic systems. This makes our experiment the primary demonstration of Rydberg quantum memory of entanglement, making a primary step toward the construction of a hybrid quantum interface., Comment: Final version

The non-Markovianity is a prominent concept of the dynamics of the open quantum systems, which is of fundamental importance in quantum mechanics and quantum information. Despite of lots of efforts, the experimentally measuring of non-Markovianity of an open system is still limited to very small systems. Presently, it is still impossible to experimentally quantify the non-Markovianity of high dimension systems with the widely used Breuer-Laine-Piilo (BLP) trace distance measure. In this paper, we propose a method, combining experimental measurements and numerical calculations, that allow quantifying the non-Markovianity of a $N$ dimension system only scaled as $N^2$, successfully avoid the exponential scaling with the dimension of the open system in the current method. After the benchmark with a two-dimension open system, we demonstrate the method in quantifying the non-Markovanity of a high dimension open quantum random walk system.

Biexciton cascade process in self-assembled quantum dots (QDs) provides an ideal system for deterministic entangled photon pair source, which is essential in quantum information science. The entangled photon pairs have recently be realized in experiments after eliminating the FSS of exciton using a number of different methods. However, so far the QDs entangled photon sources are not scalable, because the wavelengths of the QDs are different from dot to dot. Here we propose a wavelength tunable entangled photon emitter on a three dimensional stressor, in which the FSS and exciton energy can be tuned independently, allowing photon entanglement between dissimilar QDs. We confirm these results by using atomistic pseudopotential calculations. This provides a first step towards future realization of scalable entangled photon generators for quantum information applications.

We investigate the electric field tuning of the phonon-assisted hole spin relaxation in single self-assembled In$_{1-x}$Ga$_{x}$As/GaAs quantum dots, using an atomistic empirical pseudopotential method. We find that the electric field along the growth direction can tune the hole spin relaxation time for more than one order of magnitude. The electric field can prolong or shorten the hole spin lifetime and the tuning shows an asymmetry in terms of the field direction. The asymmetry is more pronounced for the taller the dot. The results show that the electric field is an effective way to tune the hole spin-relaxation in self-assembled QDs.

We show that noncollinear Andreev reflections can be induced at interfaces of semiconductor nanowires with spin-orbit coupling, Zeeman splitting and proximity-induced superconductivity. In a noncollinear local Andreev reflection, the spin polarizations of the injected and the retro-reflected carriers are typically at an angle which is tunable via system parameters. While in a nonlocal transport, this noncollinearity enables us to identify and block, at different voltage configurations, the noncollinear cross Andreev reflection and the direct charge transfer processes. We demonstrate that the intriguing noncollinearity originates from the spin-dependent coupling between carriers in the lead and the lowest discrete states in the wire, which, for a topological superconducting nanowire, are related to the overlap-induced hybridization of Majorana edge states in a finite system. These interesting phenomena can be observed in semiconductor nanowires of experimentally relevant lengths, and are potentially useful for spintronics., Comment: 7 pages, 5 figures. With significant modifications

Recently, a series of different measures quantifying memory effects in the quantum dynamics of open systems has been proposed. Here, we derive a mathematical representation for the non-Markovianity measure based on the exchange of information between the open system and its environment which substantially simplifies its numerical and experimental determination, and fully reveals the locality and universality of non-Markovianity in the quantum state space. We further illustrate the application of this representation by means of an all-optical experiment which allows the measurement of the degree of memory effects in a photonic quantum process with high accuracy., Comment: 5 pages, 5 figures

We have investigated the magnetic structure and ferroelectricity in RbFe(MoO$_4$)$_2$ via first-principles calculations. Phenomenological analyses have shown that ferroelectricity may arise due to both the triangular chirality of the magnetic structure, and through coupling between the magnetic helicity and the ferroaxial structural distortion. Indeed, it was recently proposed that the structural distortion plays a key role in stabilising the chiral magnetic structure itself. We have determined the relative contribution of the two mechanisms via \emph{ab-initio} calculations. Whilst the structural axiality does induce the magnetic helix by modulating the symmetric exchange interactions, the electric polarization is largely due to the in-plane spin triangular chirality, with both electronic and ionic contributions being of relativistic origin. At the microscopic level, we interpret the polarization as a secondary steric consequence of the inverse Dzyaloshinskii-Moriya mechanism and accordingly explain why the ferroaxial component of the electric polarization must be small.

We propose a linear compression technique for the time interval distribution of photon pairs. Using a partially frequency-entangled two-photon (TP) state with appropriate mean time width, the compressed TP time interval width can be kept in the minimum limit set by the phase modulation, and is independent of its initial width. As a result of this effect, ultra-narrow TP time interval distribution can be compressed with relatively slow phase modulators to decrease the damage of the phase-instability arising from the phase modulation process., Comment: 4 pages, 8 figures

In this Letter, we proposed and experimentally demonstrated a method to detect vector magnetic field with a single nitrogen vacancy (NV) center in diamond. The magnetic field in parallel with the axis of the NV center can be obtained by detecting the electron Zeeman shift, while the Larmor precession of an ancillary nuclear spin close to the NV center can be used to measure the field perpendicular to the axis. Experimentally, both the Zeeman shift and Larmor precession can be measured through the fluorescence from the NV center. By applying additional calibrated magnetic fields, complete information of the vector magnetic field can be achieved with such a method. This vector magnetic field detection method is insensitive to temperature fluctuation and it can be applied to nanoscale magnetic measurement., Comment: 5 pages, 5 figures

We study the phase separation of a spin polarized Fermi gas with spin-orbit coupling near a wide Feshbach resonance. As a result of the competition between spin-orbit coupling and population imbalance, the phase diagram for a uniform gas develops a rich structure of phase separation involving gapless superfluid states which are topologically non-trivial. We find that these novel gapless phases can be stabilized by intermediate spin-orbit coupling strengths. We then demonstrate the phase separation induced by an external trapping potential and discuss the optimal parameter region for the experimental observation of the gapless superfluid phases., Comment: 4.2 pages, 5 figures, replaced with the published version

We present an efficient scheme for accurate electronic structure interpolations based on the systematically improvable optimized atomic orbitals. The atomic orbitals are generated by minimizing the spillage value between the atomic basis calculations and the converged plane wave basis calculations on some coarse $k$-point grid. They are then used to calculate the band structure of the full Brillouin zone using the linear combination of atomic orbitals (LCAO) algorithms. We find that usually 16 -- 25 orbitals per atom can give an accuracy of about 10 meV compared to the full {\it ab initio} calculations. The current scheme has several advantages over the existing interpolation schemes. The scheme is easy to implement and robust which works equally well for metallic systems and systems with complex band structures. Furthermore, the atomic orbitals have much better transferability than the Shirley's basis and Wannier functions, which is very useful for the perturbation calculations.

We have measured a graphene double quantum dot device with multiple electrostatic gates that are used to enhance control to investigate it. At low temperatures the transport measurements reveal honeycomb charge stability diagrams which can be tuned from weak to strong interdot tunnel coupling regimes. We precisely extract a large interdot tunnel coupling strength for this system allowing for the observation of tunnel-coupled molecular states extending over the whole double dot. This clean, highly controllable system serves as an essential building block for quantum devices in a nuclear-spin-free world., Comment: 10 pages, 14 figures

We present full atomistic calculations of the spin-flip time (T$_{1}$) of electrons and holes mediated by acoustic phonons in self-assembled In$_{1-x}$Ga$_x$As/GaAs quantum dots at zero magnetic field. At low magnetic field, the first-order process is suppressed, and the second-order process becomes dominant. We find that the spin-phonon-interaction induced spin relaxation time is 40 - 80 s for electrons, and 1 - 20 ms for holes at 4.2 K. The calculated hole-spin relaxation times are in good agreement with recent experiments, which suggests that the two-phonon process is the main relaxation mechanism for hole-spin relaxation in the self-assembled quantum dots at zero field. We further clarify the structural and alloy composition effects on the spin relaxation in the quantum dots.

We present a comprehensive study of the optical properties of InAs/InP self-assembled quantum dots (QDs) using an empirical pseudopotential method and configuration interaction treatment of the many-particle effects. The results are compared to those of InAs/GaAs QDs. The main results are: (i) The alignment of emission lines of neutral exciton, charged exciton and biexciton in InAs/InP QDs is quite different from that in InAs/GaAs QDs. (ii) The hidden correlation in InAs/InP QDs is 0.7 - 0.9 meV, smaller than that in InAs/GaAs QDs. (iii) The radiative lifetimes of neutral exciton, charged exciton and biexciton in InAs/InP QDs are about twice longer than those in InAs/GaAs QDs. (v) The phase diagrams of few electrons and holes in InAs/InP QDs differ greatly from those in InAs/GaAs QDs. The filling orders of electrons and holes are shown to obey the Hund's rule and Aufbau principle, and therefore the photoluminescence spectra of highly charged excitons are very different from those of InAs/GaAs QDs., Comment: 10 pages, 11 figures

Plasmon mode in a silver nanowire is theoretically studied when the nanowire is placed on or near a silica substrate. It is found that the substrate has much influence on the plasmon mode. For the nanowire on the substrate, the plasmon (hybrid) mode possesses not only a long propagation length but also an ultrasmall mode area. From the experimental point of view, this cavity-free structure holds a great potential to study a strong coherent interaction between the plasmon mode and single quantum system (for example, quantum dots) embedded in the substrate., Comment: 3 pages, 3 figures

We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the {\it spillage} of the wave functions between the atomic orbital calculations and the converged plane wave calculations for dimer systems. The quality of the bases can be systematically improved by increasing the size of the bases within the same framework. The scheme is easy to implement and very flexible. We have done extensive tests of this scheme for wide variety of systems. The results show that the obtained atomic basis sets are very satisfactory for both accuracy and transferability.

The mechanism of unidirectional emission of high Q Whispering Gallery mode in deformed circular micro- cavities is studied and firstly presented in this paper. In phase space, light in the chaotic sea leaks out the cavity through the refraction regions, whose positions are controlled by stable islands. Moreover, the positions of fixed points according to the critical line in unstable manifolds mainly determines the light leak out from which refraction region and the direction of the emission. By controlling the cavity shape, we can tune the leaky regions, as well as the positions of fixed points, to achieve unidirectional emission high Q cavities with narrow angular divergence both in high and low refractive index mater

We propose an efficient method to realize a large-scale one-way quantum computer in a two-dimensional (2D) array of coupled cavities, based on coherent displacements of an arbitrary state of cavity fields in a closed phase space. Due to the nontrivial geometric phase shifts accumulating only between the qubits in nearest-neighbor cavities, a large-scale 2D cluster state can be created within a short time. We discuss the feasibility of our method for scale solid-state quantum computation, Comment: 5 pages, 3 figures

Resistively Detected Nuclear Magnetic Resonance (RD-NMR) has been used to investigate a two-subband electron system in a regime where quantum Hall pseudo-spin ferromagnetic (QHPF) states are prominently developed. It reveals that the easy-axis QHPF state around the total filling factor $\nu =4 $ can be detected by the RD-NMR measurement. Approaching one of the Landau level (LL) crossing points, the RD-NMR signal strength and the nuclear spin relaxation rate $1/T_{1}$ enhance significantly, a signature of low energy spin excitations. However, the RD-NMR signal at another identical LL crossing point is surprisingly missing which presents a puzzle.

We propose a scheme to implement a heralded quantum memory for single-photon polarization qubits with a single atom trapped in an optical cavity. In this scheme, an injected photon only exchanges quantum state with the atom, so that the heralded storage can be achieved by detecting the output photon. We also demonstrate that the scheme can be used for realizing the heralded quantum state transfer, exchange and entanglement distribution between distant nodes. The ability to detect whether the operation has succeeded or not is crucial for practical application., Comment: 5 pages, 6 figures

Temperature dependence of the longitudinal and Hall resistance is studied in the regime of localization-delocalization transition. We carry out measurements of a scaling exponent $\kappa$ in the Landau level mixing region at several filling factors. The localization exponent $\gamma$ is extracted using an approach based on the variable range hopping theory. The values of $\gamma$ and $\kappa$ are found to be universal, independent of filling factor in our sample. We can conclude that although Landau level mixing can change the degeneracy of a quantum Hall state, the value of the scaling exponent remains the same for a given sample that contains a fixed disorder profile., Comment: 11 pages, 4 figures

We describe and examine entanglement between different degrees of freedom in multiphoton states based on the permutation properties. From the state description, the entanglement comes from the permutation asymmetry. According to the different permutation properties, the multiphoton states can be divided into several parts. It will help to deal with the multiphoton interference, which can be used as the measurement of the entanglement., Comment: Final version

We propose a re-encoder to generate a refreshed parity encoded state from an existing parity encoded state. This is the simplest case of the scheme by Gilchrist et al. (Phys. Rev. A 75, 052328). We show that it is possible to demonstrate with existing technology parity encoded quantum gates and teleportation., Comment: 8 pages, 4 figures

We propose and demonstrate experimentally a projection scheme to measure the quantum phase with a precision beating the standard quantum limit. The initial input state is a twin Fock state $|N,N>$ proposed by Holland and Burnett [Phys. Rev. Lett. {\bf 71}, 1355 (1993)] but the phase information is extracted by a quantum state projection measurement. The phase precision is about $1.4/N$ for large photon number $N$, which approaches the Heisenberg limit of 1/N. Experimentally, we employ a four-photon state from type-II parametric down-conversion and achieve a phase uncertainty of $0.291\pm 0.001$ beating the standard quantum limit of $1/\sqrt{N} = 1/2$ for four photons., Comment: 5 figures

In condensed matter physics, the study of electronic states with SU(N) symmetry has attracted considerable and growing attention in recent years, as systems with such a symmetry can often have a spontaneous symmetry-breaking effect giving rise to a novel ground state. For example, pseudospin quantum Hall ferromagnet of broken SU(2) symmetry has been realized by bringing two Landau levels close to degeneracy in a bilayer quantum Hall system. In the past several years, the exploration of collective states in other multi-component quantum Hall systems has emerged. Here we show the conventional pseudospin quantum Hall ferromagnetic states with broken SU(2) symmetry collapsed rapidly into an unexpected state with broken SU(4) symmetry, by in-plane magnetic field in a two-subband GaAs/AlGaAs two-dimensional electron system at filling factor around $\nu=4$. Within a narrow tilting range angle of 0.5 degrees, the activation energy increases as much as 12 K. While the origin of this puzzling observation remains to be exploited, we discuss the possibility of a long-sought pairing state of electrons with a four-fold degeneracy., Comment: 13 pages, 4 figures

By using an asymmetric beam splitter, we observe the generalized Hong-Ou-Mandel effects for three and four photons, respectively. Furthermore, we can use this generalized Hong-Ou-Mandel interferometer to characterize temporal distinguishability., Comment: to be published in the proceedings of Coherence and Quantum Optics 9

We construct a linear optics measurement process to determine the entanglement measure, named \emph{I-concurrence}, of a set of $4 \times 4$ dimensional two-photon entangled pure states produced in the optical parametric down conversion process. In our experiment, an \emph{equivalent} symmetric projection for the two-fold copy of single subsystem (presented by L. Aolita and F. Mintert, Phys. Rev. Lett. \textbf{97}, 050501 (2006)) can be realized by observing the one-side two-photon coincidence without any triggering detection on the other subsystem. Here, for the first time, we realize the measurement for entanglement contained in bi-photon pure states by taking advantage of the indistinguishability and the bunching effect of photons. Our method can determine the \emph{I-concurrence} of generic high dimensional bipartite pure states produced in parametric down conversion process., Comment: 4 figures

In this paper, photonic entanglement and interference are described and analyzed with the language of quantum information process. Correspondingly, a photon state involving several degrees of freedom is represented in a new expression based on the permutation symmetry of bosons. In this expression, each degree of freedom of a single photon is regarded as a qubit and operations on photons as qubit gates. The two-photon Hong-Ou-Mandel interference is well interpreted with it. Moreover, the analysis reveals the entanglement between different degrees of freedom in a four-photon state from parametric down conversion, even if there is no entanglement between them in the two-photon state. The entanglement will decrease the state purity and photon interference visibility in the experiments on a four-photon polarization state., Comment: 11 pages and 2 figures

Stimulated emission of two photons is observed experimentally in the parametric amplification process and is compared to a three-photon interference scheme. We find that the underlying physics of stimulated emission is simply the constructive interference due to photon indistinguishability. So the observed signal enhancement upon the input of photons is a result of multi-photon interference of the input photons and the otherwise spontaneously emitted photon from the amplifier.

Two experiments of four-photon interference are performed with two pairs of photons from parametric down-conversion with the help of asymmetric beam splitters. The first experiment is a generalization of the Hong-Ou-Mandel interference effect to two pairs of photons while the second one utilizes this effect to demonstrate a four-photon de Broglie wavelength of $\lambda/4$ by projection measurement.

Two schemes of projection measurement are realized experimentally to demonstrate the de Broglie wavelength of three photons without the need for a maximally entangled three-photon state (the NOON state). The first scheme is based on the proposal by Wang and Kobayashi (Phys. Rev. A {\bf 71}, 021802) that utilizes a couple of asymmetric beam splitters while the second one applies the general method of NOON state projection measurement to three-photon case. Quantum interference of three photons is responsible for projecting out the unwanted states, leaving only the NOON state contribution in these schemes of projection measurement., Comment: 8 pages

Many of the properties of the partial transposition are not clear so far. Here the number of the negative eigenvalues of K(T)(the partial transposition of K) is considered carefully when K is a two-partite state. There are strong evidences to show that the number of negative eigenvalues of K(T) is N(N-1)/2 at most when K is a state in Hilbert space N*N. For the special case, 2*2 system(two qubits), we use this result to give a partial proof of the conjecture sqrt(K(T))(T)>=0. We find that this conjecture is strongly connected with the entanglement of the state corresponding to the negative eigenvalue of K(T) or the negative entropy of K.

Multi-photon interference is at the heart of the recently proposed linear optical quantum computing scheme and plays an essential role in many protocols in quantum information. Indistinguishability is what leads to the effect of quantum interference. Optical interferometers such as Michaelson interferometer provide a measure for second-order coherence at one-photon level and Hong-Ou-Mandel interferometer was widely employed to describe two-photon entanglement and indistinguishability. However, there is not an effective way for a system of more than two photons. Recently, a new interferometric scheme was proposed to quantify the degree of multi-photon distinguishability. Here we report an experiment to implement the scheme for three-photon case. We are able to generate three photons with different degrees of temporal distinguishability and demonstrate how to characterize them by the visibility of three-photon interference. This method of quantitative description of multi-photon indistinguishability will have practical implications in the implementation of quantum information protocols.

In this paper, we report an experiment, which demonstrates computation of topological charges of two optical vortices via non-degenerate four-wave-mixing process. We show that the output signal beam carries orbital angular momentum which equals to the subtraction of the orbital angular momenta of the probe light and the backward pump light. The ⁸⁵Rb atoms are used as the nonlinear medium, which transfer the orbital angular momenta of lights., Comment: 3 pages, 3 figures

An experiment is performed to demonstrate the temporal distinguishability of a four-photon state and a six-photon state, both from parametric down-conversion. The experiment is based on a multi-photon interference scheme in a recent discovered NOON-state projection measurement. By measuring the visibility of the interference dip, we can distinguish the various scenarios in the temporal distribution of the pairs and thus quantitatively determine the degree of temporal (in)distinguishability of a multi-photon state.

A measurement process is constructed to project an arbitrary two-mode $N$-photon state to a maximally entangled $N$-photon state (the {\it NOON}-state). The result of this projection measurement shows a typical interference fringe with an $N$-photon de Broglie wavelength. For an experimental demonstration, this measurement process is applied to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. Generalization to arbitrary $N$-photon states projection measurement can be easily made and may have wide applications in quantum information. As an example, we formulate it for precision phase measurement.

In this Letter we discuss the possibility of producing Bragg solitons in an electromagnetically induced transparency medium. We show that this coherent medium can be engineered to be a Bragg grating with a large Kerr nonlinearity through proper arrangements of light fields. Unlike in previous studies, the parameters of the medium can be easily controlled through adjusting the intensities and detunings of lasers. Thus this scheme may provide an opportunity to study the dynamics of Bragg solitons. And doing experiments with low power lights is possible., Comment: 4 pages, 3 figures

We construct a projection measurement process for the maximally entangled N-photon state (the NOON-state) with only linear optical elements and photodetectors. This measurement process will give null result for any N-photon state that is orthogonal to the NOON state. We examine the projection process in more detail for N=4 by applying it to a four-photon state from type-II parametric down-conversion. This demonstrates an orthogonal projection measurement with a null result. This null result corresponds to a dip in a generalized Hong-Ou-Mandel interferometer for four photons. We find that the depth of the dip in this arrangement can be used to distinguish a genuine entangled four-photon state from two separate pairs of photons. We next apply the NOON state projection measurement to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. A successful NOON state projection is demonstrated with the appearance of the four-photon de Broglie wavelength in the interference fringe pattern., Comment: 8 pages, 3 figures, new title, some content change, replaced Fig.1

The influence of a repump laser on a nearly degenerate four-wave-mixing (NDFWM) spectrum was investigated. We found the amplitude and line shape of the NDFWM depended strongly on the detuning of the repump field. A five-peak structure was observed. And at some certain repump detuning a dip appeared at the central peak. A rough analysis was proposed to explain this effect.

We consider a two-qubit unitary operation along with arbitrary local unitary operations acts on a two-qubit pure state, whose entanglement is C_0. We give the conditions that the final state can be maximally entangled and be non-entangled. When the final state can not be maximally entangled, we give the maximal entanglement C_max it can reach. When the final state can not be non-entangled, we give the minimal entanglement C_min it can reach. We think C_max and C_min represent the entanglement changing power of two-qubit unitary operations. According to this power we define an order of gates., Comment: 11 pages