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The real world obeys quantum physics and quantum computing presents an alternative way to map physical problems to systems that follow the same laws. Such computation fundamentally constitutes a better way to understand the most challenging quantum problems. One such problem is the accurate simulation of highly correlated quantum systems. Due to the high dimensionality of the problem classical computers require considerable computer power to accurately predict material properties, especially when strong electron interactions are present. Still, modern day quantum hardware has many limitations and only allows for modeling of very simple systems. Here we present for the first time a quantum computer model simulation of a complex hemocyanin molecule, which is an important respiratory protein involved in various physiological processes such as oxygen transport and immune defence, and is also used as a key component in therapeutic vaccines for cancer. To better characterise the mechanism by which hemocyanin transports oxygen, variational quantum eigensolver (VQE) based on fermionic excitations and quantum embedding methods is used in the context of dynamic mean field theory to solve Anderson impurity model (AIM). Finally, it is concluded that the magnetic structure of hemocyanin is largely influenced by the many-body correction and that the computational effort for solving correlated electron systems could be substantially reduced with the introduction of quantum computing algorithms. We encourage the use of the Hamiltonian systems presented in this paper as a benchmark for testing quantum computing algorithms efficiency for chemistry applications.

Continuous-time quantum walks provide an alternative method for quantum search problems. Most of the earlier studies confirmed that quadratic speedup exists in some synthetic Hamiltonians, but whether there is quadratic speedup in real physical systems is elusive. Here, we investigate three physical systems with long-range atom-atom interaction which are possible good candidates for realizing the quantum search, including one-dimensional atom arrays either trapped in an optical lattice or coupled to waveguide near band edge or dispersively coupled to a good cavity. We find that all three systems can provide near-optimal quantum search if there is no dissipation. However, if the dissipation is considered only the latter two systems (i.e., waveguide-QED and cavity-QED systems) can still have high success probabilities because the latter two systems can significantly enhance the atom-atom interaction even if they are far apart and the spectra gap can be much larger which can reduce the search time and the effects of dissipation significantly. Our studies here can provide helpful instructions for realizing quantum search in real physical systems in the noisy intermediate-scale quantum era.

We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger (SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exactly expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. However, some regions where the Berry curvature is identically zero in the first Brillouin zone results in the degeneracy of the quantum metric, which leads to ill-defined non-integer topological Euler numbers. Nevertheless, the non-integer "Euler number" provides valuable insights and provide an upper bound for absolute values of the Chern numbers.

A key challenge in realizing practical quantum networks for long-distance quantum communication involves robust entanglement between quantum memory nodes connected via fiber optical infrastructure. Here, we demonstrate a two-node quantum network composed of multi-qubit registers based on silicon-vacancy (SiV) centers in nanophotonic diamond cavities integrated with a telecommunication (telecom) fiber network. Remote entanglement is generated via the cavity-enhanced interactions between the SiV's electron spin qubits and optical photons. Serial, heralded spin-photon entangling gate operations with time-bin qubits are used for robust entanglement of separated nodes. Long-lived nuclear spin qubits are used to provide second-long entanglement storage and integrated error detection. By integrating efficient bi-directional quantum frequency conversion of photonic communication qubits to telecom frequencies (1350 nm), we demonstrate entanglement of two nuclear spin memories through 40 km spools of low-loss fiber and a 35 km long fiber loop deployed in the Boston area urban environment, representing an enabling step towards practical quantum repeaters and large-scale quantum networks.

The emerging hybrid integrated quantum photonics combines advantages of different functional components into a single chip to meet the stringent requirements for quantum information processing. Despite the tremendous progress in hybrid integrations of III-V quantum emitters with silicon-based photonic circuits and superconducting single-photon detectors, on-chip optical excitations of quantum emitters via miniaturized lasers towards single-photon sources (SPSs) with low power consumptions, small device footprints and excellent coherence properties is highly desirable yet illusive. In this work, we present realizations of bright semiconductor singe-photon sources heterogeneously integrated with on-chip electrically-injected microlasers. Different from previous one-by-one transfer printing technique implemented in hybrid quantum dot (QD) photonic devices, multiple deterministically coupled QD-circular Bragg Grating (CBG) SPSs were integrated with electrically-injected micropillar lasers at one time via a potentially scalable transfer printing process assisted by the wide-field photoluminescence (PL) imaging technique. Optically pumped by electrically-injected microlasers, pure single photons are generated with a high-brightness of a count rate of 3.8 M/s and an extraction efficiency of 25.44%. Such a high-brightness is due to the enhancement by the cavity mode of the CBG, which is confirmed by a Purcell factor of 2.5. Our work provides a powerful tool for advancing hybrid integrated quantum photonics in general and boosts the developments for realizing highly-compact, energy-efficient and coherent SPSs in particular.

We investigate the adiabatic evolution of light in nonlinear waveguide couplers via resonance-locked inverse engineering based on stimulated Raman adiabatic passage (STIRAP). The longitudinal varying detunings of the propagation coefficients are designed to eliminate dynamically the nonlinear effect, which induce the non-adiabatic oscillations. We show that different light evolutions such as complete light transfer, light split and light return can be realized adiabatically with appropriate choices of the detunings even in the nonlinear regime. The features open new opportunities for the realization of all-optical nonlinear devices with high fidelity in integrated optics.

Pressure-induced magnetic phase transition is attracting interest due to its ability to detect superconducting behaviour at high pressures in diamond anvil cells. However, detection of the local sample magnetic properties is a great challenge due to the small sample chamber volume. Recently, optically detected magnetic resonance (ODMR) of nitrogen vacancy (NV) centers in diamond have been used for in-situ pressure-induced phase transition detection. However, owing to their four orientation axes and temperature-dependent zero-field-splitting, interpreting the observed ODMR spectra of NV centers remain challenging. Here, we study the optical and spin properties of implanted silicon vacancy defects in 4H-SiC, which is single-axis and temperature-independent zero-field-splitting. Using this technique, we observe the magnetic phase transition of Nd2Fe14B at about 7 GPa and map the critical temperature-pressure phase diagram of the superconductor YBa2Cu3O6.6. These results highlight the potential of silicon vacancy-based quantum sensors for in-situ magnetic detection at high pressures.

Large-photon-number quantum state is a fundamental but non-resolved request for practical quantum information applications. Here we propose an N-photon state generation scheme that is feasible and scalable, using lithium niobate on insulator circuits. Such scheme is based on the integration of a common building block called photon-number doubling unit (PDU), for deterministic single-photon parametric down-conversion and up-conversion. The PDU relies on 10^7-optical-quality-factor resonator and mW-level on-chip power, which is within the current fabrication and experiment limits. N-photon state generation schemes, with cluster and GHZ state as examples, are shown for different quantum tasks.

Multiparty quantum communication is an important branch of quantum networks. It enables private information transmission with information-theoretic security among legitimate parties. We propose a sender-controlled measurement-device-independent multiparty quantum communication protocol. The sender Alice divides a private message into several parts and delivers them to different receivers for secret sharing with imperfect measurement devices and untrusted ancillary nodes. Furthermore, Alice acts as an active controller and checks the security of quantum channels and the reliability of each receiver before she encodes her private message for secret sharing, which makes the protocol convenient for multiparity quantum communication.

We investigate high-fidelity multiple beam splitting in Hermitian and non-Hermitian symmetric coupled waveguides with one input and 2N output waveguide channels. In Hermitian systems, we realize adiabatically light splitting in resonant case based on the stimulated Raman adiabatic passage (STIRAP) and arbitrary proportion from the middle waveguide to outer waveguides in propagation coefficients mismatch case using shortcuts to adiabaticity (STA) technique. In non-Hermitian systems with even waveguides being dissipative, the compact and robust beam splitting can be achieved by eliminating the non-adiabatic coupling via the non-Hermitian STA method. We further verify the feasibility of our theoretical predictions by means of the beam propagation method (BPM). The suggested multiple beam splitters open new opportunities for the realization of on-chip high-bandwidth photonics with high fidelity in short distances.

Developing nano-mechanical oscillators for ultrasensitive force detection is of great importance in exploring science. We report our achievement of ultrasensitive detection of the external force regarding the radio-frequency electric field by a nano-sensor made of a single trapped $^{40}$Ca$^{+}$ ion under injection-locking, where squeezing is additionally applied to detection of the smallest force in the ion trap. The employed ion is confined stably in a surface electrode trap and works as a phonon laser that is very sensitive to the external disturbance. The injection-locking drove the ion's oscillation with phase synchronization, yielding the force detection with sensitivity of 347 $\pm$ 50 yN/$\sqrt{Hz}$. Further with 3 dB squeezing applied on the oscillation phase variance, we achieved a successful detection of the smallest force to be 86.5 $\pm$ 70.1 yN.

Based on the optical Raman lattice technique, we experimentally realize the Qi-Wu-Zhang model for quantum anomalous Hall phase in ultracold fermions with two-dimensional (2D) spin-orbit (SO) coupling. We develop a novel protocol of pump-probe quench measurement to probe, with minimal heating, the resonant spin flipping on particular quasi-momentum subspace called band-inversion surfaces. With this protocol we demonstrate the first Dirac-type 2D SO coupling in a fermionic system, and detect non-trivial band topology by observing the change of band-inversion surfaces as the two-photon detuning varies. The non-trivial band topology is also observed by slowly loading the atoms into optical Raman lattices and measuring the spin textures. Our results show solid evidence for the realization of the minimal SO-coupled quantum anomalous Hall model, which can provide a feasible platform to investigate novel topological physics including the correlation effects with SO-coupled ultracold fermions.

The coherent interaction of electromagnetic fields with solid-state two-level systems can yield deterministic quantum light sources for photonic quantum technologies. To date, the performance of semiconductor single-photon sources based on three-level systems is limited mainly due to a lack of high photon indistinguishability. Here, we tailor the cavity-enhanced spontaneous emission from a ladder-type three-level system in a single epitaxial quantum dot (QD) through stimulated emission. After populating the biexciton (XX) of the QD through two-photon resonant excitation (TPE), we use another laser pulse to selectively depopulate the XX state into an exciton (X) state with a predefined polarization. The stimulated XX-X emission modifies the X decay dynamics and yields improved polarized single-photon source characteristics such as a source brightness of 0.030(2), a single-photon purity of 0.998(1), and an indistinguishability of 0.926(4). Our method can be readily applied to existing QD single-photon sources and expands the capabilities of three-level systems for advanced quantum photonic functionalities.

Optical microcavities have widely been employed to enhance either the optical excitation or the photon emission processes for boosting light matter interactions at nanoscale. When both the excitation and emission processes are simultaneously facilitated by the optical resonances provided by the microcavities, as referred to the dual-resonance condition in this article, the performances of many nanophotonic devices approach to the optima. In this work, we present versatile accessing of dual-resonance conditions in deterministically coupled quantum-dot(QD)-micopillars, which enables emission from exciton (X) - charged exciton (CX) transition with improved single-photon purity. In addition, the rarely observed up-converted single-photon emission process is achieved under dual-resonance condition. We further exploit the vectorial nature of the high-order cavity modes to significantly improve the excitation efficiency under the dual-resonance condition. The dual-resonance enhanced light-matter interactions in the quantum regime provides a viable path for developing integrated quantum photonic devices based on cavity quantum electrodynamics (QED) effect e.g., highly-efficient quantum light sources and quantum logical gates.

We interface a spontaneous parametric down conversion (SPDC) crystal and a cold atomic ensemble and demonstrate a highly efficient quantum memory through polarization-encoded single-photon qubits. Specifically, narrowband heralded single photons from a cavity-enhanced SPDC source is stored using cold atomic ensemble, with ~70% storage-and-retrieval efficiency and ~10$\mu$s storage time at 50% efficiency. To prevent the degradation after storage, we also manipulate the single-photon wave profile so that the retrieved non-classical nature of single photon is preserved. On the other hand, the dual-rail storage is used for storing polarization-encoded qubits, and the corrected fidelity of flying qubits after storage reaches ~97%. The results pave the way toward large-scale quantum network.

We discuss a general interaction quench in a Luttinger liquid described by a paired bosonic Hamiltonian. By employing $\mathsf{su}(1,1)$ Lie algebra, the post-quench time-evolved wavefunctions are obtained analytically, from which the time evolution of the entanglement in momentum space can be investigated. We note that depending on the choice of Bogoliubov quasiparticles, the expressions of wavefunctions, which describe time-evolved paired states, can take different forms. The correspondence between the largest entanglement eigenvalue in momentum space and the wavefunction overlap in quench dynamics is discussed, which generalizes the results of Dóra \em et al [2016, \em Phys. Rev. Lett. \textbf117, 010603]. A numerical demonstration on an XXZ lattice model is presented via the exact diagonalization method.

Quantum memories, devices that can store and retrieve photonic quantum states on demand, are essential components for scalable quantum technologies. It is desirable to push the memory towards the broadband regime in order to increase the data rate. Here, we present a theoretical and experimental study on the broadband optical memory based on electromagnetically-induced-transparency (EIT) protocol. We first provide a theoretical analysis on the issues and requirements to achieve a broadband EIT memory. We then present our experimental efforts on EIT memory in cold atoms towards the broadband or short-pulse regime. A storage efficiency of ~ 80 % with a pulse duration of 30 ns (corresponding to a bandwidth of 14.7 MHz) is realized. Limited by the available intensity of the control beam, we could not conduct an optimal storage for the even shorter pulses but still obtain an efficiency of larger than 50 % with a pulse duration of 14 ns (31.4 MHz). The achieved time-bandwidth-product at the efficiency of 50 % is 1267.

We present a theoretical study on the efficiency variation of coherent light conversion based on optical memories using the electromagnetically induced transparency (EIT) protocol in an atomic system with degenerate Zeeman states. Based on the Maxwell-Bloch equation, we obtain an approximate analytic solution for the converted light pulses which clarifies that two major factors affecting the efficiency of the converted pulses. The first one is the finite bandwidth effect of the pulses and the difference in the delay-bandwidth product of the writing and reading channel due to the difference in the transition dipole moment. The second one is the mismatch between the stored ground-state coherence and the ratio of the Clebsch-Gordan coefficient for the probe and control transition in the reading channel which results in a non-adiabatic energy loss. To correspond to real experimental conditions, we also perform a numerical calculation of the variation in conversion efficiency versus the Zeeman population distribution under the Zeeman-state optical pumping in storing a $\sigma^{+}$-polarized pulse and retrieving with $\sigma^{-}$ polarization in cesium atoms. Our work provides essential physical insights and quantitative knowledge for the development of a coherent optical converter based on EIT-memory.

Recent progress on qubit manipulation allows application of periodic driving signals on qubits. In this study, a harmonic driving field is added to a Rabi dimer to engineer photon and qubit dynamics in a circuit quantum electrodynamics device. To model environmental effects, qubits in the Rabi dimer are coupled to a phonon bath with a sub-Ohmic spectral density. A non-perturbative treatment, the Dirac-Frenkel time-dependent variational principle together with the multiple Davydov D$_2$ \it Ansatz is employed to explore the dynamical behavior of the tunable Rabi dimer. In the absence of the phonon bath, the amplitude damping of the photon number oscillation is greatly suppressed by the driving field, and photons can be created thanks to resonances between the periodic driving field and the photon frequency. In the presence of the phonon bath, one still can change the photon numbers in two resonators, and indirectly alter the photon imbalance in the Rabi dimer by directly varying the driving signal in one qubit. It is shown that qubit states can be manipulated directly by the harmonic driving. The environment is found to strengthen the interqubit asymmetry induced by the external driving, opening up a new venue to engineer the qubit states.

The generation of high-quality entangled photon pairs has been being a long-sought goal in modern quantum communication and computation. To date, the most widely-used entangled photon pairs are generated from spontaneous parametric downconversion, a process that is intrinsically probabilistic and thus relegated to a regime of low pair-generation rates. In contrast, semiconductor quantum dots can generate triggered entangled photon pairs via a cascaded radiative decay process, and do not suffer from any fundamental trade-off between source brightness and multi-pair generation. However, a source featuring simultaneously high photon-extraction efficiency, high-degree of entanglement fidelity and photon indistinguishability has not yet been reported. Here, we present an entangled photon pair source with high brightness and indistinguishability by deterministically embedding GaAs quantum dots in broadband photonic nanostructures that enable Purcell-enhanced emission. Our source produces entangled photon pairs with a record pair collection probability of up to 0.65(4) (single-photon extraction efficiency of 0.85(3)), entanglement fidelity of 0.88(2), and indistinguishabilities of 0.901(3) and 0.903(3), which immediately creates opportunities for advancing quantum photonic technologies.

We study the spatiotemporal Bloch states of a high-frequency driven two-component Bose-Einstein condensate (BEC) with spin-orbit coupling (SOC) in an optical lattice. By adopting the rotating-wave approximation (RWA) and applying an exact trial-solution to the corresponding quasistationary system, we establish a different method for tuning SOC via external field such that the existence conditions of the exact particular solutions are fitted. Several novel features related to the exact states are demonstrated, such as SOC leads to spin-motion entanglement for the spatiotemporal Bloch states, SOC increases the population imbalance of the two-component BEC and SOC can be applied to manipulate the stable atomic flow which is conducive to control quantum transport of the BEC for different application purposes.

A Rabi dimer is used to model a recently reported circuit quantum electrodynamics system composed of two coupled transmission-line resonators with each coupled to one qubit. In this study, a phonon bath is adopted to mimic the multimode micromechanical resonators and is coupled to the qubits in the Rabi dimer. The dynamical behavior of the composite system is studied by the Dirac-Frenkel time-dependent variational principle combined with the multiple Davydov D$_{2}$ ansätze. Initially all the photons are pumped into the left resonator, and the two qubits are in the down state coupled with the phonon vacuum. In the strong qubit-photon coupling regime, the photon dynamics can be engineered by tuning the qubit-bath coupling strength $\alpha$ and photon delocalization is achieved by increasing $\alpha$. In the absence of dissipation, photons are localized in the initial resonator. Nevertheless, with moderate qubit-bath coupling, photons are delocalized with quasiequilibration of the photon population in two resonators at long times. In this case, high frequency bath modes are activated by interacting with depolarized qubits. For strong dissipation, photon delocalization is achieved via frequent photon-hopping within two resonators and the qubits are suppressed in their initial down state.

Quantum state transfer from flying photons to stationary matter qubits is an important element in the realization of quantum networks. Self-assembled semiconductor quantum dots provide a promising solid-state platform hosting both single photon and spin, with an inherent light-matter interface. Here, we develop a method to coherently and actively control the single-photon frequency bins in superposition using electro-optic modulators, and measure the spin-photon entanglement with a fidelity of $0.796\pm0.020$. Further, by Greenberger-Horne-Zeilinger-type state projection on the frequency, path and polarization degrees of freedom of a single photon, we demonstrate quantum state transfer from a single photon to a single electron spin confined in an InGaAs quantum dot, separated by 5 meters. The quantum state mapping from the photon's polarization to the electron's spin is demonstrated along three different axis on the Bloch sphere, with an average fidelity of $78.5\%$.

We report optical positioning single quantum dots (QDs) in planar cavity with an average position uncertainty $<$20 nm using an optimized two-color photoluminescence imaging technique. We create single-photon sources based on these QDs in determined micropillar cavities. The brightness of the QD fluorescence is greatly enhanced on resonance with the fundamental mode of the cavity, leading to an high extraction efficiency of 68%$\pm$6% into a lens with numerical aperture of 0.65, and simultaneously exhibiting low multi-photon probability ($g^{2}(0)$=0.144$\pm$0.012) at this collection efficiency.

In this comment, we point out some shortcomings in two papers "Fractional quantum mechanics" [Phys. Rev. E 62, 3135 (2000)] and "Fractional Schroedinger equation" [Phys. Rev. E 66, 056108 (2002)]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from one place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to a destination.

In this paper, we introduce the Schrodinger equation with a general kinetic energy operator. The conservation law is proved and the probability continuity equation is deducted in a general sense. Examples with a Hermitian kinetic energy operator include the standard Schrodinger equation, the relativistic Schrodinger equation, the fractional Schrodinger equation, the Dirac equation, and the deformed Schrodinger equation. We reveal that the Klein-Gordon equation has a hidden non-Hermitian kinetic energy operator. The probability continuity equation with sources indicates that there exists a different way of probability transportation, which is probability teleportation. An average formula is deducted from the relativistic Schrodinger equation, the Dirac equation, and the K-G equation.

We report the first experimental demonstration of interference-induced spectral line elimination predicted by Zhu and Scully [Phys. Rev. Lett. 76, 388 (1996)] and Ficek and Rudolph [Phys. Rev. A 60, 4245 (1999)]. We drive an exciton transition of a self-assembled quantum dot in order to realize a two-level system exposed to bichromatic laser field and observe nearly complete elimination of the resonance fluorescence spectral line at the driving laser frequency. This is caused by quantum interference between coupled transitions among the doubly dressed excitonic states, without population trapping. We also demonstrate multiphoton ac Stark effect with shifted subharmonic resonances and dynamical modifications of resonance fluorescence spectra by using double dressing.

Single quantum emitters (SQEs) are at the heart of quantum optics and photonic quantum information technologies. To date, all demonstrated solid-state single-photon sources are confined in three-dimensional materials. Here, we report a new class of SQEs based on excitons that are spatially localized by defects in two-dimensional tungsten-diselenide monolayers. The optical emission from these SQEs shows narrow linewidths of ~0.13 meV, about two orders of magnitude smaller than that of delocalized valley excitons. Second-order correlation measurements reveal strong photon anti-bunching, unambiguously establishing the single photon nature of the emission. The SQE emission shows two non-degenerate transitions, which are cross-linearly polarized. We assign this fine structure to two excitonic eigen-modes whose degeneracy is lifted by a large ~0.71 meV coupling, likely due to the electron-hole exchange interaction in presence of anisotropy. Magneto-optical measurements also reveal an exciton g-factor of ~8.7, several times larger than that of delocalized valley excitons. In addition to their fundamental importance, establishing new SQEs in 2D quantum materials could give rise to practical advantages in quantum information processing, such as efficient photon extraction and high integratability and scalability.

We demonstrate deterministic and robust generation of pulsed resonance fluorescence single photons from a single InGaAs quantum dot using the method of rapid adiabatic passage. Comparative study is performed with transform-limited, negatively chirped and positively chirped pulses, identifying the last one to be the most robust against fluctuation of driving strength. The generated single photons are background free, have a vanishing two-photon emission probability of 0.3% and a raw (corrected) two-photon Hong-Ou-Mandel interference visibility of 97.9% (99.5%), reaching a precision that places single photons at the threshold for fault-tolerant surface-code quantum computing. The single-photon source can be readily scaled up to multi-photon entanglement and used for quantum metrology, boson sampling and linear optical quantum computing.

We investigate temperature-dependent resonance fluorescence spectra obtained from a single self-assembled quantum dot. A decrease of the Mollow triplet sideband splitting is observed with increasing temperature, an effect we attribute to a phonon-induced renormalisation of the driven dot Rabi frequency. We also present first evidence for a non-perturbative regime of phonon coupling, in which the expected linear increase in sideband linewidth as a function of temperature is cancelled by the corresponding reduction in Rabi frequency. These results indicate that dephasing in semiconductor quantum dots may be less sensitive to changes in temperature than expected from a standard weak-coupling analysis of phonon effects.

Single photon sources based on semiconductor quantum dots offer distinct advantages for quantum information, including a scalable solid-state platform, ultrabrightness, and interconnectivity with matter qubits. A key prerequisite for their use in optical quantum computing and solid-state networks is a high level of efficiency and indistinguishability. Pulsed resonance fluorescence (RF) has been anticipated as the optimum condition for the deterministic generation of high-quality photons with vanishing effects of dephasing. Here, we generate pulsed RF single photons on demand from a single, microcavity-embedded quantum dot under s-shell excitation with 3-ps laser pulses. The pi-pulse excited RF photons have less than 0.3% background contributions and a vanishing two-photon emission probability. Non-postselective Hong-Ou-Mandel interference between two successively emitted photons is observed with a visibility of 0.97(2), comparable to trapped atoms and ions. Two single photons are further used to implement a high-fidelity quantum controlled-NOT gate.

We suggest the symmetrized Schrödinger equation and propose a general complex solution which is characterized by the imaginary units $i$ and $\epsilon$. This symmetrized Schrödinger equation appears some interesting features.