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Parity-time ($\mathcal{PT}$)-symmetric systems, featuring real eigenvalues despite their non-Hermitian nature, undergo spontaneous $\mathcal{PT}$ symmetry breaking at the exceptional point (EP). The phase transition from $\mathcal{PT}$ symmetry to $\mathcal{PT}$ symmetry breaking has shown exotic functionalities in the classical realm, such as loss-induced transparency or lasing revival. This transition is also expected to produce a more unconventional effect in pure quantum $\mathcal{PT}$ devices. Here, we report experimental evidences of spontaneous $\mathcal{PT}$ symmetry breaking in a single cold $^{40}\mathrm{Ca}^{+}$ ion and, more importantly, a counterintuitive effect of perfect quantum coherence occurring at the EP. Excellent agreement between experimental results and theoretical predictions is identified. In view of the versatile role of cold ions in building a quantum memory or processor, our experiment provides an alternative platform to explore $\mathcal{PT}$-symmetric physics and utilize pure quantum EP effects.

Decoherence induced by the laser frequency noise is one of the most important obstacles in the quantum information processing. In order to suppress this decoherence, the noise power spectral density needs to be accurately characterized. In particular, the noise spectrum measurement based on the coherence characteristics of qubits would be a meaningful and still challenging method. Here, we theoretically analyze and experimentally obtain the spectrum of laser frequency noise based on the continuous dynamical decoupling technique. We first estimate the mixture-noise (including laser and magnetic noises) spectrum up to $(2\pi)$530 kHz by monitoring the transverse relaxation from an initial state $+X$, followed by a gradient descent data process protocol. Then the contribution from the laser noise is extracted by enconding the qubits on different Zeeman sublevels. We also investigate two sufficiently strong noise components by making an analogy between these noises and driving lasers whose linewidth assumed to be negligible. This method is verified experimentally and finally helps to characterize the noise., Comment: 7 pages, 5 figures

In this paper, we propose a handy method to discriminate and estimate the dephasing noise sources of trapped ion qubits, which are mainly magnetic field noise and laser frequency noise. In our method, the conventional Ramsey experiment is used to measure the dephasing time $$T_2^*$$ and calculate the total linewidth of dephasing noise. Transitions with different magnetic field sensitivities and error propagation theory are employed to quantitatively estimate the linewidth of each noise. We experimentally demonstrated this method by taking advantage of five magnetically sensitive transitions of single trapped $$^{40}$$Ca$$^+$$, and the linewidth of the laser frequency noise and magnetic field noise is determined to be 493.3 ± 8.1 Hz and 181.4 ± 3.5 $$\upmu $$G, respectively, in our system. This method also can be used to separate magnetic field noise and other dephasing noise in other atomic system such as neutral atoms.

In this paper, we explore the possibilities of realizing weak value amplification (WVA) using purely atomic degrees of freedom. Our scheme identifies the internal electronic states and external motional states of a single trapped $^{40}$Ca$^+$ ion as the system degree and pointer degree respectively, and their controllable weak coupling is provided by a bichromatic light field. In our experimental demonstration, by performing appropriate postselection on the internal states, a position displacement of 4 angstroms (in phase space) of the trapped ion is amplified to 10 nanometers. The sensitivity of the amplification effect to the relative phase of the quantum state is also demonstrated. The high operational flexibility of this procedure allows fully exploration of the peculiarities of WVA., 8 pages, 8 figures

Quantum measurement remains a puzzle through its stormy history from the birth of quantum mechanics to state-of-the-art quantum technologies. Two complementary measurement schemes have been widely investigated in a variety of quantum systems: von Neumann's projective 'strong' measurement and Aharonov's weak measurement. Here, we report the observation of a weak-to-strong measurement transition in a single trapped $40Ca^+$ ion system. The transition is realized by tuning the interaction strength between the ion's internal electronic state and its vibrational motion, which play the roles of the measured system and the measuring pointer, respectively. By pre- and post-selecting the internal state, a pointer state composed of two of the ion's motional wavepackets is obtained, and its central-position shift, which corresponds to the measurement outcome, demonstrates the transition from the weak-value asymptotes to the expected-value asymptotes. Quantitatively, the weak-to-strong measurement transition is characterized by a universal transition factor $e^{-\Gamma^2}$, where $\Gamma$ is a dimensionless parameter related to the system-apparatus coupling. This transition, which continuously connects weak measurements and strong measurements, may open new experimental possibilities to test quantum foundations and prompt us to re-examine and improve the measurement schemes of related quantum technologies., Comment: 6 pages, 3 figures, accepted by Nature Physics

In order to understand our previous numerical finding that steady-state entanglement along the instability boundary remains unchanged in a three-mode optomechanical system [Phys. Rev. A 101 023838 (2020)], we investigate in detail the boundary entanglement in a simpler two-mode optomechanical system. Studies show that both the mechanism to generate entanglement and the parameter dependence of boundary entanglement are quite similar in these two models. Therefore, the two-mode system has captured the main features in the three-mode system. With the help of analytical calculations and discussing in a much bigger parameter interval, we find that the unchanging behavior previously discovered is actually an extremely slow changing behavior of the boundary entanglement function, and most importantly, this nearly invariant boundary entanglement is a general phenomenon via parametric down conversion process in the weak dissipation regime. This is by itself interesting as threshold quantum signatures in optomechanical phonon lasers, or may have potential value in related applications based on boundary quantum properties.

By using the perturbation expansion method and self-consistent iterative method, we evaluate the effect of the conduction band nonprabolicity on the wave vector ( k t ) dependent Rashba coefficient ( α ) and nonlinear Rashba spin splitting (Δ E ) in the Al 0.5 Ga 0.5 N/GaN quantum well (QW). The effective mass (energy) under the first order approximation m t1 ( E k1 ) is in proximity to the iterative result m tp ( E kp ) and m t1 > m tp , E k1 E kp , showing the higher order contributions to m t ( E k ) are small. The sign of the nonparabolic correction to E k is just opposite to that of the correction to m t . The increase of α and Δ E due to the conduction band nonparabolicity reaches about 3% at k t =1 nm −1 . Around the left heterointerface, the probability density is high and E k0 > E kp > E k1 , so α 0 α p α 1 , Δ E 0 E p E 1 . With increasing k t , α decreases, and Δ E increases slowly. For small k t , α 0 (Δ E 0 ), α 1 (Δ E 1 ) and α p (Δ E p ) are nearly the same. While for large k t , the difference between α 0 and α 1 ( α p ) increases rapidly, but the difference between Δ E 0 and Δ E 1 (Δ E p ) increases slowly.

Localized surface plasmon resonances (LSPRs) of Ag-dielectric-Ag multi-layered nanoshell are studied by quasi-static approximation and plasmon hybridization theory. Absorption properties of multi-layered nanoshell with the silver core and nanoshell separated by a dielectric layer exhibit strong coupling between the core and nanoshell. The result shows absorption spectrum of LSPRS is influenced by the refractive index of surrounding medium, the dielectric constant of middle dielectric layer, the thickness of inner core radius and outer shell layer. LSPR shift of the longest wavelength $\left |\omega _{-}^{-}\right >$ is red-shifted with increasing the inner core radius. It is interesting to find that longer wavelength $\left |\omega _{-}^{+}\right >$ mode is mainly effected by the ratio constant of the surrounding medium refractive index e 4 to the middle layer dielectric constant e 2. $\left |\omega _{-}^{+}\right >$ mode takes place a blue-shift with increasing inner core radius when e 2 > e 4, a red-shift when e 2 < e 4, and no-shifting when e 2 = e 4. However, the influence of dielectric layer radius to $\left |\omega _{-}^{+}\right >$ mode shows the different property as that of increasing the inner core radius. The underlying mechanisms are analyzed with the plasmon hybridization theory and the distribution of induced charge interaction between the inner core and outer shell. In addition, the influence of core radius, middle dielectric layer radius and outer shell radius to sensitivity of Ag-dielectric-Ag multi-layered nanoshell are also reported, a higher sensitivity could be gotten by adjusting geometrical parameters. Our theoretical study could give an easy way to analyze properties of the core-shell nanosphere based on plasmon hybridization theory and the induced charge interaction, and usefully broaden the applications in nano-optics.

A complete quantum cooling cycle may be a useful platform for studying quantum thermodynamics just as the quantum heat engine does. Entropy change is an important feature which can help us to investigate the thermodynamic properties of the single ion cooling process. Here, we analyze the entropy change of the ion and laser field in the single ion cooling cycle by generalizing the idea in Reference (Phys. Rev. Lett. 2015, 114, 043002) to a single ion system. Thermodynamic properties of the single ion cooling process are discussed and it is shown that the Second and Third Laws of Thermodynamics are still strictly held in the quantum cooling process. Our results suggest that quantum cooling cycles are also candidates for the investigation on quantum thermodynamics besides quantum heat engines.

Adiabatic quantum computing (AQC) is an approach for solving optimization problems and has advantages against environmental decoherence and certain kinds of random unitary perturbations; however, long coherence time of quantum systems is required to meet the adiabatic criteria for the implementation of AQC. To break the dilemma of evolution time in AQC, the method of shortcuts to adiabaticity (STA) is employed to speed up the evolution process and suppress the nonadiabatic transitions. In this work we demonstrate the application of STA in AQC by implementing a fast two-bit Grover's algorithm with STA in an ion trap system, and the method here is also applicable for realizing Grover's algorithm with more entries.

A quantum algorithm of SU(N) Yang-Mills theory is formulated in terms of quantum circuits. It can nonperturbatively calculate the Dyson series and scattering amplitudes with polynomial complexity. The gauge fields in the interaction picture are discretized on the same footing with the lattice fermions in momentum space to avoid the fermion doubling and the gauge symmetry breaking problems. Applying the algorithm to the quantum simulation of quantum chromodynamics, the quark and gluon's wave functions evolved from the initial states by the interactions can be observed and the information from wave functions can be extracted at any discrete time. This may help us understand the natures of the hadronization which has been an outstanding question of significant implication on high energy phenomenological studies., 9 pages, 1 figure

In quantum mechanics, the expectation value of an operator can be measured by using the projective measurement, if the coupling between the measured system and pointer is strong enough. However in the weak coupling regime, the pointer can not show all the eigenvalue of the physical quantity directly due to the overlapping among the pointer states, which makes the measurement of the expectation value difficult. In this paper, we propose an expectation value measurement method in the weak coupling regime inspired by the weak measurement scheme. Compared to the projective measurement, our scheme has two obvious advantages. Experimentally we use the internal state and motional state of a single trapped 40Ca+ to establish the measurement scheme and realize the proof of principle demonstration of the scheme.

A near-band digital predistortion technique is proposed to linearise a wideband power amplifier (PA) with millimetre wave (mmWave) non-contiguous carrier aggregation (CA). The proposed method employs low-bandwidth linearisation architecture to only focus on the in-band compensation and part of the out-of-band (OOB) distortion suppression, which largely alleviate the bandwidth limitation for baseband operation. Experiments have been carried out on an mmWave PA with the centre frequency of 41 GHz. Good measurement results can be achieved when the PA is excited by a very wideband modulated signal with 1001 CA configuration and the total bandwidth of 640 MHz.

The Weyl equation describes chiral massless relativistic particles, called Weyl fermions, which have important relations to neutrinos. A direct observation of the dynamics of Weyl fermions in an experiment is difficult to achieve. This study investigates a method of simulating the Weyl equation in 1+2-dimension by a single trapped ion. The predictions about a two-dimensional Zitterbewegung and an especially interesting phenomenon of Weyl fermions can be tested by the future trapped ion experiment, which might enhance our understanding of neutrinos., 6 pages, 3 figures

A feedback control method for producing an equidistant ion string in a surface-electrode ion trap has been experimentally demonstrated. This method features three advantages: (i) The optimal voltage can be constrained within the specified reachable range. (ii) The height of trapped ions from the trap surface can be maintained at the same value when strings with different number of ions or with different ion spacings are to be trapped. (iii) This method is resistant to a stray electric field near the trap. By this method, the asymmetry of the ion string caused by a stray field is minimized. The robustness of trapping a variable number of ions at the same potential and the dependency of the axial frequency on the number of ions are also investigated experimentally. This work would be a practical method to create a linear ion string with a large number of ions and may find applications in large-scale quantum computing, quantum simulation, and phase transition studies utilizing homogeneous ion strings.

Entangled light beams are important resources for quantum information processing. For some applications like teleportation, only the entanglement between two wave packets (two harmonic oscillators) is needed. So the calculation of output-photon entanglement involves projecting continuous output modes onto wave-packet modes by filter functions, thus resulting in a strong dependence of entanglement on the filter functions. In this paper, we aim at optimizing the filter functions to obtain a large entanglement in a relatively short time, which is important for utilizing the entangled light beams more efficiently in real experiments. We outline the general optimization procedures based on our previous schemes of generating entangled beams in a multimode optomechanical system. Moreover, we give analytic insights into as well as physical explanations of the wave-packet optimization, which are helpful for experimental estimations.

Based on a variant of 2-site Jaynes-Cummings-Hubbard model, which is constructed using superconducting circuits, we propose a method to coherently superpose the localized and delocalized phases of photons. In our model, two nonlinear superconducting stripline resonators are coupled by an interfacial circuit composed of parallel combination of a superconducting qubit and a capacitor, which plays the role of a quantum knob for the photon hopping rate: with the knob qubit in its ground/excited state, the injected photons tend to be localized/delocalized in the resonators. We show that, by applying a microwave field with appropriate frequency on the knob qubit, we could demonstrate Rabi oscillation between photonic localized phase and delocalized phase. Furthermore, this set-up offers advantages (e. g. infinite on/off ratio) over other proposals for the realization of scalable quantum computation with superconducting qubits., Comment: 4 pages, 4 figures

We propose a method for implementing the Grover search algorithm directly in a database containing any number of items based on multi-level systems. Compared with the searching procedure in the database with qubits encoding, our modified algorithm needs fewer iteration steps to find the marked item and uses the carriers of the information more economically. Furthermore, we illustrate how to realize our idea in cavity QED using Zeemanʼs level structure of atoms. And the numerical simulation under the influence of the cavity and atom decays shows that the scheme could be achieved efficiently within current state-of-the-art technology.

Wave function is important for determining decay constants fD−S and fD−. Using the 5 types of D meson wave functions in the heavy quark limit, we studied the uncertainties of radiative pure-leptonic decays of D−S(D−) mesons. The branching ratios are (1.025390−1.706812)×10−5 and (0.953498−1.576725)×10−6 for D−S and D− decays, respectively, which are sensitive to the type of wave function.

We investigate the possibility of enhancement of cooling a trapped ion by combining the electromagnetically induced transparency (EIT) effect with the standing-wave coupling. Our study shows that the quantum destructive interference which is caused by the EIT effect and the standing-wave coupling can cancel all the dominant heating effects if appropriate parameters are chosen. The analytical predictions and numerical simulations show that the final temperature can be much lower than the recoil energy. In addition, this fast-cooling scheme is robust against fluctuations of the strength of the laser beams, which makes it more feasible for experimental realization.

To explore the value of diffusion-weighted imaging (DWI) and magnetic resonance imaging (MRI) on the follow-up of nasopharyngeal carcinoma (NPC) after radiotherapy.Eighty-three NPC patients after radiotherapy were divided into two groups: 4 cases of residual tumor and 33 cases of non-residual within 6 months, the cases of recurrent and non-recurrent were 5 and 41 over 6 months, respectively. MRI and DWI imaging of these cases were closely analyzed, and the apparent diffusion coefficient (ADC) of the nasopharyngeal residual mass and nasopharyngeal wall thickening, skull base destruction and lateral pterygoid muscle were measured.The ADC of the lateral pterygoid muscle was (1.501 ± 0.069) × 10formula^{ - 3}/formulammformula^{2}/formula/s in 83 cases. The ADCs of the non-residual group, residual group, non-recurrent group and recurrent group were (1.843 ± 0.133.4) × 10formula^{ - 3}/formulammformula^{2}/formula/s, (1.097 ± 0.183) × 10formula^{ - 3}/formulammformula^{2}/formula/s, (1.884 ± 0.134) × 10formula^{ - 3}/formulammformula^{2}/formula/s and (0.787 ± 0.067) × 10formula^{ - 3}/formulammformula^{2}/formula/s respectively.The ADCs of the residual group and recurrent group were lower than that of the lateral pterygoid muscle, while the ADCs of the non-residual group and non-recurrent group were higher than that of the lateral pterygoid muscle.The differences were statistically significant (P0.05).DWI can provide qualitative and quantitative information about the tumor cellular level; it can also identify residual, local fibrosis and recurrence after NPC radiotherapy sensitively and accurately by measuring the ADC of the region of interest.

The application of the 1.2-m altazimuth telescope of the Yunnan Observatory to astronomical observation and the method of image acquisition and processing are described. A new distinctive global pointing model has greatly improved the pointing accuracy of the telescope to 1" and this has been verified in the practical application over many years.

We investigate the cooling dynamics of a trapped $\ensuremath{\Lambda}$-configuration atom coupling to a high-finesse cavity. We find that the heating effects due to diffusion and heating transitions can be simultaneously suppressed by the cavity-induced transparency and the electromagnetically induced transparency effects, respectively. Compared to the current cavity cooling schemes, the trapped atom in our scheme can be cooled to a relatively lower final temperature.

We propose a theoretical scheme to generate flux-qubit clusters using $\mathit{XY}$ interactions. In our scheme, two neighboring qubits are coupled via a dc superconducting quantum interference device (SQUID). All flux qubits are always biased at their optimal points. The $\mathit{XY}$ interaction can be controlled by the bias current applied to the SQUID for the two coupled qubits with the same resonance frequencies or by the frequency of a microwave pulse applied to the SQUID for the two coupled qubits with unequal resonance frequencies. The generation of a $d$-dimensional cluster state needs only $2d$ steps. Existing technology allows us to rapidly modulate the bias current and easily control the frequency of the pulse, and thus our scheme is experimentally feasible.

For the transmon, its dephasing has experimentally been suppressed to an extent that dephasing time is mainly limited by the relaxation process [Schreier et al., Phys. Rev. B 77, 180502(R) (2008)]. In the Hilbert space of two transmons, there exists a two-dimensional subspace immune to the collective relaxation. In this paper, by encoding a logical qubit in this subspace, we demonstrate how to realize universal quantum computation in the decoherence-free subspace. In our scheme, the transmons are coupled through a one-dimensional superconducting transmission-line resonator. With the help of some classical driving fields, two noncommutable single-logical-qubit rotation operators and a controlled-phase gate between two logical qubits are obtained. We always work in the detuning regime, which largely decreases relaxation induced by the Purcell effect.

Cooling mechanical resonators to a quantum regime at high temperatures is important in terms of exploring and applying their quantum effects unrestricted by low environmental temperatures. It has been suggested by M. Bhattacharya et al. [Phys. Rev. A 77, 033819 (2008)] that quadratic coupling could be used to help cool a membrane in membrane-in-the-middle optomechanical systems (MMOSs) at room temperature to a state with a mean phonon number smaller than 1. Its cooling effect is actually overestimated because of the unconsidered factor that it is limited by the small frequency difference between the quadratically coupled cavity mode and its neighboring mode, which imposes an upper bound on the input trapping laser power and therefore restricts its cooling effect. Based on the MMOS and by taking the above factors into consideration, we have concretely investigated the performance of this cooling method by a more rigorous calculation. Our calculation shows that the cooling effect is indeed ultimately limited by the input trapping laser power, but one can still cool a membrane close to a quantum regime at 77 K with parameters approaching experimental values.

We propose a scalable and robust architecture for one-way quantum computation using coupled networks of superconducting transmission line resonators. In our protocol, quantum information is encoded into the long-lived photon states of the resonators, which have a much longer coherence time than the usual superconducting qubits. Each resonator contains a charge qubit used for the state initialization and local projective measurement of the photonic qubit. Any pair of neighboring photonic qubits are coupled via a mediator charge qubit, and large photonic cluster states can be created by applying Stark-shifted Rabi pulses to these mediator qubits. The distinct advantage of our architecture is that it combines both the excellent scalability of the solid-state systems and the long coherence time of the photonic qubits. Furthermore, this architecture is very robust against the parameter variations., 6 pages, 3 figures

We study the dynamics of the multipartite systems nonresonantly interacting with electromagnetic fields and show that, since the coupling strength $g$ is collectively enhanced by the square root of the number of microparticles involved, the more rigorous large detuning condition for neglecting the rapidly oscillating terms for the effective Hamiltonian should be $\Delta\gg\sqrt{N}g$, instead of $\Delta\gg g$ usually used in the literature even in the case of multipartite systems, with $\Delta$ the detuning and and $N$ the number of microparticles. This result is significant since merely the satisfaction of the original condition will result in the invalidity of the effective Hamiltonian and the errors of the parameters associated with the detuning in the multipartite case.

We give a concrete experimental scheme for engineering the insulator-superfluid transition of light in a one-dimensional (1D) array of coupled superconducting stripline resonators. In our proposed architecture, the on-site interaction and the photon-hopping rate can be tuned independently by adjusting the transition frequencies of the charge qubits inside the resonators and at the resonator junctions, respectively, which permits us to systematically study the quantum phase transition of light in a complete parameter space. By combining the techniques of photon-number-dependent qubit transition and fast readout of the qubit state using a separate low-$Q$ resonator mode, the statistical property of the excitations in each resonator can be obtained with a high efficiency. An analysis of the various decoherence sources and disorders shows that our scheme can serve as a guide to upcoming experiments involving a small number of coupled resonators.

We propose a scheme for storing arbitrary states of two superconducting charge qubits in a single Rb-87 cold-atom ensemble. The information of the two charge qubits is transferred sequentially into the single atomic ensemble, via a transmission line resonator serving as "data bus." We simulate the storage process by integrating the master equation that takes into account all kinds of decoherence mechanisms, and show that the mean storage fidelity is very high with the present experimental parameters. Moreover, the storage efficiency of the single ensemble in our scheme is double that of previous schemes. Finally, we also briefly discuss the possibilities and difficulties of extending it to multiqubit cases.

We propose a theoretical protocol for a quantum phase gate between two transmon qubits capacitively coupled to a superconducting transmission line resonator driven by a strong microwave field. Compared with previous protocols involving a dispersive regime, our protocol works at a small detuning, {Delta}{approx}g, and the nontrivial two-qubit gates can be realized in a short time, {approx}1/g, where g is the qubit-resonator coupling strength. Our analysis shows that the protocol is robust against the main decoherence sources and unavoidable parameter variations. Moreover, our protocol can be implemented using the current experimental design of circuit QED.

In this Brief Report, we propose a potential scheme to implement one-way quantum computation with circuit quantum electrodynamics (QED). Large cluster states of charge qubits can be generated in just one step with a superconducting transmission line resonator (TLR) playing the role of a dispersive coupler. A single-qubit measurement in the arbitrary basis can be implemented using a single electron transistor with the help of one-qubit gates. By examining the main decoherence sources, we show that circuit QED is a promising architecture for one-way quantum computation.

We present a method to implement the quantum partial search of the database separated into any number of blocks with qudits, D-level quantum systems. Compared with the partial search using qubits, our method needs fewer iteration steps and uses the carriers of the information more economically. To illustrate how to realize the idea with concrete physical systems, we propose a scheme to carry out a twelve-dimensional partial search of the database partitioned into three blocks with superconducting quantum interference devices (SQUIDs) in cavity QED. Through the appropriate modulation of the amplitudes of the microwave pulses, the scheme can overcome the non-identity of the cavity—SQUID coupling strengths due to the parameter variations resulting from the fabrication processes. Numerical simulation under the influence of the cavity and SQUID decays shows that the scheme could be achieved efficiently within current state-of-the-art technology.

In this paper, we study the slow propagation characteristics of surface electromagnetic waves according to theoretical analysis in the MNG (μ-negative)-DPS (double-positive)-MNG waveguide, which is composed of two-dimensional (2D) metamaterials. The dispersion curves of this waveguide vary with circuit parameter (unit capacitors) of MNG metamaterial. At the cutoff frequency of the dispersion curve the group velocity of electromagnetic wave is equal to zero in theory. So we can obtain slow propagation of the surface waves at different cutoff frequencies just by changing the unit capacitor of the MNG metamaterial. Theoretical analysis also shows that the step changes in slow waves are obtained at some fixed frequencies through changing the unit circuit parameters. The experimental results are in good agreement with simulation results.

A GaAs MESFET monolithic variable attenuator has been developed covering 2-20GHz bandwidth. A novel DC biasing and control scheme, by applying control voltage to the gate as well as the drain/source nodes of the MESFETs, allows the biasing and control of the IC through a single positive external voltage source combined with a variable voltage divider. The attenuation is variable from 2.4dB to 14.0dB, at 20GHz. The attenuation flatness versus frequency is within +?0.5dB, and the input and output VSWRs are less than 2:1, over the entire frequency and control range.