Transparency and amplification in a hybrid system of mechanical resonator and circuit QED

We theoretically study the transparency and amplification of a weak probe field applied to the cavity in hy- brid systems formed by a driven superconducting circuit QED system and a mechanical resonator, or a driven optomechanical system and a superconducting qubit. We find that both the mechanical resonator and the su- perconducting qubit can result in the transparency to a weak probe field in such hybrid systems when a strong driving field is applied to the cavity. We also find that the weak probe field can be amplified in some parameter regimes. We further study the statistical properties of the output field via the degrees of second-order coherence. We find that the nonclassicality of the output field strongly depends on the system parameters. Our studies show that one can control single-photon transmission in the optomechanical system via a tunable artificial atom or in the circuit QED system via a mechanical resonator.Comment: 9 pages, 9 figure

Engineering of nonclassical motional states in optomechanical systems

We propose to synthesize arbitrary nonclassical motional states in optomechanical systems by using sideband excitations and photon blockade. We first demonstrate that the Hamiltonian of the optomechanical systems can be reduced, in the strong single-photon optomechanical coupling regime when the photon blockade occurs, to one describing the interaction between a driven two-level trapped ion and the vibrating modes, and then show a method to generate target states by using a series of classical pulses with desired frequencies, phases, and durations. We further analyze the effect of the photon leakage, due to small anharmonicity, on the fidelity of the expected motional state, and study environment induced decoherence. Moreover, we also discuss the experimental feasibility and provide operational parameters using the possible experimental data.Comment: 11 pages, 4 figure

All-optical transistor based on Rydberg atom-assisted opto-mechanical system

We study the optical response of double optomechanical cavity system assisted by Rydberg atomic ensembles. And atomic ensembles are only coupled with one side cavity by a single cavity mode. It has been realized that a long-range manipulation for optical properties of hybrid system, by controlling the Rydberg atomic ensembles decoupled with the optomechanical cavity. Switching on the coupling between atoms and cavity mode, the original time reversal symmetry of double cavity structure has been broken. Based on the controlled optical non-reciprocity, we put forward the theoretical schemes of all-optical controlled diode, rectifier and transistor

Active User Detection of Uplink Grant-Free SCMA in Frequency Selective Channel

Massive machine type communication (mMTC) is one of the three fifth generation mobile networking (5G) key usage scenarios, which is characterized by a very large number of connected devices typically transmitting a relatively low volume of non-delay sensitive data. To support the mMTC communication, an uplink (UL) grant-free sparse code multiple access (SCMA) system has been proposed. In this system, the knowledge of user equipments' (UEs') status should be obtained before decoding the data by a message passing algorithm (MPA). An existing solution is to use the compressive sensing (CS) theory to detect active UEs under the assumed condition of flat fading channel. But the assumed condition is not suitable for the frequency selective channel and will decrease the accuracy of active UEs detection. This paper proposes a new simple module named refined active UE detector (RAUD), which is based on frequency selective channel gain analyzing. By making full use of the channel gain and analyzing the difference between characteristic values of the two status of UEs, RAUD module can enhance the active UEs detection accuracy. Meanwhile, the addition of the proposed module has a negligible effect on the complexity of UL grant-free SCMA receiver

Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry

We carefully study how the fermion-fermion interactions affect the low-energy states of a two-dimensional spin-$1/2$ fermionic system on the kagom\'{e} lattice with a quadratic band crossing point. With the help of the renormalization group approach, we can treat all kinds of fermionic interactions on the the same footing and then establish the coupled energy-dependent flows of fermionic interaction parameters via collecting one-loop corrections, from which a number of interesting results are extracted in the low-energy regime. At first, various sorts of fermion-fermion interactions furiously compete with each other and are inevitably attracted by certain fixed point in the parameter space, which clusters into three qualitatively distinct regions relying heavily upon the structure parameters of materials. In addition, we notice that an instability accompanied by some symmetry breaking is triggered around different sorts of fixed points. Computing and comparing susceptibilities of twelve potential candidates indicates that charge density wave always dominates over all other instabilities. Incidently, there exist several subleading ones including the $x$-current, bond density, and chiral plus s-wave superconductors. Finally, we realize that strong fluctuations nearby the leading instability prefer to suppress density of states and specific heat as well compressibility of quasiparticles in the lowest-energy limit.Comment: 22 pages, 12 figures; Nulcear Physics B 966, 115371 (2021

Statistical Methods and Computing for Big Data

Big data are data on a massive scale in terms of volume, intensity, and complexity that exceed the capacity of standard software tools. They present opportunities as well as challenges to statisticians. The role of computational statisticians in scientific discovery from big data analyses has been under-recognized even by peer statisticians. This article reviews recent methodological and software developments in statistics that address the big data challenges. Methodologies are grouped into three classes: subsampling-based, divide and conquer, and sequential updating for stream data. Software review focuses on the open source R and R packages, covering recent tools that help break the barriers of computer memory and computing power. Some of the tools are illustrated in a case study with a logistic regression for the chance of airline delay

Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity

In this paper, a pricing formula for volatility swaps is delivered when the underlying asset follows the stochastic volatility model with jumps and stochastic intensity. By using Feynman-Kac theorem, a partial integral differential equation is obtained to derive the joint moment generating function of the previous model. Moreover, discrete and continuous sampled volatility swap pricing formulas are given by employing transform techniques and the relationship between two pricing formulas is discussed. Finally, some numerical simulations are reported to support the results presented in this paper.Comment: 15PAGE

Ice-Flower Systems And Star-graphic Lattices

Lattice theory has been believed to resist classical computers and quantum computers. Since there are connections between traditional lattices and graphic lattices, it is meaningful to research graphic lattices. We define the so-called ice-flower systems by our uncolored or colored leaf-splitting and leaf-coinciding operations. These ice-flower systems enable us to construct several star-graphic lattices. We use our star-graphic lattices to express some well-known results of graph theory and compute the number of elements of a particular star-graphic lattice. For more researching ice-flower systems and star-graphic lattices we propose Decomposition Number String Problem, finding strongly colored uniform ice-flower systems and connecting our star-graphic lattices with traditional lattices

Phonon amplification in two coupled cavities containing one mechanical resonator

We study a general theory of phonon lasing [I. S. Grudinin et al., Phys. Rev. Lett. 104, 083901 (2010)] in coupled optomechancial systems. We derive the dynamical equation of the phonon lasing using supermodes formed by two cavity modes. A general threshold condition for phonon lasing is obtained. We also show the differences between phonon lasing and photon lasing, generated by photonic supermodes and two-level atomic systems, respectively. We find that the phonon lasing can be realized in certain parameter regime near the threshold. The phase diagram and second-order correlation function of the phonon lasing are also studied to show some interesting phenomena that cannot be observed in the common photon lasing with the two-level systems.Comment: 11 pages, 8 figure

Creation of a new vector field and focusing engineering

Recently many methods have been proposed to create the vector fields, due to the academic interest and a variety of attractive applications such as for particle acceleration, optical trapping, particle manipulation, and fluorescence imaging. For the most of the created vector fields, the spatial distribution in states of polarization (SoPs) is dependent of azimuthal angle only. It is very interesting and crucial that if we can introduce the radial controlling freedom, which undoubtedly opens a new way to provide the flexibility for creating the desired vector fields and for fulfilling the requirement on a variety of applications. Here we present a new idea to create a new kind of vector filed with the radial-variant SoPs. This idea also permits to create flexibly vector fields with arbitrarily complex distribution of SoPs, based on a combination of radial and azimuthal dependency. This realization in both principle and experiment is paramount to be able to implement the focusing engineering for applications in a variety of realms. Specially arranging the SoPs of vector fields, purposefully and carefully, is anticipated to lead to new effects and phenomena that can expand the functionality and enhance the capability of optical systems, such as the optical trapping.Comment: 13 pages, 8 figure