Despite abundant accessible traffic data, researches on traffic flow estimation and optimization still face the dilemma of detailedness and integrity in the measurement. A dataset of city-scale vehicular continuous trajectories featuring the finest r
esolution and integrity, as known as the holographic traffic data, would be a breakthrough, for it could reproduce every detail of the traffic flow evolution and reveal the personal mobility pattern within the city. Due to the high coverage of Automatic Vehicle Identification (AVI) devices in Xuancheng city, we constructed one-month continuous trajectories of daily 80,000 vehicles in the city with accurate intersection passing time and no travel path estimation bias. With such holographic traffic data, it is possible to reproduce every detail of the traffic flow evolution. We presented a set of traffic flow data based on the holographic trajectories resampling, covering the whole 482 road segments in the city round the clock, including stationary average speed and flow data of 5-minute intervals and dynamic floating car data.
We propose an experimentally accessible superconducting quantum circuit, consisting of two coplanar waveguide resonators (CWRs), to enhance the microwave squeezing via parametric down-conversion (PDC). In our scheme, the two CWRs are nonlinearly coup
led through a superconducting quantum interference device embedded in one of the CWRs. This is equivalent to replacing the transmission line in a flux-driven Josephson parametric amplifier (JPA) by a CWR, which makes it possible to drive the JPA by a quantized microwave field. Owing to this design, the PDC coefficient can be considerably increased to be about tens of megahertz, satisfying the strong-coupling condition. Using the Heisenberg-Langevin approach, we numerically show the enhancement of the microwave squeezing in our scheme. In contrast to the JPA, our proposed system becomes stable around the critical point and can generate stronger transient squeezing. In addition, the strong-coupling PDC can be used to engineer the photon blockade.
Let $f_0$ be a polynomial of degree $d_1+d_2$ with a periodic critical point $0$ of multiplicity $d_1-1$ and a Julia critical point of multiplicity $d_2$. We show that if $f_0$ is primitive, free of neutral periodic points and non-renormalizable at t
he Julia critical point, then the straightening map $chi_{f_0}:mathcal C(lambda_{f_0}) to mathcal C_{d_1}$ is a bijection. More precisely, $f^{m_0}$ has a polynomial-like restriction which is hybrid equivalent to some polynomial in $mathcal C_{d_1}$ for each map $f in mathcal C(lambda_{f_0})$, where $m_0$ is the period of $0$ under $f_0$. On the other hand, $f_0$ can be tuned with any polynomial $gin mathcal C_{d_1}$. As a consequence, we conclude that the straightening map $chi_{f_0}$ is a homeomorphism from $mathcal C(lambda_{f_0})$ onto the Mandelbrot set when $d_1=2$. This together with the main result in [SW] solve the problem for primitive tuning for cubic polynomials with connected Julia sets thoroughly.
In this paper, we consider the renormalization operator $mathcal R$ for multimodal maps. We prove the renormalization operator $mathcal R$ is a self-homeomorphism on any totally $mathcal R$-invariant set. As a corollary, we prove the existence of the
full renormalization horseshoe for multimodal maps.
Using quasiconformal surgery, we prove that any primitive, postcritically-finite hyperbolic polynomial can be tuned with an arbitrary generalized polynomial with non-escaping critical points, generalizing a result of Douady-Hubbard for quadratic poly
nomials to the case of higher degree polynomials. This solves affirmatively a conjecture by Inou and Kiwi on surjectivity of the renormalization operator on higher degree polynomials in one complex variable.
A cavity quantum electrodynamical (QED) system beyond the strong-coupling regime is expected to exhibit intriguing quantum phenomena. Here we report a direct measurement of the photon-dressed qubit transition frequencies up to four photons by harness
ing the same type of state transitions in an ultrastrongly coupled circuit-QED system realized by inductively coupling a superconducting flux qubit to a coplanar-waveguide resonator. This demonstrates a convincing observation of the photon-dressed Bloch-Siegert shift in the ultrastrongly coupled quantum system. Moreover, our results show that the photon-dressed Bloch-Siegert shift becomes more pronounced as the photon number increases, which is a characteristic of the quantum Rabi model.
We explore the quantum criticality of a two-site model combining quantum Rabi models with hopping interaction. Through a combination of analytical and numerical approaches, we find that the model allows the appearance of a superradiant quantum phase
transition (QPT) even in the presence of strong $mathbf{A}^2$ terms, preventing single-site superradiance. In the two-site model the effect of $mathbf{A}^2$ terms can be surmounted by the photon delocalization from hopping, and a reversed superradiant QPT occurs as a consequence of the competition between $mathbf{A}^2$ terms and the hopping interaction. We characterize the phase diagram and scaling functions, and extract the critical exponents in the vicinity of the critical point, thus establishing the universal behavior of the second-order phase transition. Remarkably the effective hopping strength will be enhanced if more cavities are cascaded. We also prove that the multi-qubit counterpart of the quantum Rabi dimer, i.e., the Dicke dimer, has the same properties in beating the $mathbf{A}^2$ effect. Our work provides a way to the study of phase transitions in presence of the $mathbf{A}^2$ terms and offers the prospect of investigating quantum-criticality physics and quantum devices in many-body systems.
We present an analytical method for the two-qubit quantum Rabi model. While still operating in the frame of the generalized rotating-wave approximation (GRWA), our method further embraces the idea of introducing variational parameters. The optimal va
lue of the variational parameter is determined by minimizing the energy function of the ground state. Comparing with numerical exact results, we show that our method evidently improves the accuracy of the conventional GRWA in calculating fundamental physical quantities, such as energy spectra, mean photon number, and dynamics. Interestingly, the accuracy of our method allows us to reproduce the asymptotic behavior of mean photon number in large frequency ratio for the ground state and investigate the quasi-periodical structure of the time evolution, which are incapable of being predicted by the GRWA. The applicable parameter ranges cover the ultrastrong coupling regime, which will be helpful to recent experiments.
We explore the fidelity susceptibility and the quantum coherence along with the entanglement entropy in the ground-state of one-dimensional spin-1 XXZ chains with the rhombic single-ion anisotropy. By using the techniques of density matrix renormaliz
ation group, effects of the rhombic single-ion anisotropy on a few information theoretical measures are investigated, such as the fidelity susceptibility, the quantum coherence and the entanglement entropy. Their relations with the quantum phase transitions are also analyzed. The phase transitions from the Y-N{e}el phase to the Large-$E_x$ or the Haldane phase can be well characterized by the fidelity susceptibility. The second-order derivative of the ground-state energy indicates all the transitions are of second order. We also find that the quantum coherence, the entanglement entropy, the Schmidt gap can be used to detect the critical points of quantum phase transitions. Conclusions drawn from these quantum information observables agree well with each other. Finally we provide a ground-state phase diagram as functions of the exchange anisotropy $Delta$ and the rhombic single-ion anisotropy $E$.
Promising applications of the anisotropic quantum Rabi model (AQRM) in broad parameter ranges are explored, which is realized with superconducting flux qubits simultaneously driven by two-tone time-dependent magnetic fields. Regarding the quantum pha
se transitions (QPTs), with assistant of fidelity susceptibility, we extract the scaling functions and the critical exponents, with which the universal scaling of the cumulant ratio is captured with rescaling of the parameters due to the anisotropy. Moreover, a fixed point of the cumulant ratio is predicted at the critical point of the AQRM. In respect to quantum information tasks, the generation of the macroscopic Schr{o}dinger cat states and quantum controlled phase gates are investigated in the degenerate case of the AQRM, whose performance is also investigated by numerical calculation with practical parameters. Therefore, our results pave a way to explore distinct features of the AQRM in circuit QED systems for QPTs, quantum simulations and quantum information processings.
