Quantum memory and non-demolition measurement of single phonon state with nitrogen-vacancy centers ensemble

In diamond, the mechanical vibration induced strain can lead to interaction between the mechanical mode and the nitrogen-vecancy (NV) centers. In this work, we propose to utilize the strain induced coupling for the quantum non-demolition (QND) single phonon measurement and memory in diamond. The single phonon in a diamond mechanical resonator can be perfectly absorbed and emitted by the NV centers ensemble (NVE) with adiabatically tuning the microwave driving. An optical laser drives the NVE to the excited states, which have much larger coupling strength to the mechanical mode. By adiabatically eliminating the excited states under large detuning limit, the effective coupling between the mechanical mode and the NVE can be used for QND measurement of the single phonon state. Under realistic experimental conditions, we numerically simulate the scheme. It is found that the fidelity of the absorbing and emitting process can reach a much high value. The overlap between the input and the output phonon shapes can reach $98.57\%$.Comment: 7 pages, 3 figure

Topolgical Charged Black Holes in Generalized Horava-Lifshitz Gravity

As a candidate of quantum gravity in ultrahigh energy, the $(3+1)$-dimensional Ho\v{r}ava-Lifshitz (HL) gravity with critical exponent $z\ne 1$, indicates anisotropy between time and space at short distance. In the paper, we investigate the most general $z=d$ Ho\v{r}ava-Lifshitz gravity in arbitrary spatial dimension $d$, with a generic dynamical Ricci flow parameter $\lambda$ and a detailed balance violation parameter $\epsilon$. In arbitrary dimensional generalized HL$_{d+1}$ gravity with $z\ge d$ at long distance, we study the topological neutral black hole solutions with general $\lambda$ in $z=d$ HL$_{d+1}$, as well as the topological charged black holes with $\lambda=1$ in $z=d$ HL$_{d+1}$. The HL gravity in the Lagrangian formulation is adopted, while in the Hamiltonian formulation, it reduces to Dirac$-$De Witt's canonical gravity with $\lambda=1$. In particular, the topological charged black holes in $z=5$ HL$_6$, $z=4$ HL$_5$, $z=3,4$ HL$_4$ and $z=2$ HL$_3$ with $\lambda=1$ are solved. Their asymptotical behaviors near the infinite boundary and near the horizon are explored respectively. We also study the behavior of the topological black holes in the $(d+1)$-dimensional HL gravity with $U(1)$ gauge field in the zero temperature limit and finite temperature limit, respectively. Thermodynamics of the topological charged black holes with $\lambda=1$, including temperature, entropy, heat capacity, and free energy are evaluated.Comment: 51 pages, published version. The theoretical framework of z=d HL gravity is set up, and higher curvature terms in spatial dimension become relevant at UV fixed point. Lovelock term, conformal term, new massive term, and Chern-Simons term with different critical exponent z are studie

Thermodynamics of Black Holes in Massive Gravity

We present a class of charged black hole solutions in an ($n+2)$-dimensional massive gravity with a negative cosmological constant, and study thermodynamics and phase structure of the black hole solutions both in grand canonical ensemble and canonical ensemble. The black hole horizon can have a positive, zero or negative constant curvature characterized by constant $k$. By using Hamiltonian approach, we obtain conserved charges of the solutions and find black hole entropy still obeys the area formula and the gravitational field equation at the black hole horizon can be cast into the first law form of black hole thermodynamics. In grand canonical ensemble, we find that thermodynamics and phase structure depends on the combination $k -\mu^2/4 +c_2 m^2$ in the four dimensional case, where $\mu$ is the chemical potential and $c_2m^2$ is the coefficient of the second term in the potential associated with graviton mass. When it is positive, the Hawking-Page phase transition can happen, while as it is negative, the black hole is always thermodynamically stable with a positive capacity. In canonical ensemble, the combination turns out to be $k+c_2m^2$ in the four dimensional case. When it is positive, a first order phase transition can happen between small and large black holes if the charge is less than its critical one. In higher dimensional ($n+2 \ge 5$) case, even when the charge is absent, the small/large black hole phase transition can also appear, the coefficients for the third ($c_3m^2$) and/or the fourth ($c_4m^2$) terms in the potential associated with graviton mass in the massive gravity can play the same role as the charge does in the four dimensional case.Comment: Latex 19 pages with 8 figure

Study on dynamic response of track structures under a variable speed moving harmonic load

Basing on the dynamic response characteristics of the periodic structure under a moving harmonic load in frequency domain and the superposition principle, the dynamic response of track structure under variable speeds moving harmonic load is investigated. Firstly, the track is simplified as an Euler beam model periodically supported by continuous discrete point, the dynamic differential equation of vertical vibration for the track structure is formulated. Secondly, for convenience of analysis, the analytical expression for the amplitude-frequency response of any point on the track structure under the moving harmonic load is derived in frequency domain. Based on the theory of the infinite periodic structure, the dynamic responses of the track structure under the variable speed moving harmonic load are analyzed theoretically. Finally, the influences of velocity and acceleration on the dynamic response of track structure are numerically analyzed in detail. The research results indicate that the amplitude-frequency response peaks of the track under moving harmonic load with variable and constant speeds occur near the excitation frequency. The displacement response of the track increases slightly with increase of the acceleration, and the variation trend of dynamic response is basically similar. The vibration displacement response of the rail can be effectively improved by increasing the initial velocity of the moving harmonic load, while the peak value of amplitude-frequency response remained constant