Entanglements in a Coupled Cavity-Array with One Oscillating End-Mirror

Entanglements in a coupled cavity-array with one oscillating end-mirror

Wu Qin, Xiao Yin, Zhang Zhi-Ming Citation:Chin. Phys. B . 2015, 24(10): 104208. doi: 10.1088/1674-1056/24/10/104208

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Phys. B Vol. 24, No. 10 (2015) 104208

Entanglements in a coupled cavity–array with one oscillating end-mirror∗

Wu Qin(吴琴)a)b), Xiao Yin(肖银)a), and Zhang Zhi-Ming(张智明)a)†

a)Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices (SIPSE), Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China b)School of Information Engineering, Guangdong Medical University, Dongguan 523808, China

(Received 6 March 2015; revised manuscript received 21 April 2015; published online 20 August 2015)

We theoretically investigate the entanglement properties in a hybrid system consisting of an optical cavity–array coupled to a mechanical resonator. We show that the steady state of the system presents bipartite continuous variable entanglement in an experimentally accessible parameter regime. The effects of the cavity–cavity coupling strength on the bipartite entanglements in the field–mirror subsystem and in the field–field subsystem are studied. We further find that the entanglement between the adjacent cavity and the movable mirror can be entirely transferred to the distant cavity and mirror by properly choosing the cavity detunings and the coupling strength in the two-cavity case. Surprisingly, such a remote macroscopic entanglement tends to be stable in the large coupling regime and persists for environment temperatures at above 25 K in the three-cavity case. Such optomechanical systems can be used for the realization of continuous variable quantum information interfaces and networks.

Keywords: entanglement, coupled-cavity array, optomechanical system PACS: 42.50.Wk, 46.80.+j, 41.20.Cv DOI: 10.1088/1674-1056/24/10/104208

1. Introduction the field–mirror entanglement,[15–20] and the mirror–mirror entanglement.[21–24] These studies show that entanglement Entanglement, an important trait in quantum mechanics, can be influenced by the factors of the cavity optomechanical has become a key resource for many quantum processes.[1] system such as the intensity of incident laser and the cavity– Entanglement can be experimentally prepared and manipu- pump field detuning. In fact, entangled optomechanical sys- lated in microscopic systems, such as photons, ions, and tems have potential profitable applications in realizing quan- atoms.[2] However, it is not yet completely clear to what extent tum communication networks, in which the mechanical modes quantum mechanics applies to macroscopic objects. Quan- play the vital role of local nodes where quantum information tum phenomena such as entanglement generally do not appear can be stored and retrieved, and optical modes carry the infor- in the macroscopic world due to environment-induced deco- mation between the nodes. This allows the implementation of herence, which is thought to be the main cause that reduces continuous variable (CV) quantum teleportation,[25,26] quan- [3] any quantum superposition to a classical statistical mixture. tum telecloning,[27] and entanglement swapping.[28] Nonetheless, with the spectacular level of experimental ad- Recently, much attention has been focused on the coupled vancements, it has been possible to see macroscopic quantum cavity–array (CCA),[29,30] for which some potential technolo- [4] superpositions. gies have been demonstrated in experiment.[31,32] The system Cavity optomechanical systems have become important is thought to be suitable for building a large-scale architecture candidates for exploring what extent of quantum entangle- for quantum information processing.[33] These observations [5–13] ment we can obtain at the macroscopic level due to remind us of the necessity to explore the entanglement proper- the rapid progress of nanotechnology. The simplest scheme ties in a CCA with one oscillating end-mirror. Different from capable of generating stationary optomechanical entangle- the conventional CCA with a fixed end-mirror, the end mirror ment is studied in a typical optomechanical setup,[14] where in our system is modelled as a quantum-mechanical harmonic the entanglement between the cavity and the movable mir- oscillator. Due to the long decoherence of the mechanical har- ror is remarkable for its simplicity and robustness against monic oscillator, the information storage time of the mechan- temperature. In recent years, various schemes to gener- ical harmonic oscillator is longer than the field. Hence, it is ate bipartite entanglements have been proposed, such as helpful to the study of information transfer and information ∗Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91121023), the National Natural Science Foundation of China (Grant Nos. 61378012 and 60978009), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20124407110009), the National Basic Research Program of China (Grant Nos. 2011CBA00200 and 2013CB921804), and the Program for Changjiang Scholar and Innovative Research Team in Universities, China (Grant No. IRT1243). †Corresponding author. E-mail: [email protected] © 2015 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb http://cpb.iphy.ac.cn 104208-1 Chin. Phys. B Vol. 24, No. 10 (2015) 104208

† storage in the quantum information processing. In this paper, p˙ = −ωmq + ga aN − γm p + ξ, N √ we investigate the stationary bipartite CV entanglement in this in a˙1 = −i∆1a1 − iJa2 + E − κa1 + 2κa1 , coupled system quantified by the logarithmic negativity. We . . also show how the stationary entanglement between the adja- √ in cent optical cavity field and the mirror can be transferred to a˙ j = −i∆ ja j − iJa j−1 − iJa j+1 − κa j + 2κa j , the remote optical cavity field and the mirror by selecting ap- . . propriately the cavity–pump field detunings and the coupling √ in strength between coupled cavities. However, the field–field a˙N = −i∆NaN − iJaN−1 + igaNq − κaN + 2κaN , (2) entanglement is small at the same time. Moreover, such dis- in which we have assumed that all cavity–fields have the same tant entanglement between two non-interacting subsystems is decay rate κ. The mechanical oscillator is connected to a ther- robust against temperature above 25 K. mal bath at a damping rate γ with a mean thermal excitation The remainder of this paper is organized as follows. In m numbern ¯ = 1/(eh¯ωm/kBT − 1), where k is the Boltzmann con- Section 2 we present the model under study and the analytical B stant and T is the temperature of the mechanical bath. The expressions of the optomechanical system, derive the quantum mechanical mode is also affected by a random Brownian force Langevin equations and the steady state of the system. In Sec- with correlation function h (t) (t0)i ' (2n ¯ + 1) (t −t0). tion 3, we quantify the entanglement properties of the system ξ ξ ξ γm δ ain by using the logarithmic negativity. Finally we draw our con- Furthermore, j represents the input vacuum noise opera- hain(t)a†in(t0)i = clusions in Section 4. tor and its nonzero correlation function is j j δ(t − t0). In the following, we will focus on the case of two 2. Model and equations of motion coupled cavities (N = 2) and the case of three coupled cavities (N = 3). As schematically shown in Fig.1, the system consists of n coupled cavities (1,2,3,...,N) with coupling constant J. Cav- 2.1. The case of two coupled cavities ity 1 is driven by a pump field, and cavity N consists of an os- The steady-state mean values of the system can be ob- cillating mirror at one end, modelled as a quantum-mechanical tained by setting the time derivatives to zero: harmonic oscillator. In the rotating frame with frequency ω0 of the pump field, the Hamilton is given by ps = 0, 2 N N−1 g|a2s| † † † qs = , H = ∑ h¯∆ ja j a j + ∑ hJ¯ (a j a j+1 + a j+1a j) ωm j=1 j=1 −iJa a = 1s , h¯ωm 2 2 † † 2s κ + i∆ 0 + (p + q ) − hga¯ NaNq + ihE¯ (a1 − a1), (1) 2 2 E a = , (3) a (a†) 1s 2 0 where j j is the annihilation (creation) operator for the κ + i∆1 + J /(κ + i∆2) j-th cavity mode, and ∆ j = ω j − ω0 is the detuning of its fre- where ∆ 0 = ∆ − gq is the effective cavity detuning. quencies from the pump laser, which couples to cavity 1 with 2 2 s We can divide each Heisenberg operator as a steady-state amplitude E. E is related to the input power P and the cavity p p value plus an additional fluctuation operator with zero-mean damping rate κ by |E| = 2Pκ/h¯ω0. g = (ω0/L) h¯/mωm value, i.e., q = q +δq, p = p +δ p,a = a +δa ( j = 1,2), denotes the coupling between the mirror and cavity N, the op- s s j js j and get the linearized Langevin equations by neglecting some erator q (p) is the dimensionless position (momentum) of the small quantities mechanical oscillator with frequency ωm.

δq˙ = ωmδ p, 1 2 N † E, ω0 δ p˙ = −ωmδq + G1(δa2 + δa ) − γmδ p + ξ, 2 √ in δa˙1 = −(κ + i∆1)δa1 − iJδa2 + 2κa , 1 √ 0 in δa˙2 = −(κ + i∆2)δa2 − iJδa1 + iG1δq + 2κa2 , (4) Fig. 1. The model: A coupled cavity–array with one oscillating end-mirror. where G1 = ga2s is the effective coupling strength. Using the Heisenberg equations of motion, and taking 2.2. The case of three coupled cavities into account the corresponding damping and noise terms, we can get the quantum Langevin equations for the operators of In a similar way, we can get the steady-state mean values the mechanical and optical modes in the case of three cavities

q˙ = ωm p, ps = 0, 104208-2 Chin. Phys. B Vol. 24, No. 10 (2015) 104208

2 g|a3s| in the case of three coupled cavities. The matrix A in these two qs = , ωm cases can be given by −iJa2s   a = , 0 ωm 0 0 0 0 3s κ + i∆ 0 3  −ωm −γm 0 0 G2m 0    −iJa1s  0 0 −κ ∆1 0 J  a2s = 2 0 , A =   (12) κ + i∆2 + J /(κ + i∆3)  0 0 −∆1 −κ −J 0   0  E  0 0 0 J −κ ∆2  a1s = , (5) 0 2 2 0 G2m 0 −J 0 −∆ −κ κ + i∆1 + J /[κ + i∆2 + J /(κ + i∆3)] 2 and and the linearized Langevin equations   0 ωm 0 0 0 0 0 0  −ωm −γm 0 0 0 0 G3m 0  δq˙ = ωmδ p,    0 0 −κ ∆1 0 J 0 0  p˙ = − q + G ( a + a†) − p + ,   δ ωmδ 2 δ 3 δ 3 γmδ ξ  0 0 −∆1 −κ −J 0 0 0  √ A =   (13) a = − a − J a − a + a ,  0 0 0 J −κ ∆2 0 J  δ ˙1 i∆1δ 1 i δ 2 κδ 1 2κ 1in   √  0 0 −J 0 −∆2 −κ −J 0  δa˙2 = −i∆2δa2 − iJδa1 − iJδa3 − κδa2 + 2κa2in,  0  √  0 0 0 0 0 J −κ ∆3  0 0 δa˙3 = −i∆3δa3 − iJδa2 + iG2δq − κδa3 + 2κa3in, (6) G3m 0 0 0 −J 0 −∆3 −κ √ √ 0 respectively, where G2m = 2G2, G3m = 2G3. The solution where ∆3 = ∆3 − gqs, G2 = ga3s. of Eq. (9) can be expressed as Z t 3. Entanglement u(t) = M(t)u(0) + dt0M(t0)n(t −t0), (14) 0 In this section we mainly study the entanglement between where M(t) = exp(At). The system is stable only if the real any two subsystems in this system. Here we define the cavity parts of all the eigenvalues of matrix A are negative, which field quadratures can be derived by applying the Routh–Hurwitz criterion.[34] √ † We will choose the parameters so that the system is subse- δXj = (δa j + δa j )/ 2, √ quently in a steady state. We define Vi j = hui(∞)u j(∞) + δY = (δa − δa†)/i 2, (7) j j j u j(∞)ui(∞)i/2, which is a 6 × 6 (8 × 8) correlation matrix (CM). Here and the corresponding Hermitian input noise operators T √ u (∞) = (δq(∞),δ p(∞),δX1(∞),δY1(∞),δX2(∞),δY2(∞)) in in †in Xj = (a j + a )/ 2, j √ or in in †in Yj = (a j − a j )/i 2. (8) T u (∞) = (δq(∞),δ p(∞),δX1(∞),δY1(∞), Then equations (4) and (6) can be rewritten as a matrix δX2(∞),δY2(∞),δX3(∞),δY3(∞)) form is the vector of continuous variables fluctuations operators at u˙(t) = Au(t) + n(t), (9) the steady state. When the system is stable (t → ∞), we get Z ∞ Z ∞ V = dt dt0M (t)M (t0) (t −t0), (15) in which the transposes of the column vector u(t), n(t) can be i j ∑ ik jl Φkl k,l 0 0 expressed as 0 0 0 where Φkl(t − t ) = (hnk(t)nl(t ) + nl(t )nk(t)i)/2 is the T steady-state noise CM. When the stability conditions are sat- u (t) = (δq(t),δ p(t),δX1(t),δY1(t),δX2(t),δY2(t)), √ √ T in in isfied, the steady-state CM satisfies a Lyapunov equation n (t) = (0,ξ(t), 2κX1 (t), 2κY1 (t), √ √ in in AV +VAT = −D, (16) 2κX2 (t), 2κY2 (t)), (10)

where D = diag[0,γm(2n ¯ + 1),κ,κ,κ,κ] (N = 2) (or D = in the case of two coupled cavities, and diag[0,γm(2n ¯ + 1),κ,κ,κ,κ,κ,κ](N = 3)). We can straight- T forwardly have the solution of the CM with Eq. (16). How- u (t) = (δq(t),δ p(t),δX1(t),δY1(t),δX2(t), ever, the explicit expression is too complicated and will not be δY2(t),δX3(t),δY3(t)), √ √ √ reported here. T in in in n (t) = (0,ξ(t), 2κX1 (t), 2κY1 (t), 2κX2 (t), Then we will examine the entanglement properties of the √ √ √ in in in 2κY2 (t), 2κX3 (t), 2κY3 (t)), (11) steady state of the tripartite system under consideration. For 104208-3 Chin. Phys. B Vol. 24, No. 10 (2015) 104208 this purpose, we consider the entanglement of the possible bi- Table 1. The parameters used in our numerical calculations, taken from partite subsystems that can be obtained by tracing over the re- the experiments in Ref. [35]. maining degrees of the freedom. This bipartite entanglement Paramter Symbol Value Mechanical mass m 5 ng will be quantified by using the logarithmic negativity Mechanical frequency ωm/2π 100 Hz Mechanical damping rate /2 100 Hz − γm π EN = max[0,−ln2η ], (17) Cavity length L 1 mm Input power P 50 mW where Cavity–field wavelength λ 810 nm h q i1/2 Optical damping rate κ 34.1 MHz − −1/2 2 η ≡ 2 ∑(Vbp) − Σ(Vbp) − 4det(Vbp) For the sake of simplicity, we assume −∆ = ∆ 0 = ∆. In is the lowest symplectic eigenvalue of the partial transpose of 1 2 Fig.2, we have plotted the three bipartite logarithmic negativ- the 4×4 CM, Vbp, associated with the selected bipartition, ob- ities E1 (dashed curves), E2 (solid curves), and E3 (dash– tained by neglecting the rows and columns of the uninteresting N N N dotted curves), versus the normalized detuning ∆/ω at a mode, m fixed temperature of T = 400 mK for four values of the cou- BC V = , (18) pling strength J = 0.4ωm (Fig. 2(a)), J = 0.6ωm (Fig. 2(b)), bp C B0 T J = 0.8ωm (Fig. 2(c)), and J = ωm (Fig. 2(d)). It can be 1 0 clearly seen that the bipartite entanglement E is enhanced and Σ(Vbp) ≡ detB + detB − 2detC. N 2 while the bipartite entanglement EN is decreased and the bi- 3 3.1. Numerical calculation for two-cavity case partite entanglement EN is almost unchanged with the increase Firstly, we will study the optomechanical entanglement of J. That is to say, the entanglement between mirror and in two coupled cavities case. In order to investigate the behav- cavity 1 (remote cavity) increases at the expense of mirror ior of CV entanglement between the elements of the tripartite and cavity 2 (adjacent cavity) entanglement, and the adjacent system in this case, we will denote the logarithmic negativity cavity serves as an entanglement transmitter in this process. for the mirror–cavity 1, mirror–cavity 2, and cavity 1–cavity More importantly, under the increasing action of cavity–cavity 1 2 3 2 entanglements as EN,EN, and EN, respectively. In our nu- coupling, the range of the entanglement between two distant merical calculations, we will use the set of parameters for the subsystems (mirror and cavity 1) can be broader, i.e., from optomechanical system given in Table1, which match the cur- ∆/ωm ∈ [0.5,1.5] in Fig. 2(a) to ∆/ωm ∈ [0.3,2] in Fig. 2(d). rent experimental state, thus making our proposal very close The more broader effective detuning is obtained, the more eas- to feasibility. ily it is realized in experiment.

0.3 0.3 1 (b) 1 (a) EN EN 2 2 EN EN 3 3 0.2 EN 0.2 EN N N E E 0.1 0.1

0 0 0 1 2 3 0 1 2 3

∆/ωm ∆/ωm 0.3 0.3 (c) 1 1 EN (d) EN 2 2 EN EN 3 3 0.2 EN 0.2 EN N N E E 0.1 0.1

0 0 0 1 2 3 0 1 2 3 ∆/ω m ∆/ωm

1 2 3 Fig. 2. (color online) Plot of the logarithmic negativity EN (dashed curves), EN (solid curves) and EN (dash–dotted curves) as a function of the normalized detuning ∆/ωm at a ﬁxed temperature T = 400 mK. (a) J = 0.4ωm, (b) J = 0.6ωm, (c) J = 0.8ωm, (d) J = ωm. 104208-4 Chin. Phys. B Vol. 24, No. 10 (2015) 104208

scheme there is no direct interaction between the cavity 1 and 1 0.20 EN mirror, so one may say that the entanglement is entirely trans- 2 EN ferred from the adjacent cavity to the distant cavity due to the 3 0.16 EN cavity–cavity coupling. Hence, the optomechanical entanglement between the mechanical mode and the optical mode is 0.12

N very sensitive to the coupling strength J. This result reveals E 0.08 that by changing the value of J, one can control the entanglement distribution in the tripartite system, which implies that 0.04 we can transfer the entanglement to two indirectly coupled subsystems through the coupling of two cavities. 0 0 1 2 3 4 It is also important to understand the behavior of entan-

J/ω m glement with respect to the temperature T. We ﬁnally discuss 1 2 1 the robustness of optomechanical entanglement (E and E ) Fig. 3. (color online) Plot of the logarithmic negativity EN (dashed N N 2 3 curves), EN (solid curves), and EN (dash–dotted curves) versus the cou- with respect to the environmental temperature, which is shown pling strength J when ∆1 = −ωm,∆2 = ωm. in Fig.4. We can see that the optomechanical entanglement

0.25 between mirror and cavity 1 persists for temperatures above (a) J=0.6ωm 19 K, as illustrated in Fig. 4(a). Moreover, the logarithmic neg- =0.8ω 1 0.20 J m ativity EN and its critical value of temperature Tc increase with J=ω m the increase of J (Tc is deﬁned as T > Tc,EN = 0). However 0.15 the entanglement of mirror–ﬁeld 2 is fragile to the environ- 1 N ment temperature which disappears at about 2 K. In addition, E 0.10 the stronger the coupling strength, the smaller the logarithmic 1 negativity EN, and the lower the critical value of temperature 0.05 Tc, as seen in Fig. 4(b).

0 3.2. Numerical calculation for three-cavity case 0 10 20 30 T/K Then we will investigate the optomechanical entanglement properties in the case of three coupled cavities. In this 0.12 (b) case, we mainly discuss the entanglement between the three J=0.6ωm cavities and mirror since the entanglement between three cav- J=0.8ωm J=ω ities is too small. We will denote the logarithmic negativities 0.08 m for the mirror–field 1, mirror–field 2, and mirror–field 3 bi- 2 N modal partitions as E1 , E2 , E3 , respectively. In the following

E N N N numerical calculations, the system parameters are taken as the 0.04 same as the case of two coupled cavities. We also assume 0 ∆1 = −∆2 = ∆3 = ∆ for simplicity. The three bipartite log- 1 2 arithmic negativities EN (dashed curves), EN (solid curves), 0 0 1 2 3 3 and EN (dash–dotted curves) versus the normalized detuning /K T ∆/ωm are shown in Fig.5. It is clearly seen that the optimal 1 Fig. 4. (color online) Plot of the logarithmic negativities EN (a) and entanglement is reached at about ∆/ωm = 0.5. Moreover, the 2 EN (b) versus the environment temperature when ∆1 = −ωm, ∆2 = ωm. largest entanglement is the one between the mirror and cav- The solid, dashed, and dash–dotted lines are corresponding to different coupling strengths J = 0.6ωm, 0.8ωm, and ωm, respectively. ity 2 when J = ωm, which are indirectly coupled, as seen in Fig. 5(a). With the increasing of coupling strength, the loga- For clearly presenting the effect of cavity–cavity coupling rithmic negativity E2 decreases, while the logarithmic nega- strength on the optomechanical entanglement, we plot E1 , E2 , N N N tivities E1 and E3 increase. We also observed in Fig. 5(d) that and E3 with respect to J in Fig.3 where cavity 1 is driven on N N N the degree of entanglement for mirror–cavity 1 has a similar the blue sideband, ∆1 = −ωm, and cavity 2 on the red side- curve to that of mirror–cavity 3 for a large coupling strength. band, ∆2 = ωm. This ﬁgure shows that the three bipartite entanglements increase ﬁrst and go through a peak at about When J = 5ωm, the entanglement between mirror and cavity 1 (3) reaches its maximum 0.15 at about ∆ = 0.5ωm. At the J = ωm (dashed line), J = 0.5ωm (solid line), J = 0.75ωm (dash–dotted line), then drop close to zero. It is worth not- same time, the entanglement between mirror and cavity 2 de- ing that the optimal entanglement between mirror and cavity creases to 0.02. This indicates that the entanglement is trans- 1 is reached at J = ωm when the entanglement between mir- ferred from the middle cavity 2 to cavities (1 and 3) on both ror and cavity 2 disappears completely at this point. In our sides of cavity 2 with the increase of the coupling strength. 104208-5 Chin. Phys. B Vol. 24, No. 10 (2015) 104208

0.20 0.20 (a) 1 (b) 1 EN EN 0.16 2 0.16 2 EN EN 3 3 EN EN 0.12 0.12 N N E 0.08 E 0.08

0.04 0.04

0 0 0 1 2 3 0 1 2 3 ∆/ω m ∆/ωm 0.20 0.20 (c) 1 (d) 1 EN EN 0.16 2 0.16 2 EN EN 3 3 EN EN 0.12 0.12 N N E E 0.08 0.08

0.04 0.04

0 0 0 1 2 3 0 1 2 3 ∆/ω m ∆/ωm

1 2 3 Fig. 5. (color online) Plot of the logarithmic negativity EN (dashed curves), EN (solid curves), and EN (dash–dotted curves) as a function of the normalized detuning ∆/ωm. (a) J = ωm, (b) J = 1.5ωm, (c) J = 2.5ωm, (d) J = 5ωm.

1 In Fig.6, we also plot the logarithmic negativity EN, 7(b), respectively. From this ﬁgure, we can see that the en- 2 3 EN, and EN as a function of the coupling strength J when tanglement between mirror and cavity 1 rapidly decreases 0 ∆1 = ∆3 = 0.5ωm, ∆2 = −ωm, and T = 400 mK. It is seen from 0.09 to zero with the environment temperature from obviously from the ﬁgure that the maximum entanglement be- 0.1 mK to 3 K when J = 2ωm (dash–dotted line in Fig. 7(a)). tween the mirror and cavity 2 is obtained near J/ωm = 1, and 0.10 the logarithmic negativity E2 disappears rapidly with the suf- (a) N J=ω m

ﬁciently large coupling strength J (solid curve). However, the 0.08 J=1.5ωm =2ω entanglement between the mirror and cavity 1 (3) is enhanced J m and becomes more stable with the increase of J, which is quite 0.06 1 N different from Fig.4. This implies that we can obtain sta- E 0.04 tionary entanglement between two distant subsystems through adjusting the parameter J. 0.02

0.16 0 0 1 2 3 1 /K EN T 2 0.12 EN 3 EN (b) 0.16 J=ω m J=1.5ω N 0.08 m

E =2ω 0.12 J m

0.04 2 N

E 0.08

0 0 5 10 15 0.04

J/ω m

1 0 Fig. 6. (color online) Plot of the logarithmic negativity EN (dashed 0 10 20 30 40 50 2 3 curve), EN (solid curve), and EN (dash–dotted curve) versus the cou- 0 T/K pling strength J when ∆1 = ∆3 = 0.5ωm,∆2 = −ωm. 1 Fig. 7. (color online) Plot of the logarithmic negativity EN (a) and 2 0 1 EN (b) versus the environment temperature when ∆1 = ∆3 = 0.5ωm, The robustness of the optomechanical entanglement EN, ∆2 = −ωm. Solid, dashed, and dash–dotted curves refer to different 2 EN with respect to temperature T is shown in Figs. 7(a) and coupling strengths J = ωm, 1.5ωm, 2ωm. 104208-6 Chin. Phys. B Vol. 24, No. 10 (2015) 104208

1 Furthermore, the logarithmic negativity EN and its critical [3] Zurek W H 2003 Rev. Mod. Phys. 75 715 [4] Friedman J R, Patel V, Chen W, Tolpygo S K and Lukens J E 2000 value of temperature Tc increase with the value of J. It is Nature 406 43 worth noticing that the entanglement of mirror–cavity 2 be- [5] Huang S and Agarwal G S 2011 Phys. Rev. A 83 043826 comes more robust to temperature (Tc = 40 K, as shown in [6] Brown K R, Ospelkaus C, Colombe Y, et al. 2011 Nature 471 196 Fig. 7(b)) although the degree of entanglement decreases with [7] Liao J Q and Law C K 2011 Phys. Rev. A 83 033820 [8] Ma Y H and Zhou L 2013 Chin. Phys. B 22 024204 J the increasing of . [9] Zhang D and Zheng Q 2013 Chin. Phys. Lett. 30 024213 [10] Shi Z S, Xia Y and Song J 2013 Quantum Inf. Process. 12 3179 4. Conclusion [11] Dalaﬁ A, Naderi M H, Soltanolkotabi M and Barzanjeh Sh 2013 J. Phys. B: At. Mol. Opt. Phys. 46 235502 In conclusion, we have studied the properties of optome- [12] Asjad M, Shahzad M A and Saif F 2013 Eur. Phys. J. D 67 198 chanical entanglement in a coupled cavity–array with a mov- [13] Sete E A and Eleuch H 2014 Phys. Rev. A 89 013841 [14] Vitali D, Gigan S, Ferreira A, Bohm¨ H R, Tombesi P, Guerreiro A, Ve- able mirror through the logarithmic negativity. We mainly dral V, Zeilinger A and Aspelmeyer M 2007 Phys. Rev. Lett. 98 030405 considered two cases of a different number of coupled cavity [15] Genes C, Mari A, Tombesi P and Vitali D 2008 Phys. Rev. A 78 032316 ¨ (two and three cavities). Our results show that the entangle- [16] Joshi C, Larson J, Jonson M, Andersson E and Ohbreg P 2012 Phys. Rev. A 85 033805 ment of the adjacent cavity and mirror can be entirely trans- [17] Akram U, Munro W, Nemoto K and Milburn G J 2012 Phys. Rev. A 86 ferred to the remote cavity and mirror due to cavity–cavity 042306 [18] Mi X W, Bai J X and Song K H 2013 Eur. Phys. J. D 67 115 coupling in the case of two coupled cavities. Such an op- [19] Zhang D, Zhang X P and Zheng Q 2013 Chin. Phys. B 22 064206 tomechanical entanglement between the distant cavity mode [20] Ma Y H and Wu E 2015 Int. J. Theor. Phys. 54 1334 and the mechanical mode of the mirror is sensitive to cavity– [21] Joshi C, Akram U and Milburn G J 2014 New. J. Phys. 16 023009 cavity coupling strength and cavity–pump detunings. The sta- [22] Liao J Q, Wu Q Q and Nori F 2014 Phys. Rev. A 89 014302 [23] Ge W C, Al-Amri M, Nha H and Zubairy M S 2013 Phys. Rev. A 88 tionary distant entanglement can be achievable through strong 022338 0 [24] Huang S and Agarwal G S 2009 New. J. Phys. 11 103044 cavity–cavity coupling when ∆1 = ∆3 = 0.5ωm,∆2 = −ωm in the case of three coupled cavities. It is worth noting that the [25] Mancini S, Vitali D and Tombesi P 2003 Phys. Rev. Lett. 90 137901 [26] Pirandola S, Mancini S, Vitali D and Tombesi P 2003 Phys. Rev. A 68 generated remote entanglement is surprisingly robust against 062317 increasing temperature: entanglement may persist above 19 K [27] Pirandola S, Mancini S, Vitali D and Tombesi P 2004 J. Mod. Opt. 51 901 and 25 K in the two cases. According to our theoretical calcu- [28] Pirandola S, Vitali D, Tombesi P and Lloyd S 2006 Phys. Rev. Lett. 97 lations and analyses, we believe that if we continue to increase 150403 the number of cavities, the middle cavities can serve as a signal [29] Seraﬁni A, Mancini S and Bose S 2006 Phys. Rev. Lett. 96 010503 [30] Cho J, Angelakis D G and Bose S 2008 Phys. Rev. A 78 022323 transmission medium to realize quantum information transfer [31] Hartmann M J, Brandao˜ F G S L and Plenio M B 2006 Nat. Phys. 2 processing from the nearest cavity to the farthest cavity. 849 [32] Hartmann M J, Brandao˜ F G S L and Plenio M B 2008 Laser Photon. Rev. 2 527 References [33]Y onac¨ M, Yu T and Eberly H J 2006 J. Phys. B: At. Mol. Opt. Phys. 39 [1] Nielson M A and Chuang I L 2000 Quantum Computation and Quan- S621 tum Information (Cambridge: Cambridge University Press) [34] DeJesus E X and Kaufman C 1987 Phys. Rev. A 35 5288 [2] Horodechi R, Horodecki P, Horodecki M andHorodecki K 2009 Rev. [35] Kleckner D, Marshall W, Dood M, et al. 2006 Phys. Rev. Lett. 96 Mod. Phys. 81 865 173901

104208-7 Chinese Physics B

Volume 24 Number 10 October 2015

GENERAL 100101 Rapid identifying high-inﬂuence nodes in complex networks Song Bo, Jiang Guo-Ping, Song Yu-Rong and Xia Ling-Ling 100201 Singular and non-topological soliton solutions for nonlinear fractional differential equations Ozkan Guner 100202 Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method Cheng Yu-Min, Liu Chao, Bai Fu-Nong and Peng Miao-Juan 100203 Conservative method for simulation of a high-order nonlinear Schrodinger¨ equation with a trapped term Cai Jia-Xiang, Bai Chuan-Zhi and Qin Zhi-Lin 100204 Transformation optics for efﬁcient calculation of transmembrane voltage induced on cells Liao Yin-Hong, Zhu Hua-Cheng, Tang Zheng-Ming and Huang Ka-Ma 100301 Time-domain nature of group delay Wang Jian-Wu and Feng Zheng-He 100302 A new kind of special function and its application Fan Hong-Yi, Wan Zhi-Long, Wu Ze and Zhang Peng-Fei 100303 Shannon information entropies for position-dependent mass Schrodinger¨ problem with a hyperbolic well Sun Guo-Hua, Dusanˇ Popov, Oscar Camacho-Nieto and Dong Shi-Hai 100304 Characterizing the dynamics of quantum discord under phase damping with POVM measurements Jiang Feng-Jian, Ye Jian-Feng, Yan Xin-Hu and Lu¨ Hai-Jiang 100305 Non-Markovianity of a qubit coupled with an isotropic Lipkin–Meshkov–Glick bath Tian Li-Jun, Ti Min-Min and Zhai Xiang-Dong 100306 Scheme for purifying a general mixed entangled state and its linear optical implementation Dong Dong, Zhang Yan-Lei, Zou Chang-Ling, Zou Xu-Bo and Guo Guang-Can 100307 Deterministic joint remote state preparation of arbitrary single- and two-qubit states Chen Na, Quan Dong-Xiao, Xu Fu-Fang, Yang Hong and Pei Chang-Xing 100501 A perturbation method to the tent map based on Lyapunov exponent and its application Cao Lv-Chen, Luo Yu-Ling, Qiu Sen-Hui and Liu Jun-Xiu 100502 A novel adaptive-impulsive synchronization of fractional-order chaotic systems Leung Y. T. Andrew, Li Xian-Feng, Chu Yan-Dong and Zhang Hui 100503 Synchronization of coupled chaotic Hindmarsh Rose neurons: An adaptive approach Wei Wei 100504 Dynamics and stabilization of peak current-mode controlled buck converter with constant current load Leng Min-Rui, Zhou Guo-Hua, Zhang Kai-Tun and Li Zhen-Hua

(Continued on the Bookbinding Inside Back Cover) ATOMIC AND MOLECULAR PHYSICS

103201 The ac Stark shifts of the terahertz clock transitions of barium Yu Geng-Hua, Geng Ying-Ge, Li Long, Zhou Chao, Duan Cheng-Bo, Chai Rui-Peng and Yang Yong-Ming 103202 Extreme ultraviolet and x-ray transition wavelengths in Rb XXIV Indu Khatri, Arun Goyal, Sunny Aggarwal, A. K. Singh and Man Mohan 103203 Role of elastic scattering in high-order above threshold ionization Chen Zhang-Jin, Ye Jian-Mian and Xu Yang-Bing

7 103204 The VMI study on angular distribution of ejected electrons from Eu 4f 6p1/26d autoionizing states Zhang Kai, Shen Li, Dong Cheng and Dai Chang-Jian 103401 Resonant charge transfer in slow Li+–Li(2s) collisions Li Tie-Cheng, Liu Chun-Hua, Qu Yi-Zhi, Liu Ling, Wu Yong, Wang Jian-Guo, Liebermann H. P. and Buenker R. J.

103402 Site preferences and lattice vibrations of Nd6Fe13−푥T푥Si (푇 = Co, Ni) Huang Tian-Shun, Cheng Hai-Xia, Wang Xiao-Xu, Zhang Zhen-Feng, An Zhi-Wei and Zhang Guo-Hua 103403 Single ionization of helium atoms by energetic fully stripped carbon ions Ebrahim Ghanbari-Adivi and Sadjad Eskandari 103601 Modeling the interaction of nitrate anions with ozone and atmospheric moisture A. Y. Galashev

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

104101 Reciprocity principle-based model for shielding effectiveness prediction of a rectangular cavity with a covered aperture Jiao Chong-Qing and Li Yue-Yue 104102 Design and development of high linearity millimeter wave traveling-wave tube for satellite communica- tions He Jun, Huang Ming-Guang, Li Xian-Xia, Li Hai-Qiang, Zhao Lei, Zhao Jian-Dong, Li Yue and Zhao Shi-Lei 104103 Exploring electromagnetic response of tellurium dielectric resonator metamaterial at the infrared wavelengths Song Jia-Kun, Song Yu-Zhi, Li Kang-Wen, Zhang Zu-Yin, Xu Yun, Wei Xin and Song Guo-Feng 104104 Tunable wideband absorber based on resistively loaded lossy high-impedance surface Dang Ke-Zheng, Shi Jia-Ming, Wang Jia-Chun, Lin Zhi-Dan and Wang Qi-Chao

104201 Absorption enhancement in thin ﬁlm a-Si solar cells with double-sided SiO2 particle layers Chen Le, Wang Qing-Kang, Shen Xiang-Qian, Chen Wen, Huang Kun and Liu Dai-Ming 104202 Superscattering-enhanced narrow band forward scattering antenna Hu De-Jiao, Zhang Zhi-You and Du Jing-Lei 104203 Ghost imaging with broad distance Duan De-Yang, Zhang Lu, Du Shao-Jiang and Xia Yun-Jie

(Continued on the Bookbinding Inside Back Cover) 104204 An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems Liu Hua-Wei, Zheng Shu and Zhou Huai-Chun 104205 Field-free orientation of diatomic molecule via the linearly polarized resonant pulses Li Su-Yu, Guo Fu-Ming, Wang Jun, Yang Yu-Jun and Jin Ming-Xing 104206 Photon pair source via two coupling single quantum emitters Peng Yong-Gang and Zheng Yu-Jun 104207 Movement of a millimeter-sized oil drop pushed by optical force Zhang Li and She Wei-Long 104208 Entanglements in a coupled cavity–array with one oscillating end-mirror Wu Qin, Xiao Yin and Zhang Zhi-Ming 104209 Plasmonic emission and plasma lattice structures induced by pulsed laser in Purcell cavity on silicon Huang Wei-Qi, Huang Zhong-Mei, Miao Xin-Jian, Liu Shi-Rong and Qin Chao-Jian 104210 Analysis of gain distribution in cladding-pumped thulium-doped ﬁber laser and optical feedback inhibi- tion problem in ﬁber-bulk laser system Ji En-Cai, Liu Qiang, Hu Zhen-Yue and Gong Ma-Li 104211 Arbitrary frequency stabilization of a diode laser based on visual Labview PID VI and sound card output Feng Guo-Sheng, Wu Ji-Zhou, Wang Xiao-Feng, Zheng Ning-Xuan, Li Yu-Qing, Ma Jie, Xiao Lian-Tuan and Jia Suo-Tang 104212 Broadband and high-speed swept external-cavity laser using a quantum-dot superluminescent diode as gain device Hu Fa-Jie, Jin Peng, Wu Yan-Hua, Wang Fei-Fei, Wei Heng and Wang Zhan-Guo

104213 An optical fiber spool for laser stabilization with reduced acceleration sensitivity to 10−12/g Hu Yong-Qi, Dong Jing, Huang Jun-Chao, Li Tang and Liu Liang 104214 V–L decomposition of a novel full-waveform lidar system based on virtual instrument technique Xu Fan and Wang Yuan-Qing 104215 Confinement-induced nanocrystal alignment of conjugated polymer by the soft-stamped nanoimprint lithography Li Xiao-Hui, Yu Ji-Cheng, Lu Nai-Yan, Zhang Wei-Dong, Weng Yu-Yan and Gu Zhen 104216 Analysis of the spatial filter of a dielectric multilayer film reflective cutoff filter-combination device Zhang Ying, Qi Hong-Ji, Yi Kui, Wang Yan-Zhi, Sui Zhan and Shao Jian-Da 104301 Quantitative calculation of reaction performance in sonochemical reactor by bubble dynamics Xu Zheng, Yasuda Keiji and Liu Xiao-Jun 104302 Wavefront modulation of water surface wave by a metasurface Sun Hai-Tao, Cheng Ying, Wang Jing-Shi and Liu Xiao-Jun

(Continued on the Bookbinding Inside Back Cover) 104303 Temperature imaging with speed of ultrasonic transmission tomography for medical treatment control: A physical model-based method Chu Zhe-Qi, Yuan Jie, Stephen Z. Pinter, Oliver D. Kripfgans, Wang Xue-Ding, Paul L. Carson and Liu Xiao- Jun 104501 Nonlinear parametrically excited vibration and active control of gear pair system with time-varying characteristic Liu Shuang, Wang Jin-Jin, Liu Jin-Jie and Li Ya-Qian 104502 Skew-gradient representation of generalized Birkhoffian system Mei Feng-Xiang and Wu Hui-Bin 104701 Effects of the computational domain on the secondary flow in turbulent plane Couette flow Gai Jie, Xia Zhen-Hua and Cai Qing-Dong 104702 Ferrofluid nucleus phase transitions in an external uniform magnetic field B. M. Tanygin, S. I. Shulyma, V. F. Kovalenko and M. V. Petrychuk

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

105101 Dynamic mechanical analysis of single walled carbon nanotubes/polymethyl methacrylate nanocompos- ite ﬁlms Ali Badawi and N. Al-Hosiny 105102 Effect of microwave frequency on plasma formation in air breakdown at atmospheric pressure Zhao Peng-Cheng, Guo Li-Xin and Li Hui-Min 105201 Investigation of high sensitivity radio-frequency readout circuit based on AlGaN/GaN high electron mo- bility transistor Zhang Xiao-Yu, Tan Ren-Bing, Sun Jian-Dong, Li Xin-Xing, Zhou Yu, Lu¨ Li and Qin Hua

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

106101 Complementary method to locate atomic coordinates by combined searching method of structure- sensitive indexes based on bond valence method Song Zhen, Liu Xiao-Lang, He Li-Zhu, Xia Zhi-Guo and Liu Quan-Lin 106102 Inﬂuences of surface and ﬂexoelectric polarization on the effective anchoring energy in nematic liquid crystal Guan Rong-Hua, Ye Wen-Jiang and Xing Hong-Yu

106103 Determination of electrostatic parameters of a coumarin derivative compound C17H13NO3 by x-ray and density functional theory Youcef Megrouss, Nadia Benhalima, Rawia Bahoussi, Nouredine Boukabcha, Abdelkader Chouaih and Fodil Hamzaoui 106104 New crystal structure and physical properties of TcB from ﬁrst-principles calculations Zhang Gang-Tai, Bai Ting-Ting, Yan Hai-Yan and Zhao Ya-Ru ′ 106105 Inﬂuences of neutral oxygen vacancies and 퐸1 centers on 훼-quartz Li Hui-Ran, Cheng Xin-Lu, Zhang Hong and Zhao Feng

(Continued on the Bookbinding Inside Back Cover) 106106 Analysis of functional failure mode of commercial deep sub-micron SRAM induced by total dose irradi- ation Zheng Qi-Wen, Cui Jiang-Wei, Zhou Hang, Yu De-Zhao, Yu Xue-Feng, Lu Wu, Guo Qi and Ren Di-Yuan 106601 Analysis of recoverable and permanent components of threshold voltage shift in NBT stressed p-channel power VDMOSFET Danijel Dankovic,´ Ninoslav Stojadinovic,´ Zoran Prijic,´ Ivica Manic,´ Vojkan Davidovic,´ Aneta Prijic,´ Snezanaˇ Djoric-Veljkovi´ c´ and Snezanaˇ Golubovic´

106801 Mechanical strains in pecvd SiN푥:H ﬁlms for nanophotonic application O. Semenova, A. Kozelskaya, Li Zhi-Yong, and Yu Yu-De

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTI- CAL PROPERTIES

107101 Structural, elastic, and electronic properties of sodium atoms encapsulated type-I silicon–clathrate compound under high pressure Zhang Wei, Chen Qing-Yun, Zeng Zhao-Yi and Cai Ling-Cang

107102 Nano LaAlO3 buffer layer-assisted tunneling current in manganite p–n heterojunction Ma Jun-Jie, Wang Deng-Jing, Huang Hai-Lin, Wang Ru-Wu and Li Yun-Bao 107301 Influences of Pr and Ta doping concentration on the characteristic features of FTO thin film deposited by spray pyrolysis Guven¨ Turgut, Adem Koçyigit˘ and Erdal Sonmez¨ 107302 High response Schottky ultraviolet photodetector formed by PEDOT:PSS transparent electrode contacts

to Mg0.1Zn0.9O Hu Zuo-Fu, Wu Huai-Hao, Lv Yan-Wu and Zhang Xi-Qing 107303 Effect of the annealing temperature on the long-term thermal stability of Pt/Si/Ta/Ti/4H–SiC contacts Cheng Yue, Zhao Gao-Jie, Liu Yi-Hong, Sun Yu-Jun, Wang Tao and Chen Zhi-Zhan 107304 Rectification and electroluminescence of nanostructured GaN/Si heterojunction based on silicon nanoporous pillar array Wang Xiao-Bo, Li Yong, Yan Ling-Ling and Li Xin-Jian 107305 A C-band 55% PAE high gain two-stage power amplifier based on AlGaN/GaN HEMT Zheng Jia-Xin, Ma Xiao-Hua, Lu Yang, Zhao Bo-Chao, Zhang Hong-He, Zhang Meng, Cao Meng-Yi and Hao Yue 107306 Fermi level pinning effects at gate–dielectric interfaces influenced by interface state densities Hong Wen-Ting, Han Wei-Hua, Lyu Qi-Feng, Wang Hao and Yang Fu-Hua 107307 Lateral resistance reduction induced by light-controlled leak current in silicon-based Schottky junction Wang Shuan-Hu, Zhang Xu, Zou Lv-Kuan, Zhao Jing, Wang Wen-Xin and Sun Ji-Rong 107501 Magnetic hysteresis, compensation behaviors, and phase diagrams of bilayer honeycomb lattices Ersin Kantar

(Continued on the Bookbinding Inside Back Cover) 107502 Exact solution of Heisenberg model with site-dependent exchange couplings and Dzyloshinsky–Moriya interaction Yang Li-Jun, Cao Jun-Peng and Yang Wen-Li

107503 Effects of oxidation of DyH3 in Nd–Fe–B sintered magnets Yan Gao-Lin and Fang Zhi-Hao

107504 Effects of R-site compositions on the meta-magnetic behavior of Tb1−푥Pr푥(Fe0.4Co0.6)1.88C0.05 (푥 = 0, 0.8, and 1) Huang Jun-Wei, Xia Zheng-Cai, Cheng Gang, Shi Li-Ran, Jin Zhao, Shang Cui and Wei Meng

107505 Magnetic optical bifunctional CoPt333/Co multilayered nanowire arrays Su Yi-Kun, Yan Zhi-Long, Wu Xi-Ming, Liu Huan, Ren Xiao and Yang Hai-Tao 107506 Lumped-equivalent circuit model for multi-stage cascaded magnetoelectric dual-tunable bandpass ﬁlter Zhang Qiu-Shi, Zhu Feng-Jie and Zhou Hao-Miao

107701 The interface density dependence of the electrical properties of 0.9Pb(Sc0.5Ta0.5)O3–

0.1PbTiO3/0.55Pb(Sc0.5Ta0.5)O3–0.45PbTiO3 multilayer thin ﬁlms Li Xue-Dong, Liu Hong, Wu Jia-Gang, Liu Gang, Xiao Ding-Quan and Zhu Jian-Guo

107702 Nanoscale domain switching mechanism of Bi3.15Eu0.85Ti3O12 thin ﬁlm under the different mechanical forces Zhu Zhe, Chen Yu-Bo and Zheng Xue-Jun 107703 Effects of surface adsorbed oxygen, applied voltage, and temperature on UV photoresponse of ZnO nanorods Zong Xian-Li and Zhu Rong 107704 C H complex defects and their inﬂuence in ZnO single crystal Xie Hui, Zhao You-Wen, Liu Tong, Dong Zhi-Yuan, Yang Jun and Liu Jing-Ming

107705 Temperature dependences of ferroelectricity and resistive switching behavior of epitaxial BiFeO3 thin films Lu Zeng-Xing, Song Xiao, Zhao Li-Na, Li Zhong-Wen, Lin Yuan-Bin, Zeng Min, Zhang Zhang, Lu Xu-Bing, Wu Su-Juan, Gao Xing-Sen, Yan Zhi-Bo and Liu Jun-Ming 107801 Multifunctional disk device for optical switch and temperature sensor Bian Zhen-Yu, Liang Rui-Sheng, Zhang Yu-Jing, Yi Li-Xuan, Lai Gen and Zhao Rui-Tong 107802 Single-layer dual-band terahertz filter with weak coupling between two neighboring cross slots Qi Li-Mei, Li Chao, Fang Guang-You and Li Shi-Chao 107803 Simulation of positron backscattering and implantation profiles using Geant4 code Huang Shi-Juan, Pan Zi-Wen, Liu Jian-Dang, Han Rong-Dian and Ye Bang-Jiao 107804 Exploring positron characteristics utilizing two new positron–electron correlation schemes based on mul- tiple electronic structure calculation methods Zhang Wen-Shuai, Gu Bing-Chuan, Han Xiao-Xi, Liu Jian-Dang and Ye Bang-Jiao

(Continued on the Bookbinding Inside Back Cover) INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

108101 Temperature-dependent photoluminescence spectra of GaN epitaxial layer grown on Si (111) substrate Zhao Dan-Mei, Zhao De-Gang, Jiang De-Sheng, Liu Zong-Shun, Zhu Jian-Jun, Chen Ping, Liu Wei, Li Xiang and Shi Ming

108102 Influences of hydrogen dilution on microstructure and optical absorption characteristics of nc-SiO푥:H film Zhao Wei, Du Lin-Yuan, Jiang Zhao-Yi, Yin Chen-Chen, Yu Wei and Fu Guang-Sheng 108201 Ion and water transport in charge-modified graphene nanopores Qiu Ying-Hua, Li Kun, Chen Wei-Yu, Si Wei, Tan Qi-Yan and Chen Yun-Fei 108202 Surface morphology and electrochemical characterization of electrodeposited Ni Mo nanocomposites as cathodes for hydrogen evolution Elhachmi Guettaf Temam, Hachemi Ben Temam and Said Benramache 108203 Closed-form solution of mid-potential between two parallel charged plates with more extensive application Shang Xiang-Yu, Yang Chen and Zhou Guo-Qing

108401 Dual-band LTCC antenna based on 0.95Zn2SiO4-0.05CaTiO3 ceramics for GPS/UMTS applications Dou Gang, Li Yu-Xia and Guo Mei 108402 Charge and spin-dependent thermal efficiency of polythiophene molecular junction in presence of de- phasing Z. Golsanamlou, M. Bagheri Tagani and H. Rahimpour Soleimani 108501 Simulation study of the losses and influences of geminate and bimolecular recombination on the perfor- mances of bulk heterojunction organic solar cells Zhu Jian-Zhuo, Qi Ling-Hui, Du Hui-Jing and Chai Ying-Chun 108502 An improved GGNMOS triggered SCR for high holding voltage ESD protection applications Zhang Shuai, Dong Shu-Rong, Wu Xiao-Jing, Zeng Jie, Zhong Lei and Wu Jian 108503 A novel diode string triggered gated-PiN junction device for electrostatic discharge protection in 65-nm CMOS technology Zhang Li-Zhong, Wang Yuan, Lu Guang-Yi, Cao Jian and Zhang Xing 108504 Electrical properties of zinc-oxide-based thin-film transistors using strontium-oxide-doped semiconductors Wu Shao-Hang, Zhang Nan, Hu Yong-Sheng, Chen Hong, Jiang Da-Peng and Liu Xing-Yuan 108505 A threshold voltage model of short-channel fully-depleted recessed-source/drain (Re-S/D) SOI MOS- FETs with high-푘 dielectric Gopi Krishna Saramekala, Sarvesh Dubey and Pramod Kumar Tiwari 108506 Fabrication and characterization of novel high-speed InGaAs/InP uni-traveling-carrier photodetector for high responsivity Chen Qing-Tao, Huang Yong-Qing, Fei Jia-Rui, Duan Xiao-Feng, Liu Kai, Liu Feng, Kang Chao, Wang Jun- Chu, Fang Wen-Jing and Ren Xiao-Min

(Continued on the Bookbinding Inside Back Cover) 108701 Ultrafast structural dynamics studied by kilohertz time-resolved x-ray diffraction Guo Xin, Jiang Zhou-Ya, Chen Long, Chen Li-Ming, Xin Jian-Guo, Peter M. Rentzepis and Chen Jie 108702 Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method Bao Yuan, Wang Yan, Gao Kun, Wang Zhi-Li, Zhu Pei-Ping and Wu Zi-Yu 108703 Flexible-reduced ﬁeld of view magnetic resonance imaging based on single-shot spatiotemporally en- coded technique Li Jing, Cai Cong-Bo, Chen Lin, Chen Ying, Qu Xiao-Bo and Cai Shu-Hui 108801 Analysis of the interdigitated back contact solar cells: The n-type substrate lifetime and wafer thickness Zhang Wei, Chen Chen, Jia Rui, Sun Yun, Xing Zhao, Jin Zhi, Liu Xin-Yu and Liu Xiao-Wen 108802 GaInP/GaAs tandem solar cells with highly Te- and Mg-doped GaAs tunnel junctions grown by MBE Zheng Xin-He, Liu San-Jie, Xia Yu, Gan Xing-Yuan, Wang Hai-Xiao, Wang Nai-Ming and Yang Hui 108901 Improved routing strategy based on gravitational ﬁeld theory Song Hai-Quan and Guo Jin

GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS

109201 Spatiotemporal distribution characteristics and attribution of extreme regional low temperature event Feng Tai-Chen, Zhang Ke-Quan, Su Hai-Jing, Wang Xiao-Juan, Gong Zhi-Qiang and Zhang Wen-Yu