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Advanced materials for electrocatalytic water splitting applications have been sought-after considering both environmental and economic requirements. However, the traditional materials design concept limits the exploration of high-performance catalysts. The born of a materials design concept based on multiple elements, high-entropy materials, provides a promising path to break the shackles of compositional design in materials science. A number of high-entropy materials were reported to show remarkable properties for electrocatalytic water splitting applications. High-entropy materials were widely confirmed to be one kind of the best electrocatalysts for water splitting applications. Due to the synergy of multiple metal components, they show excellent catalytic activity. Several nontraditional methods were developed and reported to prepare high-performance high-entropy materials. This review article presents the recent progress on high-entropy materials for electrocatalytic water splitting applications. Moreover, it presents the research interests and future prospects in this field.

The electron heat transport plays an important role in laser driven inertial confinement fusion. For the plasmas created by intense laser, the traditional Spitzer–Härm theory cannot accurately describe the electron heat transport process mainly due to two physical effects. First, the electron distribution function would significantly differ from the Maxwellian distribution because of the inverse bremsstrahlung heating. Second, the long mean free paths of heat carrying electrons relative to the temperature scale length indicate that the electron heat flux has the nonlocal feature. In 2020, we have developed a nonlocal electron heat transport model based on the non-Maxwellian electron distribution function (NM-NL model) to describe the electron heat flux in laser plasmas. Recently, this model is successfully incorporated into our radiation hydrodynamical code RDMG. In this article, we numerically investigated the electron heat flux in laser plasmas, especially the nonlocal feature of heat flux and the influence of the non-Maxwellian distribution. The influence of electron heat transport on laser ablation is also discussed. The simulated plasma conditions based on different electron heat transport models are presented and compared with experiments. Our results show that the nonlocal feature of heat flux and the influence of non-Maxwellian distribution function are considerable in plasmas heated by intense lasers.

In 2021, the fusion yield of 1.35 MJ was produced at NIF by using indirect drive inertial confinement fusion (ICF), indicating that indirect drive ICF has reached ignition. However, the driving radiation flux on capsule inside Hohlraums is still a puzzle in indirect drive ICF studies. The energy deficit at NIF is still neither well understood nor solved. In this paper, we proposed a scheme to determine the driving radiation flux on the capsule by using the combination of the shock wave technique and the reemitted radiation flux measurement. In this scheme, a witness sample is placed in the Hohlraum center as the surrogate of the capsule. The shock velocity in the witness sample is measured by a streaked optical pyrometer from one side, and the temporal reemitted radiation flux is measured by a space-resolved flat response x-ray detector. Then, the peak of the radiation flux is determined by the shock velocity, and the time behavior of the radiation flux is determined by the reemitted flux through the numerical simulation of radiation hydrodynamic code. The rules for designing the witness sample and an example of applying this scheme to determine the driving radiation flux on capsule inside the octahedral spherical Hohlraum are presented in detail.

In inertial confinement approaches to fusion, the asymmetry of target implosion is a major obstacle to achieving high gain in the laboratory. A recently proposed octahedral spherical hohlraum makes it possible to naturally create spherical target irradiation without supplementary symmetry control. Before any decision is made to pursue an ignition-scale laser system based on the octahedral hohlraum, one needs to test the concept with the existing facilities. Here, we report a proof-of-concept experiment for the novel octahedral hohlraum geometry on the cylindrically configured SGIII laser facility without a symmetry control. All polar and equatorial self-emission images of the compressed target show a near round shape of convergence ratio 15 under both square and shaped laser pulses. The observed implosion performances agree well with the ideal spherical implosion simulation. It also shows limitations with using the existing facilities and adds further weight to the need to move to a spherical port geometry for future ignition laser facilities.

Recently, high entropy alloy (HEA) based materials have been vigorously explored as viable catalysts in water electrolysis for their unique properties. However, the synthesis of efficient and robust high entropy catalysts remains a challenge. Here a facile and scalable approach is reported to synthesize advanced HEA (CoNiCuMnAl)/C nanoparticles from the polymetallic Metal–organic framework (MOF). The novel core-shell nanoarchitectures feature face-centered cubic HEA wrapped in ultra-thin carbon shell. The optimized catalyst (deposited upon Ni foam) boosted alkaline Oxygen evolution reaction (OER) (in 1.0 M KOH) with an ultralow overpotential of 215 mV at 10 mA/cm2 (also by a low Tafel slope of 35.6 mV dec−1). The enhanced performance is closely tied to surface reconstruction (i.e., formation of oxyhydroxide catalytic active species) and the high entropy effect, revealed by Fourier-transformed alternating current voltammetry (FTACV) and in-situ Raman spectrum analysis, in conjunction with Density Functional Theory (DFT) computations. Furthermore, the new design showed excellent long-term OER stability with negligible decay through 30 h testing (under 200 mA cm−2). The present work demonstrates the feasibility and advantage of utilizing highly efficient and durable high entropy alloys for catalyzing electrochemical water splitting process.

Cr6+ and Pb2+ are both highly toxic pollutants and commonly co-exist in some industrial effluents and contaminated waters. In this study, simultaneous removal of Cr6+ and Pb2+ by a novel sewage sludge-derived biochar immobilized nanoscale zero-valent iron (SSB-nZVI) was systematically investigated. It was well demonstrated that a porous structure was successfully formed on the SSB-nZVI when the starch was used as an additive. A synergistic effect on the adsorption and reduction over the SSB-nZVI was achieved, resulting in nearly 90 and 82% of Cr6+ and Pb2+ removal within 30 min, respectively. Cr6+ was reduced prior to Pb2+. A low pH could accelerate the corrosion of nZVI as well as phosphate leaching. When Malachite green was added as a coexisting organic pollutant, its effective removal was found due to the formation of a Fenton-like system. The SSB-nZVI could be run consecutively three times with a relatively satisfactory performance. Most of Cr6+ was converted into Cr2O3 and Cr(OH)3 on the SSB-nZVI surface, whereas most of Pb2+ species existed as Pb(OH)2 (or PbO). A possible reaction mechanism on the SSB-nZVI involved the adsorption, reduction and precipitation of both Cr6+ and Pb2+ over the particles. Present study sheds light on the insight of the fate and transport of Cr6+ and Pb2+ in aquatic environment, as well provides helpful guide for the remediation of coexistence of pollutants in real applications.

In this study, a novel biochar-supported zero valent iron (BC-nZVI) was synthesized through a green method. A high performance on the simultaneous removal of Cu2+ and bisphenol A (BPA) by a combination of BC-nZVI with persulfate (BC-nZVI/PS) system was successfully achieved. The simultaneous efficiencies of Cu2+ and BPA could reach 96 and 98% within 60 min, respectively. Both HO• and SO4•− were two major reactive species in BC-nZVI/PS system, and SO4•− was primary radical responsible for the degradation of BPA. Four kinds of Cu species, such as Cu(OH)2, CuO, Cu2O and Cu0 were generated via the adsorption and reduction of the BC-nZVI, whereas six kinds of products of BPA including p-isopropenyl phenol and 4-isopropylphenol were generated via the combined oxidation of SO4•− and HO•. The possible reaction mechanism for the simultaneous removal of Cu2+ and BPA by BC-nZVI/PS system contained a synergistic effect between the reduction of Cu2+ and the oxidation of BPA. This is the first report on the feasibility of the remediation of coexistence of heavy metal and organic compound in aquatic environment using the BC-nZVI/PS system.

In this paper, we study the influence of three different electron heat conduction models on the laser ablation of gold plane target. Different from previous studies, we concentrate on the plasma conditions, the conversion efficiency from laser into soft x rays and the scaling relation of mass ablation, which are relevant to hohlraum physics study in indirect drive inertial confinement fusion. We find that the simulated electron temperature in corona region is sensitive to the electron heat conduction models. For different electron heat conduction models, there are obvious differences in magnitude and spatial profile of electron temperature. For the flux limit model, the calculated conversion efficiency is sensitive to flux limiters. In the laser ablation of gold, most of the laser energies are converted into x rays. So the scaling relation of mass ablation rate is quite different from that of low Z materials.

The coupling evolutions of stimulated Raman scattering (SRS) and Raman rescattering (re-SRS) are investigated under the parameter conditions of relevance to the gas-filled hohlraum experiments at the National Ignition Facility by using the nonenveloped fluid code FLAME. It is found that re-SRS works as a frequency filter of the backscattered light of SRS in the gas region. The low frequency modes of scattered light originated from a higher density region would stimulate re-SRS and be heavily depleted by re-SRS near the region of their quarter critical density. The energy in daughter waves of re-SRS is deposited in the gas plasmas. The large amplitude of the daughter Langmuir wave of re-SRS would stimulate cascade Langmuir decay instabilities and induce obvious low frequency density modulations, which can further result in the inflation of high frequency modes of scattered light of SRS at densities lower than the growth region of re-SRS.

In this paper, we give a review of our theoretical and experimental progress in octahedral spherical hohlraum study. From our theoretical study, the octahedral spherical hohlraums with 6 Laser Entrance Holes (LEHs) of octahedral symmetry have robust high symmetry during the capsule implosion at hohlraum-to-capsule radius ratio larger than 3.7. In addition, the octahedral spherical hohlraums also have potential superiority on low backscattering without supplementary technology. We studied the laser arrangement and constraints of the octahedral spherical hohlraums, and gave a design on the laser arrangement for ignition octahedral hohlraums. As a result, the injection angle of laser beams of 50°–60° was proposed as the optimum candidate range for the octahedral spherical hohlraums. We proposed a novel octahedral spherical hohlraum with cylindrical LEHs and LEH shields, in order to increase the laser coupling efficiency and improve the capsule symmetry and to mitigate the influence of the wall blowoff on laser transport. We studied on the sensitivity of the octahedral spherical hohlraums to random errors and compared the sensitivity among the octahedral spherical hohlraums, the rugby hohlraums and the cylindrical hohlraums, and the results show that the octahedral spherical hohlraums are robust to these random errors while the cylindrical hohlraums are the most sensitive. Up till to now, we have carried out three experiments on the spherical hohlraum with 2 LEHs on Shenguang(SG) laser facilities, including demonstration of improving laser transport by using the cylindrical LEHs in the spherical hohlraums, spherical hohlraum energetics on the SGIII prototype laser facility, and comparisons of laser plasma instabilities between the spherical hohlraums and the cylindrical hohlraums on the SGIII laser facility. PACS codes: 52.70.La, 52.35.Tc, 47.40.Nm, Keywords: Indirect-drive inertial confinement fusion, Novel spherical hohlraum with 6 LEHs, High and robust radiation symmetry, High energy coupling efficiency, Theoretical study, Experiments

In laser plasmas, the electron distribution function is not Maxwellian but super-Gaussian due to the inverse bremsstrahlung heating, and the electron heat transport is generally nonlocal because of the large Knudsen number. Starting from the Fokker–Planck equation, we develop a nonlocal electron heat transport model based on the non-Maxwellian distribution function. In our study, we follow the method in Schurtz et al. [Phys. Plasmas 7, 4238 (2000)] and derive a differential equation for calculating the nonlocal electron heat flux based on the non-Maxwellian distribution function. The numerical results show that the non-Maxwellian distribution function would reduce the nonlocal heat flux in the laser heated region. The preheat effect due to nonlocal electron heat transport in the conduction region is also reduced by the non-Maxwellian distribution function. This nonlocal electron heat transport model can be easily implemented in two-dimensional and three-dimensional hydrodynamics codes.

The first octahedral spherical hohlraum energetics experiment is accomplished at the SGIII laser facility. For the first time, the 32 laser beams are injected into the octahedral spherical hohlraum through six laser entrance holes. Two techniques are used to diagnose the radiation field of the octahedral spherical hohlraum in order to obtain comprehensive experimental data. The radiation flux streaming out of laser entrance holes is measured by six flat-response x-ray detectors (FXRDs) and four M-band x-ray detectors, which are placed at different locations of the SGIII target chamber. The radiation temperature is derived from the measured flux of FXRD by using the blackbody assumption. The peak radiation temperature inside hohlraum is determined by the shock wave technique. The experimental results show that the octahedral spherical hohlraum radiation temperature is in the range of 170-182 eV with drive laser energies of 71 kJ to 84 kJ. The radiation temperature inside the hohlraum determined by the shock wave technique is about 175 eV at 71 kJ. For the flat-top laser pulse of 3 ns, the conversion efficiency of gas-filled octahedral spherical hohlraum from laser into soft x rays is about 80% according to the two-dimensional numerical simulation.

Cr

In this study, a novel biochar-supported zero valent iron (BC-nZVI) was synthesized through a green method. A high performance on the simultaneous removal of Cu

We investigate a new laser-driven spherically convergent plasma fusion scheme (SCPF) that can produce thermonuclear neutrons stably and efficiently. In the SCPF scheme, laser beams of nanosecond pulse duration and 10^{14}-10^{15} W/cm^{2} intensity uniformly irradiate the fuel layer lined inside a spherical hohlraum. The fuel layer is ablated and heated to expand inwards. Eventually, the hot fuel plasmas converge, collide, merge, and stagnate at the central region, converting most of their kinetic energy to internal energy, forming a thermonuclear fusion fireball. With the assumptions of steady ablation and adiabatic expansion, we theoretically predict the neutron yield Y_{n} to be related to the laser energy E_{L}, the hohlraum radius R_{h}, and the pulse duration τ through a scaling law of Y_{n}∝(E_{L}/R_{h}^{1.2}τ^{0.2})^{2.5}. We have done experiments at the ShengGuangIII-prototype facility to demonstrate the principle of the SCPF scheme. Some important implications are discussed.

Octahedral spherical hohlraums with a single laser ring at an injection angle of 55^{∘} are attractive concepts for laser indirect drive due to the potential for achieving the x-ray drive symmetry required for high convergence implosions. Laser-plasma instabilities, however, are a concern given the long laser propagation path in such hohlraums. Significant stimulated Raman scattering has been observed in cylindrical hohlraums with similar laser propagation paths during the ignition campaign on the National Ignition Facility (NIF). In this Rapid Communication, experiments demonstrating low levels of laser-driven plasma instability (LPI) in spherical hohlraums with a laser injection angle of 55^{∘} are reported and compared to that observed with cylindrical hohlraums with injection angles of 28.5^{∘} and 55^{∘}, similar to that of the NIF. Significant LPI is observed with the laser injection of 28.5^{∘} in the cylindrical hohlraum where the propagation path is similar to the 55^{∘} injection angle for the spherical hohlraum. The experiments are performed on the SGIII laser facility with a total 0.35-μm incident energy of 93 kJ in a 3 nsec pulse. These experiments demonstrate the role of hohlraum geometry in LPI and demonstrate the need for systematic experiments for choosing the optimal configuration for ignition studies with indirect drive inertial confinement fusion.

The first spherical hohlraum energetics experiment is accomplished on the SGIII-prototype laser facility. In the experiment, the radiation temperature is measured by using an array of flat-response x-ray detectors (FXRDs) through a laser entrance hole at four different angles. The radiation temperature and M-band fraction inside the hohlraum are determined by the shock wave technique. The experimental observations indicate that the radiation temperatures measured by the FXRDs depend on the observation angles and are related to the view field. According to the experimental results, the conversion efficiency of the vacuum spherical hohlraum is in the range from 60% to 80%. Although this conversion efficiency is less than the conversion efficiency of the near vacuum hohlraum on the National Ignition Facility, it is consistent with that of the cylindrical hohlraums used on the NOVA and the SGIII-prototype at the same energy scale.

We propose a scheme for generating squeezed states in solid state circuits which consist a superconducting transmission line resonator (STLR), a superconducting Cooper-pair box (CPB) and a nanoelectromechanical resonator (NMR). The nonlinear interaction between the STLR and the CPB can be implemented by setting the external biased flux of the CPB at some certain points. The interaction Hamiltonian between the STLR and the NMR is derived by performing Frohlich transformation on the total Hamiltonian of the combined system. Just by adiabatically keeping the CPB at the ground state, we get the standard parametric down-conversion Hamiltonian, and the squeezed states of the STLR can be easily generated, which is similar to the three-wave mixing in quantum optics.

We propose an efficient scheme to generate quantum entanglement in scalable superconducting charge qubits with a one-dimensional superconducting transmission line resonator (STLR) as data bus. The coupling between qubit and data bus may be turned on and off by controlling the DC gate voltage and externally applied flux of the superconducting charge qubit. In our proposal, the entanglement between two arbitrary qubits and W states of three qubits can be generated quickly and easily.

Alloy cladding coatings are widely prepared on the surface of tools and machines. High-entropy alloys are potential replacements of nickel-, iron-, and cobalt-base alloys in machining due to their excellent strength and toughness. In this work, CoCrFeMnNbNi HEA coating was produced on AISI 304 steel by tungsten inert gas cladding. The microstructure and wear behavior of the cladding coating were studied by X-ray diffraction, scanning electron microscopy, energy dispersive spectrometer, microhardness tester, pin-on-ring wear tester, and 3D confocal laser scanning microscope. The microstructure showed up as a nanoscale lamellar structure matrix which is a face-centered-cubic solid solution and niobium-rich Laves phase. The microhardness of the cladding coating is greater than the structure. The cladding coating has excellent wear resistance under the condition of dry sliding wear, and the microploughing in the worn cladding coating is shallower and finer than the worn structure, which is related to composition changes caused by forming the nanoscale lamellar structure of Laves phase.

Compared with cylindrical hohlraums, the octahedral spherical hohlraums have natural superiority in maintaining high radiation symmetry during the whole capsule implosion process in indirect drive inertial confinement fusion. However, the narrow space between laser beams and the hohlraum wall may disturb laser propagation inside the spherical hohlraum. In this work, the laser propagation inside the spherical hohlraum and cylindrical hohlraum is investigated experimentally by measuring laser spot movement at the SGIII-prototype laser facility. The experimental results show that the laser propagations inside the spherical hohlraum and the cylindrical hohlraum are totally different from each other due to different hohlraum structures. For the spherical hohlraum, although the laser energy is mainly deposited in the initial position of the laser spot during the whole laser pulse, some laser energies are absorbed by the ablated plasmas from the hohlraum wall. Because the laser beam is refracted by the thin plasmas near the laser entrance hole (LEH) region, the laser spot in the spherical hohlraum moves toward the opposite LEH. In contrast, the laser spot in the cylindrical hohlraum moves toward the LEH along the laser path due to the plasma expansion. When the laser is to be turned off, the accumulated plasmas near the LEH region in the cylindrical hohlraum absorb a majority of laser energy and hinder the laser arriving at the appointed position on the hohlraum wall.

We study the theory of degenerate three-wave mixing and the generation of squeezed microwaves using circuit quantum electrodynamics in solid state circuits. The Hamiltonian for degenerate three-wave mixing, which seemed to be given phenomenologically in quantum optics, is derived by quantum mechanical calculations. The nonlinear medium needed in three-wave mixing is composed of a series of superconducting charge qubits which are located inside two superconducting transmission-line resonators. Here, the multiqubit ensemble is present to enhance the effective coupling constant between the two modes in the transmission-line resonators. In the squeezing process, the qubits are kept in their ground states so that their decoherence does not corrupt the squeezing. The main obstacle preventing a large squeezing efficiency is the decay rate of the transmission-line resonator.

We investigate the dynamics of a system consisting of a Cooper‐pair box and two superconducting transmission line resonators. There exist both linear and nonlinear interactions in such a system. We show that single‐photon entanglement state can be generated in a simple way in the linear interaction regime. In nonlinear interaction regime, we derive the Hamiltonian of degenerate three‐wave mixing and propose a scheme for generating squeezed state of microwave using the three‐wave mixing in solid state circuits. In the following, we design a system for generating squeezed states of nanamechanical resonator.

An electron thermal transport theory based on the super-Gaussian electron distribution function f0∝e−vm is investigated for magnetized laser plasmas in order to obtain accurate transport coefficients used in the radiation hydrodynamic codes. It is found that the super-Gaussian distribution suppresses the diffusive heat flow and the Righi-Leduc heat flow. The diffusive heat flow and Righi-Leduc heat flow can be suppressed by as much as 50% and 75% under the typical hohlraum plasma condition, respectively. The super-Gaussian distribution introduces isothermal heat flows associated with the gradients of electron density and the super-Gaussian exponential factor m. And the isothermal heat flows induce the anomalous Nernst effects. Moreover, the self-generated magnetic field in laser plasmas can be generated not only by the thermalelectric effect but also by the nonparallel gradients of electron temperature and the super-Gaussian exponential factor m, the nonparallel gradients of electron density, and the supe...

The random radiation asymmetry in the octahedral spherical hohlraum [K. Lan et al., Phys. Plasmas 21, 0 10704 (2014)] arising from the power imbalance, pointing accuracy of laser quads, and the assemblage accuracy of capsule is investigated by using the 3-dimensional view factor model. From our study, for the spherical hohlraum, the random radiation asymmetry arising from the power imbalance of the laser quads is about half of that in the cylindrical hohlraum; the random asymmetry arising from the pointing error is about one order lower than that in the cylindrical hohlraum; and the random asymmetry arising from the assemblage error of capsule is about one third of that in the cylindrical hohlraum. Moreover, the random radiation asymmetry in the spherical hohlraum is also less than the amount in the elliptical hohlraum. The results indicate that the spherical hohlraum is more insensitive to the random variations than the cylindrical hohlraum and the elliptical hohlraum. Hence, the spherical hohlraum can relax the requirements to the power imbalance and pointing accuracy of laser facility and the assemblage accuracy of capsule.

The radiation temperature TR and M-band fraction fM inside the vacuum Au hohlraum have been experimentally determined by a shock wave technique and a broadband soft x-ray spectrometer (SXS) on the SGIII-prototype laser facility. From the results of the shock wave technique, TR is about 202 eV, and fM is about 9% for the hohlraums driven by a 1 ns flattop pulse of 6 kJ laser energy. The Continuous Phase Plate (CPP) for beam smoothing is applied in the experiment, which increases TR to 207 eV while has almost no influence on fM . Comparisons between the results from the two kinds of technologies show that TR from the shock wave technique is lower than that from SXS whether with CPP or not. However, fM from the shock wave technique is consistent with that from SXS without CPP, but obviously lower than the SXS's result with CPP. The preheat effect on exterior surface of witness plate is reduced by thicker thickness of witness plate designed for higher laser driven energy.

Some of our recent studies on hohlraum physics are presented, mainly including simulation study on hohlraum physics experiments on SGIII prototype, the design of Au + U + Au sandwich hohlraum for ignition target, and an initial design of elliptical hohlraum and pertinent drive laser power in order to generate an ignition radiation profile.

An electron transportmodel based on the non-Maxwellian distribution f 0 ∝ e - ν m (NM model), caused by the inverse bremsstrahlung heating, is used in 1-D plane target and 2-D hohlraum simulations. In the NM model, the electron heat flux depends not only on the gradient of electron temperature T e but also on the gradients of electron number density and the index m. From 1-D simulations, the spatial distribution of T e is dune-like and T e decreases obviously in the flux-heated region, which is very different from the flat profile obtained by using the flux limit model (FL model) but similar to the experimental observations [Gregori et al., Phys. Rev. Lett. 92, 205006 (2004)] and the nonlocal results [Rosen et al., High Energy Density Phys. 7, 180 (2011)]. The reason which causes the dune-like profile of T e is discussed in the paper. From 2-D hohlraum simulations, the NM results of the plasma status, the emission peak and profile inside hohlraum are very different from the FL model results. Finally, it is hard to use an average flux limiter in the FL model to obtain the same hohlraumplasma status and emission with those under the NM model.

The Hohlraum physics experiments performed on the SGIII-prototype laser facility are simulated by using our two-dimensional radiation hydrodynamic code LARED-H, and the influence of laser intensity on the two-dimensional Hohlraum simulations is studied. Both the temporal radiation temperature and the x-ray spectrum from the simulations agree well with the observations, except that the simulated M-band fraction (greater than 2 keV) is obviously smaller than the observation. According to our study, the coupling efficiency from laser to x-ray is around 70% for SGIII-prototype laser facility Hohlraums.

In this letter, we report an experimental demonstration of single-step realization of universal quantum gate in a nuclear magnetic resonance quantum information processor. The scheme uses a constant Hamiltonian evolution and is robust against decoherence. Our work focuses on the implementation of the controlled-NOT gate. Several sets of parameters are obtained and they provide flexibility to suppress decoherence for quantum computation.

In this paper, we study the dynamical decoupling method for suppressing the decoherence of a Δ-type three-level atom. We consider a realistic situation that the pulse length of radio-frequency pulse (RF pulse) is finite. A dynamical decoupling group is given for designing the RF pulse sequences. Our analytical results show that the corresponding decoupling operations can suppress the decoherence completely in ideal conditions. In the realistic situation, the numerical results indicate that the decoherence can also be suppressed effectively.

We propose a scheme for generating squeezed states of nanomechanical resonator in a solid state circuit system which consists of a nanomechanical resonator, a superconducting Cooper-pair box, and a superconducting transmission line resonator. The nonlinear interaction between the nanomechanical resonator and superconducting transmission line resonator can be implemented by setting the external biased flux of the Cooper-pair box at some special values. The squeezed states of the nanomechanical resonator can be generated by degenerate three-wave mixing and the Cooper-pair box plays the role of “nonlinear medium” in the squeezing process.