We present a detailed analysis of spin squeezing of the one-axis twisting model with a many-body phase dephasing, which is induced by external field fluctuation in a two-mode Bose-Einstein condensates. Even in the presence of the dephasing, our analy
tical results show that the optimal initial state corresponds to a coherent spin state $|theta_{0}, phi_0rangle$ with the polar angle $theta_0=pi/2$. If the dephasing rate $gammall S^{-1/3}$, where $S$ is total atomic spin, we find that the smallest value of squeezing parameter (i.e., the strongest squeezing) obeys the same scaling with the ideal one-axis twisting case, namely $xi^2propto S^{-2/3}$. While for a moderate dephasing, the achievable squeezing obeys the power rule $S^{-2/5}$, which is slightly worse than the ideal case. When the dephasing rate $gamma>S^{1/2}$, we show that the squeezing is weak and neglectable.
Squeezed spin states possess unique quantum correlation or entanglement that are of significant promises for advancing quantum information processing and quantum metrology. In recent back to back publications [C. Gross textit{et al, Nature} textbf{46
4}, 1165 (2010) and Max F. Riedel textit{et al, Nature} textbf{464}, 1170 (2010)], reduced spin fluctuations are observed leading to spin squeezing at -8.2dB and -2.5dB respectively in two-component atomic condensates exhibiting one-axis-twisting interactions (OAT). The noise reduction limit for the OAT interaction scales as $propto 1/{N^{2/3}}$, which for a condensate with $Nsim 10^3$ atoms, is about 100 times below standard quantum limit. We present a scheme using repeated Rabi pulses capable of transforming the OAT spin squeezing into the two-axis-twisting type, leading to Heisenberg limited noise reduction $propto 1/N$, or an extra 10-fold improvement for $Nsim 10^3$.
Including collisional decoherence explicitly, phase sensitivity for estimating effective scattering strength $chi$ of a two-component Bose-Einstein condensate is derived analytically. With a measurement of spin operator $hat{J}_{x}$, we find that the
optimal sensitivity depends on initial coherent spin state. It degrades by a factor of $(2gamma)^{1/3}$ below super-Heisenberg limit $propto 1/N^{3/2}$ for particle number $N$ and the dephasing rate $1<!<gamma<N^{3/4}$. With a $hat{J}_y$ measurement, our analytical results confirm that the phase $phi=chi tsim 0$ can be detected at the limit even in the presence of the dephasing.
Based upon standard angular momentum theory, we develop a framework to investigate polarization squeezing and multipartite entanglement of a quantum light field. Both mean polarization and variances of the Stokes parameters are obtained analytically,
with which we study recent observation of triphoton states [L. K. Shalm {it et al}, Nature textbf{457}, 67 (2009)]. Our results show that the appearance of maximally entangled NOON states accompanies with a flip of mean polarization and can be well understood in terms of quantum Fisher information.
Micro-indentation test with a micro flat-end cone indenter was employed to simulate micro embossing process and investigate the thermo-mechanical response of ceramic green substrates. The laminated low temperature co-fired ceramic green tapes were us
ed as the testing material ; the correlations of indentation depth versus applied force and applied stress at the temperatures of 25 degrees C and 75degrees C were studied. The results showed that permanent indentation cavities could be formed at temperatures ranging from 25 degrees C to 75 degrees C, and the depth of cavities created was applied force, temperature and dwell time dependent. Creep occurred and made a larger contribution to the plastic deformation at elevated temperatures and high peak loads. There was instantaneous recovery during the unloading and retarded recovery in the first day after indentation. There was no significant pile-up due to material flow observed under compression at the temperature up to 75 degrees C. The plastic deformation was the main cause for formation of cavity on the ceramic green substrate under compression. The results can be used as a guideline for embossing ceramic green substrates.
In large area micro hot embossing, the process temperature plays a critical role to both the local fidelity of microstructure formation and global uniformity. The significance of low temperature hot embossing is to improve global flatness of embossed
devices. This paper reports on experimental studies of polymer deformation and relaxation in micro embossing when the process temperatures are below or near its glass transition temperature (Tg). In this investigation, an indentation system and a micro embosser were used to investigate the relationship of microstructure formation versus process temperature and load pressure. The depth of indentation was controlled and the load force at a certain indentation depth was measured. Experiments were carried out using 1 mm thick PMMA films with the process temperature ranging from Tg-55 degrees C to Tg +20 degrees C. The embossed structures included a single micro cavity and groups of micro cavity arrays. It was found that at temperature of Tg-55 degrees C, elastic deformation dominated the formation of microstructures and significant relaxation happened after embossing. From Tg-20 degrees C to Tg, plastic deformation dominated polymer deformation, and permanent cavities could be formed on PMMA substrates without obvious relaxation. However, the formation of protrusive structures as micro pillars was not complete since there was little polymer flow. With an increase in process temperature, microstructure could be formed under lower loading pressure. Considering the fidelity of a single microstructure and global flatness of embossed substrates, micro hot embossing at a low process temperature, but with good fidelity, should be preferred.
