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A dynamics regime of Rydberg atoms, unselective ground-state blockade (UGSB), is proposed in the context of Rydberg antiblockade (RAB), where the evolution of two atoms is suppressed when they populate in an identical ground state. UGSB is used to implement a SWAP gate in one step without individual addressing of atoms. Aiming at circumventing common issues in RAB-based gates including atomic decay, Doppler dephasing, and fluctuations in the interatomic coupling strength, we modify the RAB condition to achieve a dynamical SWAP gate whose robustness is much greater than that of the nonadiabatic holonomic one in the conventional RAB regime. In addition, on the basis of the proposed SWAP gates, we further investigate the implementation of a three-atom Fredkin gate by combining Rydberg blockade and RAB. The present work may facilitate to implement the RAB-based gates of strongly coupled atoms in experiment.
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Mouse embryonic stem (ES) cells are locked into self-renewal by shielding from inductive cues. Release from this ground state in minimal conditions offers a system for delineating developmental progression from naïve pluripotency. Here, we examine the initial transition process. The ES cell population behaves asynchronously. We therefore exploited a short-half-life Rex1::GFP reporter to isolate cells either side of exit from naïve status. Extinction of ES cell identity in single cells is acute. It occurs only after near-complete elimination of naïve pluripotency factors, but precedes appearance of lineage specification markers. Cells newly departed from the ES cell state display features of early post-implantation epiblast and are distinct from primed epiblast. They also exhibit a genome-wide increase in DNA methylation, intermediate between early and late epiblast. These findings are consistent with the proposition that naïve cells transition to a distinct formative phase of pluripotency preparatory to lineage priming.
These results reveal that TFs associated with pluripotency display individual expression behaviour as ES cells transition from the ground state. RGd2 downregulation appears to reflect aggregate loss of naïve TFs against a background of persistent Oct4 and Sox2 expression.
To determine the time of exit from the ground state, entire cultures or subpopulations sorted on the basis of RGd2 expression at selected time points were re-plated at single cell density in serum/LIF (serum/L) and 2i/LIF (2i/L). Resulting colonies were stained for alkaline phosphatase (AP) activity (Fig. 4A).
To examine global expression dynamics, we carried out microarray profiling using three biological replicates. We also performed RNA-seq on independently derived RGd2 ES cell lines. We found a total of 8810 genes in the microarray that were differentially expressed between at least two subpopulations (Table S3). Consistent with the activation of MEK/ERK and GSK3 upon 2i withdrawal, we observed changes in the expression of components of the pathway and transcriptional targets. Activation of MEK/ERK is reflected in the upregulation of immediate ERK response genes, such as Egr1, Fos, Myc and Jun (Murphy et al., 2004), and of negative-feedback regulators Spry2 and the ERK phosphatases Dusp4 and Dusp6 (Fig. 5A). mRNAs for the canonical Wnt targets T, Axin2, Cdx1 and Cdx2 are detected at low levels in 2i, consistent with inhibition of Gsk3 (Marucci et al., 2014) (Fig. 5A). Expression is reduced upon 2i withdrawal, indicating reduction of β-catenin-dependent transcription during transition from the ground state. Lef1 is upregulated, however, suggesting increased potential for Wnt-stimulated transcriptional regulation after exit.
At the onset of this transition, the molecular network that sustains naïve pluripotency is dismantled (Buecker et al., 2014; Kalkan and Smith, 2014; Leeb et al., 2014). Apparently co-incident with acute downregulation of the critical naïve TFs, post-implantation epiblast markers are up-regulated (Acampora et al., 2016; Boroviak et al., 2015). Increased differentiation when transferred to serum suggests enhanced sensitivity to inductive cues before cells have fully extinguished ES cell identity. However, for as long as Rex1 is expressed, cells retain in full the ability to regain the ground state. Such reactivation of self-renewal, despite marked reduction in the levels of functionally important naïve TFs, is consistent with evidence that the mouse ES cell state is founded on a highly flexible transcription factor circuitry (Dunn et al., 2014; Martello and Smith, 2014; Young, 2011; Niwa, 2014). We surmise that loss of Rex1 reflects a cumulative reduction of the suite of factors below a critical threshold. From this point, the naïve TF network cannot be reactivated and is subsumed by an emerging new circuitry. The apparent gradual loss of self-renewal gleaned from whole population analyses arises from asynchronous single cell dynamics and at the level of individual cells the exit from ES cell identity may be precipitate.
The electronic structure of cyclopentadienyl nickel nitrosyl (1) in the ground state as well as the cationic states of 1 are investigated by means of a semiempirical INDO Hamiltonian and many body perturbation theory. It is demonstrated that the nature of the NiNO coupling is largely covalent while the interaction between the 3d center and the cyclopentadienyl ligand is predominantly of ionic type. The ground state MO sequence of the Ni 3d orbitals is 4e2(3dx-y/3dxy) below 7e1
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In atomic physics, Hund's rules refers to a set of rules that German physicist Friedrich Hund formulated around 1927, which are used to determine the term symbol that corresponds to the ground state of a multi-electron atom. The first rule is especially important in chemistry, where it is often referred to simply as Hund's Rule.
As an example, consider the ground state of silicon. The electronic configuration of Si is 1s2 2s2 2p6 3s2 3p2 (see spectroscopic notation). We need to consider only the outer 3p2 electrons, for which it can be shown (see term symbols) that the possible terms allowed by the Pauli exclusion principle are 1D , 3P , and 1S. Hund's first rule now states that the ground state term is 3P (triplet P), which has S = 1. The superscript 3 is the value of the multiplicity = 2S + 1 = 3. The diagram shows the state of this term with ML = 1 and MS = 1.
For silicon there is only one triplet term, so the second rule is not required. The lightest atom that requires the second rule to determine the ground state term is titanium (Ti, Z = 22) with electron configuration 1s2 2s2 2p6 3s2 3p6 3d2 4s2. In this case the open shell is 3d2 and the allowed terms include three singlets (1S, 1D, and 1G) and two triplets (3P and 3F). (Here the symbols S, P, D, F, and G indicate that the total orbital angular momentum quantum number has values 0, 1, 2, 3 and 4, respectively, analogous to the nomenclature for naming atomic orbitals.)
We deduce from Hund's first rule that the ground state term is one of the two triplets, and from Hund's second rule that this term is 3F (with L = 3 \displaystyle L=3 ) rather than 3P (with L = 1 \displaystyle L=1 ). There is no 3G term since its ( M L = 4 , M S = 1 ) \displaystyle (M_L=4,M_S=1) state would require two electrons each with ( M L = 2 , M S = + 1 / 2 ) \displaystyle (M_L=2,M_S=+1/2) , in violation of the Pauli principle. (Here M L \displaystyle M_L and M S \displaystyle M_S are the components of the total orbital angular momentum L and total spin S along the z-axis chosen as the direction of an external magnetic field.)
The value of ζ ( L , S ) \displaystyle \zeta (L,S) changes from plus to minus for shells greater than half full. This term gives the dependence of the ground state energy on the magnitude of J \displaystyle J\, .
The 3 P \displaystyle ^3\!P\, lowest energy term of Si consists of three levels, J = 2 , 1 , 0 \displaystyle J=2,1,0\, . With only two of six possible electrons in the shell, it is less than half-full and thus 3 P 0 \displaystyle ^3\!P_0\, is the ground state.
If the shell is half-filled then L = 0 \displaystyle L=0\, , and hence there is only one value of J \displaystyle J\, (equal to S \displaystyle S\, ), which is the lowest energy state. For example, in phosphorus the lowest energy state has S = 3 / 2 , L = 0 \displaystyle S=3/2,\ L=0 for three unpaired electrons in three 3p orbitals. Therefore, J = S = 3 / 2 \displaystyle J=S=3/2 and the ground state is 4 S 3 / 2 \displaystyle ^4\!S_3/2\, . 2ff7e9595c
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