101 research outputs found

### (a) Potential curve of the well state in the <em>x</em>ā<em>y</em> plane

<p><strong>Figure 2.</strong>Ā (a) Potential curve of the well state in the <em>x</em>ā<em>y</em> plane. The potential is azimuthally symmetric around the <em>z</em>-axis, giving rise to a doughnut-shaped potential well. (b) Potential curve of the well state in the <em>x</em>ā<em>z</em> plane. Two pronounced minima occur on the Ā±<em>x</em>-axes. In (a) and (b), we set Ī = ā3|Ī“|.</p> <p><strong>Abstract</strong></p> <p>We show that the dipoleādipole interaction between two Rydberg atoms can lead to substantial Abelian and non-Abelian gauge fields acting on the relative motion of the two atoms. We demonstrate how the gauge fields can be evaluated by numerical techniques. In the case of adiabatic motion in a single internal state, we show that the gauge fields give rise to a magnetic field that results in a Zeeman splitting of the rotational states. In particular, the ground state of a molecular potential well is given by the first excited rotational state. We find that our system realizes a synthetic spināorbit coupling where the relative atomic motion couples to two internal two-atom states. The associated gauge fields are non-Abelian.</p

### (a) The system under consideration consists of two Rydberg atoms

<p><strong>Figure 1.</strong>Ā (a) The system under consideration consists of two Rydberg atoms. \boldsymbol{R} is the relative position of atom 2 with respect to atom 1. An external electric field \boldsymbol{E} is applied in the <em>z</em>-direction. Ļ is the distance of atom 2 from the <em>z</em>-axis. (b) An internal level structure of each Rydberg atom. The Stark shifts Ī“ ā” <em>W</em><sub>p ā 1/2</sub> ā <em>W</em><sub>p ā 3/2</sub> and Ī ā” <em>W</em><sub>p + 1/2</sub> ā <em>W</em><sub>p + 3/2</sub> are negative. We assume \delta \not=\Delta. The dipole transitions indicated by solid, blue dotted and red dashed lines couple to Ļ, Ļ<sup>ā</sup> and Ļ<sup>+</sup> polarized fields, respectively.</p> <p><strong>Abstract</strong></p> <p>We show that the dipoleādipole interaction between two Rydberg atoms can lead to substantial Abelian and non-Abelian gauge fields acting on the relative motion of the two atoms. We demonstrate how the gauge fields can be evaluated by numerical techniques. In the case of adiabatic motion in a single internal state, we show that the gauge fields give rise to a magnetic field that results in a Zeeman splitting of the rotational states. In particular, the ground state of a molecular potential well is given by the first excited rotational state. We find that our system realizes a synthetic spināorbit coupling where the relative atomic motion couples to two internal two-atom states. The associated gauge fields are non-Abelian.</p

### (a) Lowest vibrational states in the potential shown in figure 3(a) for Ī = ā3|Ī“| and Ī©<sub>L</sub>/|Ī“| = 2.8 <b>Ć</b> 10<sup>ā6</sup>

<p><strong>Figure 4.</strong>Ā (a) Lowest vibrational states in the potential shown in figure <a href="http://iopscience.iop.org/0953-4075/46/13/134008/article#jpb460426f3" target="_blank">3</a>(a) for Ī = ā3|Ī“| and Ī©<sub>L</sub>/|Ī“| = 2.8 <b>Ć</b> 10<sup>ā6</sup>. The energy difference of the vibrational states is Ļ<sub>vib</sub> ā 0.015|Ī“|. (b) Lowest vibrational state for different quantum numbers \mathcal {M} and on an energy scale defined by Ī©<sub>L</sub>.</p> <p><strong>Abstract</strong></p> <p>We show that the dipoleādipole interaction between two Rydberg atoms can lead to substantial Abelian and non-Abelian gauge fields acting on the relative motion of the two atoms. We demonstrate how the gauge fields can be evaluated by numerical techniques. In the case of adiabatic motion in a single internal state, we show that the gauge fields give rise to a magnetic field that results in a Zeeman splitting of the rotational states. In particular, the ground state of a molecular potential well is given by the first excited rotational state. We find that our system realizes a synthetic spināorbit coupling where the relative atomic motion couples to two internal two-atom states. The associated gauge fields are non-Abelian.</p

### (a) Three potential wells in the <em>x</em>ā<em>y</em> plane corresponding to three different eigenstates of <em>H</em><sub>int</sub>

<p><strong>Figure 5.</strong>Ā (a) Three potential wells in the <em>x</em>ā<em>y</em> plane corresponding to three different eigenstates of <em>H</em><sub>int</sub>. The solid red, black dashed and blue dotted lines correspond to |Ļ<sub>1</sub>ć, |Ļ<sub>2</sub>ć and |Ļ<sub>3</sub>ć, respectively. The black dot indicates the initial position of the system for the dynamics discussed in figure <a href="http://iopscience.iop.org/0953-4075/46/13/134008/article#jpb460426f6" target="_blank">6</a> and the arrow indicates the direction of motion. (b) Imaginary part of \tilde{A}_{12}^{(1)}=[\tilde{A}_{21}^{(1)}]^* for = 0. (c) Real parts of \tilde{A}_{11}^{(2)} (solid red line), \tilde{A}_{22}^{(2)} (dashed black line) and \tilde{A}_{12}^{(2)}=[\tilde{A}_{21}^{(2)}]^* (dotted blue line) for = 0. (d) Matrix elements of the commutator <em>C</em> in equation (<a href="http://iopscience.iop.org/0953-4075/46/13/134008/article#jpb460426eqn34" target="_blank">34</a>). The red solid line shows <em>C</em><sub>11</sub> = ā<em>C</em><sub>22</sub> and the black dashed line represents <em>C</em><sub>12</sub> = <em>C</em><sub>21</sub>. In (a)ā(d), we set Ī = ā1.13|Ī“|. All components of \boldsymbol{\tilde{A}} that are not shown in (b) and (c) are zero.</p> <p><strong>Abstract</strong></p> <p>We show that the dipoleādipole interaction between two Rydberg atoms can lead to substantial Abelian and non-Abelian gauge fields acting on the relative motion of the two atoms. We demonstrate how the gauge fields can be evaluated by numerical techniques. In the case of adiabatic motion in a single internal state, we show that the gauge fields give rise to a magnetic field that results in a Zeeman splitting of the rotational states. In particular, the ground state of a molecular potential well is given by the first excited rotational state. We find that our system realizes a synthetic spināorbit coupling where the relative atomic motion couples to two internal two-atom states. The associated gauge fields are non-Abelian.</p

### Estimation of Heterosis and Comparison of True Breed Difference.

<p>Estimation of Heterosis and Comparison of True Breed Difference.</p

### Predicted Means (Ā± Standard Error) for Fixed Effects plus the Significance of any Two-way Interactions.

<p>Predicted Means (Ā± Standard Error) for Fixed Effects plus the Significance of any Two-way Interactions.</p

### Number of Animals and Data Structure for the AG, AGG, and GG Genotypes involved in the Investigation over Five Years.

<p>Number of Animals and Data Structure for the AG, AGG, and GG Genotypes involved in the Investigation over Five Years.</p

### Predicted Means (Ā± Standard Error) for Wool Traits plus Significance of Two-way Interactions of Fixed Effects.

<p>Predicted Means (Ā± Standard Error) for Wool Traits plus Significance of Two-way Interactions of Fixed Effects.</p

### Sequences of specific primer pairs used for RT- and qRT-PCR amplification.

<p>Sequences of specific primer pairs used for RT- and qRT-PCR amplification.</p

### Gene classification based on Gene ontology (GO) enrichment for differentially expressed genes.

<p>Gene classification based on Gene ontology (GO) enrichment for differentially expressed genes.</p

- ā¦