We report on spectroscopic measurements on the
This content will become publicly available on September 22, 2023
The midIR spectroscopic properties of
 Publication Date:
 NSFPAR ID:
 10372091
 Journal Name:
 Journal of the Optical Society of America B
 Volume:
 40
 Issue:
 1
 Page Range or eLocationID:
 Article No. A1
 ISSN:
 07403224; JOBPDE
 Publisher:
 Optical Society of America
 Sponsoring Org:
 National Science Foundation
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$4{f}^{7}6{s}^{2}{\phantom{\rule{thickmathspace}{0ex}}}^{8}{\phantom{\rule{negativethinmathspace}{0ex}}S}_{7/2}^{\circ <\#comment/>}\to <\#comment/>4{f}^{7}{(}^{8}\phantom{\rule{negativethinmathspace}{0ex}}{S}^{\circ <\#comment/>})6s6p{(}^{1}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{negativethinmathspace}{0ex}}{P}^{\circ <\#comment/>}){\phantom{\rule{thinmathspace}{0ex}}}^{8}\phantom{\rule{negativethinmathspace}{0ex}}{P}_{9/2}$ transition in neutral europium151 and europium153 at 459.4 nm. The center of gravity frequencies for the 151 and 153 isotopes, reported for the first time in this paper, to our knowledge, were found to be 652,389,757.16(34) MHz and 652,386,593.2(5) MHz, respectively. The hyperfine coefficients for the$6s6p{(}^{1}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{negativethinmathspace}{0ex}}{P}^{\circ <\#comment/>}){\phantom{\rule{thinmathspace}{0ex}}}^{8}\phantom{\rule{negativethinmathspace}{0ex}}{P}_{9/2}$ state were found to be$\mathrm{A}(151)=<\#comment/>228.84(2)\phantom{\rule{thickmathspace}{0ex}}\mathrm{M}\mathrm{H}\mathrm{z}$ ,$\mathrm{B}(151)=226.9(5)\phantom{\rule{thickmathspace}{0ex}}\mathrm{M}\mathrm{H}\mathrm{z}$ and$\mathrm{A}(153)=<\#comment/>101.87(6)\phantom{\rule{thickmathspace}{0ex}}\mathrm{M}\mathrm{H}\mathrm{z}$ ,$\mathrm{B}(153)=575.4(1.5)\phantom{\rule{thickmathspace}{0ex}}\mathrm{M}\mathrm{H}\mathrm{z}$ , which all agree with previously published results except for A(153), which shows a small discrepancy. The isotope shift is found to be 3163.8(6) MHz, which also has a discrepancy with previously published results. 
Electrooptic quantum coherent interfaces map the amplitude and phase of a quantum signal directly to the phase or intensity of a probe beam. At terahertz frequencies, a fundamental challenge is not only to sense such weak signals (due to a weak coupling with a probe in the nearinfrared) but also to resolve them in the time domain. Cavity confinement of both light fields can increase the interaction and achieve strong coupling. Using this approach, current realizations are limited to low microwave frequencies. Alternatively, in bulk crystals, electrooptic sampling was shown to reach quantumlevel sensitivity of terahertz waves. Yet, the coupling strength was extremely weak. Here, we propose an onchip architecture that concomitantly provides subcycle temporal resolution and an extreme sensitivity to sense terahertz intracavity fields below 20 V/m. We use guided femtosecond pulses in the nearinfrared and a confinement of the terahertz wave to a volume of
${V}_{\mathrm{T}\mathrm{H}\mathrm{z}}\sim <\#comment/>{10}^{<\#comment/>9}({\mathrm{\lambda <\#comment/>}}_{\mathrm{T}\mathrm{H}\mathrm{z}}/2{)}^{3}$ in combination with ultraperformant organic molecules (${r}_{33}=170\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{p}\mathrm{m}/\mathrm{V}$ ) and accomplish a recordhigh singlephoton electrooptic coupling rate of${g}_{\phantom{\rule{negativethinmathspace}{0ex}}\mathrm{e}\mathrm{o}}=2\mathrm{\pi <\#comment/>}\times <\#comment/>0.043\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{G}more\xbb$ , 10,000 times higher than in recent reports of sensing vacuum field fluctuations in bulk media. Via homodyne detection implemented directly on chip, the interaction results into an intensity modulation of the femtosecond pulses. The singlephoton cooperativity is${C}_{0}=1.6\times <\#comment/>{10}^{<\#comment/>8}$ , and the multiphoton cooperativity is$C=0.002$ at room temperature. We show$><\#comment/>70\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ dynamic range in intensity at 500 ms integration under irradiation with a weak coherent terahertz field. Similar devices could be employed in future measurements of quantum states in the terahertz at the standard quantum limit, or for entanglement of subsystems on subcycle temporal scales, such as terahertz and nearinfrared quantum bits. 
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$\mathrm{\varphi <\#comment/>}$ is a key quantity in the physics of light propagating through a turbulent medium. In certain respects, however, the statistics of the phasefactor ,$\mathrm{\psi <\#comment/>}=\mathrm{exp}<\#comment/>(i\mathrm{\varphi <\#comment/>})$ , are more relevant than the statistics of the phase itself. Here, we present a theoretical analysis of the 2D phasefactor spectrum${F}_{\mathrm{\psi <\#comment/>}}(\mathit{\kappa <\#comment/>})$ of a random phase screen. We apply the theory to four types of phase screens, each characterized by a powerlaw phase structure function,${D}_{\mathrm{\varphi <\#comment/>}}(r)=(r/{r}_{c}{)}^{\mathrm{\gamma <\#comment/>}}$ (where${r}_{c}$ is the phase coherence length defined by${D}_{\mathrm{\varphi <\#comment/>}}({r}_{c})=1\phantom{\rule{thickmathspace}{0ex}}{\mathrm{r}\mathrm{a}\mathrm{d}}^{2}$ ), and a probability density function${p}_{\mathrm{\alpha <\#comment/>}}(\mathrm{\alpha <\#comment/>})$ of the phase increments for a given spatial lag. We analyze phase screens with turbulent ($\mathrm{\gamma <\#comment/>}=5/3$ ) and quadratic ($\mathrm{\gamma <\#comment/>}=2$ ) phase structure functions and with normally distributed (i.e., Gaussian) versus Laplacian phase increments. We find that there is a pronounced bump in each of the four phasefactor spectra${F}_{\mathrm{\psi <\#comment/>}}(\mathrm{\kappa <\#comment/>})$ . The precise location and shape of the bump are different for the four phasescreen types, but in each case it occurs at$\mathrm{\kappa <\#comment/>}\sim <\#comment/>1/{r}_{c}$ . The bump is unrelated to the wellknownmore »