We show that a transition metal dichalcogenide monolayer with a radiatively broadened exciton resonance would exhibit perfect extinction of a transmitted field. This result holds for s-or p-polarized weak resonant light fields at any incidence angle, due to the conservation of in-plane momentum of excitons and photons in a flat defect-free two dimensional crystal. In contrast to extinction experiments with single quantum emitters, exciton-exciton interactions lead to an enhancement of reflection with increasing power for incident fields that are blue detuned with respect to the exciton resonance. We show that the interactions limit the maximum reflection that can be achieved by depleting the incoming coherent state into an outgoing two-mode squeezed state. In this Letter we show that a TMD monolayer acts as a perfect atomically-thin mirror for radiation that is resonant with radiatively broadened excitonic resonances. In the limit of weak resonant incident laser field, destructive interference between the transmitted field and the field generated by the TMD excitons leads to perfect extinction. In-plane momentum conservation ensures that the transmitted field vanishes for any incidence angle as long as the generated 2D excitons have a perfect overlap with the incident field polarization: this is the case for an incident s-polarized field. Remarkably, p-polarized fields also yield perfect extinction since the generated longitudinally-polarized exciton couples exclusively to ppolarized outgoing radiation. On the other hand, any superposition of s-and p-polarized fields will have finite transmission: this is a consequence of finite energy splitting of the transverse and longitudinal exciton resonances induced by the electron-hole exchange interaction [7]. MonolayersThe exciton-exciton interactions ensure that there will be a non-zero transmitted field as the intensity of the field is increased: this is the analog of saturation induced reduction in extinction observed in resonantly driven single quantum emitters. Unlike the latter however, strong extinction of the mean transmitted field is possible in the TMD case by tuning the incident field to blue (red) side of the resonance for repulsive (attractive) exciton-exciton interactions. We find that for laser detunings and intensities where the exciton system approaches bistability, the extinction of the mean field is only limited by the deple -FIG. 1: (a) The schematic of the experimental setup. A collimated coherent laser field is incident on a transition metal dichalcogenide (TMD) monolayer. In addition to coherent transmitted and reflected fields, a two-mode squeezed-state (TMSS) is generated due to exciton-exciton interactions. Unlike the coherent fields, the TMSS is emitted into a large solid-angle. Electromagnetic field can be characterized as consisting of right (left) propagating input rin (lin) and output rout (lout) modes. (b) The reflection from the 2D TMD layer for weak near resonant drive. Destructive interference between the directly transmitted field an...

High-harmonic generation (HHG) is widely used for up-conversion of amplified (near) infrared ultrafast laser pulses to short wavelengths. We demonstrate that Ramsey-comb spectroscopy, based on two such pulses derived from a frequency-comb laser, enables us to observe phase effects in this process with a few mrad precision. As a result, we could perform the most accurate spectroscopic measurement based on light from HHG, illustrated with a determination of the 5p 6 → 5p 5 8s 2 [3/2]1 transition at 110 nm in 132 Xe. We improve its relative accuracy 10 4 times to a value of 2.3 × 10 −10 . This is 3.6 times better than shown before involving HHG, and promising to enable 1S − 2S spectroscopy of He + for fundamental tests.High-precision spectroscopy in calculable atomic and molecular systems is at the heart of the most precise tests of bound-state quantum electrodynamics (QED) and searches for new physics beyond the Standard Model [1][2][3][4][5][6]. Instrumental in this development was the invention of the optical frequency comb (FC) [7,8] which enables precise optical frequency measurements referenced to an atomic clock. However, uncertainties in finite nuclearsize effects are hampering further progress [9]. Instead, spectroscopy has been used to measure the proton size in atomic and muonic hydrogen, but with partly conflicting results [10][11][12][13][14][15][16]. High-precision spectroscopy of the 1S − 2S transition in He + would provide new possibilities for fundamental tests as the uncertainty there is less dominated by nuclear size effects [17]. Combined with muonic He + spectroscopy [18,19] one can extract e.g. the alpha particle radius or the Rydberg constant. A major experimental challenge arises from the requirement of extreme ultraviolet (XUV) light at 60 nm (or shorter), to excite the transition. A similar challenge exist for spectroscopy of highly-charged ions [5], or the Thorium nuclear clock transition near 150 nm in the vacuum ultraviolet (VUV) [20,21]. At those wavelengths a relative accuracy of 0.1 ppm has been achieved with Fouriertransform spectroscopy techniques [22], and 0.03 ppm with low harmonics from nanosecond pulsed lasers [23]. A higher accuracy can be reached with light from highharmonic generation (HHG), induced by focusing ultrafast high-energy laser pulses in a noble gas at intensities of ∼ 10 14 W/cm 2 . The process can be understood using the three-step model [24,25], involving tunnel-ionization and recollision of an electron. This highly coherent process leads to the generation of a series of odd harmonics, which are tightly linked to the fundamental wave [26][27][28][29][30]. In combination with frequency-comb lasers, it has been used to achieve a spectroscopic accuracy of about 1 ppb at VUV and XUV wavelengths [31,32]. To improve on this we recently developed the Ramseycomb spectroscopy (RCS) method [33,34], based on pairs of powerful amplified FC pulses in a Ramsey-type [35] excitation scheme. Using only two pulses can compro-mise the accuracy provided by the FC laser [31], but th...

High-precision laser spectroscopy of atomic hydrogen has led to an impressive accuracy in tests of bound-state quantum electrodynamics (QED). At the current level of accuracy many systematics have to be studied very carefully and only independent measurements provide the ultimate cross-check. This has been proven recently by measurements in muonic hydrogen, eventually leading to a significant shift of the CODATA recommended values of the proton charge radius and the Rydberg constant. We aim to contribute to tests of fundamental physics by measuring the 1S-2S transition in the He + ion for the first time. Combined with measurements in muonic helium ions this can probe the value of the Rydberg constant, test higher-order QED terms, or set benchmarks for ab initio nuclear polarizability calculations. We extend the Ramsey-comb spectroscopy method to the XUV using high-harmonic generation in order to excite a single, trapped He + ion.

Experimental level s of the co nfiguration s 3d" 4p, 3d"5p, 3d"6p, 3d"4s4p, 3d "4f, and 3d"5f of Cu II we re compared with co rresponding calculated values. The e lectrostatI c Inter~ctlons between the configuration 3d"4s4p and th e con fi gura tion s 3d"4p, 3d"5p, and 3d"6p were conS Idered exp hcltl y. It was shown that the configuration s 3d 94f and 3d 9 5f of Cu II do not interact strongly with other co nfigurations.

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