We present a novel approach for solving numerically one-dimensional scattering problems and apply it for computing the emission probability of an ultracold atom interacting with an arbitrary field mode of a high-$Q$ cavity. Our method is efficient, stable and succeeds when other numerical integration methods fail. It also replaces and improves advantageously the WKB approximation. The cases of sinusoidal, $\mathrm{sech}^2$ and Gaussian field modes are studied and compared. Divergences with previous works, where WKB was used, are found.
In order to probe the transitions of a nuclear spin $s$ from one of its substate quantum numbers $m$ to another substate $m'$, the experimenter applies a magnetic field ${\bm B}_0$ in some particular direction, such along $\hat{\bm z}$, and then applies an weaker field ${\bm B}_1(t)$ that is oscillatory in time with the angular frequency $ω$, and is normally perpendicular to ${\bm B}_0$, such as ${\bm B}_1(t)=B_1\hat{\bm x}\cos(ωt)$. In the rotating wave approximation, ${\bm B}_1(t)=B_1[\hat{\bm x}\cos(ωt)+\hat{\bm y}\sin(ωt)]$. Although this problem is solved for spin $\frac{1}{2}$ in every q…
Inspired by the unique nonclassical character of two-photon interactions induced by entangled photons, we develop a new comprehensive Förster-type formulation for entangled two-photon resonance energy transfer (E2P-RET) mediated by inhomogeneous, dispersive and absorptive media with any space-dependent and frequency-dependent dielectric function and with any size of donor/acceptor. In our theoretical framework, two uncoupled particles are jointly excited by the temporally entangled field associated with two virtual photons that are produced by three-level radiative cascade decay in a donor par…
With the purpose to devise a novel lasing scheme, we consider a two level system with both a transversal and longitudinal coupling to the electromagnetic field. If the longitudinal coupling is sufficiently strong, multi-photon transitions become possible. We assume furthermore that the electromagnetic environment has a spectrum with a single sharp resonance, which serves as a lasing cavity. Additionally, the electromagnetic environment should have a very broad resonance around a frequency which differs form the sharp resonance. We use the polaron transformation and derive a rate equation to de…
The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of scattering resonances in the complex plane of the wavenumber without finding them one by one. The method is applied to two collision models for the individual scatterers, namely a resonant model, and a non-resonant hard-sphere model. The results obtained with the former are compared to the literature. In particular, the spiral arms surrounding the single-scatterer …
Zero-field nuclear magnetic resonance (NMR) provides complementary analysis modalities to those of high-field NMR and allows for ultra-high-resolution spectroscopy and measurement of untruncated spin-spin interactions. Unlike for the high-field case, however, universal quantum control -- the ability to perform arbitrary unitary operations -- has not been experimentally demonstrated in zero-field NMR. This is because the Larmor frequency for all spins is identically zero at zero field, making it challenging to individually address different spin species. We realize a composite-pulse technique f…
Long-range interactions between cold Rydberg atoms, which are used in many important applications, can be enhanced using Förster resonances between collective many-body states controlled by an external electric field. Here we report on the first experimental observation of highly-resolved radio-frequency-assisted Förster resonances in a few cold Rb Rydberg atoms. We also observed radio-frequency-induced Förster resonances which cannot be tuned by a dc electric field. They imply an efficient transition from van der Waals to resonant dipole-dipole interaction due to Floquet sidebands of Rydberg …
