J.-Ph. Karr

Optical bistability in semiconductor microcavities

We report the observation of polaritonic bistability in semiconductor microcavities in the strong-coupling regime. The origin of bistability is the polariton-polariton interaction, which gives rise to a Kerr-like nonlinearity. The experimental results are in good agreement with a simple model taking transverse effects into account.

Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD

The simplest molecules in nature, molecular hydrogen ions in the form of H2+ and HD+, provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, we report on such a test based on a frequency measurement of a vibrational overtone transition in HD+ by laser spectroscopy. We find that the theoretical and experimental frequencies are equal to within 0.6(1.1) parts per billion, which represents the most stringent test of molecular theory so far. Our measurement not only confirms the validity of high-order quantum electrodynamics in molecules, but also enables the long predicted determination of the proton-to-electron mass ratio from a molecular system, as well as improved constraints on hypothetical fifth forces and compactified higher dimensions at the molecular scale. With the perspective of comparisons between theory and experiment at the 0.01 part-per-billion level, our work demonstrates the potential of molecular hydrogen ions as a probe of fundamental physical constants and laws.

High accuracy results for the energy levels of the molecular ions H+2, D+2 and HD+, up to J = 2

We present a nonrelativistic calculation of the rotation-vibration levels of the molecular ions H+2, D+2 and HD+, relying on the diagonalization of the exact three-body Hamiltonian in a variational basis. The J = 2 levels are obtained with a very high accuracy of 10−14 au (for most levels) representing an improvement by five orders of magnitude over previous calculations. The accuracy is also improved for the J = 1 levels of H+2 and D+2 with respect to earlier works. Moreover, we have computed the sensitivities of the energy levels with respect to the mass ratios, allowing these levels to be used for metrological purposes.

H2+ and HD+: Candidates for a molecular clock

Abstract We investigate the leading systematic effects in ro-vibrational spectroscopy of the molecular hydrogen ions H 2 + and HD + , in order to assess their potential for the realization of optical clocks that would be sensitive to possible variations of the proton-to-electron mass ratio. Both two-photon (2E1) and quadrupole (E2) transitions are considered. In view of the weakness of these transitions, most attention is devoted to the light shift induced by the probe laser, which we express as a function of the transition amplitude, differential dynamic polarizability and clock interrogation times. Transition amplitudes and dynamic polarizabilites including the effect of hyperfine structure are then calculated in a full three-body approach to get a precise evaluation of the light shift. Together with the quadrupole and Zeeman shifts that are obtained from previous works, these results provide a realistic estimate of the achievable accuracy. We show that the lightshift is the main limiting factor in the case of two-photon transitions, both in H 2 + and HD + , leading to expected accuracy levels close to 5 × 10 - 16 in the best cases. Quadrupole transitions have even more promising properties and may allow reaching or going beyond 1 × 10 - 16 .

Squeezed states and the quantum noise of light in semiconductor microcavities

A theoretical investigation of the quantum noise in the light reflected by a microcavity containing a semiconductor quantum well is presented. Squeezing is predicted when scattering processes have a low efficiency. Exciton-phonon scattering is shown to destroy the non-classical effects and to yield excess noise in the output field.

Twin polaritons in semiconductor microcavities

The quantum correlations between the beams generated by polariton pair scattering in a semiconductor microcavity above the parametric oscillation threshold are computed analytically. The influence of various parameters, including the cavity-exciton detuning, the intensity mismatch between the signal and idler beams, and the amount of spurious noise, is analyzed. We show that very strong quantum correlations between the signal and idler polaritons can be achieved. However, the quantum effects in the outgoing light fields are strongly reduced due to the large mismatch in the coupling of the signal and idler polaritons to the external photons.

Energy levels and two-photon transition probabilities in the HD+ ion

We present a fully exact non-relativistic calculation of the energies and wavefunctions of the J = 1 states of the HD+ molecular ion. The energies are obtained with a very high accuracy of 10−14 au, representing, for most levels, an improvement by several orders of magnitude over previous calculations. We compute the static polarizabilities of the J = 0 states, which are in agreement with the literature, with an improved accuracy, as well as the two-photon transition probabilities and light shifts between J = 0 states. Finally, we extend our study to transitions between higher J states, using an approximate expression of the transition probability, and discuss the feasibility of a two-photon spectroscopy experiment in HD+.

Fundamental Transitions and Ionization Energies of the Hydrogen Molecular Ions with Few ppt Uncertainty

We calculate ionization energies and fundamental vibrational transitions for H_{2}^{+}, D_{2}^{+}, and HD^{+} molecular ions. The nonrelativistic quantum electrodynamics expansion for the energy in terms of the fine structure constant α is used. Previous calculations of orders mα^{6} and mα^{7} are improved by including second-order contributions due to the vibrational motion of nuclei. Furthermore, we evaluate the largest corrections at the order mα^{8}. That allows us to reduce the fractional uncertainty to the level of 7.6×10^{-12} for fundamental transitions and to 4.5×10^{-12} for the ionization energies.

Hydrogen molecular ions for improved determination of fundamental constants

An experimental scheme is proposed to help resolve the proton- (deuteron-) radius puzzle with rovibrational two-photon spectroscopy of hydrogen molecular ions measured at high precision. The technique is also expected to measure other fundamental constants, such as the Rydberg constant and the electron-proton mass ratio, at a competitive level of precision compared to the existing schemes.

Calculation of the relativistic Bethe logarithm in the two-center problem

We present a variational approach to evaluate relativistic corrections of order \alpha^2 to the Bethe logarithm for the ground electronic state of the Coulomb two center problem. That allows to estimate the radiative contribution at m\alpha^7 order in molecular-like three-body systems such as hydrogen molecular ions H_2^+ and HD^+, or antiprotonic helium atoms. While we get 10 significant digits for the nonrelativistic Bethe logarithm, calculation of the relativistic corrections is much more involved especially for small values of bond length R. We were able to achieve a level of 3-4 significant digits starting from R=0.2 bohr, that will allow to reach 10^{-10} relative uncertainty on transition frequencies.