Test of quantum chemistry in vibrationally-hot hydrogen molecules

Precision measurements are performed on highly excited vibrational quantum states of molecular hydrogen. The $v=12, J=0-3$ rovibrational levels of H$_2$ ($X^1\Sigma_g^+$), lying only $2000$ cm$^{-1}$ below the first dissociation limit, were populated by photodissociation of H$_2$S and their level energies were accurately determined by two-photon Doppler-free spectroscopy. A comparison between the experimental results on $v=12$ level energies with the best \textit{ab initio} calculations shows good agreement, where the present experimental accuracy of $3.5 \times10^{-3}$ cm$^{-1}$ is more precise than theory, hence providing a gateway to further test theoretical advances in this benchmark quantum system.Comment: 5 pages, 4 figures, and 2 table

Qudit-Basis Universal Quantum Computation using χ(2)\chi^{(2)} Interactions

We prove that universal quantum computation can be realized---using only linear optics and $\chi^{(2)}$ (three-wave mixing) interactions---in any $(n+1)$-dimensional qudit basis of the $n$-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that $\chi^{(2)}$ Hamiltonians and photon-number operators generate the full $\mathfrak{u}(3)$ Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-$Z$ gate can be implemented with only linear optics and $\chi^{(2)}$ interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection/subtraction, a technique enabled by $\chi^{(2)}$ interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states.Comment: 9 pages, 3 figure

High-precision laser spectroscopy of the CO A1Π^1\Pi - X1Σ+^1\Sigma^+ (2,0), (3,0) and (4,0) bands

High-precision two-photon Doppler-free frequency measurements have been performed on the CO A$^1\Pi$ - X$^1\Sigma^+$ fourth-positive system (2,0), (3,0), and (4,0) bands. Absolute frequencies of forty-three transitions, for rotational quantum numbers up to $J = 5$, have been determined at an accuracy of $1.6\times10^{-3}$ cm$^{-1}$, using advanced techniques of two-color 2+1' resonance-enhanced multi-photon ionization, Sagnac interferometry, frequency-chirp analysis on the laser pulses, and correction for AC-Stark shifts. The accurate transition frequencies of the CO A$^1\Pi$ - X$^1\Sigma^+$ system are of relevance for comparison with astronomical data in the search for possible drifts of fundamental constants in the early universe. The present accuracies in laboratory wavelengths of $\Delta\lambda/\lambda = 2 \times 10^{-8}$ may be considered exact for the purpose of such comparisons.Comment: 13 pages, 6 figures, The Journal of Chemical Physics (2015) accepte

High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position sensitive detection

We present a method of performing high-speed rotational anisotropy nonlinear optical harmonic generation experiments at rotational frequencies of several hertz by projecting the harmonic light reflected at different angles from a sample onto a stationary position sensitive detector. The high rotational speed of the technique, $10^3$ to $10^4$ times larger than existing methods, permits precise measurements of the crystallographic and electronic symmetries of samples by averaging over low frequency laser power, beam pointing, and pulse width fluctuations. We demonstrate the sensitivity of our technique by resolving the bulk four-fold rotational symmetry of GaAs about its [001] axis using second harmonic generation

Berry phases in superconducting transitions

I generalize the concept of Berry's geometrical phase for quasicyclic Hamiltonians to the case in which the ground state evolves adiabatically to an excited state after one cycle, but returns to the ground state after an integer number of cycles. This allows to extend the charge Berry phase gamma_c related to the macroscopic polarization, to many-body systems with fractional number of particles per site. Under certain conditions, gamma_c and the spin Berry phase gamma_s jump in pi at the boundary of superconducting phases. In the extended Hubbard chain with on-site attraction U and nearest-neighbor interaction V at quarter filling, the transitions detected agree very well with exact results in two limits solved by the Bethe ansatz, and with previous numerical studies. In chains with spin SU(2) symmetry, gamma_s jumps when a spin gap opens.Comment: 5 pages, 3 figures, accepted in Europhys. Let