Two-color Polarization Spectroscopy Research Articles

Two-color polarization spectroscopy measurements of Zeeman state-to-state collision induced transitions of nitric oxide in binary gas mixtures.

We investigated collision induced transitions in the (0, 0) band of the A2Σ+-X2Π electronic transition of nitric oxide (NO) using two-color polarization spectroscopy (TCPS). Two sets of TCPS spectra for 1% NO, diluted in different buffer gases at 295K and 1 atm, were obtained with the pump beam tuned to the R11(11.5) and OP12(1.5) transitions. The buffer gases were He, Ar, and N2. The probe was scanned while the pump beam was tuned to the line center. Theoretical TCPS spectra, calculated by solving the density matrix formulation of the time-dependent Schrödinger wave equation, were compared with the experimental spectra. A collision model based on the modified exponential-gap law was used to model the rotational level-to-rotational level collision dynamics. A model for collisional transfer from an initial to a final Zeeman state was developed based on the difference in cosine of the rotational quantum number J projection angle with the z-axis for the two Zeeman states. Rotational energy transfer rates and Zeeman state collisional dynamics were varied to obtain good agreement between theory and experiment for the two different TCPS pump transitions and for the three different buffer gases. One key finding, in agreement with quasi-classical trajectory calculations, is that the spin-rotation changing transition rate in the A2Σ+ level of NO is almost zero for rotational quantum numbers ≥8. It was necessary to set this rate to near zero to obtain agreement with the TCPS spectra.

Artificial modulation-free Pound-Drever-Hall method for laser frequency stabilization.

We have proposed an artificial modulation-free Pound-Drever-Hall (PDH) method for laser frequency stabilization and demonstrated it via two-color polarization spectroscopy of Rydberg electromagnetically induced transparency (EIT) resonance in a room-temperature rubidium vapor. Due to the unique error signal profile, the conventional PDH method owns a large capture range in laser frequency locking. Here we manually construct a PDH error signal via a linear combination of polarization spectroscopies of the Rydberg EIT resonances without and with a magnetic field applied. The artificial modulation-free PDH error signal owns a subnatural linewidth dispersion curve as well as a large capture range with which we successfully stabilize the laser to an absolute atomic frequency reference in a long running time, immune to environmental fluctuation and even manmade impulse perturbation. This method can provide an absolute frequency reference based on atomic transition while keeping similar locking ability to provide corrections for frequency fluctuations over a broad bandwidth as the conventional PDH.

Investigation of the two-color polarization spectroscopy between the excited states based on cesium atoms

Two-color polarization spectroscopy (TCPS) of cesium 6S<sub>1/2</sub>-6P<sub>3/2</sub>-8S<sub>1/2</sub> (852.3 nm + 794.6 nm) ladder-type system in a room-temperature vapor cell are investigated. The frequency of 852.3 nm laser used as a pump beam is locked on one of the hyperfine transitions between the ground state 6S<sub>1/2</sub> and excited state 6P<sub>3/2</sub> by the saturated absorption spectroscopy technique, which can populate some atoms on the 6P<sub>3/2</sub> excited state and induce anisotropy in the atomic medium. The frequency of 794.6 nm laser serving as a probe beam is scanned across the whole 6P<sub>3/2</sub>→8S<sub>1/2</sub> transition to ascertain this anisotropy, and thus the TCPS is obtained. In experiment, we measure and analyse the influence of frequency detuning of 852.3 nm pump laser on TCPS, and especially reveal that some of hyperfine energy levels of intermediate excited state 6P<sub>3/2</sub>, which has no direct interaction with the 852.3 nm pump laser, are also populated by a small fraction of atoms with a specific speed in the direction of pump laser beam due to Doppler effect, so they also have contribution to the TCPS when the 794.6 nm probe laser is scanned to the resonance transition line between the 6P<sub>3/2</sub> and 8S<sub>1/2</sub> states after the Doppler frequency shift has been considered. In addition, we prove that the atomic coherence like electromagnetically induced transparency effect obviously results in a narrower line width of TCPS in the case of counter-propagating experimental configuration than that in the case of pump beam co-propagating with the probe beam in the Cs vapor cell. Finally, we apply the TCPS with dispersive shaped feature to frequency stabilization with no modulation, and the frequency fluctuations of 794.6 nm laser are ～0.5 MHz and ～9.2 MHz for the frequency-locking and free running in ～225 s, respectively. The above research work is expected to play a role in precisely measuring the atomic energy level structure and its related hyperfine structure constant (magnetic dipole and electric quadrupole coupling constants), and also in stabilizing the laser frequency to the excited state transition especially for the optical fiber communication, two-color laser cooling/trapping neutral atoms, optical filter, etc.

Narrow linewidth two-color polarization spectroscopy due to the atomic coherence effect in a ladder-type atomic system

An experimental investigation of two-color polarization spectroscopy (TCPS) is presented based on the cesium 6S1/2 – 6P3/2 – 8S1/2 (852.3 nm + 794.6 nm) ladder-type system in a room-temperature vapor cell. The dependency of line shapes of TCPS on the power of a 852.3 nm pump and a 794.6 nm probe laser is measured in detail, and we confirm that the linewidth of TCPS in a counter-propagating configuration between the pump and probe laser beams is obviously narrower than that of a co-propagating configuration, due to the atomic coherence effect. It is helpful for laser stabilization of the excited state transition using TCPS without frequency modulation.

Laser frequency offset locking by marrying modulation sideband with the two-color polarization spectroscopy in a ladder-type atomic system

We present an investigation of two-color polarization spectroscopy (TCPS) based on cesium 6S1/2–6P3/2–7S1/2 (852nm+1470nm) ladder-type system in a room-temperature vapor cell. The 1470nm laser can be offset locked by TCPS combining with frequency modulation sideband. This locking scheme offers a method of modulation-free and conveniently tunable the lock point of laser frequency relative to an excited state transition, and may have many applications such as in two-color magneto-optical trap, diamond-level structure four-wave mixing experiments.

Lineshapes in two-color polarization spectroscopy for cesium

We present a theoretical study of lineshape in polarization spectroscopy for the 6S₁/₂-6P₃/₂-7S₁/₂ transition line in cesium atoms. A circularly polarized pump beam is tuned either to the lower or the upper transition line, while a linearly polarized probe beam is tuned to the other transition line. The polarization rotation of the probe beam is accurately calculated using a semi-classical density-matrix formalism taking into account all relaxation processes.

Rotationally elastic and inelastic dynamics of NO(X2Π, v = 0) in collisions with Ar

A combined theoretical and experimental study of the depolarization of selected NO(X(2)Π, v = 0, j, F, ɛ) levels in collisions with a thermal bath of Ar has been carried out. Rate constants for elastic depolarization of rank K = 1 (orientation) and K = 2 (alignment) were extracted from collision-energy-dependent quantum scattering calculations, along with those for inelastic population transfer to discrete product levels. The rate constants for total loss of polarization of selected initial levels, which are the sum of elastic depolarization and population transfer contributions, were measured using a two-color polarization spectroscopy technique. Theory and experiment agree qualitatively that the rate constants for total loss of polarization decline modestly with j, but the absolute values differ by significantly more than the statistical uncertainties in the measurements. The reasons for this discrepancy are as yet unclear. The lack of a significant K dependence in the experimental data is, however, consistent with the theoretical prediction that elastic depolarization makes only a modest contribution to the total loss of polarization. This supports a previous conclusion that elastic depolarization for NO(X(2)Π) + Ar is significantly less efficient than for the electronically closely related system OH(X(2)Π) + Ar [P. J. Dagdigian and M. H. Alexander, J. Chem. Phys. 130, 204304 (2009)].

Tensor cross sections and collisional depolarization of OH(X 2Π) in collisions with helium

Tensor cross sections for collisions of OH(X (2)Pi) with helium are computed using accurate ab initio potential energy surfaces computed by Lee et al. We use these cross sections to predict rate constants for collisional depolarization of specific rotational fine-structure levels of OH(X (2)Pi) in collisions with helium. Good agreement is found with the results of the two-color polarization spectroscopy experiments of Paterson et al. [J. Chem. Phys. 129, 074304 (2008)]. By examination of partial cross sections, the range of impact parameters at which collisional depolarization occurs is shown to be similar to that for rotationally inelastic collisions.

Tensor cross sections and the collisional evolution of state multipoles: OH(XΠ2)–Ar

By means of a kinetic analysis, we show that the overall rate constant for the collisional loss of orientation or alignment of a rotational level is the sum of the rate constant for elastic depolarization and the sum of the rate constants for all rotationally inelastic transitions out of the level under consideration. An expression for the depolarization cross section is derived in terms of tensor cross sections, and the relationship of depolarization to m-resolved transitions is discussed. We use this formalism in simulations, based on high-quality ab initio potential energy surfaces, of the depolarization of the open-shell molecule OH(X (2)Pi) through collisions with Ar. Good agreement is seen with the results of the two-color polarization spectroscopy experiments of Paterson et al. [J. Chem. Phys. 129, 074304 (2008)]. In addition, we show that the major contribution to elastic collisional depolarization occurs not from weak, glancing collisions but from encounters which probe the inner wall of the potential energy surface.

Orientation and alignment depolarization in OH(X Π2)+Ar/He collisions

The depolarization of OH(X (2)Pi(3/2),v=0,J=1.5-6.5,e) rotational angular momentum (RAM) in collisions with He and Ar under thermal conditions (298 K) has been studied using two-color polarization spectroscopy (PS). Orientation or alignment of the OH RAM was achieved using circularly or linearly polarized pulsed excitation, respectively, on the off-diagonal OH A (2)Sigma(+)-X (2)Pi(1,0) band. The evolution of the ground-state OH(X) RAM polarization, exclusively, was probed using an independent, linearly polarized pulse tuned to the diagonal OH A (2)Sigma(+)-X (2)Pi(0,0) band. The PS signal decay rate constant k(PS) decreases with increasing rotational quantum number for OH(X)+Ar but does not vary monotonically for OH(X)+He. The measured k(PS) equals the sum k(RET)+k(Lambda)+k(dep), where k(RET), k(Lambda), and k(dep) are the rate constants for rotational energy transfer, Lambda-doublet changing collisions, and rotationally elastic depolarization (of orientation or alignment of the OH(X) angular momentum, as specified), respectively. Values of k(dep) can be extracted from the measured k(PS) with prior knowledge of k(RET) and k(Lambda). Because k(RET) and k(Lambda) were not previously available for collisions of Ar with OH(X, v=0), we performed exact, fully quantum-mechanical scattering calculations on a new potential energy surface (PES) presented here for the first time. The raw experimental results show that k(dep) is systematically markedly higher for alignment than for orientation for OH(X)+Ar but much more weakly so for OH(X)+He. Calculated k(RET) and k(Lambda) values at 298.15 K are consistent with a substantial contribution from k(dep) for OH(X)+Ar but not for OH(X)+He. This may point to the role of attractive forces in elastic depolarization. The experimental results provide a very sensitive test of the ability of the most recent ab initio OH(X)-He PES of Lee et al. [J. Chem. Phys. 113, 5736 (2000)] to reproduce k(RET)+k(Lambda) accurately.

Orientation and alignment moments in two-color polarization spectroscopy

A theoretical analysis of two-color polarization spectroscopy (TCPS) is presented as an extension of a previous analysis of one-color PS. Three commonly used schemes in which pump and probe transitions share a common level are considered. Diagrammatic techniques are used to isolate the photon interaction sequences that can contribute to the signal. A perturbation-theory analysis expressing the signal in terms of spherical tensor moments is applied. The analysis emphasises the significance of orientation and alignment tensor moments of rotational angular momentum and their collisional evolution. The assumed context is transitions between single rotational states of gas-phase molecules that subsequently suffer discrete collisions. The time scale of the measurements is assumed to be long relative to the periods of molecular motion, as would typically be the case for signals excited by nanosecond-pulsed lasers from samples at moderate pressures. The Doppler motion of the probed species is included, as is an analytical solution to the integration over the Maxwell-Boltzmann distribution of velocities. The effects of nuclear hyperfine depolarization and velocity-changing collisions are discussed. It is shown that when pump- and probe-laser pulses are separated in time, TCPS creates and probes either orientation or alignment of rotational angular momentum in the common level shared by pump and probe transitions. Example simulations of one- and two-color polarization spectroscopies are included to demonstrate the resulting simplification of the measured signal using TCPS. TCPS is therefore a viable spectroscopic technique for the determination of rotational angular momentum orientation and alignment relaxation rates in molecular gases, of interest because they are sensitive probes of inelastic collisions.

Time-domain investigation of OH ground-state energy transfer using picosecond two-color polarization spectroscopy

Two-color polarization spectroscopy was used to investigate rotational energy transfer (RET) and relaxation of orientation and alignment in the ground electronic state of OH in an atmospheric-pressure methane–air flame. Two independently tunable lasers produced nearly transform-limited infrared and ultraviolet pulses of 50 ps duration. The infrared laser excited rovibrational transitions, and delayed ultraviolet pulses probed electronic transitions from either the directly pumped or collisionally populated states. Alignment and orientation relaxation times were measured for individual rotational levels in OH X 2 Π 3/2(v=1) , and the feasibility of time-domain investigation of state-to-state energy transfer processes was demonstrated.

Coherent infrared–ultraviolet double-resonance spectroscopy of CH 3

Two-color polarization spectroscopy (TC-PS) and two-color resonant four-wave mixing spectroscopy (TC-RFWM) are used to detect photolytically produced CH 3 radicals. An infrared laser pumps individual lines in the ν 3 fundamental of the X ̃ 2 A 2″ state, and an ultraviolet laser probes the pumped levels to reveal rotationally resolved spectra of transitions to the predissociated B ̃ 2 A 1 ′ state. The spectra are fit with a complex Lorentzian lineshape and yield an updated value of 46 239.4±1.2 cm −1 for T 0 of the B ̃ state. A detection limit of 2×10 13 CH 3 molecules per cm 3 per quantum state is observed for these coherent double-resonance techniques.

Infrared–ultraviolet double-resonance spectroscopy of OH in a flame

We have experimentally investigated three types of two-color techniques for the detection of the hydroxyl radical using an infrared laser to pump individual ground-state rovibrational transitions and an ultraviolet laser to probe electronic transitions from the pumped intermediate levels. Signal scaling relations and saturation studies are compared for the following techniques: two-color laser-induced fluorescence (TC-LIF), polarization spectroscopy (TC-PS), and resonant four-wave mixing (TC-RFWM). Collisional effects are observed, but the time resolution set by the 1.5-ns laser pulses is not sufficient to determine state-to-state energy transfer rates in an atmospheric pressure flame.

Laser spectroscopy of spontaneous coherence transfer and optically induced polarization rotation in [formula omitted

Spontaneous coherence transfer in 87 Rb atoms has been studied experimentally using a two-color laser polarization spectroscopy. Two classes of optical transitions were investigated for that the theory predicts a presence or absence of anisotropy of a ground state hyperfine sublevel 5 S 1/2 (F=1) populated via spontaneous decay of the 5 P 1/2 (F ′=1,2) excited states optically pumped by a strong linearly polarized laser beam. The anisotropy was controlled by the polarization rotation of another weak probe laser beam. A qualitative agreement with theory has been found at low ( 3–10 mW/ cm 2 ) pumping intensity. However, no significant changes in the rotation angles were observed after increasing the intensity to 70 mW/ cm 2 . A conclusion has been made that the spatial distribution of the pumping beam became important at high intensity.