^{1,a)}, S. Ashman

^{1,b)}, J. Bai

^{2}, B. Beser

^{2}, E. H. Ahmed

^{2}, A. M. Lyyra

^{2}and J. Huennekens

^{1,c)}

### Abstract

Collisional satellite lines with |Δ*J*| ≤ 58 have been identified in recent polarizationspectroscopy V-type optical–optical double resonance (OODR) excitation spectra of the Rb_{2} molecule [H. Salami *et al.*, Phys. Rev. A80, 022515 (2009)]. Observation of these satellite lines clearly requires a transfer of population from the rotational level directly excited by the pump laser to a neighboring level in a collision of the molecule with an atomic perturber. However to be observed in polarizationspectroscopy, the collision must also partially preserve the angular momentum orientation, which is at least somewhat surprising given the extremely large values of Δ*J* that were observed. In the present work, we used the two-step OODR fluorescence and polarizationspectroscopy techniques to obtain quantitative information on the transfer of population and orientation in rotationally inelastic collisions of the NaK molecules prepared in the 2(*A*)^{1}Σ^{+}(*v*′ = 16, *J*′ = 30) rovibrational level with argon and potassium perturbers. A rate equation model was used to study the intensities of these satellite lines as a function of argon pressure and heat pipe oven temperature, in order to separate the collisional effects of argon and potassium atoms. Using a fit of this rate equation model to the data, we found that collisions of NaK molecules with potassium atoms are more likely to transfer population and destroy orientation than collisions with argon atoms. Collisions with argon atoms show a strong propensity for population transfer with Δ*J* = even. Conversely, collisions with potassium atoms do not show this Δ*J* = even propensity, but do show a propensity for Δ*J* = positive compared to Δ*J* = negative, for this particular initial state. The density matrix equations of motion have also been solved numerically in order to test the approximations used in the rate equation model and to calculate fluorescence and polarizationspectroscopy line shapes. In addition, we have measured rate coefficients for broadening of NaK 3^{1}Π ← 2(*A*)^{1}Σ^{+}spectral lines due to collisions with argon and potassium atoms. Additional broadening, due to velocity changes occurring in rotationally inelastic collisions, has also been observed.

We would like to thank Dr. Amanda Ross, Professor Robert W. Field and Professor A. Peet Hickman for many valuable discussions. This work was supported by the National Science Foundation through Grant Nos. PHY-0652938, PHY-0968898, PHY-0555608, and PHY-0855502.

I. INTRODUCTION

II. EXPERIMENT

III. THEORY

A. Polarizationspectroscopy lineshapes

B. Empirical model to describe collisional population and orientation transfer

IV. RESULTS AND DISCUSSION

A. Collisional transfer of population and orientation

B. Line-broadening measurements

C. Assignment of uncertainties

V. CONCLUSIONS

### Key Topics

- Potassium
- 67.0
- Polarization
- 52.0
- Fluorescence spectroscopy
- 17.0
- Fluorescence
- 15.0
- Heat pipes
- 15.0

## Figures

Rb_{2} *A* ^{1}Σ_{ u } ^{+} ← *X* ^{1}Σ_{ g } ^{+} spectrum recorded using polarization spectroscopy showing collisional transfer of population and orientation with |Δ*J*| up to 58. The pump laser was tuned to the *B* ^{1}Π_{ u }(*v* ^{′} = 2, *J* ^{ ′ } = 70) ← *X* ^{1}Σ_{ g } ^{+}(*v* ^{″} = 0, *J* ^{ ″ } = 71) transition, creating orientation in the *X* ^{1}Σ_{ g } ^{+}(*v* ^{″} = 0, *J* ^{ ″ } = 71) level. The probe laser was scanned over the various *A* ^{1}Σ_{ u } ^{+}(*v* ^{′}, *J* ^{ ′ }) ← *X* ^{1}Σ_{ g } ^{+}(*v* ^{″} = 0, *J* ^{ ″ }) transitions. Signals could be identified for collisionally populated ground state levels with .

Rb_{2} *A* ^{1}Σ_{ u } ^{+} ← *X* ^{1}Σ_{ g } ^{+} spectrum recorded using polarization spectroscopy showing collisional transfer of population and orientation with |Δ*J*| up to 58. The pump laser was tuned to the *B* ^{1}Π_{ u }(*v* ^{′} = 2, *J* ^{ ′ } = 70) ← *X* ^{1}Σ_{ g } ^{+}(*v* ^{″} = 0, *J* ^{ ″ } = 71) transition, creating orientation in the *X* ^{1}Σ_{ g } ^{+}(*v* ^{″} = 0, *J* ^{ ″ } = 71) level. The probe laser was scanned over the various *A* ^{1}Σ_{ u } ^{+}(*v* ^{′}, *J* ^{ ′ }) ← *X* ^{1}Σ_{ g } ^{+}(*v* ^{″} = 0, *J* ^{ ″ }) transitions. Signals could be identified for collisionally populated ground state levels with .

Experimental setup. The white light and monochromator are used in measurements of atomic potassium density using the absorption equivalent width technique.

Experimental setup. The white light and monochromator are used in measurements of atomic potassium density using the absorption equivalent width technique.

Energy level diagram for fluorescence experiment. The frequency of the pump laser is fixed to line center of the *A* ^{1}Σ^{+}(*v*′ = 16, *J*′ = 30) ← *X* ^{1}Σ^{+}(*v*″ = 0, *J*″ = 29) transition. The frequency of the probe laser is scanned over the “direct” line 3^{1}Π(*v* = 6 or 7, *J* = 29) ← *A* ^{1}Σ^{+}(*v*′ = 16, *J*′ = 30) and over the “collisional” lines 3^{1}Π(*v* = 6 or 7, *J* = 29 + Δ*J*) ← *A* ^{1}Σ^{+}(*v*′ = 16, *J*′ = 30 + Δ*J*). Excitation is detected by monitoring total violet 3^{1}Π → *X* ^{1}Σ^{+} fluorescence.

Energy level diagram for fluorescence experiment. The frequency of the pump laser is fixed to line center of the *A* ^{1}Σ^{+}(*v*′ = 16, *J*′ = 30) ← *X* ^{1}Σ^{+}(*v*″ = 0, *J*″ = 29) transition. The frequency of the probe laser is scanned over the “direct” line 3^{1}Π(*v* = 6 or 7, *J* = 29) ← *A* ^{1}Σ^{+}(*v*′ = 16, *J*′ = 30) and over the “collisional” lines 3^{1}Π(*v* = 6 or 7, *J* = 29 + Δ*J*) ← *A* ^{1}Σ^{+}(*v*′ = 16, *J*′ = 30 + Δ*J*). Excitation is detected by monitoring total violet 3^{1}Π → *X* ^{1}Σ^{+} fluorescence.

A comparison of fluorescence (lower trace) and polarization spectroscopy (upper trace) signals showing collisional lines corresponding to Δ*J* = ±1, ±2, ±3, ±4. The direct lines (Δ*J* = 0) go far off scale in both traces.

A comparison of fluorescence (lower trace) and polarization spectroscopy (upper trace) signals showing collisional lines corresponding to Δ*J* = ±1, ±2, ±3, ±4. The direct lines (Δ*J* = 0) go far off scale in both traces.

Illustration of absorption of left and right circularly polarized light giving rise to the polarization spectroscopy signal. Arrows labeled *F* ^{ L } and *F* ^{ R } represent probe laser absorptions for left and right circularly polarized light, respectively, and the represent absorption coefficients.

Illustration of absorption of left and right circularly polarized light giving rise to the polarization spectroscopy signal. Arrows labeled *F* ^{ L } and *F* ^{ R } represent probe laser absorptions for left and right circularly polarized light, respectively, and the represent absorption coefficients.

Fluorescence data *R* _{F} vs *n* _{Ar} for Δ*J* = +2, with the potassium density fixed at (a) *n* _{K} = 4.1 × 10^{14} cm^{−3}; (b) *n* _{K} = 1.8 × 10^{15} cm^{−3}; (c) *n* _{K} = 5.1 × 10^{15} cm^{−3}; and (d) *n* _{K} = 8.7 × 10^{15} cm^{−3}; and as a function of *n* _{K} for data obtained in the heat pipe mode (e).

Fluorescence data *R* _{F} vs *n* _{Ar} for Δ*J* = +2, with the potassium density fixed at (a) *n* _{K} = 4.1 × 10^{14} cm^{−3}; (b) *n* _{K} = 1.8 × 10^{15} cm^{−3}; (c) *n* _{K} = 5.1 × 10^{15} cm^{−3}; and (d) *n* _{K} = 8.7 × 10^{15} cm^{−3}; and as a function of *n* _{K} for data obtained in the heat pipe mode (e).

Polarization data *R* _{P} vs *n* _{Ar} for Δ*J* = +2, with the potassium density fixed at (a) *n* _{K} = 3.2 × 10^{14} cm^{−3}; (b) *n* _{K} = 1.8 × 10^{15} cm^{−3}; (c) *n* _{K} = 5.1 × 10^{15} cm^{−3}; and (d) *n* _{K} = 8.7 × 10^{15} cm^{−3}.

Polarization data *R* _{P} vs *n* _{Ar} for Δ*J* = +2, with the potassium density fixed at (a) *n* _{K} = 3.2 × 10^{14} cm^{−3}; (b) *n* _{K} = 1.8 × 10^{15} cm^{−3}; (c) *n* _{K} = 5.1 × 10^{15} cm^{−3}; and (d) *n* _{K} = 8.7 × 10^{15} cm^{−3}.

Fitted values of (a) and (b) plotted against Δ*J*.

Fitted values of (a) and (b) plotted against Δ*J*.

Fitted values of (a) and (b) plotted against Δ*J*.

Fitted values of (a) and (b) plotted against Δ*J*.

Plot of the homogeneous linewidths of the “direct” probe transition, 3^{1}Π(*v* = 7, *J* = 29) ← 2(*A*)^{1}Σ^{+}(*v*′ = 16, *J*′ = 30), as a function of argon density, for *n* _{K} = 5.1 × 10^{15} cm^{−3}. The slope of the least-squares straight line fit of these data is (7.05 ± 0.11) × 10^{−9} cm^{3} s^{−1} and the intercept is (5.96 ± 0.08) × 10^{8} s^{−1}.

Plot of the homogeneous linewidths of the “direct” probe transition, 3^{1}Π(*v* = 7, *J* = 29) ← 2(*A*)^{1}Σ^{+}(*v*′ = 16, *J*′ = 30), as a function of argon density, for *n* _{K} = 5.1 × 10^{15} cm^{−3}. The slope of the least-squares straight line fit of these data is (7.05 ± 0.11) × 10^{−9} cm^{3} s^{−1} and the intercept is (5.96 ± 0.08) × 10^{8} s^{−1}.

*n* _{Ar} = 0 intercepts of the homogeneous linewidths vs argon density of the “direct” probe transition, 3^{1}Π(*v* = 7, *J* = 29) ← 2(*A*)^{1}Σ^{+}(*v*′ = 16, *J*′ = 30), plus linewidths recorded in heat pipe mode, plotted as a function of potassium density. The slope of the least-squares straight line fit of these data is cm^{3} s^{−1} with an intercept of (3.2 ± 0.3) × 10^{8} s^{−1}.

*n* _{Ar} = 0 intercepts of the homogeneous linewidths vs argon density of the “direct” probe transition, 3^{1}Π(*v* = 7, *J* = 29) ← 2(*A*)^{1}Σ^{+}(*v*′ = 16, *J*′ = 30), plus linewidths recorded in heat pipe mode, plotted as a function of potassium density. The slope of the least-squares straight line fit of these data is cm^{3} s^{−1} with an intercept of (3.2 ± 0.3) × 10^{8} s^{−1}.

Velocity changes (as manifested in additional Doppler broadening of collisional lines) due to (a) argon collisions and (b) potassium collisions.

Velocity changes (as manifested in additional Doppler broadening of collisional lines) due to (a) argon collisions and (b) potassium collisions.

level population distribution in the intermediate 2(*A*)^{1}Σ^{+}(*v* ^{′} = 16, *J* ^{ ′ } = 30) level calculated using the density matrix equations of motion for the NaK OODR transition 3^{1}Π(*v* = 7, *J* = 29) ← 2(*A*)^{1}Σ^{+}(*v* ^{′} = 16, *J* ^{ ′ } = 30) ← 1(*X*)^{1}Σ^{+}(*v* ^{″} = 0, *J* ^{ ″ } = 29). (a) Pump laser power 100 mW, probe laser power 0 mW. Net orientation . (b) Pump laser power 100 mW, probe laser power 1 mW. Net orientation . The conditions of case (b) are similar to those used in the present experiment.

level population distribution in the intermediate 2(*A*)^{1}Σ^{+}(*v* ^{′} = 16, *J* ^{ ′ } = 30) level calculated using the density matrix equations of motion for the NaK OODR transition 3^{1}Π(*v* = 7, *J* = 29) ← 2(*A*)^{1}Σ^{+}(*v* ^{′} = 16, *J* ^{ ′ } = 30) ← 1(*X*)^{1}Σ^{+}(*v* ^{″} = 0, *J* ^{ ″ } = 29). (a) Pump laser power 100 mW, probe laser power 0 mW. Net orientation . (b) Pump laser power 100 mW, probe laser power 1 mW. Net orientation . The conditions of case (b) are similar to those used in the present experiment.

## Tables

*f*(*J*, *J*′) values for ^{1}Σ → ^{1}Σ and ^{1}Σ → ^{1}Π transitions.

*f*(*J*, *J*′) values for ^{1}Σ → ^{1}Σ and ^{1}Σ → ^{1}Π transitions.

Parameters obtained from empirical global fit to the data, using Γ = 4.4 × 10^{7} s^{−1}.

Parameters obtained from empirical global fit to the data, using Γ = 4.4 × 10^{7} s^{−1}.

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