DOI: 10.5061/dryad.g4f4qrg0j
title: Quantum interference observed in state-resolved molecule-surface scattering

description: While the dynamics of collisions between a molecule and a solid surface
 are ultimately quantum mechanical, decohering effects owing to the large
 number of interacting degrees of freedom typically obscure the wave-like
 nature of these events. However, a partial decoupling of internal
 molecular motion from external degrees of freedom can permit striking
 interference effects to be manifest despite significant momentum exchange
 between the molecule and the bath of surface vibrations. We report
 state-prepared and state-resolved measurements of methane scattering from
 a gold surface which demonstrate total destructive interference between
 molecular states related by a reflection symmetry operation. High contrast
 interference effects prevail for all processes investigated, including
 vibrationally excited and vibrationally inelastic collisions. The results
 demonstrate the uniquely quantum mechanical effect of discrete symmetries
 in molecular collision dynamics.
description: # Quantum interference observed in state-resolved molecule-surface
 scattering
 [https://doi.org/10.5061/dryad.g4f4qrg0j](https://doi.org/10.5061/dryad.g4f4qrg0j) ## Description of the data and file structure Folders in the data archive correspond to particular subfigures from the main text and supplementary materials. **README files for respective files are included within each folder**. ### Files and variables #### File: data-archive-2024-10-18.zip **Description:** This main folder consists of 8 sub-folders. The sub-folder consists of tabular data files and the corresponding README files. * **fig3d**: each dataset corresponds to a particular tagging transition. for each dataset there is generated two files: \* %%metadata.txt \* %%data.tsv the data file contains (by column number): 1 : frequency offset of the tagging laser that is being tuned over a rovibrational transition 2 : lockin x component of lockin amplifier output that is in-phase with the reference clock. lockin amplifier receives bolometer detector amplifier output as input signal. 3 : lockin y component of lockin amplifier output that is 90 degrees out-of-phase with the reference clock the metadata contains the following fields (by line number): 1 : tag vib level vibrational quanta of lower tagging level code: 0 : ground vibrational state ( v = 0 ) 1 : v1 symmetric stretch fundamental 3 : v3 antisymmetric stretch fundamental 24 : v2 + v4 combination band (F2 symmetry) 2 : tag j angular momentum quantum number j'' of lower tagging level 3 : tag sym CH4 molecular symmetry group Td(M) classification of lower tagging level To determine inversion parity of a level, use the following correspondance: A1: P = -1 A2: P = +1 F1: P = +1 F2: P = -1 4 : tag branch difference j' - j'' between upper tagging level angular momentum quantum number j' and lower tagging level angular momentum quantum number j'' 5 : tag level energy energy of lower tagging level as quoted in CH4 HITEMP database (doi 10.3847/1538-4365/ab7a1a) 6 : tag database transition frequency frequency of tagging transition as quoted in HITEMP. 7 : tag obseved transition frequency frequency of tagging transition as observed in our bolometric tagging-based scattering measurements 8 : tag einstein coefficient einstein coefficient of tagging transition as quoted in HITEMP 9 : pump vib level vibrational quanta of upper pumping level [lower level is always 0 (v=0)] 10 : pump j angular momentum quantum number j'' of lower pumping level 11 : pump sym CH4 molecular symmetry group Td(M) classification of lower pumping level for upper level symmetry, use following correspondance: (lower) A1 -&gt; A2 (upper) A2 -&gt; A1 F1 -&gt; F2 F2 -&gt; F1 12 : pump branch difference j' - j'' between upper pumping level angular momentum quantum number j' and lower pumping level angular momentum quantum number j'' 13 : pump level energy energy of lower pumping level from HITRAN database (doi 10.1016/j.jqsrt.2021.107949) 14 : pump transition frequency frequency of pumping transition from HITRAN 15 : bolometer sensitivity timestamp timestamp of creation of dataset (not included) of bolometer sensitivity measurements (BSM-DS). bolometer sensitivity estimations only permit comparison of relative collisional transition probabilities measured with in the same (BSM-DS). that is, relative collisional transition probabilities should only be compared when their associated bolometer sensitivity timestamps are identical. see doi 10.1063/5.0150009 for more on bolometer sensitivity correction method. 16 : bolometer sensitivity value measured bolometer sensitivity for detector measurements under consideration 17 : incident kinetic energy kinetic energy of incident molecular beam 18 : incident angle angle formed between surface normal and the incident molecule beam 19 : scattering angle angle formed between direction of scattered molecules being probed and surface normal. at angle of specular scattering, scattering angle equals incident angle 20 : surface temperature temperature of Au(111) surface 21 : lockin phase rephasing of lockin output signals to obtain signal V(f) which is fit to determine relative transition probabilities, where: f : lockin frequency offset V(f) = Vx(f) cos(phi) + Vy(f) sin(phi), where: Vx : lockin x Vy : lockin y phi : lockin phase * **fig4b**: each dataset corresponds to a particular surface orientation (theta_i). for the measurements presented in figure 4a, there is no pump laser. the rovibrational levels populated in the incident molecular beam that contribute to the scattered flux in the v=0 (Jf=6,Pi=-1) meta-CH4 rovibrational level probed consist of: \* &gt;90% : v=0 (Ji=0,Pi=-1) \* &lt;9% : v=0 (Ji=3,Pi=+1) \* &lt;1% : all other levels where the percentage indicates the fractional population in the incident beam. for each dataset there are two files generated: \* %%data.tsv \* %%metadata.txt the data file contains (by column number): 1 : tagging polarization angle angle made between the tagging laser polarization and surface normal. 2 : lockin x component of lockin amplifier output that is in-phase with the reference clock. lockin amplifier receives bolometer detector amplifier output as input signal. 3 : lockin y component of lockin amplifier output that is 90 degrees out-of-phase with the reference clock chronologically, a tagging laser frequency scan is first performed. after the frequency scan is completed, the tagging laser is tuned to the frequency of maximum absorption and then the tagging laser polarization scan is performed. information on the tagging transition: \* tag vib level : 0 \* tag j : 6 \* tag sym : A1 \* tag branch : -1 \* tag level energy : 219.94510 cm-1 \* tag transition frequency : 2958.017263 cm-1 \* tag einstein coefficient : 2.195E+01 s-1 other fixed parameters: surface temperature : 300 K kinetic energy : 210 meV since the plotted polarization response curves R(theta_t) are normalized, detector sensitivity factors were not measured. the lockin x-y phase is 0.0 degrees for all datasets (i.e. only the x channel is analyzed). to compensate for the gradually decreasing bolometer sensitivity over the course of the slow polarization scans, the raw data V(theta_n), where theta_n denotes the nth measurement, are fit to the expression v(theta) = sum(n=0,1,2) b_n cos(2n (theta-thetao)) d(theta;alpha) where d(theta;alpha) = (1 - alpha (theta-thetamin) / (thetamax - thetamin)) describes the bolometer sensitivity decay, with thetamin and thetamax being respectively the first and last polarization angles measured. the fit returns an estimation of the parameters b_0, b_1, b_2, thetao, and alpha. we note that the best-fit values for the parameter alpha are consistent with independent determinations of the long-term rate of bolometer sensitivity decay with exposure to CH4. the plotted results are that obtained by dividing the raw measurements V(theta_n) by the factor b_0 d(theta_n;alpha). the metadata file contains (indexed by row): 1 : theta_i angle made between surface normal and direction of incident molecular beam 2 : theta_s angle made between surface normal and direction of scattered molecular beam being probed * **fig4c:** the measurements presented in figure 4c are in many respects identical to those present in figure 4b. the differences are: \* theta_i is fixed at 35.0 degrees \* theta_s is fixed at 36.4 degrees \* there are two meta-CH4 rovibrational levels probed: \* v=0 (Jf=6,Pf=-1) (A1 symmetry) \* v=0 (Jf=6,Pf=+1) (A2 symmetry) \* the detection scheme employs the heterodyning technique described in main text which acts to isolate the contribution from the state v=0 (Ji=0,Pi=-1) \* see the data archive for fig2b for details on the pumping transition for each dataset there are two files generated: \* %%data-freq.tsv \* %%data-pol.tsv the data-freq file is the same format as the data file of the data files for figs 2 and 3 the data-pol file is the same format as the data file of the fig 4b data the small offset is subtracted from the raw data before normalization. it is not clear to us what the origin of this offset is, but the fact that it persists when the tagging laser is tuned far off-resonance leads us to conclude that its subtraction is justified. to determine the offset, the frequency scan (tabulated in the data-freq file) data at a fixed tagging laser polarization are fit to a derivative-gaussian (i.e. FM) lineshape with constant offset included as a fit parameter. no compensation for decaying bolometer sensitivity is attempted. information on the tagging transitions: \* file prefix 00 \* tag vib level : 0 \* tag j : 6 \* tag sym : A1 \* tag branch : -1 \* tag level energy : 219.94510 cm-1 \* tag transition frequency : 2958.017263 cm-1 \* tag einstein coefficient : 2.195E+01 s-1 \* file prefix 01 \* tag vib level : 0 \* tag j : 6 \* tag sym : A2 \* tag branch : -1 \* tag level energy : 219.91970 cm-1 \* tag transition frequency : 2958.536362 cm-1 \* tag einstein coefficient : 2.206E+01 s-1 other fixed parameters: surface temperature : 300 K kinetic energy : 210 meV * **figs2:** each dataset corresponds to a particular tagging transition. the tagging transitions are identical to those used in fig4c. see the accompanying data archive for information on these tagging transitions. these measurements use the same heterodyning technique of figs 2b and 4c. see the data archive for 2b for information on the pumping transition. fixed parameters: incident angle theta_i : 25 degrees incident kinetic energy : 100 meV surface temperature : 300 K for each dataset there is one file generated: \* %%data.tsv with the file prefix %% key indicating the tagging transition: \* 00 : A1 symmetry [bolometer sensitivity of 31 (arb. units)] \* 01 : A2 symmetry [bolometer sensitivity of 27 (arb. units)] the data file contains (by column number): 1 : scattering angle theta_s angle made between the surface normal and the scattered angle being probed. specular scattering corresponds to a scattered angle equal to the incident angle theta_i. 2 : lockin x component of lockin amplifier output that is in-phase with the reference clock. lockin amplifier receives bolometer detector amplifier output as input signal. 3 : lockin y component of lockin amplifier output that is 90 degrees out-of-phase with the reference clock chronologically, a tagging laser frequency scan at fixed scattering angle is first performed. after the frequency scan is completed, the tagging laser is tuned to the frequency of maximum absorption and then the scan over scattering angles is performed. the lockin x-y phase is 0.0 degrees for all datasets (i.e. only the x channel is analyzed). * **fig3b**:  each dataset corresponds to a particular tagging transition. for each dataset there is generated two files: \* %%metadata.txt \* %%data.tsv the data file contains (by column number): 1 : frequency offset of the tagging laser that is being tuned over a rovibrational transition 2 : lockin x component of lockin amplifier output that is in-phase with the reference clock. lockin amplifier receives bolometer detector amplifier output as input signal. 3 : lockin y component of lockin amplifier output that is 90 degrees out-of-phase with the reference clock the metadata contains the following fields (by line number): 1 : tag vib level vibrational quanta of lower tagging level code: 0 : ground vibrational state ( v = 0 ) 1 : v1 symmetric stretch fundamental 3 : v3 antisymmetric stretch fundamental 24 : v2 + v4 combination band (F2 symmetry) 2 : tag j angular momentum quantum number j'' of lower tagging level 3 : tag sym CH4 molecular symmetry group Td(M) classification of lower tagging level To determine inversion parity of a level, use the following correspondance: A1: P = -1 A2: P = +1 F1: P = +1 F2: P = -1 4 : tag branch difference j' - j'' between upper tagging level angular momentum quantum number j' and lower tagging level angular momentum quantum number j'' 5 : tag level energy energy of lower tagging level as quoted in CH4 HITEMP database (doi 10.3847/1538-4365/ab7a1a) 6 : tag database transition frequency frequency of tagging transition as quoted in HITEMP. 7 : tag obseved transition frequency frequency of tagging transition as observed in our bolometric tagging-based scattering measurements 8 : tag einstein coefficient einstein coefficient of tagging transition as quoted in HITEMP 9 : pump vib level vibrational quanta of upper pumping level [lower level is always 0 (v=0)] 10 : pump j angular momentum quantum number j'' of lower pumping level 11 : pump sym CH4 molecular symmetry group Td(M) classification of lower pumping level for upper level symmetry, use following correspondance: (lower) A1 -&gt; A2 (upper) A2 -&gt; A1 F1 -&gt; F2 F2 -&gt; F1 12 : pump branch difference j' - j'' between upper pumping level angular momentum quantum number j' and lower pumping level angular momentum quantum number j'' 13 : pump level energy energy of lower pumping level from HITRAN database (doi 10.1016/j.jqsrt.2021.107949) 14 : pump transition frequency frequency of pumping transition from HITRAN 15 : bolometer sensitivity timestamp timestamp of creation of dataset (not included) of bolometer sensitivity measurements (BSM-DS). bolometer sensitivity estimations only permit comparison of relative collisional transition probabilities measured with in the same (BSM-DS). that is, relative collisional transition probabilities should only be compared when their associated bolometer sensitivity timestamps are identical. see doi 10.1063/5.0150009 for more on bolometer sensitivity correction method. 16 : bolometer sensitivity value measured bolometer sensitivity for detector measurements under consideration 17 : incident kinetic energy kinetic energy of incident molecular beam 18 : incident angle angle formed between surface normal and the incident molecule beam 19 : scattering angle angle formed between direction of scattered molecules being probed and surface normal. at angle of specular scattering, scattering angle equals incident angle 20 : surface temperature temperature of Au(111) surface 21 : lockin phase rephasing of lockin output signals to obtain signal V(f) which is fit to determine relative transition probabilities, where: f : lockin frequency offset V(f) = Vx(f) cos(phi) + Vy(f) sin(phi), where: Vx : lockin x Vy : lockin y phi : lockin phase * **fig3c**: each dataset corresponds to a particular tagging transition. for each dataset there is generated two files: \* %%metadata.txt \* %%data.tsv the data file contains (by column number): 1 : frequency offset of the tagging laser that is being tuned over a rovibrational transition 2 : lockin x component of lockin amplifier output that is in-phase with the reference clock. lockin amplifier receives bolometer detector amplifier output as input signal. 3 : lockin y component of lockin amplifier output that is 90 degrees out-of-phase with the reference clock the metadata contains the following fields (by line number): 1 : tag vib level vibrational quanta of lower tagging level code: 0 : ground vibrational state ( v = 0 ) 1 : v1 symmetric stretch fundamental 3 : v3 antisymmetric stretch fundamental 24 : v2 + v4 combination band (F2 symmetry) 2 : tag j angular momentum quantum number j'' of lower tagging level 3 : tag sym CH4 molecular symmetry group Td(M) classification of lower tagging level To determine inversion parity of a level, use the following correspondance: A1: P = -1 A2: P = +1 F1: P = +1 F2: P = -1 4 : tag branch difference j' - j'' between upper tagging level angular momentum quantum number j' and lower tagging level angular momentum quantum number j'' 5 : tag level energy energy of lower tagging level as quoted in CH4 HITEMP database (doi 10.3847/1538-4365/ab7a1a) 6 : tag database transition frequency frequency of tagging transition as quoted in HITEMP. 7 : tag obseved transition frequency frequency of tagging transition as observed in our bolometric tagging-based scattering measurements 8 : tag einstein coefficient einstein coefficient of tagging transition as quoted in HITEMP 9 : pump vib level vibrational quanta of upper pumping level [lower level is always 0 (v=0)] 10 : pump j angular momentum quantum number j'' of lower pumping level 11 : pump sym CH4 molecular symmetry group Td(M) classification of lower pumping level for upper level symmetry, use following correspondance: (lower) A1 -&gt; A2 (upper) A2 -&gt; A1 F1 -&gt; F2 F2 -&gt; F1 12 : pump branch difference j' - j'' between upper pumping level angular momentum quantum number j' and lower pumping level angular momentum quantum number j'' 13 : pump level energy energy of lower pumping level from HITRAN database (doi 10.1016/j.jqsrt.2021.107949) 14 : pump transition frequency frequency of pumping transition from HITRAN 15 : bolometer sensitivity timestamp timestamp of creation of dataset (not included) of bolometer sensitivity measurements (BSM-DS). bolometer sensitivity estimations only permit comparison of relative collisional transition probabilities measured with in the same (BSM-DS). that is, relative collisional transition probabilities should only be compared when their associated bolometer sensitivity timestamps are identical. see doi 10.1063/5.0150009 for more on bolometer sensitivity correction method. 16 : bolometer sensitivity value measured bolometer sensitivity for detector measurements under consideration 17 : incident kinetic energy kinetic energy of incident molecular beam 18 : incident angle angle formed between surface normal and the incident molecule beam 19 : scattering angle angle formed between direction of scattered molecules being probed and surface normal. at angle of specular scattering, scattering angle equals incident angle 20 : surface temperature temperature of Au(111) surface 21 : lockin phase rephasing of lockin output signals to obtain signal V(f) which is fit to determine relative transition probabilities, where: f : lockin frequency offset V(f) = Vx(f) cos(phi) + Vy(f) sin(phi), where: Vx : lockin x Vy : lockin y phi : lockin phase * **fig3a**: each dataset corresponds to a particular tagging transition. for each dataset there is generated two files: \* %%metadata.txt \* %%data.tsv the data file contains (by column number): 1 : frequency offset of the tagging laser that is being tuned over a rovibrational transition 2 : lockin x component of lockin amplifier output that is in-phase with the reference clock. lockin amplifier receives bolometer detector amplifier output as input signal. 3 : lockin y component of lockin amplifier output that is 90 degrees out-of-phase with the reference clock the metadata contains the following fields (by line number): 1 : tag vib level vibrational quanta of lower tagging level code: 0 : ground vibrational state ( v = 0 ) 1 : v1 symmetric stretch fundamental 3 : v3 antisymmetric stretch fundamental 24 : v2 + v4 combination band (F2 symmetry) 2 : tag j angular momentum quantum number j'' of lower tagging level 3 : tag sym CH4 molecular symmetry group Td(M) classification of lower tagging level To determine inversion parity of a level, use the following correspondance: A1: P = -1 A2: P = +1 F1: P = +1 F2: P = -1 4 : tag branch difference j' - j'' between upper tagging level angular momentum quantum number j' and lower tagging level angular momentum quantum number j'' 5 : tag level energy energy of lower tagging level as quoted in CH4 HITEMP database (doi 10.3847/1538-4365/ab7a1a) 6 : tag database transition frequency frequency of tagging transition as quoted in HITEMP. 7 : tag obseved transition frequency frequency of tagging transition as observed in our bolometric tagging-based scattering measurements 8 : tag einstein coefficient einstein coefficient of tagging transition as quoted in HITEMP 9 : pump vib level vibrational quanta of upper pumping level [lower level is always 0 (v=0)] 10 : pump j angular momentum quantum number j'' of lower pumping level 11 : pump sym CH4 molecular symmetry group Td(M) classification of lower pumping level for upper level symmetry, use following correspondance: (lower) A1 -&gt; A2 (upper) A2 -&gt; A1 F1 -&gt; F2 F2 -&gt; F1 12 : pump branch difference j' - j'' between upper pumping level angular momentum quantum number j' and lower pumping level angular momentum quantum number j'' 13 : pump level energy energy of lower pumping level from HITRAN database (doi 10.1016/j.jqsrt.2021.107949) 14 : pump transition frequency frequency of pumping transition from HITRAN 15 : bolometer sensitivity timestamp timestamp of creation of dataset (not included) of bolometer sensitivity measurements (BSM-DS). bolometer sensitivity estimations only permit comparison of relative collisional transition probabilities measured with in the same (BSM-DS). that is, relative collisional transition probabilities should only be compared when their associated bolometer sensitivity timestamps are identical. see doi 10.1063/5.0150009 for more on bolometer sensitivity correction method. 16 : bolometer sensitivity value measured bolometer sensitivity for detector measurements under consideration 17 : incident kinetic energy kinetic energy of incident molecular beam 18 : incident angle angle formed between surface normal and the incident molecule beam 19 : scattering angle angle formed between direction of scattered molecules being probed and surface normal. at angle of specular scattering, scattering angle equals incident angle 20 : surface temperature temperature of Au(111) surface 21 : lockin phase rephasing of lockin output signals to obtain signal V(f) which is fit to determine relative transition probabilities, where: f : lockin frequency offset V(f) = Vx(f) cos(phi) + Vy(f) sin(phi), where: Vx : lockin x Vy : lockin y phi : lockin phase * **fig2b**: each dataset corresponds to a particular tagging transition. for each dataset there is generated two files: \* %%metadata.txt \* %%data.tsv the data file contains (by column number): 1 : frequency offset of the tagging laser that is being tuned over a rovibrational transition 2 : lockin x component of lockin amplifier output that is in-phase with the reference clock. lockin amplifier receives bolometer detector amplifier output as input signal. 3 : lockin y component of lockin amplifier output that is 90 degrees out-of-phase with the reference clock the metadata contains the following fields (by line number): 1 : tag vib level vibrational quanta of lower tagging level code: 0 : ground vibrational state ( v = 0 ) 1 : v1 symmetric stretch fundamental 3 : v3 antisymmetric stretch fundamental 24 : v2 + v4 combination band (F2 symmetry) 2 : tag j angular momentum quantum number j'' of lower tagging level 3 : tag sym CH4 molecular symmetry group Td(M) classification of lower tagging level To determine inversion parity of a level, use the following correspondance: A1: P = -1 A2: P = +1 F1: P = +1 F2: P = -1 4 : tag branch difference j' - j'' between upper tagging level angular momentum quantum number j' and lower tagging level angular momentum quantum number j'' 5 : tag level energy energy of lower tagging level as quoted in HITRAN database (doi 10.1016/j.jqsrt.2021.107949) 6 : tag transition frequency frequency of tagging transition as quoted in HITRAN 7 : tag einstein coefficient einstein coefficient of tagging transition as quoted in HTIRAN 8 : pump vib level vibrational quanta of upper pumping level [lower level is always 0 (v=0)] 9 : pump j angular momentum quantum number j'' of lower pumping level 10 : pump sym CH4 molecular symmetry group Td(M) classification of lower pumping level for upper level symmetry, use following correspondance: (lower) A1 -&gt; A2 (upper) A2 -&gt; A1 F1 -&gt; F2 F2 -&gt; F1 11 : pump branch difference j' - j'' between upper pumping level angular momentum quantum number j' and lower pumping level angular momentum quantum number j'' 12 : pump level energy energy of lower pumping level 13 : pump transition frequency frequency of pumping transition 14 : bolometer sensitivity timestamp timestamp of creation of dataset (not included) of bolometer sensitivity measurements (BSM-DS). bolometer sensitivity estimations only permit comparison of relative collisional transition probabilities measured with in the same (BSM-DS). that is, relative collisional transition probabilities should only be compared when their associated bolometer sensitivity timestamps are identical. see doi 10.1063/5.0150009 for more on bolometer sensitivity correction method. 15 : bolometer sensitivity value measured bolometer sensitivity for detector measurements under consideration 16 : incident kinetic energy kinetic energy of incident molecular beam 17 : incident angle angle formed between surface normal and the incident molecule beam 18 : scattering angle angle formed between direction of scattered molecules being probed and surface normal. at angle of specular scattering, scattering angle equals incident angle 19 : surface temperature temperature of Au(111) surface 20 : lockin phase rephasing of lockin output signals to obtain signal V(f) which is fit to determine relative transition probabilities, where: f : lockin frequency offset V(f) = Vx(f) cos(phi) + Vy(f) sin(phi), where: Vx : lockin x Vy : lockin y phi : lockin phase