Collisional relaxation of vibrational states of SrOH with He at 2 K

Vibrational relaxation of strontium monohydroxide (SrOH) molecules in collisions with helium (He) at 2 K is studied. We find the diffusion cross section of SrOH at 2.2 K to be &sgr; d = ( 5 ± 2 ) × 10 − 14 cm 2 ?> and the vibrational quenching cross section for the (100) Sr–O stretching mode to be &sgr; q ?> = ( 7 ± 2 ) × 10 − 17 cm 2 ?> . The resulting ratio γ 100 ?> = &sgr; d / &sgr; q ∼ 700 ?> is more than an order of magnitude smaller than for previously studied few-atom radicals (Au et al 2014 Phys. Rev. A 90 032703 ). We also determine the Franck–Condon factor for SrOH ( A ˜ 2 &Pgr; 1 / 2 ( 100 ) ← X ˜ 2 &Sgr; + ( 000 ) ?> ) to be ( 4.8 ± 0.8 ) × 10 − 2 ?> .


Introduction
The study and control of cold atom-molecule collisions lies at the interface of physics and chemistry [1][2][3]. The diversity and complexity of internal molecular structures and molecular interactions provide new possibilities in precision measurement [4,5], quantum information science [6,7], condensed-matter physics [8], and controlled chemistry [3]. Detailed understanding of low temperature molecular collisions provides important information necessary for further development of these applications.
Compared to atomic collisions [9], low-temperature collisions of diatomic molecules are much less understood. Recently, however, significant progress has been made [10][11][12]. Experimental measurements of low energy collisions between simple polyatomic species (like linear triatomics) and atoms can provide crucial input for advancing theoretical models. Supersonic jet beams (sometimes Stark decelerated [13,14]), atom association [15][16][17], and buffer-gas cooling [18][19][20] are the main experimental tools for exploring molecular collisions in the cold (1 K) and ultracold ( μ 1 K) temperature regimes. The cold, rarefied buffer-gas environment offers a way to study cooling and molecular collisions with precise control of helium buffer-gas density and cell temperature. The efficiency of quenching vibrational motion during the atom-molecule collisional process at low temperature has been recently measured for several systems [21][22][23][24].
In this paper, we explore inelastic collisions between strontium monohydroxide (SrOH) and helium ( 4 He) at 2.2 K. Our measurements probe the intermediate range of vibrational energy spacings, compared to previous low temperature collisional results [22][23][24][25]. For the excited Sr-O stretching vibrational mode of SrOH, we observe rapid rotational quenching and translational cooling followed by a slower vibrational quenching to the ground vibrational level. Vibrational quenching cross sections are determined with high accuracy. Our work extends the study of vibrational relaxation in cold atom-molecule collisions to linear polyatomic radicals and contributes to an overall physical picture of the dependence of quenching rates on vibrational energy spacing in low energy collisions, providing an important benchmark for theory.

Experiment
To create cold SrOH molecules we use laser ablation in combination with buffer-gas cooling [26]. A schematic diagram of the experimental apparatus is shown in figure 1. SrOH ( Σ + X 2 ) molecules are introduced into the gas phase using pulsed Nd:YAG laser ablation at 532 nm of a Sr(OH) 2 solid precursor with a pulse energy of ∼15 mJ and duration of ∼5 ns. We continuously flow 4 He buffer gas into a 2.5 cm-diameter cell at rates of 0.5-10 standard cubic centimeters per minute (SCCM). The cell is thermally anchored to a pumped helium reservoir at a temperature of ∼ T 2.2 K. The helium density in the cell can be varied between ≈ × − × − n 1 10 1 10 cm He 15 16 3 , resulting in the mean time between molecule-helium diffusive collisions of τ μ ∼ − 0.6 0.06 s. The typical SrOH density in our experiment is a very small fraction of the helium density ≈ − n 10 cm SrOH 9 3 . A detailed description of the cryogenic apparatus used in this experiment is provided by [27].
Laser absorption spectroscopy is performed in the cell to monitor molecule production and thermalization dynamics. SrOH in the ground and excited vibrational levels is detected using transitions. We use external-cavity diode lasers at 688 nm with a typical detection power of μ ∼ P 5 W and a beam diameter of ∼ ø 1 mm. We employ the 'off-diagonal' excitation Π Σ ← + A X (100)˜(000)  1)is shown in figure 3. The time decay profile of the molecules in the X(000) vibronic state is governed by the diffusion to the walls and pump-out of the cell through the aperture: Figure 1. Schematic of the apparatus. Hot SrOH molecules produced during laser ablation of a Sr(OH) 2 target quickly cool translationally and rotationally after colliding with cold (∼2 K) helium buffer gas. Thermalization dynamics are studied using a probe laser to observe molecular absorption. An optical pumping beam is used to populate the X (100) vibrational level to measure the quenching rate.
where τ 000 , τ d , and τ p are the timescales for the decay of (000) vibrational mode molecules (τ 000 ) due to diffusion (τ d ) and cell pump-out (τ p ). By measuring the on-resonance absorption time profile (figure 4(a)) we can extract the diffusion lifetime of SrOH: . For low buffer-gas flows τ τ < 1 d p [29], and the molecule loss is primarily due to diffusion to the cell walls. Therefore, from our measurements of τ 000 we can directly determine the diffusion lifetime of the molecules in our cell: τ τ ≈ d 000 . At long times after laser ablation (⩾10 ms), when higher-order diffusion modes have decayed, the in-cell X(000) population profile is well fitted by a single exponential (figure 4(a)). We determine the SrOH-He momentum transfer cross section by measuring the diffusion lifetime of SrOH (000) mode molecules at different densities of helium buffer gas. From figure 4(b) we find that τ 000 has a linear dependence on the helium density and conclude that (000) mode molecule loss is primarily dominated by diffusion. For a cylindrical cell of length L and radius r the time constant of the exponential decay for molecules diffusing through helium gas of density (n He ) is given by [30]: d He d is the mean SrOH- 4 He collision velocity at temperature T with reduced mass of the atom-molecule system μ and the diffusion cross ). From equation (2) we determine that in the diffusive regime (τ τ < 1 d p ) the in-cell lifetime is directly proportional to the helium density, as seen in our data.
From the measurement of τ 000 as a function of the helium density (figure 4(b)) using equation (2)  agrees with the theoretical prediction for larger polyatomic molecules colliding with helium [31].

Vibrational quenching cross sections
Vibrationally excited SrOH molecules are produced during the process of laser ablation. As can be seen from figure 5, vibrationally excited molecules of the (100) Sr-O stretching mode quickly ( μ <500 s) thermalize rotationally to = ± T 2.8 0.7 K r and translationally to a temperature ⩽5.6 K. We place a bound on the translational temperature from the Doppler fit. Additional linewidth broadening mechanisms are present inside buffer-gas cells as has been seen repeatedly [25]. Vibrational temperature remains out of thermal equilibrium ( ∼ T 400 K v ) with other degrees of freedom. In order to populate the X(100) state we optically pump SrOH molecules from the (000) mode to the (100) mode using Π Σ ← + A X (100)˜(000) 2 1 2 2 electronic excitation (figure 2). The optical pumping process increases the population in X(100) state by an order of magnitude. After the optical pumping laser is turned off, SrOH molecules in the (100) mode decay faster than those in the (000) mode ( figure 6). The additional effect that leads to the faster decay for the (100) molecules is vibrational quenching with timescale τ q . Using equation (1), we can write the decay rate of the (100) molecules in the buffer-gas cell: . As can be seen from figure 7(a), the in-cell lifetime of the molecules in the = X Ñ(100), 1 state is inversely proportional to the helium density which indicates that (100) molecule loss is dominated by vibrational quenching.
The dimensionless ratio of elastic to inelastic collision rates γ 100 indicates the rate of translational versus vibrational equilibration of a molecular sample and can be determined from our measurements by:  where we used equation (2) in the last step. After extracting lifetimes for the decays of the (000) and (100) vibrational modes ( figure 7(b)), we calculate γ 100 using an approximate form of equation (5): We can also place an upper bound on γ 010 for the excited bending mode. The number of collisions necessary for translational cooling of vibrationally excited SrOH molecules produced during laser ablation is given by [32]: SrOH He . Therefore, if γ > 100, the sample will cool translationally and rotationally, before collision-induced vibrational relaxation, leaving a metastable population, as was seen in the (100) mode of SrOH. However, if γ < 100 vibrationally excited molecules will quench before they cool translationally and rotationally. Molecules in the Π X (010) 2 vibronic  state were previously detected in supersonic beams for SrOH [33] and CaOH [34] produced using pulsed laser ablation at 300 K. Experimentally, when measuring absorption on the Σ Π ← band we saw no evidence of molecules in the excited bending mode. This rapid vibrational thermalization is due to inelastic vibrational collisions with helium. This allows us to place an upper bound γ < 100 010 , which is consistent with direct experimental measurements for low-lying bending modes in large molecules [24]. In addition to vibrational quenching, there could potentially be other unexpected contributions to the loss of (010) molecules in our experiment like state dependent chemical reactions.
The measured values of γ can be used to calculate the absolute values of collisional quenching cross sections:

Rotational thermalization
Rotational thermalization dynamics for SrOH molecules in the (100) and (000) vibrational modes can be extracted by monitoring ″ Q J ( ) 11 transitions for different rotational levels. From the data shown in figures 5 and 8, we estimate that the rotational temperature thermalizes to ∼ T 3 K r within 1 ms after ablation. Since the mean time between collisions is μ <1 s we conclude that fewer than 1000 collisions are necessary for complete rotational thermalization after laser ablation. The initial rotational temperature following laser ablation process in a similar experiment was measured to be >300 K [35]. Typically, initial translational temperature of species immediately after the ablation process is ∼1000 K [26,36].

Franck-Condon (FC) factor measurements
Diagonal FC factors are required for scattering thousands of photons necessary for laser cooling or slowing of molecules [37]. Experimental measurements of these factors have focused on diatomic molecules thus far [38][39][40]. We measure the ratio of FC factors by comparing the ratio of the absorption signals R sig for Π Σ ← + A X (100)˜(000) lines shown in figure 9(b). Since the absorption cross section σ for a Doppler broadened line in an electronic transition is proportional to the product of the excitation frequency (ν) and FC factor ( [41] 3 , the ratio of FC factors from our measurements is given by: in the harmonic oscillator model [43] 4 . Our result indicates that the SrOH − A X˜FC array is highly diagonal, and it should be possible to scatter ∼10 3 photons for SrOH using two lasers (λ ← A X(000)˜(000) and λ ← A X(000)˜(100) ) before the molecules will decay to the X(200) state. In order to determine branching ratios to the excited bending vibrations in the X state a more detailed experimental and theoretical analysis is necessary, which is beyond the scope of this paper. By driving ′ = ← ″ = N N 0 1transitions, the rotational loss channel can be eliminated [44]. In addition to the possibility of laser cooling, this may also have important applications for sensitive molecule detection in the magnetic trap environment [45].

Conclusions
Our measurement of the collisional quenching coefficient γ 100 and an upper bound on γ 010 in SrOH-4 He collisions provide important information on the interactions between polyatomic molecules and S 1 -state atoms at temperatures near 1 K. Below we compare our measurements with other experimental values for diatomics in the similar collisional energy regime (multiple-partial waves): Since SrOH is a relatively heavy molecule with a large density of rovibrational states it is not surprising that vibrational quenching proceeds relatively quickly. Our results indicate that buffer-gas cooling with helium can efficiently thermalize not only translational and rotational but also vibrational degrees of freedom in polyatomic molecules with low frequency vibrational modes (ω < − 600 cm 1 ) at timescales <1 ms. Study of SrOH-He cold collisions provides benchmark information on the dependence of vibrational quenching rates on the frequencies of molecular vibrations. The experimental techniques demonstrated in this work can be easily and off-diagonal Π Σ ← + A X (100)˜(000) 2 1 2 2 electronic transitions. We observe an average value of 5.2% with a standard deviation of 0.2%. Figure (b) shows the corresponding absorption signals as a function of time. To determine the histogram of the measured ratios, only the signal between 0.5 and 10 ms is used in the analysis. extended to the study of buffer-gas cooling and inelastic collisions for other linear polyatomic molecules (for example CaOH and BaOH). Future work can include experimental investigation of vibrational quenching for different modes in planar (e.g. SrNH 2 ) and symmetric-top (e.g. SrCH 3 ) molecules.