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A: Spectroscopy, Photochemistry, and Excited States 40

+

Rovibronic Spectroscopy of Sympathetically Cooled CaH Aaron T. Calvin, Smitha S. Janardan, John J. Condoluci, Rene Rugango, Eric Pretzsch, Gang Shu, and Kenneth R. Brown

J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b12823 • Publication Date (Web): 09 Mar 2018 Downloaded from http://pubs.acs.org on March 10, 2018

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The Journal of Physical Chemistry

Rovibronic Spectroscopy of Sympathetically Cooled 40CaH+ †

Aaron T. Calvin,

†

Smitha S. Janardan,

‡

Pretzsch,

†School

†

Gang Shu,

John J. Condoluci,

†

and Kenneth R. Brown

†

Réne Rugango,

Eric

∗,†,‡,¶,§

of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA

‡School ¶School

of Physics, Georgia Institute of Technology, Atlanta, GA

of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA

§Departments

of Electrical and Computer Engineering and Chemistry, Duke University, Durham, NC

E-mail: [email protected]

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 17

Abstract We measure the rovibronic transitions

3, J 0

+

of CaH

X 1 Σ+ , v 00 = 0, J 00 → A 1 Σ+ , v 0 = 0, 1, 2, and

and obtain rotational constants for the

obtained using two-photon photodissociation of CaH

+.

Ca

+

A 1 Σ+

state.

The spectrum is

co-trapped with Doppler cooled

The excitation is driven by a mode-locked, frequency-doubled Ti:Sapph laser,

which is then pulse shaped to narrow the spectral bandwidth. The measured values of the rotational constants are in agreement with

ab initio

theory.

Introduction Ion traps provide a well-isolated environment that allows for the creation of reactive chemical species and localizes ions for enhanced spectroscopic signals.

14

Co-trapping molecular ions

with laser cooled atomic ions adds the advantage of sympathetically cooling the molecular ions to millikelvin temperatures which minimizes Doppler shifts and allows cooling to the translational ground state.

5,6

Spectroscopy of molecular ions using this platform has gained

attention in the past few years for applications in thermometry, initio molecular theory,

9

cold reactions,

8,10

7

astrochemistry,

8

test of ab

and proposed probes for fundamental physics.

11,12

In particular, the test of the time dependence of the mass of the electron to the mass of the proton,

µ = me /mp ,

using alkaline-earth hydrides requires ecient precision measurements

of generally weak clock transitions using quantum logic spectroscopy. logic operations on CaH

+

13

Current quantum

+ 14 15 and MgH demonstrate progress toward this goal. However,

ecient spectroscopy requires rotational state preparation of these diatomic hydrides. Several methods are available for rotational state control including the recent probabilistic state preparation in CaH

+

by projective measurement, which should allow coherent preparation

of the molecule into any pure state on timescales faster than the blackbody rethermalization time.

14

Our work is aimed at providing a method to verify rotational cooling by methods

such as state projection,

14

optical pumping

Astrochemical relevance of CaH

+

9,16,17

or by a buer gas of laser cooled atoms.

stems from detection of the CaH radical on sunspots

2


18,19 20,21

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and the surfaces of other stars.

22,23

The low ionization potential

24

of CaH suggests the

+

presence of CaH . Identication has so far been stalled by the lack of spectroscopic data on this species. Our method provides a general and versatile method to obtain spectra of molecular ions with rotational resolution. The rst bound transition in CaH

+

was observed for two vibrational overtone transitions

within the ground electronic state for a single CaH

+

+ 25 sympathetically cooled by two Ca .

Four vibronic peaks were previously measured for the and

3 electronic transition 26

ated isotopologue.

27

X 1 Σ+ , v 00 = 0 → A 1 Σ+ , v 0 = 0, 1, 2,

and the peak assignment was recently veried using the deuter-

The bandwidth of the frequency doubled laser was too broad to resolve

rotational transitions

Figure 1a.

femtosecond optical waveforms

28

diagonal Franck-Condon factors.

Femtosecond pulse shaping is widely used to modulate

and has use in rotationally cooling molecules with nearly

29

In our experiment, this pulse shaping technique spec-

trally narrows the probe beam to obtain rotational resolution of the

1

Σ+ , v 0 = 0, 1, 2,

and

3

X 1 Σ+ , v 00 = 0 → A

transition.

Methods The experiment uses a linear Paul trap

30

in a spherical octagon vacuum chamber (Kimball

Physics MCF800-SphOct-G2C8) held at a base pressure of

10−10

torr.

+ Ca is generated

by photoionizing a neutral beam with 423 and 379 nm lasers and subsequently trapped. The ions are Doppler cooled with a 397 nm laser scattering on the main cooling transition (S1/2

→ P1/2 )

and an 866 nm repump beam.

+ Ca is directly imaged by detecting the

scattered 397 nm photons. Hydrogen gas is leaked into the chamber to achieve a pressure of 10

−8

+ torr suitable for reactions to form CaH .

CaH

+

is co-trapped with Ca

+ translationally cooled by the Coulomb interaction with the laser cooled Ca ,

+

and is

Figure 2a.

A frequency doubled Ti:Sapph laser was chosen for the spectroscopy of CaH

+

because of

the large range of frequency tunability and ease of frequency doubling when mode-locked.

3



Page 4 of 17

After frequency doubling, the laser has a pulse width of around 300 fs and a linewidth too broad to resolve rotational transitions. 4-f pulse shaping system.

28

In order to narrow the linewidth, we employed a

The pulsed laser is angularly dispersed by a holographic grating

(Thorlabs GH25 with 3600 lines/mm). At a focal point away, a cylindrical lens (f=500mm) performs a Fourier transform to convert angular dispersion to spatial dispersion. A 76

µm

slit spatial mask lies at the focal point of the lens and is used to pick out desired frequency components. The slit lies directly in front of a mirror and the second pass recombines the selected frequency components into a collimated beam.

The mirror is tilted vertically to

spatially separate the outgoing pulse shaped beam from the incoming beam in order to pick the beam with a D-shaped mirror and send to the trap

Figure 1b.

76

µm

is the

narrowest slit width achieved without spatial diraction of the outgoing beam.

The slit

Figure 1c.

For this,

position is correlated to wavelength by the calibration curve shown in

the pulse shaped beam is sent to a commercial spectrometer (Ocean Optics Spectrometer model HR2000+). The center wavelength is estimated for various slit positions. The input power to the 4-f system was 500 mW and the output was typically 50

µW.

The pulse shaped beam is co-aligned to the axial direction of the trap. A shutter (Vincent Associates Model V51452T0 Serial 11355) is used to switch the beam. The beam switching sequence,

Figure 2b,

exposes the molecular ions to the dissociating beam and Ca

uorescence is measured to obtain the uorescence recovery scan shown in

Figure 2c

+

Figure 2c.

compares the rate of dissociation at dierent excitation wavelengths.

The

uorescence increase is t to an exponential curve to model a rst order dissociation process:

A(t) = A∞ − (A∞ − A0 )e−Γ(λ)t where

A(t)

represents the time dependent uorescence,

the steady state orescence, and the spectrum.

Γ(λ) is the

A0

is the initial uorescence,

(1)

A∞

is

wavelength dependent rate recorded to produce

When the laser is o resonance, the uorescence increase is negligible and

in these cases, the error in

Γ(λ)

is larger than 30% and the dissociation value is consistent

4


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with 0.

The data points for the spectrum

Figure 3

are the average of ve data points

and vertical error bars are the standard deviation. The entire range previously studied with vibronic resolution

26,27

was remeasured with rotational resolution.

Results and discussion Measuring the dissociation rate as a function of wavelength yielded a series of peaks

3, corresponding to transitions from X 1 Σ, v00 = 0, J 00 → A 1 Σ+ , v0 = 0−4, J 0 .

Figure

The horizontal

error bars are the standard error of the residuals from the calibration curve. Up to two or three rovibronic peaks are taken each day with a new calibration curve created every time the Ti:sapph laser central wavelength changed.

The measured dissociation rate is not a

quantitative indication of the transition strength or relative population in the rotational levels due to uncertainty of laser intensity in the current setup. Rates are extracted from a rst order t of the uorescence recovery curve, experiments on this electronic transition.

26,27

Equation 1,

consistent with previous

The dissociation pathway is currently unknown

and the dissociation is complicated by rethermalization of rotational levels populated in the ground state by blackbody radiation and collisions with the background gas. Nonetheless, the measured rate does provide a means to extract transition frequencies and spectroscopic constants. To extract rotational constants from the experimental data, the measured transitions were assigned to an initial rotational state to plot a Fortrat diagram shown in

Figure 4.

The experimental transitions were t to the rst order equation to obtain the rotational constants,

B0:

νP,R = νvibronic + (B 0 + B 00 )m + (B 0 − B 00 )m2 Here,

m

(2)

is for the rotational quantum number where m=J of the excited state for the R

branch and for m=-J of the ground state for the P branch. After an initial guess, measured

5



transitions were re-assigned with

m

Page 6 of 17

to give a reasonable rotational constant, vibrational

oset, and an improved parabolic t. The parabolic t parameter of the second order term in

Equation 2

at the 95% condence interval is used to estimate the uncertainty of the

rotational constants. We set the rotational constant in the ground state to 4.75 cm

−1

based

on measurements by the National Institute of Standards and Technology (NIST), which were rst reported at the North American Conference on Trapped Ions

31,32

to a precision better

− −1 than 10 4 cm . As a result, we attribute all of the uncertainty to the excited state. If we t the ground state

B

independently, we measure a ground state

B

of 4.73

agreement with the NIST value and results in a shift of the exctied state

± B

−1 0.02 cm in values within

the error bars. After obtaining a rotational constant from the Fortrat diagrams, the expected P and R branches were plotted in

Figure 3.

While this t is solely a rst order approximation, it

does provide the reasonable rotational constants for the limited resolution as shown in

Table

1. Table 1: Optimized parameters for the experimental spectroscopic constants for the excited states are compared to ab initio 27 theoretical parameters for the predicted spectrum. The λ(v0 ) term is the v00 = 0, J 00 = 0 → v0 , J 0 = 0 transition. Error ranges in the experimental t constants are the standard errors in the parameters from the Fortrat curve quadratic t. All values reported are in cm−1 . v0

λ(v 0 )

0 Theory CCSDT 0 Experiment

B0

24294

24595±

1 Theory CCSDT

25073

3.047 3

1 Experiment

25370 ± 1.7

2 Theory CCSDT

25861

2 Experiment

26119 ± 1.8

3 Theory CCSDT

26655

3 Experiment

26863 ± 1.6

3.17

±

0.08

3.00 2.86

±

0.03

2.94 2.94

±

0.05

2.88 2.85

±

0.03

Finally, the results were used to extract information about the vibrational constants. Us-

0 ing the quadratic t of the vibronic transition energies (λ(v )), the optimized energy dierence

6


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between the potential minimum of the vibrational harmonic constant of the were obtained

Table 2.

X 1Σ

X 1 Σ+

and the

A 1 Σ+

electronic manifolds (T(0,1)),

state (ωe ), and the anharmonic constant (ωe xe )

The constants agree better with the ab initio calculations than re-

sults derived from vibronic spectroscopy and are more reliable since the measured transitions are largely unaected by the unknown dissociation pathway. The rovibronic results measure vibronic transition frequencies in agreement with vibronic spectroscopy

26

and measure an average shift of 310

±

3 cm

−1

in the electronic transition

relative to ab initio calculations. The rotational constants match well with theory, however higher distortion constants are not measured due to the limited resolution of the experiment. In addition, although v' = 0 was taken with the same method to yield a reasonable rotational constant, two transitions were measured that deviated far from the predicted value by calculating the P and R branches as shown in

Figure 3.

It is possible that hot bands

contribute extra rovibronic transitions from higher lying vibrational states in the ground state accessed by spontaneous decay after the initial excitation. This is more likely to occur for the excitation to the ground vibrational state of the excited electronic state due to the larger Franck-Condon overlap of that state with higher lying vibrational states in the ground electronic state. This eect could explain the relatively large discrepancy between the measured and the theoretical rotational constants for v' = 0, 1 compared to v' = 2, 3, which have predicted larger overlap with the ground vibrational state in the ground electronic state

33

as

well as the two transitions in v' = 0 that could not be assigned using the rst order model. The spacing and frequency is consistent with transitions from v = 1, at high J to v' = 4, J'. Additionally, resolving the transitions with a continuous-wave (CW) laser source would allow more accurate determination of the transition assignments and rotational constants, especially at the bandhead for the v' = 0, 1 cases where the Franck-Condon overlap is weaker.

7



Page 8 of 17

Table 2: Spectroscopic constants obtained from the rovibronic spectrum of CaH+ compared to the constants determined from vibronic spectroscopy and CCSDT. 27 All values reported are in cm−1 . CaH T(0,1)

ωe ωe x e

+

Rovibronic

CaH

±2 ± 9.6 ± 2.3

24207 786 7.8

+

Vibronic

±5 ±6 ± 1.4

Theory

24239

23907

813

772

16.8

3.8

Conclusion and Outlook The spectrum and rotational constants obtained here represent the highest precision mea-

+ surements available for an electronic transition in CaH .

The distortion constants could

be easily obtained with a CW frequency-doubled Ti:Sapph given the preliminary spectrum obtained here to facilitate the search. This method provides a convenient means of obtaining rotational resolution over a large range that is extendable to other molecular ions. The t for the v' = 0 peak suers relatively larger error due to the lack of resolution of the P and R branches, especially at the bandhead.

Nonetheless, the strong v' = 2 transition

clearly shows resolved rotational transitions and a hint at a thermal envelope of peak heights. Measurements of this transition with a pulse shaped or CW source could provide a convenient method of state readout for proposed methods of rotational cooling by a cryogenic chamber,

34,35

pumping.

sympathetic cooling with a buer gas of Doppler cooled atoms,

18

or by optical

9,16,17,29

Supporting Information Available A table with the experimental rovibronic frequency along with the associated assignment used in the creation of the Fortrat diagrams is included in the supporting information.

8


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Acknowledgement This work was supported by the Army Research Oce (ARO) (W911NF-12-1-0230), the National Science Foundation (PHY- 1404388), and an ARO Multi-University Research Initiative (W911NF-14-1-0378). initio calculations.

The authors thank David Sherrill for providing us with ab

We also thank Dr.

Chris Seck for providing guidance on the pulse

shaping setup.

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1998,

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Graphical TOC Entry

13



Page 14 of 17

a

b

Figure 1:

c

a.

The vibronic spectrum of the v'=2 transition taken with the frequency doubled −1

Ti:Sapph beam is a convolution of the mode-locked Ti:sapph spectral linewidth of 180 cm

and the underlying rotational structure. The expected P and R branches are plotted based on ab initio theory with an intensity prole based on the thermal distribution of the v = 0, J states at room temperature and the transitions are scaled to match the vibronic curve.

b.

To resolve the underlying rovibronic transitions, a 4-f pulse shaping setup is introduced.

The position of the slit yields the ne control of the laser wavelength.

c.

The wavelength

is determined from the relative slit position by a linear calibration curve. Deviations from a linear trend are due to the limited resolution of the spectrometer and error in estimating the center wavelength, which is taken into account as the uncertainty in wavelength from the standard error of regression. The slit width and resolution of the measured pulse-shaped frequency limit the resolution of the obtained spectrum.

14


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a

c

+

Ca

CaH

+

+H2

+γ +γ

25 μm

b

a.

+ and Ca + with an associated decrease of uorescence over the course of several minutes. CaH is more Figure 2:

A laser cooled Coulomb crystal of Ca

+

reacts with H2 to form CaH

+

stably trapped on the outer edge of the composite Coulomb crystal due to the increased + mass compared to Ca . The asymmetry of the crystal is due to radiation pressure on the + + + Ca . Exposure to a resonant laser photodissociates CaH resulting in the recovery of Ca .

b.

The crystal is exposed to the beam alternating between on and o with a time of 8 + uorescence is detected for 200 µs each data point and the

ms each for 10 cycles. The Ca

c

process is repeated 250 times. . Fluorescence recovers when the laser is on resonance with a + + rovibronic transition of CaH to form Ca . A typical dissociation scan for three wavelengths showing the normalized uorescence over exposure time is used to extract dissociation rates. −1 The 24539 cm scan shows no detectable dissociation. The uorescence recovery curves are t to a rst order dissociation process.

15



Figure 3: The predicted P and R branches using the rotational constant obtained with the Fortrat diagram is compared to the measured experimental transitions. The experimental transitions are centered on the weighted average of the measured dissociation rates with a width obtained from the standard error of the residuals from the calibration curve.

16


Page 16 of 17

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Figure 4: Fortrat diagrams composed for each vibronic transition were used to extract without higher order distortion terms.

17


B0

Rovibronic Spectroscopy of Sympathetically Cooled 40CaH+ - The

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