HighResolution Rotational Spectroscopy and Coherent Control of a

Motivation A general protocol for spectroscopy of molecular ions Reaching the same level of

Trapping and sympathetic laser cooling 40 Ca. H+ · Convenient to work with 40

Transferring information Quantized Harmonic Motion

Proof-of-Principle Molecule 40 Ca. H+ levels · Room. J temperature, electronic ground state Rotation

Transitions with Unique Frequencies J = 1, B = 0. 36 m. T Rotation

Transitions with Unique Frequencies J = 2, B = 0. 36 m. T Rotation

Projecting into a Pure State J = 1, B = 0. 36 m. T

Stimulated Raman Transition 1051 nm fiber laser p D ~ 2 p 500 THz

Pure Initial State High Resolution Coherent Spectra Projective measurement Rotation manifold J = 1

Rotation manifold J = 1 Rotation manifold J = 2 Transition probability Projective measurement

Transition probability Projective measurement Transition probability Coherent Manipulation Rotationmanifold. J J= =1 1 t

Directly Driving THz Rotational Transitions with a Frequency Comb Femtosecond Ti: S laser frequency

Detecting Initial and final states in Rotational Spectroscopy State preparation Comb pulse frequency comb

Complementary Rotational Spectra State preparation Prepared in J = 2 Detection probability after comb

Determination of the Rotational Constant and Centrifugal Corrections (preliminary)

Coherent Manipulation Rabi flopping between J = 2 and J = 4 levels Prepared

Entanglement between Ca. H+ and Ca+ Y. Lin et al. , in preparation Ca.

Entanglement between Ca. H+ and Ca+ Y. Lin et al. , in preparation

Summary Trapped and laser cooled translationally Probabilistic projective molecular state preparation with CW Raman

David Leibrandt Dietrich Leibfried Alejandra Collopy David Hume

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High-Resolution Rotational Spectroscopy and Coherent Control of a Single Ca. H+ James Chin-wen Chou Yiheng Lin, Alejandra Collopy, Christoph Kurz, Tara Fortier, Scott Diddams, Dietrich Leibfried, David R. Leibrandt National Institute of Standards and Technology, Boulder, Colorado, USA

Motivation A general protocol for spectroscopy of molecular ions Reaching the same level of control and measurement precision for many species of molecular ions as on atomic ions. nobelprize. org

Trapping and sympathetic laser cooling 40 Ca. H+ · Convenient to work with 40 Ca + · Form a 40 Ca. H+ by trapping two 40 Ca + ions and leaking in H 2 DC RF

Transferring information Quantized Harmonic Motion

Proof-of-Principle Molecule 40 Ca. H+ levels · Room. J temperature, electronic ground state Rotation 1 S, spin 1/2 v. Hin=nuclear 0 sublevels J 33 1. 1 % population in each sublevels at 300 K 22 ~0. 6 THz 11 00 -7/2 -5/2 -3/2 -1/2 +3/2 +5/2 +7/2 M. Abe, Y. Moriwaki, M. Hada, and M. Kajita, Chem. Phys. Lett. 521, 31– 35 (2012) m

Transitions with Unique Frequencies J = 1, B = 0. 36 m. T Rotation Nuclear spin ~ 10 k. Hz m -3/2 -1/2 +3/2

Transitions with Unique Frequencies J = 2, B = 0. 36 m. T Rotation Nuclear spin -1/2 +1/2 ~ 13 k. Hz m -5/2 -3/2 +5/2

Projecting into a Pure State J = 1, B = 0. 36 m. T motion m -3/2 -1/2 +3/2 I. S. Vogelius, L. B. Madsen, and M. Drewsen, J. Phys. B, 39, S 1259 (2006).

Projecting into a Pure State J = 1, B = 0. 36 m. T Non-destructive detection of molecular states m -3/2 -1/2 +3/2 I. S. Vogelius, L. B. Madsen, and M. Drewsen, J. Phys. B, 39, S 1259 (2006).

Stimulated Raman Transition 1051 nm fiber laser p D ~ 2 p 500 THz s- s- p l=1051 nm motion · Coherent process · Applicable to many molecular ion species m m+1 motion

Pure Initial State High Resolution Coherent Spectra Projective measurement Rotation manifold J = 1 Rotation manifold J = 2 Nature 545, 203 (2017)

Rotation manifold J = 1 Rotation manifold J = 2 Transition probability Projective measurement Transition probability Improved Contrast Raman frequency Offset (k. Hz)

Transition probability Projective measurement Transition probability Coherent Manipulation Rotationmanifold. J J= =1 1 t = 700 ms Rotationmanifold. J J= =2 2 t = 788 ms Pulse duration (in unit of time)

Directly Driving THz Rotational Transitions with a Frequency Comb Femtosecond Ti: S laser frequency comb Chirped mirrors 30: 70 splitter AO M delay p M f. Raman = M f. Rep +/- 2 f. AOM AO s. D. Hayes, et al. , Phys. Rev. Lett. 104, 140501 (2010) S. Ding and D. Matsukevich, New J. Phys. 14 023028 (2012) D. Liebfried, New J. Phys. 14 023029 (2012)

Detecting Initial and final states in Rotational Spectroscopy State preparation Comb pulse frequency comb π pulse State detection

Complementary Rotational Spectra State preparation Prepared in J = 2 Detection probability after comb pulse State detection Comb pulse J=2 Prepared in J = 4 J=4 Reduced ambiguity in line assignment J=4 Comb Raman frequency offset (k. Hz) J=2 Comb Raman frequency offset (k. Hz)

Determination of the Rotational Constant and Centrifugal Corrections (preliminary)

Coherent Manipulation Rabi flopping between J = 2 and J = 4 levels Prepared in J = 4 Detection probability after comb pulse J=4 J=2 Pulse duration (ms)

Entanglement between Ca. H+ and Ca+ Y. Lin et al. , in preparation Ca. H+ 40 Ca+ ~400 THz ~13 k. Hz molecule-motion sideband

Entanglement between Ca. H+ and Ca+ Y. Lin et al. , in preparation Ca. H+ 40 Ca+ ~400 THz ~13 k. Hz molecule-motion sideband atom-motion sideband

Entanglement between Ca. H+ and Ca+ Y. Lin et al. , in preparation

Summary Trapped and laser cooled translationally Probabilistic projective molecular state preparation with CW Raman beams Coherent manipulation of molecular states with CW and comb Raman beams Precision measurements of the THz rotational transitions Inferred molecular constants with high precision Using far-detuned Raman beams to manipulate molecular states, applicable to other molecular ion species Atom-molecule entanglement

David Leibrandt Dietrich Leibfried Alejandra Collopy David Hume