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arXiv:1501.06987 · Physical Review A

Efficient sympathetic motional-ground-state cooling of a molecular ion

Yong Wan, Florian Gebert, Fabian Wolf, Piet O. Schmidt

Published Apr 30, 2015• 49 citations
arXivHTMLPDF

Abstract

Cold molecular ions are promising candidates in various fields ranging from precision spectroscopy and test of fundamental physics to ultracold chemistry. Control of internal and external degrees of freedom is a prerequisite for many of these applications. Motional-ground-state cooling represents the starting point for quantum logic-assisted internal state preparation, detection, and spectroscopy protocols. Robust and fast cooling is crucial to maximize the fraction of time available for the actual experiment. We optimize the cooling rate of ground-state cooling schemes for single ${}^{25}{\mathrm{Mg}}^{+}$ ions and sympathetic ground-state cooling of ${}^{24}{\mathrm{MgH}}^{+}$. In particular, we show that robust cooling is achieved by combining pulsed Raman sideband cooling with continuous quench cooling. Furthermore, we experimentally demonstrate an efficient strategy for ground-state cooling outside the Lamb-Dicke regime.

DOI
10.1103/physreva.91.043425

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Cold molecular ions are promising candidates in various fields ranging from precision spectroscopy and test of fundamental physics to ultracold chemistry. Control of internal and external degrees of freedom is a prerequisite for many of these applications. Motional-ground-state cooling represents the starting point for quantum logic-assisted internal state preparation, detection, and spectroscopy protocols. Robust and fast cooling is crucial to maximize the fraction of time available for the actual experiment. We optimize the cooling rate of ground-state cooling schemes for single 25Mg+{}^{25}{\mathrm{Mg}}^{+}25Mg+ ions and sympathetic ground-state cooling of 24MgH+{}^{24}{\mathrm{MgH}}^{+}24MgH+. In particular, we show that robust cooling is achieved by combining pulsed Raman sideband cooling with continuous quench cooling. Furthermore, we experimentally demonstrate an efficient strategy for ground-state cooling outside the Lamb-Dicke regime.
Efficient cooling of trapped ions is a prerequisite for various applications of the ions in precision spectroscopy, quantum information, and coherence control. Raman sideband cooling is an effective method to cool the ions to their motional ground state. We investigate both numerically and experimentally the optimization of Raman sideband cooling strategies and propose an efficient one, which can simplify the experimental setup as well as reduce the number of cooling pulses. Several cooling schemes are tested and compared through numerical simulations. The simulation result shows that the fixed-width pulses and varied-width pulses have almost the same efficiency for both the first-order and the second-order Raman sideband cooling. The optimized strategy is verified experimentally. A single 25Mg+{^{25}\mathrm{Mg}}^{+}25Mg+ ion is trapped in a linear Paul trap and Raman sideband cooled, and the achieved average vibrational quantum numbers under different cooling strategies are evaluated. A good agreement between the experimental result and the simulation result is obtained.
We propose a method for the production of ultracold molecular ions. This method utilizes sympathetic cooling due to the strong collisions between appropriately chosen molecular ions and laser-cooled neutral atoms to realize ultracold internal ground-state molecular ions. In contrast to other experiments producing cold molecular ions, our proposed method efficiently cools both the internal and external molecular-ion degrees of freedom. The availability of an ultracold, absolute ground-state sample of molecular ions would have broad impact to fields as diverse as quantum chemistry, astrophysics, and fundamental physics and may lead to the development of a robust scalable quantum computer.
Stationary molecules in well-defined internal states are of broad interest in both physics and chemistry. Through high-resolution spectroscopy, fundamental physics can be tested and lead to, e.g., improved values of the electron-to-proton mass ratio [1], new boundaries on the electron electric dipole moment [2] and observation of the potential evolution of the fine structure constant over time [3]. Translationally and internally cold molecules have as well been considered promising candidates for qubits in new quantum computing senarios [4], and molecular ions could in the future likely become an excellent alternative to atomic qubits in the realization of a practical ion trap based quantum computer due to favourable internal state decoherence rates. In chemistry, state prepared molecular targets are an ideal starting point for uni-molecular reactions, including coherent control of photofragmentation through the application of various laser sources [5,6]. In cold bi-molecular reactions, where the effect of even tiny potential barriers becomes significant, experiments with state prepared molecules can yield important information on the details of the potential curves of the molecular complexes [7,8,9]. Furthermore, in order to learn more about the chemistry in interstellar clouds, astrochemists can benefit greatly from direct measurements on cold reactions in laboratories [9]. Working with MgH+ molecular ions in a linear Paul trap, we routinely cool their translational degree of freedom by sympathetic cooling with Doppler laser cooled Mg+ ions. Giving the time for the molecules to equilibrate internally to the room temperature blackbody radiation, the vibrational degree of freedom will freeze out, leaving only the rotational degree of freedom to be cooled. We report here on the implementation of a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ ions [10]. The scheme is based on excitation of a single rovibrational transition [11], and it should be generalizable to any diatomic polar molecular ion, given appropriate mid-infrared laser sources such as a quantum cascade laser are available. In recent experiments, a nearly 15-fold increase in the rotational ground-state population was obtained, with the resulting ground-state population of 36,7±1,2 %, equivalent to that of a thermal distribution at about 20 K. The obtained cooling results imply that, through this technique, cold molecular-ion experiments can now be carried out at cryogenic temperatures in room-temperature set-ups. References [1] Koelemeij, J. C. J., Roth, B., Wicht, A., Ernsting, I. and Schiller, S., Phys. Rev. Lett. 98, 173002 (2007). [2] Hudson, J. J., Sauer, B. E., Tarbutt, M. R. and Hinds, E. A., Phys. Rev. Lett. 89, 023003 (2002). [3] Hudson, E. R., Lewandowski, H. J., Sawyer, B. C. and Ye, J, Phys. Rev. Lett. 96, 143004 (2006). [4] DeMille, D, Phys. Rev. Lett. 88, 067901 (2002). [5] Rice, S. A. and Zaho, M. Optical control of molecular dynamics (Wiley, New York, 2000). [6] Shapiro, M. and Brumer, P. W. Principles of the Quantum Control of Molecular Processes (Wiley, New York, 2003). [7] Willitsch, S., Bell, M. T., Gingell, A. D. and Softley, T. P., Phys. Chem. Chem. Phys. 10, 7200 ( 2008). [8] Krems, R. V., Phys. Chem. Chem. Phys. 10, 4079 (2008). [9] Smith, I. W. M., Low temperatures and cold molecules (Imperial College Press, London, 2008). [10] Staanum, P. F., Højbjerre, K., Skyt, P.S., Hansen, A. K. and Drewsen, M., Nat. Phys. 6, 271 (2010). [11] Vogelius, I. S., Madsen, L. B. and Drewsen, M., Phys. Rev. Lett. 89, 173003 (2002).
We report continuous Raman sideband cooling of a long ion chain close to the motional ground state beyond the Lamb-Dicke (LD) regime. By driving multiple sideband transitions simultaneously, we show that nearly all axial modes of a 24-ion chain are cooled to the ground state, with an LD parameter as large as $\ensuremath{\eta}=1.3$, spanning a frequency bandwidth of 4 MHz. Compared to traditional ground-state cooling methods such as pulsed sideband cooling or electromagnetically-induced-transparency cooling, our method offers two key advantages: disposal of pulse optimization, and a wide bandwidth covering the entire spectrum. This technique contributes as a crucial step for large-scale quantum information processing with linear ion chains and higher dimensions alike, and can be readily generalized to other atomic and molecular systems.
Sideband cooling enables preparation of trapped ion motion near the ground state and is essential for many scientific and technological applications of trapped ion devices. Here, we study the efficiency of continuous and pulsed sideband cooling using both first- and second-order sidebands applied to an ion where the motion starts outside the Lamb-Dicke regime. We find that after optimizing these distinct cooling methods, pulsed and continuous cooling achieve similar results based on simulations and experiments with a 40^{40}40Ca+^++ ion. We consider optimization of both average phonon number n‾\overline{n}n and population in the ground state. We also demonstrate the disparity between n‾\overline{n}n as measured by the sideband ratio method of trapped ion thermometry and the n‾\overline{n}n found by averaging over the ion's motional state distribution.
Control of the external degree of freedom of trapped molecular ions is essential for their promising applications to spectroscopy, precision measurements of fundamental constants, and quantum information technology. Here, we demonstrate near ground-state cooling of the axial motional modes of a calcium mono-oxide ion via sympathetic sideband cooling with a cotrapped calcium ion. We also show that the phonon state of the axial out-of-phase mode of the ion chain is maintained while the mode frequency is adiabatically ramped up and/or down. The adiabatic ramping of the motional mode frequency is a prerequisite for searching for the proposed molecular dipole-phonon interaction [W. C. Campbell and E. R. Hudson, Phys. Rev. Lett. 125, 120501 (2020); M. Mills et al., Phys. Chem. Chem. Phys. 22, 24964 (2020)].