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arXiv:1001.4394 · Physical Review A

Molecular heat pump for rotational states

Constantinos Lazarou, Matthias Keller, B. M. Garraway

Published Jan 27, 2010• 9 citations
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Abstract

In this work, we investigate the theory for three different unidirectional population-transfer schemes in trapped multilevel systems which can be utilized to cool molecular ions. The approach we use exploits the laser-induced coupling between the internal and motional degrees of freedom so that the internal state of a molecule can be mapped onto the motion of that molecule in an external trapping potential. By sympathetically cooling the translational motion back into its ground state, the mapping process can be employed as part of a cooling scheme for molecular rotational levels. This step is achieved through a common mode involving a laser-cooled atom trapped alongside the molecule. For the coherent mapping, we will focus on adiabatic passage techniques which may be expected to provide robust and efficient population transfers. By applying far-detuned chirped adiabatic rapid passage pulses, we are able to achieve an efficiency of better than $98%$ for realistic parameters and including spontaneous emission. Even though our main focus is on cooling molecular states, the analysis of the different adiabatic methods has general features which can be applied to atomic systems.

DOI
10.1103/physreva.81.013418

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Different adiabatic passage methods are applied as part of a state mapping scheme in multilevel trapped systems. The aim is to achieve full population transfer from the rotational states of a trapped molecular ion to its translational states. Our analysis is based on numerical simulations with the master equation. We discuss how the resolved sideband condition, and spontaneous emission have an adverse effect on the efficiency for stimulated Raman adiabatic passage. Use of adiabatic rapid passage techniques, with two-photon Raman transitions results in higher efficiencies that can exceed 97%.

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In the last several years we have discovered a variety of remarkable pulse strategies for manipulating molecular motion by employing a design strategy we call “local optimization.'' Here we review the concept of local optimization and contrast it with optimal control theory. By way of background, we give highlights from two recent examples of the method: (1) a strategy for eliminating population transfer to one or many excited electronic states during strong field excitation, an effect we call ‘optical paralysis’; (2) a generalization of the counterintuitive STIRAP (stimulated Raman adiabatic passage) pulse sequence from three levels to N levels, a strategy we call ‘straddling STIRAP.' We then turn to a third example, which is the main subject of this paper: laser cooling of molecular internal degrees of freedom. We study a model that includes both coherent interaction with the radiation field and spontaneous emission; the latter is necessary to carry away the entropy from the molecule. An optimal control calculation was performed first and succeeded in producing vibrational cooling, but the resulting pulse sequence was difficult to interpret. Local optimization subsequently revealed the cooling mechanism: the instantaneous phase of the laser is locked to the phase of the transition dipole moment between the excited state amplitude and v=0 of the ground state. Thus, the molecules that reach v=0 by spontaneous emission become decoupled from the field, and no longer absorb, while molecules in all other states are continually repumped. The mechanism could be called “vibrationally selective coherent population trapping,'' in analogy to the corresponding mechanism of velocity selective coherent population trapping in atoms for sub-Doppler cooling of translations.

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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).

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Blackbody-mediated rotational laser cooling schemes in MgH+, DCl+, HCl+, LiH and CsH

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Ensembles of ultra-cold atoms, molecules and ions (both atomic and molecular) can be held in traps for increasingly long periods of time. While these trapped species remain translationally cold, for molecules the absorption of ambient black-body radiation can result in rapid thermalisation of the rotational (and vibrational) degrees of freedom. At 300 K, internal state purity is lost typically on the order of tens of seconds, inhibiting the study of quantum state selected reactions. In this paper a theoretical model is used to investigate laser-driven, blackbody-mediated, rotational cooling schemes for several (1)Σ and (2)Π diatomic species. The rotational cooling is particularly effective for DCl(+) and HCl(+), for which 92% and >99% (respectively) of the population can be driven into the rovibrational ground state. For the other systems a broadband optical pumping source (simultaneously exciting up to four transitions) is found to enhance the population that can be accumulated in the rovibrational ground state by up to 29% over that achieved when exciting a single transition. The influence of the rotational constant, dipole moments and electronic state of the diatomics on the rotational cooling achievable is also considered. An extension to polyatomic species is discussed and a combination of cold trap environments (at 77 K) and optical pumping schemes is proposed.

Physical Chemistry Chemical Physics•Jan 1, 2013•13 citations
In this work, we investigate the theory for three different unidirectional population-transfer schemes in trapped multilevel systems which can be utilized to cool molecular ions. The approach we use exploits the laser-induced coupling between the internal and motional degrees of freedom so that the internal state of a molecule can be mapped onto the motion of that molecule in an external trapping potential. By sympathetically cooling the translational motion back into its ground state, the mapping process can be employed as part of a cooling scheme for molecular rotational levels. This step is achieved through a common mode involving a laser-cooled atom trapped alongside the molecule. For the coherent mapping, we will focus on adiabatic passage techniques which may be expected to provide robust and efficient population transfers. By applying far-detuned chirped adiabatic rapid passage pulses, we are able to achieve an efficiency of better than 9898%98 for realistic parameters and including spontaneous emission. Even though our main focus is on cooling molecular states, the analysis of the different adiabatic methods has general features which can be applied to atomic systems.
Different adiabatic passage methods are applied as part of a state mapping scheme in multilevel trapped systems. The aim is to achieve full population transfer from the rotational states of a trapped molecular ion to its translational states. Our analysis is based on numerical simulations with the master equation. We discuss how the resolved sideband condition, and spontaneous emission have an adverse effect on the efficiency for stimulated Raman adiabatic passage. Use of adiabatic rapid passage techniques, with two-photon Raman transitions results in higher efficiencies that can exceed 97%.
In the last several years we have discovered a variety of remarkable pulse strategies for manipulating molecular motion by employing a design strategy we call “local optimization.'' Here we review the concept of local optimization and contrast it with optimal control theory. By way of background, we give highlights from two recent examples of the method: (1) a strategy for eliminating population transfer to one or many excited electronic states during strong field excitation, an effect we call ‘optical paralysis’; (2) a generalization of the counterintuitive STIRAP (stimulated Raman adiabatic passage) pulse sequence from three levels to N levels, a strategy we call ‘straddling STIRAP.' We then turn to a third example, which is the main subject of this paper: laser cooling of molecular internal degrees of freedom. We study a model that includes both coherent interaction with the radiation field and spontaneous emission; the latter is necessary to carry away the entropy from the molecule. An optimal control calculation was performed first and succeeded in producing vibrational cooling, but the resulting pulse sequence was difficult to interpret. Local optimization subsequently revealed the cooling mechanism: the instantaneous phase of the laser is locked to the phase of the transition dipole moment between the excited state amplitude and v=0 of the ground state. Thus, the molecules that reach v=0 by spontaneous emission become decoupled from the field, and no longer absorb, while molecules in all other states are continually repumped. The mechanism could be called “vibrationally selective coherent population trapping,'' in analogy to the corresponding mechanism of velocity selective coherent population trapping in atoms for sub-Doppler cooling of translations.
Working with MgH+molecular ions in a linear Paul trap, we routinely cool their translational degrees of freedom by sympathetic cooling with Doppler laser cooled Mg+ions. Giving the time for the molecules to equilibrate internally to room temperature blackbody radiation, the vibrational degree of freedom is frozen out, leaving only the rotational degree of freedom to be cooled. We have implemented a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ions, using a scheme based on excitation of a single rovibrational transition. This technique is generalizable to any diatomic polar molecular ion, given an appropriate mid-infrared laser source such as a quantum cascade laser.
Although ion-ion sympathetic cooling is now commonly used to reduce speeds of trapped molecular ions to milliKelvin temperatures, cooling of the decoupled internal molecular modes remains a challenge. Here, we demonstrate that a single spectrally filtered femtosecond laser, tuned to the electronic A-X transition of trapped AlH+, can efficiently cool rotations from room temperature to the ground state. Since this single-laser technique simultaneously drives rotationally de-exciting electronic excitations from all initially populated states, each parity can be cooled as quickly as 100 μs. In our current implementation, full population collection into the N = 0 positive-parity level relies on vibrational relaxation on the timescale of 100 ms. Since this technique cools by step-wise rotational pumping, it is most readily applicable to “alkali-like” molecular species, such as AlH+, with semi-closed cycling transitions. Although we currently use a destructive two-photon state readout technique, these species are also promising candidates for single-molecule fluorescence detection. The ability to quickly cool molecular rotations is expected to be important for precision spectroscopy experiments, quantum information processing applications, and for ultracold chemistry studies.
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).
Ensembles of ultra-cold atoms, molecules and ions (both atomic and molecular) can be held in traps for increasingly long periods of time. While these trapped species remain translationally cold, for molecules the absorption of ambient black-body radiation can result in rapid thermalisation of the rotational (and vibrational) degrees of freedom. At 300 K, internal state purity is lost typically on the order of tens of seconds, inhibiting the study of quantum state selected reactions. In this paper a theoretical model is used to investigate laser-driven, blackbody-mediated, rotational cooling schemes for several (1)Σ and (2)Π diatomic species. The rotational cooling is particularly effective for DCl(+) and HCl(+), for which 92% and >99% (respectively) of the population can be driven into the rovibrational ground state. For the other systems a broadband optical pumping source (simultaneously exciting up to four transitions) is found to enhance the population that can be accumulated in the rovibrational ground state by up to 29% over that achieved when exciting a single transition. The influence of the rotational constant, dipole moments and electronic state of the diatomics on the rotational cooling achievable is also considered. An extension to polyatomic species is discussed and a combination of cold trap environments (at 77 K) and optical pumping schemes is proposed.