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arXiv:1508.06060 · Physical Review A

Proposal for laser cooling of rare-earth ions

Maxence Lepers, Ye Hong, Jean-François Wyart, Olivier Dulieu

Published Jan 7, 2016• 12 citations
arXivHTMLPDF

Abstract

The efficiency of laser cooling relies on the existence of an almost closed optical-transition cycle in the energy spectrum of the considered species. In this respect, rare-earth elements exhibit many transitions which are likely to induce noticeable leaks from the cooling cycle. In this work, to determine whether laser cooling of singly ionized erbium ${\mathrm{Er}}^{+}$ is feasible, we have performed accurate electronic-structure calculations of energies and spontaneous-emission Einstein coefficients of ${\mathrm{Er}}^{+}$, using a combination of ab initio and least-squares-fitting techniques. We identify five weak closed transitions suitable for laser cooling, the broadest of which is in the kilohertz range. For the strongest transitions, by simulating the cascade dynamics of spontaneous emission, we show that repumping is necessary, and we discuss possible repumping schemes. We expect our detailed study on ${\mathrm{Er}}^{+}$ to give good insight into the laser cooling of neighboring ions such as ${\mathrm{Dy}}^{+}$.

DOI
10.1103/physreva.93.011401

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The efficiency of laser cooling relies on the existence of an almost closed optical-transition cycle in the energy spectrum of the considered species. In this respect, rare-earth elements exhibit many transitions which are likely to induce noticeable leaks from the cooling cycle. In this work, to determine whether laser cooling of singly ionized erbium Er+{\mathrm{Er}}^{+}Er+ is feasible, we have performed accurate electronic-structure calculations of energies and spontaneous-emission Einstein coefficients of Er+{\mathrm{Er}}^{+}Er+, using a combination of ab initio and least-squares-fitting techniques. We identify five weak closed transitions suitable for laser cooling, the broadest of which is in the kilohertz range. For the strongest transitions, by simulating the cascade dynamics of spontaneous emission, we show that repumping is necessary, and we discuss possible repumping schemes. We expect our detailed study on Er+{\mathrm{Er}}^{+}Er+ to give good insight into the laser cooling of neighboring ions such as Dy+{\mathrm{Dy}}^{+}Dy+.
The direct laser cooling of neutral diatomic molecules in molecular beams suggests that trapped molecular ions can also be laser cooled.The long storage time and spatial localization of trapped molecular ions provides an opportunity for multi-step cooling strategies, but also requires careful consideration of rare molecular transitions.We briefly summarize the requirements that a diatomic molecule must meet for laser cooling, and we identify a few potential molecular ion candidates.We then carry out a detailed computational study of the candidates BH + and AlH + , including improved ab initio calculations of the electronic state potential energy surfaces and transition rates for rare dissociation events.On the basis of an analysis of the population dynamics, we determine which transitions must be addressed for laser cooling, and compare experimental schemes using continuous-wave and pulsed lasers.
We present a theoretical scheme for laser cooling of rare-earth-doped solids with optical superradiance (SR), which is the coherent, sharply directed spontaneous emission of photons by a system of laser-excited rare-earth ions in the solid-state host (glass or crystal). We consider an Yb+{}^{+}+-doped ZnF4{}_{4}4​-BaF2{}_{2}2​-LaF3{}_{3}3​-AlF3{}_{3}3​-NaF (ZBLAN) sample pumped at a wavelength 1015 nm, with a rectangular pulsed source with a power of \ensuremath{\sim}433 W and a duration of 10 ns. The intensity of the SR is proportional to the square of the number of excited ions. This unique feature of SR permits an increase in the rate of the cooling process in comparison with the traditional laser cooling of the rare-earth-doped solids with anti-Stokes spontaneous incoherent radiation (fluorescence). This scheme overcomes the limitation of using only low phonon energy glasses for laser cooling.
We report on a novel mechanism that allows for strong laser cooling of atoms that do not have a closed cycling transition. This mechanism is observed in a magneto-optical trap (MOT) for erbium, an atom with a very complex energy level structure with multiple pathways for optical-pumping losses. We observe surprisingly high trap populations of over 10(6) atoms and densities of over 10(11) atoms cm(-3), despite the many potential loss channels. A model based on recycling of metastable and ground state atoms held in the quadrupole magnetic field of the trap explains the high trap population, and agrees well with time-dependent measurements of MOT fluorescence. The demonstration of trapping of a rare-earth atom such as erbium opens a wide range of new possibilities for practical applications and fundamental studies with cold atoms.
The feasibility of laser cooling MHM\mathrm{H}MH (M=Be,Mg,Ca,Sr,andBaM=\mathrm{Be},\phantom{\rule{0.16em}{0ex}}\mathrm{Mg},\phantom{\rule{0.16em}{0ex}}\mathrm{Ca},\phantom{\rule{0.16em}{0ex}}\mathrm{Sr},\phantom{\rule{0.16em}{0ex}}\mathrm{and}\phantom{\rule{0.16em}{0ex}}\mathrm{Ba}M=Be,Mg,Ca,Sr,andBa) is investigated using ab initio quantum chemistry. The ground state $X\phantom{\rule{0.16em}{0ex}}{}^{2}{\ensuremath{\Sigma}}^{+}$ and first excited state $A\phantom{\rule{0.16em}{0ex}}{}^{2}\ensuremath{\Pi}$ of MHM\mathrm{H}MH species are calculated using the multireference configuration interaction (MRCI) level of theory. For CaH\mathrm{CaH}CaH, SrH\mathrm{SrH}SrH, and BaH\mathrm{BaH}BaH, the spin-orbit coupling effects are also taken into account in electronic structure calculations at the MRCI level. Calculated spectroscopic constants for 9BeH^{9}\mathrm{BeH}9BeH, 24MgH^{24}\mathrm{MgH}24MgH, 40CaH^{40}\mathrm{CaH}40CaH, 86SrH^{86}\mathrm{SrH}86SrH, and 138BaH^{138}\mathrm{BaH}138BaH show good agreement with available theoretical and experimental results. The permanent dipole moments and transition dipole moments (TDMs) of the $X\phantom{\rule{0.16em}{0ex}}{}^{2}{\ensuremath{\Sigma}}^{+}$ and $A\phantom{\rule{0.16em}{0ex}}{}^{2}\ensuremath{\Pi}$ states of MHM\mathrm{H}MH species are also calculated at the MRCI level of theory, and they are in good agreement with previous theoretical results. With the potential energy curves and TDMs obtained, the highly diagonally distributed Franck-Condon factors f00(9BeH:0.998,24MgH:0.954,40CaH:0.961,86SrH:0.978,and138BaH:0.971){f}_{00}\left({}^{9}\mathrm{BeH}:0.998{,}^{24}\mathrm{MgH}:0.954{,}^{40}\mathrm{CaH}:0.961{,}^{86}\mathrm{SrH}:0.978,\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{and}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{138}\mathrm{BaH}:0.971\right)f00​(9BeH:0.998,24MgH:0.954,40CaH:0.961,86SrH:0.978,and138BaH:0.971) for the $A\phantom{\rule{0.16em}{0ex}}{}^{2}\ensuremath{\Pi}\left({v}^{\ensuremath{'}}=0\right)\ensuremath{\rightarrow}X\phantom{\rule{0.16em}{0ex}}{}^{2}{\ensuremath{\Sigma}}^{+}\left(v=0\right)$ transition are determined. Radiative lifetime calculations of the $A\phantom{\rule{0.16em}{0ex}}{}^{2}\ensuremath{\Pi}\left({v}^{\ensuremath{'}}=0\right)$ state (9BeH:82.0ns{}^{9}\mathrm{BeH}:82.0\phantom{\rule{0.16em}{0ex}}\mathrm{ns}9BeH:82.0ns, 24MgH:48.6ns{}^{24}\mathrm{MgH}:48.6\phantom{\rule{0.16em}{0ex}}\mathrm{ns}24MgH:48.6ns, 40CaH:33.3ns{}^{40}\mathrm{CaH}:33.3\phantom{\rule{0.16em}{0ex}}\mathrm{ns}40CaH:33.3ns, 86SrH:33.2ns{}^{86}\mathrm{SrH}:33.2\phantom{\rule{0.16em}{0ex}}\mathrm{ns}86SrH:33.2ns, and 138BaH^{138}\mathrm{BaH}138BaH: 68.6 ns) are found to be short enough for rapid laser cooling. The proposed main cycling laser drives the $X\phantom{\rule{0.16em}{0ex}}{}^{2}{\ensuremath{\Sigma}}^{+}\left(v=0\right)\ensuremath{\rightarrow}A\phantom{\rule{0.16em}{0ex}}{}^{2}\ensuremath{\Pi}\left({v}^{\ensuremath{'}}=0\right)$ transition at wavelength ${\ensuremath{\lambda}}_{00}\left({}^{9}\mathrm{BeH}:497.2\phantom{\rule{0.16em}{0ex}}\mathrm{nm}{,}^{24}\mathrm{MgH}:525.5\phantom{\rule{0.16em}{0ex}}\mathrm{nm}{,}^{40}\mathrm{CaH}:675.4\phantom{\rule{0.16em}{0ex}}\mathrm{nm}{,}^{86}\mathrm{SrH}:740.3\phantom{\rule{0.16em}{0ex}}\mathrm{nm},\phantom{\rule{0.16em}{0ex}}\mathrm{and}\phantom{\rule{0.28em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{138}\mathrm{BaH}:952.6\phantom{\rule{0.16em}{0ex}}\mathrm{nm}\right)$. The results demonstrate the possibility of laser cooling MHM\mathrm{H}MH species, and provide a promising theoretical reference for further theoretical and experimental research on alkaline-earth-metal monohydrides.
Laser cooling of rare-earth doped solids has been demonstrated across a wide range of material platforms, inspiring the development of simple phenomenological models such as the four-level model to elucidate the universal properties of laser cooling under various operating conditions. However, these models usually require the input of full absorption spectra that must be provided experimentally or by additional complicated atomic modeling. In this Letter, we propose that a four-level model, when extended to admit effective energy levels adaptive to the pumping photon energy, can accurately predict the cooling efficiency as a function of temperature and pumping frequency using only few inputs such as the absorption coefficient measured at a single frequency and temperature. Our model exploits the quasi-equilibrium properties of the excitation of rare-earth ions for the determination of the effective four energy levels. The model is validated against published experimental results for a span of materials including ytterbium/thulium-doped glass and crystals. With the verified model, we derive explicit expressions for the optimal frequency and the operating bandwidth of pumping lasers. Our model significantly simplifies the modeling process of laser cooling and is expected to stimulate further development of optical refrigeration.
The recent achievements devoted to cooling of solids with a laser are presented in this paper. We discuss the latest results of traditional laser cooling of solids based on rare earth ions and new techniques based on colloidal lead-salt quantum dots doped in a glass host, laser cooling in Tm3+-doped oxy-fluoride glass ceramic. Relatively short (microsecond) lifetime of the excited level of the PbSe QDs compared to the millisecond lifetime of the excited level of RE ions allows an acceleration of the cooling process and provides an opportunity to use new materials with higher phonon energy as hosts, which are normally considered unsuitable for cooling with RE ions. Another new approach to the laser cooling problem based on super-radiance has been considered in this paper. The advantages of optical refrigeration with rare earth doped semiconductors, in which not only optically active electrons of the 4f shell but the valence and conduction bands of the host material are involved in cooling cycle is discussed. It is shown that involving the valence and conduction bands of the host in the cooling cycle allows the pump wavelength to be shorter than mean fluorescence wavelength. Raman laser cooling of solids as well as observation of spontaneous Brillouin cooling have been presented.