Analogous to the extension of laser cooling techniques from two-level to three-level atoms, Doppler cooling of molecules with an intermediate electronic state is considered. In particular, we use a rate-equation approach to simulate cooling of SiO+, in which population buildup in the intermediate state is prevented by its short lifetime. We determine that Doppler cooling of SiO+ can be accomplished without optically repumping from the intermediate state, at the cost of causing undesirable parity flips and rotational diffusion. Since the necessary repumping would require a large number of continuous-wave lasers, optical pulse shaping of a femtosecond laser is proposed as an attractive alternative. Other candidate three-electron-level molecules are also discussed.
We propose and demonstrate a new method for Doppler cooling trapped-ion crystals where the distribution of micromotion amplitudes may be large and uneven. The technique uses pulses of Doppler cooling light synchronized with the trap RF that selectively target ions when their velocity is near a node, leading to more uniform cooling across a crystal by a single tone of cooling light. We lay out a theoretical framework that describes where this technique is practical, and provide a simple experimental demonstration.
We perform detailed analysis of sub-Doppler cooling limits for various atoms by direct solving quantum kinetic equation for atom density matrix in standing-wave light field generated by counterpropagating waves. It was demonstrated that the polarization gradient cooling effects are sensitive to atom recoil parameter (the ratio of recoil energy to natural linewidth) that results to limitation of sub-Doppler cooling and allows to outline the limits of well-known sub-Doppler cooling theory. We also give a comparison the cooling limits for well-known $σ_+-σ_-$ and $lin\perp lin$ configurations.
Doppler cooling with lasers is essential to ions' trapping and also a preliminary step towards achievement of ultracold ions. Due to lack of effective tools, experimentally monitoring the ions' temperature and the laser-ion coupling is difficult in Doppler cooling. Here we analytically explore the Doppler cooling process of trapped ions, exemplified by $^{40}$Ca$^{+}$, by solving the friction coefficient in the Doppler cooling with respect to a thermal bath, particularly, to a bath with large heating rate. We show four regions for cooling and heating induced by the three-level electromagnetica…
We study the Doppler-cooling of radial two-dimensional (2D) Coulomb crystals of trapped barium ions in a radiofrequency trap. Ions in radial 2D crystals experience micromotion of an amplitude that increases linearly with the distance from the trap center, leading to a position-dependent frequency modulation of laser light in each ion's rest frame. We use two tones of Doppler-cooling laser light separated by approximately 100~MHz to efficiently cool distinct regions in the crystals with differing amplitudes of micromotion. This technique allows us to trap and cool more than 50 ions populating 4…
We report magneto-optical trapping (MOT) of a polyatomic molecule, calcium monohydroxide (CaOH). The MOT contains $2.0(5)\times 10^4$ CaOH molecules at a peak density of $3.0(8)\times10^{6}$ cm$^{-3}$. CaOH molecules are further sub-Doppler laser cooled in an optical molasses, to a temperature of 110(4) $μ$K. The temperatures and densities achieved here make CaOH a viable candidate for a wide variety of quantum science applications, including the creation of optical tweezer arrays of CaOH molecules. This work also suggests that laser cooling and magneto-optical trapping of many other polyatomi…
We present a 3D theoretical comparison between the radiation-pressure forces exerted on an atom in an isotropic light cooling scheme and in a six-beam molasses. We demonstrate that, in the case of a background vapor where all the space directions of the atomic motion have to be considered, the mean cooling rate is equal in both configurations. Nevertheless, we also point out what mainly differentiates the two cooling techniques: the force component orthogonal to the atomic motion. If this transverse force is always null in the isotropic light case, it can exceed the radiation-pressure-force lo…
We demonstrate one-dimensional Doppler cooling of a beam of buffer-gas cooled Barium monofluoride (BaF) molecules. The dependences of the cooling efficiency with the laser detuning, the bias filed and the laser intensity are carefully measured. We numerical simulate our experiment with a Monte Carlo method, and find the theoretic predictions consists with our experimental data. This result represents a key step towards further cooling and trapping of BaF molecules.
Complex molecular structure demands customized solutions to laser cooling by extending its general set of principles and practices. Yttrium monoxide (YO) has unique intramolecular interactions. The Fermi-contact interaction dominates over the spin-rotation coupling, resulting in two manifolds of closely spaced states, with one of them possessing a negligible Landé g-factor. This unique energy level structure favors dual-frequency DC magneto-optical trapping (MOT) and gray molasses cooling (GMC). We report exceptionally robust cooling of YO at 4 $μ$K over a wide range of laser intensity, detuni…
We study the time-dependent fluorescence of an initially hot, multi-level, single atomic ion trapped in a radio-frequency Paul trap during Doppler cooling. We have developed an analytical model that describes the fluorescence dynamics during Doppler cooling which is used to extract the initial energy of the ion. While previous models of Doppler cooling thermometry were limited to atoms with a two-level energy structure and neglected the effect of the trap oscillating electric fields, our model applies to atoms with multi-level energy structure and takes into account the influence of micromotio…
A direct numerical simulation of many interacting ions in a Penning trap with a rotating wall is presented. The ion dynamics is modelled classically. Both axial and planar Doppler laser cooling are modeled using stochastic momentum impulses based on two-level atomic scattering rates. The plasmas being modeled are ultra-cold two-dimensional crystals made up of 100's of ions. We compare Doppler cooled results directly to a previous linear eigenmodes analysis. Agreement in both frequency and mode structure are obtained. Additionally, when Doppler laser cooling is applied, the laser cooled steady …
Many predictions of Doppler cooling theory of two-level atoms have never been verified in a three-dimensional geometry, including the celebrated minimum achievable temperature $\hbar Γ/2 k_B$, where $Γ$ is the transition linewidth. Here, we show that, despite their degenerate level structure, we can use Helium-4 atoms to achieve a situation in which these predictions can be verified. We make measurements of atomic temperatures, magneto-optical trap sizes, and the sensitivity of optical molasses to a power imbalance in the laser beams, finding excellent agreement with the Doppler theory. We sho…
Ultracold Rb-OH collisions and prospects for sympathetic cooling
本文计算了Rb原子与OH自由基冷碰撞的从头算截面。我们预测，在10-100 mK的温度范围内，碰撞速率常数为10^{-11} cm ^3/s，在此温度下，分子已经在实验中产生。然而，我们也发现，在这些碰撞的分子有很强的倾向，改变其内部状态，这可能会使共振冷却的Rb缓冲气体中的OH的问题，在静磁或静电陷阱。
We demonstrate simple and robust methods for Doppler cooling and obtaining high fluorescence from trapped 43Ca+ ions at a magnetic field of 146 Gauss. This field gives access to a magnetic-field-independent "atomic clock" qubit transition within the ground level hyperfine structure of the ion, but also causes the complex internal structure of the 64 states relevant to Doppler cooling to be spread over many times the atomic transition line-width. Using a time-dependent optical Bloch equation simulation of the system we develop a simple scheme to Doppler-cool the ion on a two-photon dark resonan…
We demonstrate in situ fluorescence detection of $^7$Li atoms in a 1D optical lattice with single atom precision. Even though illuminated lithium atoms tend to boil out, when the lattice is deep, molasses beams without extra cooling retain the atoms while producing sufficient fluorescent photons for detection. When the depth of the potential well at an antinode is 2.4 mK, an atom remains trapped for 30 s while scattering probe photons at the rate of $1.7 \times 10^5$ s$^{-1}$. We propose a simple model that describes the dependence of the lifetime of an atom on well depth. When the number of t…
We demonstrate sub-Doppler laser cooling of $ ^{39} $K using degenerate Raman sideband cooling via the 4S$_{1/2} \rightarrow $5P$ _{1/2} $ transition at 404.8 nm. By using an optical lattice in combination with a magnetic field and optical pumping beams, we obtain a spin-polarized sample of up to $5.6 \times 10^{7}$ atoms cooled down to a sub-Doppler temperature of 4 $μ$K, reaching a peak density of $3.9 \times 10^{9}$ atoms/cm$ ^{3} $, a phase-space density greater than $ 10^{-5} $, and an average vibrational level of $ \langle ν\rangle=0.6 $ in the lattice. This work opens up the possibility…
The ability to cool atoms below the Doppler limit -- the minimum temperature reachable by Doppler cooling -- has been essential to most experiments with quantum degenerate gases, optical lattices and atomic fountains, among many other applications. A broad set of new applications await ultracold molecules, and the extension of laser cooling to molecules has begun. A molecular magneto-optical trap has been demonstrated, where molecules approached the Doppler limit. However, the sub-Doppler temperatures required for most applications have not yet been reached. Here we cool molecules to 50 uK, we…
We propose a method of stimulated laser cooling of diatomic molecules by counter-propagating $π$-trains of ultrashort laser pulses. The cooling cycles occur on the rovibrational transitions inside the same ground electronic manifold, thus avoiding the common problem of radiative branching in Doppler cooling of molecules. By matching the frequency comb spectrum of the pulse trains to spectrum of the R-branch rovibrational transitions we show that stimulated cooling can be carried out on several rovibrational transitions simultaneously, thereby increasing number of cooled molecules. The exerted …
We report on the realization of sub-Doppler laser cooling of sodium atoms in gray molasses using the D1 optical transition ($3s\, ^2S_{1/2} \rightarrow 3p\, ^2P_{1/2}$) at 589.8 nm. The technique is applied to samples containing $3\times10^9$ atoms, previously cooled to 350 $μ$K in a magneto-optical trap, and it leads to temperatures as low as 9 $μ$K and phase-space densities in the range of $10^{-4}$. The capture efficiency of the gray molasses is larger than 2/3, and we observe no density-dependent heating for densities up to $10^{11}$ cm$^{-3}$.
Λ-enhanced Sub-Doppler Cooling of Lithium Atoms in D1 Gray Molasses
根据最近在（Fernandes et al. 2012）中证明的40 K D1线上的双色亚多普勒冷却方案，我们对7 Li原子引入了类似的技术，并获得了60 uK的温度，同时捕获了前一阶段存在的所有5x10^8原子。我们调查的两个冷却频率之间的失谐的影响，并观察到三倍的温度下降时，拉曼条件得到满足。我们解释这种效果所产生的额外的冷却，由于长寿命的超精细状态之间的凝聚力。通过求解一个简化的Λ型三能级系统的光学布洛赫方程，我们发现在拉曼条件附近存在一个有效的冷却力。转移到四极磁阱中后，我们测得相空间密度约为10^-5。这种激光冷却为锂原子在光或磁阱中的快速蒸发到量子简并提供了一条很有前途的途径。
We report on simultaneous sub-Doppler laser cooling of fermionic $^6$Li and $^{40}$K using the D$_1$ optical transitions. We compare experimental results to a numerical simulation of the cooling process applying a semi-classical Monte Carlo wavefunction method. The simulation takes into account the three dimensional optical molasses setup and the dipole interaction between atoms and the bichromatic light field driving the D$_1$ transitions. We discuss the physical mechanisms at play, we identify the important role of coherences between the ground state hyperfine levels and compare D$_1$ and D$…
Calcium monofluoride (CaF) molecules are loaded into an optical dipole trap (ODT) and subsequently laser cooled within the trap. Starting with magneto-optical trapping, we sub-Doppler cool CaF and then load $150(30)$ CaF molecules into an ODT. Enhanced loading by a factor of five is obtained when sub-Doppler cooling light and trapping light are on simultaneously. For trapped molecules, we directly observe efficient sub-Doppler cooling to a temperature of $60(5)$ $μ\text{K}$. The trapped molecular density of $8(2)\times10^7$ cm$^{-3}$ is an order of magnitude greater than in the initial sub-Dop…
We report on the efficient gray molasses cooling of sodium atoms using the $D_{2}$ optical transition at 589.1 nm. Thanks to the hyperfine split about 6$Γ$ between the $|F'=2\rangle$ and $|F'=3\rangle$ in the excited state 3$^{2}P_{3/2}$, this atomic transition is effective for the gray molasses cooling mechanism. Using this cooling technique, the atomic sample in $F = 2$ ground manifold is cooled from 700 $\upmu$K to 56 $\upmu$K in 3.5 ms. We observe that the loading efficiency into magnetic trap is increased due to the lower temperature and high phase space density of atomic cloud after gray…
We describe a simple approach to the problem of incorporating the response time of an atom or ion being Doppler-cooled into the theory of the cooling process. The system being cooled does not in general respond instantly to the changing laser frequencies it experiences in its rest frame, and this "dynamic effect" can affect significantly the temperatures attainable. It is particularly important for trapped ions when there is a slow decay out of the cooling cycle requiring the use of a repumping beam. We treat the cases of trapped ions with two and three internal states, then apply the theory t…
We propose a sub-Doppler laser cooling mechanism that takes advantage of the unique spectral features and extreme dispersion generated by the phenomenon of electromagnetically induced transparency (EIT). EIT is a destructive quantum interference phenomenon experienced by atoms with multiple internal quantum states when illuminated by laser fields with appropriate frequencies. By detuning the lasers slightly from the "dark resonance", we observe that, within the transparency window, atoms can be subject to a strong viscous force, while being only slightly heated by the diffusion caused by spont…
Gray molasses is a powerful tool for sub-Doppler laser cooling of atoms to low temperatures. For alkaline atoms, this technique is commonly implemented with cooling lasers which are blue-detuned from either the D1 or D2 line. Here we show that efficient gray molasses can be implemented on the D2 line of 40K with red-detuned lasers. We obtained temperatures of 48(2) microKelvin, which enables direct loading of 9.2(3)*10^6 atoms from a magneto-optical trap into an optical dipole trap. We support our findings by a one-dimensional model and three-dimensional numerical simulations of the optical Bl…
In addition to being suitable for laser cooling and trapping in a magneto-optical trap (MOT) using a relatively broad ($\sim$5 MHz) transition, the molecule YO possesses a narrow-line transition. This forbidden transition between the $X^{2}Σ$ and $A'^{2}Δ_{3/2}$ states has linewidth $\sim$2$π\times$160 kHz. After cooling in a MOT on the $X^{2}Σ$ to $A^{2}Π_{1/2}$ (orange) transition, the narrow (red) transition can be used to further cool the sample, requiring only minimal additions to the first stage system. The narrow line cooling stage will bring the temperature from $\sim$1 mK to $\sim$10 …
We demonstrate 1D simultaneous laser cooling of $^{87}$Rb and $^{85}$Rb atoms using an optical frequency comb. By adjusting the pulse repetition frequency and the offset frequency, the frequency comb spectrum is tuned to ensure that two distinct frequency comb modes are simultaneously red-detuned from the cooling transitions, one mode for each species. Starting from a pre-cooled cloud of $^{85,87}$Rb atoms at above-Doppler temperatures, we show simultaneous cooling of both species down to the Doppler temperature using two counter-propagating $σ$$^{+}$/$σ$$^{-}$-polarized beams from the frequen…
Second-stage laser cooling of thulium atoms at the 530.7 nm transition with a natural linewidth of 350 kHz offers an interesting possibility to study different regimes of a magneto-optical trap (MOT). The intermediate value of the spectral linewidth of the cooling transition allows the observation of three distinct regimes depending on intensity and detuning of the cooling beams. Namely, the "bowl-shaped" regime when light pressure force competes with gravity, the "double structure" regime with interplay between Doppler and polarization-gradient (sub-Doppler) cooling, and the "symmetric" regim…
