In this paper, we develop an analytical approach to Doppler cooling of atoms by one- or two-photon transitions when the natural width of the excited level is so small that the process leads to a Doppler temperature comparable to the recoil temperature. A ``quenching'' of the sharp line is introduced in order to allow control of the time scale of the problem. In such limit, the usual Fokker-Planck equation does not correctly describe the cooling process. We propose a generalization of the Fokker-Planck equation and derive a new model which is able to reproduce correctly the numerical results, up to the recoil limit. Two cases of practical interest, one-photon Doppler cooling of strontium and two-photon Doppler cooling of hydrogen are considered.
We have experimentally studied sub-Doppler laser cooling in a magneto-optical trap for thulium atoms working at the wavelength of 410.6\,nm. Without any dedicated molasses period of sub-Doppler cooling, the cloud of $3\times 10^6$ atoms at the temperature of 25(5)\,$μ$K was observed. The measured temperature is significantly lower than the Doppler limit of 240$μ$K for the cooling transition at 410.6\,nm. High efficiency of the sub-Doppler cooling process is due to a near-degeneracy of the Landé-$g$ factors of the lower $4f^{13}6s^{2}\, (J\,=\,{7}/{2})$ and the upper $4f^{12}5d_{3/2}6s^{2}\, (J…
Three-photon laser excitation of Rydberg states by three different laser beams can be arranged in a star-like geometry that simultaneously eliminates the recoil effect and Doppler broadening. Our analytical and numerical calculations for a particular laser excitation scheme 5S_{1/2}->5P_{3/2}->6S_{1/2}->nP in Rb atoms have shown that compared to the one- and two-photon laser excitation this approach provides much narrower line width and longer coherence time for both cold atom samples and hot vapors, if the intermediate one-photon resonances of the three-photon transition are detuned by more t…
The influence of photon-momentum recoil on adiabatic population transfer in an atomic three-level lambda system is studied. It is shown that the Doppler frequency shifts, due to atomic motion can play an important role in adiabatic population transfer processes of atomic internal states by a pair of laser fields. For the limiting case of slow atoms ( Doppler shift much smaller than the photon recoil energy) the atoms occupy the same target state regardless of the order of switching of laser fields, while for the case of fast atoms interacting with the intuitive sequence of pulses, the target s…
Doppler cooling the center-of-mass motion of an optically levitated microsphere via the velocity dependent scattering force from narrow whispering gallery mode (WGM) resonances is described. Light that is red detuned from the WGM resonance can be used to damp the center-of-mass motion in a process analogous to the Doppler cooling of atoms. Leakage of photons out of the microsphere when the incident field is near resonant with the narrow WGM resonance acts to damp the motion of the sphere. The scattering force is not limited by saturation, but can be controlled by the incident power. Cooling ti…
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…
Magneto-optical traps (MOTs) of Er and Dy have recently been shown to exhibit population-wide sub-Doppler cooling due to their near degeneracy of excited and ground state Lande g factors. We discuss here an additional, unusual intra-MOT sub-Doppler cooling mechanism that appears when the total Dy MOT cooling laser intensity and magnetic quadrupole gradient increase beyond critical values. Specifically, anisotropically sub-Doppler-cooled cores appear, and their orientation with respect to the quadrupole axis flips at a critical ratio of the MOT laser intensity along the quadrupole axis versus t…
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 investigate the dynamics of cavity cooling of a single ion beyond the Lamb-Dicke regime and demonstrate a cooling limit of approximately 50% of the Doppler temperature using a high finesse cavity for the first time. We also study the statistical properties of the ion-cavity emission and present a model that maps the phonon states to the photon states. With this model, we explain the super-Poissonian photon distribution observed in our experiments and propose a method to estimate the ion temperature in a real-time manner based on the statistical behavior of the photon emission from the cavit…
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…
We report enhanced sub-Doppler cooling of the bosonic atoms of $^{39}$K facilitated by formation of dark states tuned for the Raman resonance in the $Λ-$configuration near the D1 transition. Temperature of about 12 $μ$K is achieved in the two stage D2-D1 molasses and spans a very large parameter region where quantum interference persists robustly. We also present results on enhanced radiation heating with sub-natural linewidth (0.07$Γ$) and signature Fano like profile of a coherently driven 3-level atomic system. The Optical Bloch Equations relevant for the three-level atom in bichromatic ligh…
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…
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…
Optimizing Doppler laser cooling protocols for quantum sensing with 3D ion crystals in a Penning trap
University of Colorado, Boulder（科罗拉多大学博尔德分校）；Sandia National Laboratories（桑迪亚国家实验室）；Indian Institute of Technology Madras（马德拉斯印度理工学院）；National Institute of Standards and Technology（美国国家标准与技术研究院）；University of California, San Diego（加州大学圣地亚哥分校）
Sub-Doppler cooling of a trapped ion in a phase-stable polarization gradient
Massachusetts Institute of Technology（麻省理工学院）；Lincoln Laboratory, Massachusetts Institute of Technology（林肯实验室，麻省理工学院）；Clarendon Laboratory, Department of Physics, University of Oxford（克拉伦登实验室，牛津大学物理系）
Doppler and sideband cooling are long standing techniques that have been used together to prepare trapped atomic ions in their ground state of motion. In this paper we study how these techniques can be extended to cool both radial modes of motion of a single ion in a Penning trap. We numerically explore the prerequisite experimental parameters for efficient Doppler cooling in the presence of an additional oscillating electric field to resonantly couple the radial modes. The simulations are supported by experimental data for a single $^{40}$Ca$^+$ ion Doppler cooled to $\sim$100 phonons in both…
Laser cooling of translational motion of small molecules is performed by addressing transitions that ensure spontaneous emission cannot cause net rotational excitation. This will not be possible once the rotational splitting becomes comparable to the operational excitation linewidth, as will occur for large molecules or wide bandwidth lasers. We show theoretically that in this regime, angular momentum transfer from red-detuned Doppler cooling light can also exert a damping torque on linear molecules, cooling rotation to the same Doppler limit (typically $\approx$ 500 $μ$K for molecules with $\…
The problem of deep laser cooling of $^{24}$Mg atoms is theoretically studied. We propose two-stage sub-Doppler cooling strategy using electro-dipole transition $3^3P_2$$\to$$3^3D_3$ ($λ$=383.9 nm). The first stage implies exploiting magneto-optical trap with $σ^+$ and $σ^-$ light beams, while the second one uses a lin$\perp$lin molasses. We focus on achieving large number of ultracold atoms (T$_{eff}$ < 10 $μ$K) in a cold atomic cloud. The calculations have been done out of many widely used approximations and based on quantum treatment with taking full account of recoil effect. Steady-state a…
We propose a laser cooling mechanism that leads to a temperature significantly lower than the single-photon recoil limit, about $4\times 10^{-4}\,E_{r}$. This mechanism benefits from sharp and high-contrast spectra which are induced by interacting dark-state resonances. It is theoretically demonstrated that four-level atoms illuminated by two counter-propagating probe beams and two additional beams directed perpendicularly to other two, exhibit new cooling effects; For red detuned probe lasers, atoms can be subject to a strong viscous force with an extremely small diffusion, characteristic of …
In photon recoil spectroscopy, signals are extracted from recoils imparted by the spectroscopy light on the motion of trapped ions as demonstrated by C. Hempel et al., Nature Photonics 7, 630 (2013) and Y. Wan et al., Nature Communications 5, 3096 (2014). The method exploits the exquisite efficiency in the detection of phonons achievable in ion crystals, and is thus particularly suitable for species with broad non-cycling transitions where detection of fluorescence photons is impractical. Here, we develop a theoretical model for the description of photon recoil spectroscopy based on a Fokker-P…
We propose a new dark-state cooling method of trapped ion systems in the Lamb-Dicke limit. With application of microwave dressing the ion, we can obtain two electromagnetically induced transparency structures. The heating effects caused by the carrier and the blue sideband transition vanish due to the EIT effects and the final mean phonon numbers can be much less than the recoil limit. Our scheme is robust to fluctuations of microwave power and laser intensities which provides a broad cooling bandwidth to cool motional modes of a linear ion chain. Moreover, it is more suitable to cool four-lev…
Resolved sideband cooling is a standard technique for cooling trapped ions below the Doppler limit to near their motional ground state. Yet, the most common methods for sideband cooling implicitly rely on low Doppler-cooled temperatures and tightly confined ions, and they cannot be optimized for different experimental conditions. Here we introduce a framework which calculates the fastest possible pulsed sideband cooling sequence for a given number of pulses and set of experimental parameters, and we verify its improvement compared to traditional methods using a trapped $^{171}$Yb$^+$ ion. Afte…
The erbium atomic system is a promising candidate for an atomic Bose-Einstein condensate of atoms with a non-vanishing orbital angular momentum ($L \neq 0$) of the electronic ground state. In this paper we report on the frequency stabilization of a blue external cavity diode laser system on the 400.91 $nm$ laser cooling transition of atomic erbium. Doppler-free saturation spectroscopy is applied within a hollow cathode discharge tube to the corresponding electronic transition of several of the erbium isotopes. Using the technique of frequency modulation spectroscopy, a zero-crossing error sign…
A new scheme of three-dimensional (3D) all-optical (nonmagnetic) cooling and trapping of resonant atoms, based on using of so-called rectified radiation forces in non-monochromatic light fields is presented. It can be applied to the atoms with a tripod-type configuration of levels: atoms (ions) with the quantum transition F=1 \to F=0. The scheme proposed provides a long-term trapping of such atoms in deep light-induced potential wells. Moreover, the atom temperature can continuously be changed by varying field parameters in quite a large range (from super-Doppler to sub-Doppler values) without…
We provide a theoretical analysis for a recently demonstrated cooling method. Two-level particles undergo successive adiabatic transfers upon interaction with counter-propagating laser beams that are repeatedly swept over the transition frequency. We show that particles with narrow linewidth transitions can be cooled to near the recoil limit. This cooling mechanism has a reduced reliance on spontaneous emission compared to Doppler cooling, and hence shows promise for application to systems lacking closed cycling transitions, such as molecules.
Precision spectroscopy of atomic and molecular ions offers a window to new physics, but is typically limited to species with a cycling transition for laser cooling and detection. Quantum logic spectroscopy has overcome this limitation for species with long-lived excited states. Here, we extend quantum logic spectroscopy to fast, dipole-allowed transitions and apply it to perform an absolute frequency measurement. We detect the absorption of photons by the spectroscopically investigated ion through the photon recoil imparted on a co-trapped ion of a different species, on which we can perform ef…
We present a detailed numerical analysis of the temperature limit and timescale of cavity cooling of a dilute gas in the quantum regime for particles and light. For a cavity with a linewidth smaller than the recoil frequency efficient cooling towards quantum degeneracy is facilitated by applying a tailored sequence of laser pulses transferring the particles towards lower momenta. Two-particle Monte Carlo wave function simulations reveal strongly improved cooling properties for a ring versus a standing-wave geometry. Distinct quantum correlations and cooling limits for bosons and fermions demon…
Laser cooling to sub-Doppler temperatures by optical molasses is thought to be inhibited in atoms with unresolved, near-degenerate hyperfine structure in the excited state. We demonstrate that such cooling is possible in one to three dimensions, not only near the standard D2 line for laser cooling, but over a range extending to the D1 line. Via a combination of Sisyphus cooling followed by adiabatic expansion, we reach temperatures as low as 40 μK, which corresponds to atomic velocities a factor of 2.6 above the limit imposed by a single photon recoil. Our method requires modest laser power at…
We demonstrate sub-Doppler laser cooling and magneto-optical trapping of the rare earth element Holmium. Atoms are loaded from an atomic beam source and captured in six-beam $σ_+ - σ_-$ molasses using a strong $J=15/2 \leftrightarrow J=17/2$ cycling transition at $λ=410.5 \rm nm$. Due to the small difference in hyperfine splittings and Landé $g$-factors in the lower and upper levels of the cooling transition the MOT is self-repumped without additional repump light, and deep sub-Doppler cooling is achieved with the magnetic trap turned on. We measure the leakage out of the cycling transition to…
We report observation of sub-Doppler cooling of lithium using an irregular-tetrahedral laser beam arrangement, which is produced by a nanofabricated diffraction grating. We are able to capture 11(2) % of the lithium atoms from a grating magneto-optical trap into $Λ$-enhanced $D_1$ gray molasses. The molasses cools the captured atoms to a radial temperature of 60(9) $μ$K and an axial temperature of 23(3) $μ$K. In contrast to results from conventional counterpropagating beam configurations, we do not observe cooling when our optical fields are detuned from Raman resonance. An optical Bloch equat…
A novel laser cooling mechanism was recently demonstrated using a narrow-linewidth optical transition. Counter-propagating laser beams are swept in frequency to cause adiabatic transfer between a ground state and excited state, and Doppler shifts provide time-ordering that ensures the associated photon recoils oppose the particle's motion. We now expand this technique to $^{87}$Rb, which has no narrow-linewidth optical transition, by using artificially-narrow two-photon Raman transitions. The cooling mechanism is capable of exerting large forces to compress the phase-space of the atomic ensemb…
Sympathetic cooling of trapped ions has become an indispensable tool for quantum information processing and precision spectroscopy. In the simplest situation a single Doppler-cooled ion sympathetically cools another ion which typically has a different mass. We analytically investigate the effect of the mass ratio of such an ion crystal on the achievable temperature limit in the presence of external heating. As an example, we show that cooling of a single Al+ with Be+, Mg+ and Ca+ ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger…
We present a new and efficient implementation of Raman cooling of trapped atoms. It uses Raman pulses with an appropriate frequency chirp to realize a velocity selective excitation through a rapid adiabatic passage. This method allows to address in a single pulse a large number of non zero atomic velocity classes and it produces a nearly unity transfer efficiency. We demonstrate this cooling method using cesium atoms in a far-detuned crossed dipole trap. Three-dimensional cooling of $1 \times 10^{5}$ atoms down to $2 μ$K is performed in 100 ms. In this preliminary experiment the final atomic d…
