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 that in the plane of symmetry. This phenomenon can be traced to a loss of the velocity-selective resonance at zero velocity in the cooling force along directions in which the atomic polarization is oriented by the quadrupole field. We present data characterizing this anisotropic laser cooling phenomenon and discuss a qualitative model for its origin based on the extraordinarily large Dy magnetic moment and Dy's near degenerate g factors.
Magneto-optical traps (MOTs) of highly magnetic lanthanides open the door to explorations of novel phases of strongly correlated matter such as lattice supersolids and quantum liquid crystals. We recently reported the first MOTs of the five high abundance isotopes of the most magnetic atom, dysprosium. Described here are details of the experimental technique employed for repumper-free Dy MOTs containing up to half a billion atoms. Extensive characterization of the MOTs' properties---population, temperature, loading, metastable decay dynamics, trap dynamics---is provided.
We present our technique to create a magneto-optical trap for dysprosium atoms using the narrow-line cooling transition at 626$\,$nm to achieve suitable conditions for direct loading into an optical dipole trap. The magneto-optical trap is loaded from an atomic beam via a Zeeman slower using the strongest atomic transition at 421$\,$nm. With this combination of two cooling transitions we can trap up to $2.0\cdot10^8$ atoms at temperatures down to 6$\, μ$K. This cooling approach is simpler than present work with ultracold dysprosium and provides similar starting conditions for a transfer to an …
We report on an apparatus for cooling and trapping of neutral dysprosium. We characterize and optimize the performance of our Zeeman slower and 2D molasses cooling of the atomic beam by means of Doppler spectroscopy on a 136 kHz broad transition at 626 nm. Furthermore, we demonstrate the characterization and optimization procedure for the loading phase of a magneto-optical trap (MOT) by increasing the effective laser linewidth by sideband modulation. After optimization of the MOT compression phase, we cool and trap up to $10^9$ atoms within 3 seconds in the MOT at temperatures of 9 μK and phas…
A thermal atomic beam of dysprosium (Dy) atoms is cooled using the $4f^{10}6s^2 (J=8) \to 4f^{10}6s6p (J=9)$ transition at 421 nm. The cooling is done via a standing light wave orthogonal to the atomic beam. Efficient transverse cooling to the Doppler limit is demonstrated for all observable isotopes of dysprosium. Branching ratios to metastable states are demonstrated to be $<5\times10^{-4}$. A scheme for enhancement of the nonzero-nuclear-spin-isotope cooling, as well as a method for direct identification of possible trap states, is proposed.
Ultracold dysprosium gases, with a magnetic moment ten times that of alkali atoms and equal only to terbium as the most magnetic atom, are expected to exhibit a multitude of fascinating collisional dynamics and quantum dipolar phases, including quantum liquid crystal physics. We report the first laser cooling and trapping of half a billion Dy atoms using a repumper-free magneto-optical trap (MOT) and continuously loaded magnetic confinement, and we characterize the trap recycling dynamics for bosonic and fermionic isotopes. The first inelastic collision measurements in the few partial wave, 10…
The laser cooling and trapping of ultracold neutral dysprosium has been recently demonstrated using the broad, open 421-nm cycling transition. Narrow-line magneto-optical trapping of Dy on longer wavelength transitions would enable the preparation of ultracold Dy samples suitable for loading optical dipole traps and subsequent evaporative cooling. We have identified the closed 741-nm cycling transition as a candidate for the narrow-line cooling of Dy. We present experimental data on the isotope shifts, the hyperfine constants A and B, and the decay rate of the 741-nm transition. In addition, w…
A two-dimensional magneto-optical trap of dysprosium atoms as a compact source for efficient loading of a narrow-line three-dimensional magneto-optical trap
We report the Bose-Einstein condensation (BEC) of the most magnetic atom, dysprosium. The Dy BEC is the first for an open f-shell lanthanide (rare-earth) element and is produced via forced evaporation in a crossed optical dipole trap loaded by an unusual, blue-detuned and spin-polarized narrow-line magneto-optical trap. Nearly pure condensates of 1.5x10^4 164Dy atoms form below T = 30 nK. We observe that stable BEC formation depends on the relative angle of a small polarizing magnetic field to the axis of the oblate trap, a property of trapped condensates only expected in the strongly dipolar …
We characterize the anisotropic differential ac-Stark shift for the Dy $626$ nm intercombination transition, induced in a far-detuned $1070$ nm optical dipole trap, and observe the existence of a "magic polarization" for which the polarizabilities of the ground and excited states are equal. From our measurements we extract both the scalar and tensorial components of the dynamic dipole polarizability for the excited state, $α_E^\text{s} = 188 (12)\,α_\text{0}$ and $α_E^\text{t} = 34 (12)\,α_\text{0}$, respectively, where $α_\text{0}$ is the atomic unit for the electric polarizability. We also p…
We produce Bose-Einstein condensates of $^{162}$Dy atoms employing an innovative technique based on a resonator-enhanced optical trap that allows efficient loading from the magneto-optical trap and fast evaporation. We characterize the scattering properties of the ultracold atoms for magnetic fields between 6 and 30 G. In addition to the typical chaotic distribution of narrow Feshbach resonances in Lanthanides, we discover two rather isolated broad features at around 22 G and 27 G. A characterization using the complementary measurements of losses, thermalization, anisotropic expansion and mole…
The grating magneto-optical trap (GMOT) requires only one beam and three planar diffraction gratings to form a cloud of cold atoms above the plane of the diffractors. Despite the complicated polarization arrangement, we demonstrate sub-Doppler cooling of 87Rb atoms to a temperature of 7.6(0.6) uK through a multi-stage, far-detuned GMOT in conjunction with optical molasses. A decomposition of the electric field into polarization components for this geometry does not yield a mapping onto standard sub-Doppler laser-cooling configurations. With numerical simulations, we find that the polarization …
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 realization of a magneto-optical trap of mercury atoms on the intercombination line. We report on trapping of all stable mercury isotopes. We characterize the effect of laser detuning, laser intensity, and gradient field on the trapping performance of our system. The atom number for the most abundant isotope Hg-202 is 50 million atoms. Moreover, we study the difference in cooling processes for bosonic and fermionic isotopes. We observe agreement with the Doppler cooling theory for the bosonic species and show sub-Doppler cooling for the fermionic species. We reach a phase space de…
We have performed for the first time direct laser spectroscopy of the 1S0-3P0 optical clock transition at 265.6 nm in fermionic isotopes of neutral mercury laser-cooled in a magneto-optical trap. Spectroscopy is performed by measuring the depletion of the magneto-optical trap induced by the excitation of the long-lived 3P0 state by a probe at 265.6 nm. Measurements resolve the Doppler-free recoil doublet allowing for a determination of the transition frequency to an uncer- tainty well below the Doppler-broadened linewidth. We have performed absolute measurement of the frequency with respect to…
We report on the first realization of a two-species magneto-optical trap (MOT) for erbium and dysprosium. The MOT operates on an intercombination line for the respective species. Owing to the narrow-line character of such a cooling transition and the action of gravity, we demonstrate a novel trap geometry employing only five beams in orthogonal configuration. We observe that the mixture is cooled and trapped very efficiently, with up to \num{5e8} Er atoms and \num{e9} Dy atoms at temperatures of about $10\,μK$. Our results offer an ideal starting condition for the creation of a dipolar quantum…
We investigate cooling mechanisms in magneto-optically and magnetically trapped erbium. We find efficient sub-Doppler cooling in our trap, which can persist even in large magnetic fields due to the near degeneracy of two Lande g factors. Furthermore, a continuously loaded magnetic trap is demonstrated where we observe temperatures below 25 microkelvin. These favorable cooling and trapping properties suggest a number of scientific possibilities for rare-earth atomic physics, including narrow linewidth laser cooling and spectroscopy, unique collision studies, and degenerate bosonic and fermionic…
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…
Engineering controllable, strongly interacting many-body quantum systems is at the frontier of quantum simulation and quantum information processing. Arrays of laser-cooled neutral atoms in optical tweezers have emerged as a promising platform, because of their flexibility and the potential for strong interactions via Rydberg states. Existing neutral atom array experiments utilize alkali atoms, but alkaline-earth atoms offer many advantages in terms of coherence and control, and also open the door to new applications in precision measurement and timekeeping. In this work, we present a techniqu…
We theoretically investigate the damping and trapping forces in a three-dimensional magneto-optical trap (MOT), by numerically solving the optical Bloch equations. We focus on the case where there are dark states because the atom is driven on a "type-II" system where the angular momentum of the excited state, $F'$, is less than or equal to that of the ground state, $F$. For these systems we find that the force in a three-dimensional light field has very different behaviour to its one dimensional counterpart. This differs from the more commonly used "type-I" systems ($F'=F+1$) where the 1D and …
A low-light-power theory of nonlinear magneto-optical rotation of frequency-modulated light resonant with a J=1->J'=0 transition is presented. The theory is developed for a Doppler-free transition, and then modified to account for Doppler broadening and velocity mixing due to collisions. The results of the theory are shown to be in qualitative agreement with experimental data obtained for the rubidium D1 line.
Ultracold atoms at temperatures close to the recoil limit have been achieved by extending Doppler cooling to forbidden transitions. A cloud of ^40Ca atoms has been cooled and trapped to a temperature as low as 6 μK by operating a magneto-optical trap on the spin-forbidden intercombination transition. Quenching the long-lived excited state with an additional laser enhanced the scattering rate by a factor of 15, while a high selectivity in velocity was preserved. With this method more than 10% of pre-cooled atoms from a standard magneto-optical trap have been transferred to the ultracold trap. M…
We report Monte Carlo wave function simulation results on cold collisions between magnesium atoms in a strong red-detuned laser field. This is the normal situation e.g. in magneto-optical traps (MOT). The Doppler limit heating rate due to radiative collisions is calculated for Mg-24 atoms in a magneto-optical trap based on the singlet S_0 - singlet P_1 atomic laser cooling transition. We find that radiative heating does not seem to affect the Doppler limit in this case. We also describe a channelling mechanism due to the missing Q branch in the excitation scheme, which could lead to a suppress…
We report on the sub-Doppler laser cooling of neutral $^{171}$Yb and $^{173}$Yb in a magneto-optical trap using the $^{1}S_{0}$-$^{1}P_{1}$ transition at 398.9nm. We use two independent means to estimate the temperature of the atomic cloud for several of the Yb isotopes. The two methods of MOT-cloud-imaging and release-and-recapture show consistency with one another. Temperatures below 400$μ$K and 200$μ$K are recorded for $^{171}$Yb and $^{173}$Yb, respectively, while ~1mK is measured for both $^{172}$Yb and $^{174}$Yb. By comparison, the associated 1D Doppler cooling temperature limit is 694$…
Bright and dark nonlinear magneto-optical resonances associated with the ground state Hanle effect have been studied experimentally and theoretically for D1 excitation of atomic cesium. This system offers the advantage that the separation between the different hyperfine levels exceeds the Doppler width, and, hence, transitions between individual levels can be studied separately. Experimental measurements for various laser power densities and transit relaxation times are compared with a model based on the optical Bloch equations, which averages over the Doppler contour of the absorption line an…
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…
We describe the application of displaced, or misaligned, beams in a mirror-based magneto-optical trap (MOT) to enable portable and miniaturized atom chip experiments, where optical access is limited to a single window. Two different geometries of beam displacement are investigated: a variation on the well-known 'vortex-MOT', and the other a novel 'hybrid-MOT' combining Zeeman-shifted and purely optical scattering force components. The beam geometry is obtained similar to the mirror-MOT, using a planar mirror surface but with a different magnetic field geometry more suited to planar systems. Us…
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…
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…
We propose and demonstrate a laser frequency stabilization scheme which generates a dispersion-like tunable Doppler-free dichroic lock (TDFDL) signal. This signal offers a wide tuning range for lock point (i.e. zero-crossing) without compromising on the slope of the locking signal. The method involves measurement of magnetically induced dichroism in an atomic vapour for a weak probe laser beam in presence of a counter propagating strong pump laser beam. A simple model is presented to explain the basic principles of this method to generate the TDFDL signal. The spectral shift in the locking sig…
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…
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$^{-3}$.
A new configuration for observation of magneto-optical subnatural-linewidth resonances of electromagnetically induced absorption (EIA) in alkali vapor has been verified experimentally. The configuration includes using two counter-propagating pump and probe light waves with mutually orthogonal linear polarizations, exciting an open optical transition of an alkali atom in the presence of a buffer gas. The main advantage of the novel observation scheme consists in the possibility of obtaining simultaneously high-contrast and quite narrow nonlinear signals. Here a 2.5-cm long rubidium-87 vapor cel…
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…
In the presence of an external static magnetic field, an atomic gas becomes optically active, showing magneto-optical rotation. In the saturated regime, the coherences among the excited substates give a nonlinear contribution to the rotation of the light polarization. In contrast with the linear magneto-optical rotation, the nonlinear counterpart is insensitive to Doppler broadening. By varying the temperature of a cold strontium gas, we observe both regimes by driving the $J=0\rightarrow J=1$ transition on the intercombination line. For this narrow transition, the sensitivity to the static ma…
We demonstrate significantly improved magneto-optical trapping of molecules using a very slow cryogenic beam source and RF modulated and DC magnetic fields. The RF MOT confines $1.1(3) \times 10^5$ CaF molecules at a density of $4(1) \times 10^6$ cm$^{-3}$, which is an order of magnitude greater than previous molecular MOTs. Near Doppler-limited temperatures of $340(20)$ $μ$K are attained. The achieved density enables future work to directly load optical tweezers and create optical arrays for quantum simulation.
We extend the technique originally proposed by Honda et al.to measure the temperature of Ytterbium and alkine-earth atoms confined in a Magneto-Optical Trap (MOT). The method is based on the analysis of excitation spectra obtained by probing the 1S0->3P1 inter-combination line. Thanks to a careful analysis and modeling of the effects caused by the MOT light on the probe transition we overcome the resolution and precision limits encountered in previous works. Ground state light shift and Rabi broadening are measured and successfully compared with calculated values. This knowledge allows us to p…
We have detected and analysed narrow high-contrast coherent population trapping (CPT) resonances, which are induced in absorption of the weak probe light beam by the counterpropagating two-frequency pumping radiation. Our experimental investigations have been carried out on example of nonclosed three level Lambda systems formed by spectral components of the Doppler broadened D2 line of cesium atoms. We have established that CPT resonances in transmission of the probe beam (in the cesium vapor), at definite conditions, may have not only more contrast but also much lesser width in comparison wit…
Non-Hermitian physics is responsible for many of the counter-intuitive effects observed in optics research opening up new possibilities in sensing, polarization control and measurement. A hallmark of non-Hermitian matrices is the possibility of non-orthogonal eigenvectors resulting in coupling between modes. The advantages of propagation mode coupling have been little explored in magneto-optical filters and other devices based on birefringence. Magneto-optical filters select for ultra-narrow transmission regions by passing light through an atomic medium in the presence of a magnetic field. Pas…
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…
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 demonstrate a Magneto-Optical Trap (MOT) configuration which employs optical forces due to light scattering between electronically excited states of the atom. With the standard MOT laser beams propagating along the {\it x}- and {\it y}- directions, the laser beams along the {\it z}-direction are at a different wavelength that couples two sets of {\it excited} states. We demonstrate efficient cooling and trapping of cesium atoms in a vapor cell and sub-Doppler cooling on both the red and blue sides of the two-photon resonance. The technique demonstrated in this work may have applications in …
We study electromagnetically induced transparency (EIT) in a heated potassium vapor cell, using a simple optical setup with a single free-running diode laser and an acousto-optic modulator. Despite the fact that the Doppler width is comparable to the ground state hyperfine splitting, transparency windows with deeply sub-natural line widths and large group indices are obtained. A longitudinal magnetic field is used to split the EIT feature and induce magnetooptical anisotropy. Using the beat note between co-propagating coupling and probe beams, we perform a heterodyne measurement of the circula…
Experimental signals of non-linear magneto-optical resonances at D1 excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The D1 transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic fi…
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…
Spatially Resolved Temperature Measurement Using Rydberg Doppler Broadening Thermometry
Università di Pisa（比萨大学）；CNR-INO（意大利国家研究委员会光学研究所）；University of Florence（佛罗伦萨大学）；ETH Zürich（苏黎世联邦理工学院）；Universität Innsbruck（因斯布鲁克大学）；Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften（奥地利科学院量子光学与量子信息研究所）；Observatoire de Paris, Université PSL, CNRS, Sorbonne Université（巴黎天文台，巴黎文理研究大学，法国国家科学研究中心，索邦大学）
We have used diffraction gratings to simplify the fabrication, and dramatically increase the atomic collection efficiency, of magneto-optical traps using micro-fabricated optics. The atom number enhancement was mainly due to the increased beam capture volume, afforded by the large area (4cm^2) shallow etch (200nm) binary grating chips. Here we provide a detailed theoretical and experimental investigation of the on-chip magneto-optical trap temperature and density in four different chip geometries using 87Rb, whilst studying effects due to MOT radiation pressure imbalance. With optimal initial …
We describe a dynamic magneto-optical trap (MOT) suitable for the use with vacuum systems in which optical access is limited to a single window. This technique facilitates the long-standing desire of producing integrated atom chips, many of which are likely to have severely restricted optical access compared with conventional vacuum chambers. This "switching-MOT" relies on the synchronized pulsing of optical and magnetic fields at audio frequencies. The trap's beam geometry is obtained using a planar mirror surface, and does not require a patterned substrate or bulky optics inside the vacuum c…
The development of the magneto-optical trap revolutionized the fields of atomic and quantum physics by providing a simple method for the rapid production of ultracold, trapped atoms. A similar technique for producing a diverse set of dense, ultracold diatomic molecular species will likewise transform the study of strongly interacting quantum systems, precision measurement, and physical chemistry. We demonstrate one- and two-dimensional transverse laser cooling and magneto-optical trapping of the polar molecule yttrium (II) oxide (YO). Using a quasicycling optical transition we observe transver…
We demonstrated a frequency offset locking between two laser sources using a waveguide-type electro-optic modulator (EOM) with 10th-order sidebands for magneto-optical trapping of Fr atoms. The frequency locking error signal was successfully obtained by performing delayed self-homodyne detection of the beat signal between the repumping frequency and the 10th-order sideband component of the trapping light. Sweeping the trapping-light and repumping-light frequencies with keeping its frequency difference of 46 GHz was confirmed over 1 GHz by monitoring the Doppler absorption profile of I2. This t…
