Abstract The magneto-optical trap (MOT) is an essential tool for collecting and preparing cold atoms with a wide range of applications. We demonstrate a planar-integrated MOT by combining an optical grating chip with a magnetic coil chip. The flat grating chip simplifies the conventional six-beam configuration down to a single laser beam; the flat coil chip replaces the conventional anti-Helmholtz coils of a cylindrical geometry. We trap 10^{4} cold ^{87}\text{Rb} atoms in the planar-integrated MOT, at a point 3-9 mm above the chip surface. This novel configuration effectively reduces the volume, weight, and complexity of the MOT, bringing benefits to applications including gravimeter, clock and quantum memory devices.
We characterize the loading, containment and optical properties of all-optical atom traps implemented by diffractive focusing with one-dimensional (1D) microstructures milled on gold films. These on-chip Fresnel lenses with focal lengths of the order of a few hundred microns produce optical-gradient-dipole traps. Cold atoms are loaded from a mirror magneto-optical trap (MMOT) centered a few hundred microns above the gold mirror surface. Details of loading optimization are reported and perspectives for future development of these structures are discussed.
Trapping lithium with a big number in a simplified experimental setup has difficulties and challenges today. In this paper, we experimentally demonstrate the enhancement of \textsuperscript{6}Li trapping efficiency in a three-dimensional magneto-optical trap (3D MOT) by using the multiple-sideband cooling in a two-dimensional magneto-optical trap (2D MOT). To improve the number of trapped atoms, we broaden the cooling light spectrum to 102 MHz composed of seven frequency components and then trap atoms with a number of $6.0\times10^8$ which is about 4 times compared to that in the single-freque…
We study the properties of a Rb magneto-optic trap loaded from a commercial getter source which provides a large flux of atoms for the trap along with the capability of rapid turn-off necessary for obtaining long trap lifetimes. We have studied the trap loading at two different values of background pressure to determine the cross-section for Rb--N$_2$ collisions to be 3.5(4)x10^{-14} cm^2 and that for Rb--Rb collisions to be of order 3x10^{-13} cm^2. At a background pressure of 1.3x10^{-9} torr, we load more than 10^8 atoms into the trap with a time constant of 3.3 s. The 1/e lifetime of trapp…
We present an experimental study of Z-scan measurements of the nonlinear response of cold Cs atoms in a magneto-optical trap. Numerical simulations of the Z-scan signal accounting for the nonuniform atomic density agree with experimental results at large probe beam detunings. At small probe detunings a spatially varying radiation force modifies the Z-scan signal. We also show that the measured scan is sensitive to the atomic polarization distribution.
We demonstrate the possibility of trapping about one hundred million rubidium atoms in a magneto-optical trap with several of the beams passing through a transparent atom chip mounted on a vacuum cell wall. The chip is made of a gold microcircuit deposited on a silicon carbide substrate, with favorable thermal conductivity. We show how a retro-reflected configuration can efficiently address the chip birefringence issues, allowing atom trapping at arbitrary distances from the chip. We also demonstrate detection through the chip, granting a large numerical aperture. This configuration is compare…
A new geometry to trap neutral particles with an ac electric field using a simple electrodes structure is described. In this geometry, all electrodes are placed on a single chip plane, while particles are levitated above the chip. This provides an easy construction of the trap and a good optical access to the trap.
We present a magneto-optical trap (MOT) design based on millimeter ball lenses, contained within a metal cube of 0.75$^{\prime \prime}$ side length. We present evidence of trapping approximately $4.2\times 10^5$ of $^{85}$Rb atoms with a number density of $3.2\times 10^9$ atoms/cm$^{3}$ and a loading time of 1.3 s. Measurement and a kinetic laser-cooling model are used to characterize the atom trap design. The design provides several advantages over other types of MOTs: the laser power requirement is low, the small lens and cube sizes allow for miniaturization of MOT applications, and the lack…
We have studied the absorption of a weak probe beam through cold rubidium atoms in a magneto-optic trap. The absorption spectrum shows two peaks with the smaller peak having linewidth as small as 28% of the natural linewidth. The modification happens because the laser beams used for trapping also drive the atoms coherently between the ground and excited states. This creates ``dressed'' states whose energies are shifted depending on the strength of the drive. Linewidth narrowing occurs due to quantum coherence between the dressed states. The separation of the states increases with laser intensi…
We demonstrate a technique for producing a cold pulsed beam of atoms by transferring a cloud of atoms trapped in a three dimensional magneto-optic trap (MOT). The MOT is loaded by heating a getter source of Rb atoms. We show that it is advantageous to transfer with two beams (with a small angle between them) compared to a single beam, because the atoms stop interacting with the beams in the two-beam technique, which results in a Gaussian velocity distribution. The atoms are further cooled in optical molasses by turning off the MOT magnetic field before the transfer beams are turned on.
We report on the realisation of a chip-based multipole ion trap manufactured using micro-electromechanical systems (MEMS) technology. It provides ion confinement in an almost field-free volume between two planes of radiofrequency electrodes, deposited on glass substrates, which allows for optical access to the trap. An analytical model of the effective trapping potential is presented and compared with numerical calculations. Stable trapping of argon ions is achieved and a lifetime of 16s is measured. Electrostatic charging of the chip surfaces is studied and found to agree with a numerical est…
We demonstrate the use of spatial emission patterns to measure the magnetic fields used in a magneto-optical trap. The directional aspect of the Hanle effect gives a direct, visual presentation of the magnetic fields, in which brighter fluorescence indicates larger fields. It can be used to determine the direction as well as the magnitude of the field. It is particularly well suited for characterizing and aligning magneto-optical traps, requiring little additional equipment or setup beyond what is ordinarily used in a magneto-optical trap, and being most sensitive to fields of the size typical…
In order to study interactions of atomic ions with ultracold neutral atoms, it is important to have sub-$μ$m control over positioning ion crystals. Serving for this purpose, we introduce a microfabricated planar ion trap featuring 21 DC electrodes. The ion trap is controlled by a home-made FPGA voltage source providing independently variable voltages to each of the DC electrodes. To assure stable positioning of ion crystals with respect to trapped neutral atoms, we integrate into the overall design a compact mirror magneto optical chip trap (mMOT) for cooling and confining neutral $^{87}$Rb at…
We propose a method for laser cooling and trapping a substantial class of polar molecules, and in particular titanium (II) oxide (TiO). This method uses pulsed electric fields to nonadiabatically remix the ground-state magnetic sublevels of the molecule, allowing us to build a magneto-optical trap (MOT) based on a quasi-cycling $J'=J"-1$ transition. Monte-Carlo simulations of this electrostatically remixed MOT (ER-MOT) demonstrate the feasibility of cooling TiO to a temperature of 10 $\mathrmμK$ and trapping it with a radiation-pumping-limited lifetime on the order of 80 ms.
The loading dynamics of an alkali-atom magneto-optical trap can be used as a reliable measure of vacuum pressure, with loading time T indicating a pressure less than or equal to [2x10^(-8) Torr s]/T. This relation is accurate to approximately a factor of two over wide variations in trap parameters, background gas composition, or trapped alkali species. The low-pressure limit of the method does depend on the trap parameters, but typically extends to the 10^(-10) Torr range.
One path to realizing systems of trapped atomic ions suitable for large-scale quantum computing and simulation is to create a two-dimensional array of ion traps. Interactions between nearest-neighbouring ions could then be turned on and off by tuning the ions' relative positions and frequencies. We demonstrate and characterize the operation of a planar-electrode ion-trap array. Driving the trap with a network of phase-locked radio-frequency (RF) resonators which provide independently variable voltage amplitudes we vary the position and motional frequency of a 40Ca+ ion in two dimensions within…
Electromagnetically induced absorption (EIA) was observed on a sample of $% ^{85}Rb$ in a magneto-optical trap using low intensity cw copropagating pump and probe optical fields. At moderate trapping field intensity, the EIA spectrum is determined by the Zeeman effect produced on the atomic ground-state by the trapping quadrupolar magnetic field. The use of EIA spectroscopy for the magnetic field mapping of cold atomic samples is illustrated.
Measurements of rubidium lifetime in a dark magneto-optical trap (DMOT) was performed at various populations of the bright and dark hyperfine states of the trapped atoms. The rubidium lifetime in the trap appeared to be shorter if the atom spent more time in the bright state. A simple explanation of this effect is based on the increase of the cross-section of rubidium collisions with the surrounding warm atoms upon rubidium electronic excitation.
We present experimental results from a new scheme for magneto-optically trapping strontium monofluoride (SrF) molecules, which provides increased confinement compared to our original work. The improved trap employs a new approach to magneto-optical trapping presented by M. Tarbutt, \emph{arXiv preprint} 1409.0244, which provided insight for the first time into the source of the restoring force in magneto-optical traps (MOTs) where the cycling transition includes dark Zeeman sublevels (known as type-II MOTs). We measure a radial spring constant $20\times$ greater than in our original work with …
Thulium atoms are trapped in a magneto-optical trap using a strong transition at 410 nm with a small branching ratio. We trap up to $7\times10^{4}$ atoms at a temperature of 0.8(2) mK after deceleration in a 40 cm long Zeeman slower. Optical leaks from the cooling cycle influence the lifetime of atoms in the MOT which varies between 0.3 -1.5 s in our experiments. The lower limit for the leaking rate from the upper cooling level is measured to be 22(6) s$^{-1}$. The repumping laser transferring the atomic population out of the F=3 hyperfine ground-state sublevel gives a 30% increase for the lif…
Large clouds of cold atoms prepared in a magneto-optical trap can develop spatio-temporal instabilities when the frequency of the trapping lasers is brought close to the atomic resonance. This system bears close similarities with trapped plasmas, whereby effective Coulomb interactions are induced by the exchange of scattered photons and lead to collective nonlinear dynamics of the trapped atoms. We report in this paper a detailed experimental study of the instability threshold, and comparisons with three-dimensional simulations of the interacting, laser-driven cloud.
We present designs for multipole ion traps based on a set of planar, annular, concentric electrodes which require only rf potentials to confine ions. We illustrate the desirable properties of the traps by considering a few simple cases of confined ions. We predict that mm-scale surface traps may have trap depths as high as tens of electron volts, or micromotion amplitudes in a 2-D ion crystal as low as tens of nanometers, when parameters of a magnitude common in the field are chosen. Several example traps are studied, and the scaling of those properties with voltage, frequency, and trap scale,…
We investigate the scaling behavior of a very large magneto-optical trap (VLMOT) containing up to $1.4 \times 10^{11}$ Rb$^{87}$ atoms. By varying the diameter of the trapping beams, we are able to change the number of trapped atoms by more than 5 orders of magnitude. We then study the scaling laws of the loading and size of the VLMOT, and analyze the shape of the density profile in this regime where the Coulomb-like, light-mediated repulsive interaction between atoms is expected to play an important role.
An exhaustive kinetic model for the atoms in a 1D Magneto-Optical Trap is derived, without any approximations. It is shown that the atomic density is described by a Vlasov-Fokker-Planck equation, coupled with two simple differential equations describing the trap beam propagation. The analogy of such a system with plasmas is discussed. This set of equations is then simplified through some approximations, and it is shown that corrective terms have to be added to the models usually used in this context.
We confine 4 10^8 fermionic 6Li atoms simultaneously with 9 10^9 bosonic 7Li atoms in a magneto-optical trap based on an all-semiconductor laser system. We optimize the two-isotope sample for sympathetic evaporative cooling. This is an essential step towards the production of a quantum-degenerate gas of fermionic lithium atoms.
Cold ions trapped in the vicinity of conductive surfaces experience heating of their oscillatory motion. Typically, the rate of this heating is orders of magnitude larger than expected from electric field fluctuations due to thermal motion of electrons in the conductors. This effect, known as anomalous heating, is not fully understood. One of the open questions is the heating rate's dependence on the ion-electrode separation. We present a direct measurement of this dependence in an ion trap of simple planar geometry. The heating rates are determined by taking images of a single $^{172}$Yb${^+}…
We investigate the limiting factors in the standard implementation of the Ca magneto-optical trap. We find that intercombination transitions from the 4s5p 1P1 state used to repump electronic population from the 3d4s 1D2 state severely reduce the trap lifetime. We explore seven alternative repumping schemes theoretically and investigate five of them experimentally. We find all five of these schemes yield a significant increase in trap lifetime and consequently improve the number of atoms and peak atom density by as much as ~20x and ~6x, respectively. One of these transitions, at 453 nm, is show…
We demonstrate a scheme for magneto-optically trapping strontium monofluoride (SrF) molecules at temperatures one order of magnitude lower and phase space densities three orders of magnitude higher than obtained previously with laser-cooled molecules. In our trap, optical dark states are destabilized by rapidly and synchronously reversing the trapping laser polarizations and the applied magnetic field gradient. The number of molecules and trap lifetime are also significantly improved from previous work by loading the trap with high laser power and then reducing the power for long-term trapping…
We have integrated magneto-optical traps (MOTs) into an atom chip by etching pyramids into a silicon wafer. These have been used to trap atoms on the chip, directly from a room temperature vapor of rubidium. This new atom trapping method provides a simple way to integrate several atom sources on the same chip. It represents a substantial advance in atom chip technology and offers new possibilities for atom chip applications such as integrated single atom or photon sources and molecules on a chip.
A few 85Rb atoms were trapped in a micron-size magneto-optical trap with a high quadrupole magnetic-field gradient and the number of atoms was precisely controlled by suppressing stochastic loading and loss events via real-time feedback on the magnetic field gradient. The measured occupation probability of single atom was as high as 99%. Atoms up to five were also trapped with high occupation probabilities. The present technique could be used to make a deterministic atom source.
We analyze the dynamics of a paramagnetic, dipolar molecule in a generic "magneto-electrostatic'' trap where both magnetic and electric fields may be present. The potential energy that governs the dynamics of the molecules is found using a reduced molecular model that incorporates the main features of the system. We discuss the shape of the trapping potentials for different field geometries, as well as the possibility of nonadiabatic transitions to untrapped states, i.e., the analog of Majorana transitions in a quadrupole magnetic atomic trap. Maximizing the lifetime of molecules in a trap is …
We use a single ion as an movable electric field sensor with accuracies on the order of a few V/m. For this, we compensate undesired static electric fields in a planar RF trap and characterize the static fields over an extended region along the trap axis. We observe a strong buildup of stray charges around the loading region on the trap resulting in an electric field of up to 1.3 kV/m at the ion position. We also find that the profile of the stray field remains constant over a time span of a few months.
We present a theoretical model describing recently observed collective effects in large magneto-optically trapped atomic ensembles. Based on a kinetic description we develop an efficient test particle method, which in addition to the single atom light pressure accounts for other relevant effects such as laser attenuation and forces due to multiply scattered light with position dependent absorption cross sections. Our calculations confirm the existence of a dynamical instability and provide deeper insights into the observed system dynamics.
Magneto-optical trapping forces for molecules are far weaker than for alkali atoms because the photon scattering rate is reduced when there are multiple ground states, and because of optical pumping into dark states. The force is further reduced when the upper state has a much smaller Zeeman splitting than the lower state. We use a rate model to estimate the strength of the trapping and damping forces in a magneto-optical trap (MOT) of CaF molecules, using either the A$^{2}Π_{1/2}$ - X$^{2}Σ^{+}$ transition or the B$^{2}Σ^{+}$ - X$^{2}Σ^{+}$ transition. We identify a new mechanism of magneto-o…
The cloud of cold atoms produced by a Magneto-Optical Trap is known to exhibit instabilities. We examine in this paper in which limits it could be possible to realize an experimental trap similar to the configurations studied theoretically, i.e. mainly traps where one direction is privileged. We study the static behavior of an anisotropic trap, where anisotropy results essentially from the use of two different laser frequencies for the arms of the trap. Such a trap has very surprising behaviors, in particular the cloud disappears for some laser frequencies, while it exists for smaller and larg…
We describe an apparatus designed to trap and cool a Yb and Cs mixture. The apparatus consists of a dual species effusive oven source, dual species Zeeman slower, magneto-optical traps in a single ultra-high vacuum science chamber, and the associated laser systems. The dual species Zeeman slower is used to load sequentially the two species into their respective traps. Its design is flexible and may be adapted for other experiments with different mixtures of atomic species. The apparatus provides excellent optical access and can apply large magnetic bias fields to the trapped atoms. The apparat…
We study optical gain in a gas of cold 39K atoms. The gain is observed during operation of a conventional magneto-optical trap without the need for additional fields. Measurements of transmission spectra from a weak probe show that the gain is due to stimulated Raman scattering between hyperfine ground states. The experimental results are reproduced by a simplified six-level model, which also helps explain why such gain is not observed in similar experiments with rubidium or cesium.
Radiative decay from the excited $^1P_1$ state to metastable $^3P_2$ and $^3P_0$ states is expected to limit attainable trapped atomic population in a magneto-optic trap of ytterbium (Yb) atoms. In experiments we have carried out with optical repumping of $^3P_{0,2}$ states to $^3P_1$, we observe enhancement of trapped atoms yield in the excited $^1P_1$ state. The individual decay rate to each metastable state is measured and the results show an excellent agreement with the theoretical values.
We report on a novel Magneto-Optical Trap (MOT) geometry involving the retroreflection of one of the six MOT beams in order to create an atom cloud close to the surface of a prism which does not have optical access along one axis. A MOT of Rb$^{85}$ with $\sim 4 \times 10^7$ atoms can be created 700 um from the surface. The MOT lies close to the minimum of an evanescent Gravito-Optical Surface Trap (GOST) allowing for transfer into the GOST with potentially minimal losses.
We have demonstrated that the ion current resulting from collisions between metastable krypton atoms in a magneto-optical trap can be used to precisely measure the trap loading rate. We measured both the ion current of the abundant isotope Kr-83 (isotopic abundance = 11%) and the single-atom counting rate of the rare isotope Kr-85 (isotopic abundance ~ 1x10^-11), and found the two quantities to be proportional at a precision level of 0.9%. This work results in a significant improvement in using the magneto-optical trap as an analytical tool for noble-gas isotope ratio measurements, and will be…
First laser cooling and trapping of the heavy alkaline earth element barium has been achieved based on the strong 6s$^2$ $^1$S$_0$ - 6s6p $^1$P$_1$ transition for the main cooling. Due to the large branching into metastable D-states several additional laser driven transitions are required to provide a closed cooling cycle. A total efficiency of $0.4(1) \cdot 10^{-2}$ for slowing a thermal atomic beam and capturing atoms into a magneto optical trap was obtained. Trapping lifetimes of more than 1.5 s were observed. This lifetime is shortened at high laser intensities by photo ionization losses. …
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 demonstrate a 1D magneto-optical trap of the polar free radical calcium monohydroxide (CaOH). A quasi-closed cycling transition is established to scatter $\sim 10^3$ photons per molecule, predominantly limited by interaction time. This enables radiative laser cooling of CaOH while compressing the molecular beam, leading to a significant increase in on-axis beam brightness and reduction in temperature from 8.4 mK to 1.4 mK.
We have developed a unique neutralizer device that uses an yttrium target surrounded by a platinum wall to magneto-optically trap radioactive atoms. In general, the radioactive nucleus produced in a nuclear reaction is extracted and transported in ion form. For the magneto-optical trap, thermal neutralization must occur on the surface of a metal with a small work function. The converter can produce a neutral atomic beam with small angular divergence that, given the recycling of atoms and ions, converts ions into neutral atoms with remarkable efficiency. We demonstrated the ion neutralization p…
Magneto-optical trapping (MOT) is a key technique on the route towards ultracold molecular ensembles. However, the realization and optimization of magneto-optical traps with their wide parameter space is particularly difficult. Here, we present a very general method for the optimization of molecular magneto-optical trap operation by means of Bayesian optimization (BO). As an example for a possible application, we consider the optimization of a calcium fluoride (CaF) MOT for maximum capture velocity. We find that both the $X^2Σ^+\,$ to $A^2Π_{1/2}\,$ and the $X^2Σ^+\,$ to $B^2Σ^+\,$ transition …
A large cloud of $^{87}$Rb atoms confined in a magneto-optical trap exhibits, in a certain regime of parameters, spatio-temporal instabilities with a dynamics resembling that of a turbulent fluid. We apply the methods of turbulence theory based on structure function analysis to extract scaling exponents which are compared to known turbulent regimes. This analysis also allows us to make a clear distinction between different instability regimes.
We report the first observation of a non-dipole transition in an ultra-cold atomic vapor. We excite the 3P-4P electric quadrupole (E2) transition in $^{23}$Na confined in a Magneto-Optical Trap(MOT), and demonstrate its application to high-resolution spectroscopy by making the first measurement of the hyperfine structure of the 4P$_{1/2}$ level and extracting the magnetic dipole constant A $=$ 30.6 $\pm$ 0.1 MHz. We use cw OODR (Optical-Optical Double Resonance) accompanied by photoinization to probe the transition.
We demonstrate the simultaneous magneto-optical trapping (MOT) of Rb and Sr and examine the characteristic loss of Rb in the MOT due to photoionization by the cooling laser for Sr. The photoionization cross section of Rb in the $5P_{3/2}$ state at 461 nm is determined to be $1.4(1)\times10^{-17}$ cm$^2$. It is important to consider this loss rate to realize a sufficiently large number of trapped Rb atoms to achieve a quantum degenerate mixture of Rb and Sr.
We demonstrate a combined magneto-optical trap and imaging system that is suitable for the investigation of cold atoms near surfaces. In particular, we are able to trap atoms close to optically scattering surfaces and to image them with an excellent signal-to-noise ratio. We also demonstrate a simple magneto-optical atom cloud launching method. We anticipate that this system will be useful for a range of experimental studies of novel atom-surface interactions and atom trap miniaturization.
We present a study on characteristics of a magneto-optical trap (MOT) as an optical lattice. Fluorescence spectra of atoms trapped in a MOT with a passively phase-stabilized beam configuration have been measured by means of the photon-counting heterodyne spectroscopy. We observe a narrow Rayleigh peak and well-resolved Raman sidebands in the fluorescence spectra which clearly show that the MOT itself behaves as a three-dimensional optical lattice. Optical-lattice-like properties of the phase-stabilized MOT such as vibrational frequencies and lineshapes of Rayleigh peak and Raman sidebands are …
We report the laser-cooling and confinement of Cd atoms in a magneto-optical trap, and characterize the loading process from the background Cd vapor. The trapping laser drives the 1S0-1P1 transition at 229 nm in this two-electron atom and also photoionizes atoms directly from the 1P1 state. This photoionization overwhelms the other loss mechanisms and allows a direct measurement of the photoionization cross section, which we measure to be 2(1)x10^(-16)cm^(2) from the 1P1 state. When combined with nearby laser-cooled and trapped Cd^(+) ions, this apparatus could facilitate studies in ultracold …
This article presents a new experiment aiming at BEC of metastable helium atoms. It describes the design of a high flux discharge source of atoms and a robust laser system using a DBR diode coupled with a high power Yb doped fiber amplifier for manipulating the beam of metastable atoms. The atoms are trapped in a small quartz cell in an extreme high vacuum. The trapping design uses an additional laser (repumper) and allows the capture of a large number of metastable helium atoms (approximately $10^9$) in a geometry favorable for loading a tight magnetostatic trap.
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 propose different experimental methods to measure the analog of the Debye length in a very large Magneto-Optical Trap, which should characterize the spatial correlations in the atomic cloud. An analytical, numerical and experimental study of the response of the atomic cloud to an external modulation potential suggests that this Debye length, if it exists, is significantly larger than what was expected.
We present a Dual Isotope Magneto Optical Trap produced using a single diode laser. We generate all the optical frequencies needed for trapping both species using a fiber intensity modulator. All the optical frequencies are amplified simultaneously using a tapered amplifier. The independent control of each frequency is on the RF side rather than on the optical side. This introduces an enormous simplification for laser cooling applications that often require an acousto-optic modulator for each laser beam. Frequency changing capabilities are limited by the modulator bandwidth (10 GHz). Traps for…
