A method is proposed for producing atom gratings having period $λ/4$ and $λ/8$ using optical fields having wavelength $λ$. Counterpropagating optical fields drive Raman transitions between ground state sublevels. The Raman fields can be described by an effective two photon field having wave vector 2 k, where k is the propagation vector of one of the fields. By combining this Raman field with {\em another} Raman field having propagation vector -2 k, one, in effect, creates a standing wave Raman field \label{91}%which whose ``intensity'' varies as $\cos (4 k\cdot r).$ When atoms move through this standing wave field, atom gratings having period $λ/4$ are produced, with the added possibility that the total ground state population in a given ground state manifold can have $λ/8$ periodicity. The conditions required to produce such gratings are derived. Moreover, it is shown that even higher order gratings having periodicity smaller than $λ/8$ can be produced using a multicolor field geometry involving three (two-photon) Raman fields. Although most calculations are carried out in the Raman-Nath approximation, the use of Raman fields to create reduced period optical lattices is also discussed.
We measured the magnetic resonance of rubidium atoms passing through periodic magnetic fields generated by two types of multilayered transmission magnetic grating. One of the gratings reported here was assembled by stacking four layers of magnetic films so that the direction of magnetization alternated at each level. The other grating was assembled so that the magnetization at each level was aligned. For both types of grating, the experimental results were in good agreement with our calculations. We studied the feasibility of extending the frequency band of the grating and narrowing its resona…
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 demonstrate a two-dimensional grating magneto-optical trap (2D GMOT) with a single input cooling laser beam and a planar diffraction grating using $^{87}$Rb. This configuration increases experimental access when compared with a traditional 2D MOT. As described in the paper, the output flux is several hundred million rubidium atoms/s at a mean velocity of $16.5(9)$ m/s and a velocity distribution of $4(3)$ m/s standard deviation. We use the atomic beam from the 2D GMOT to demonstrate loading of a three dimensional grating MOT (3D GMOT) with $2.46(7)\times 10^8$ atoms. Methods to improve outp…
We demonstrate for the first time the two-color cooling and trapping of alkaline-earth atoms in a grating magneto-optical trap (gMOT). The trap is formed by a single incident laser beam together with four secondary beams that are generated via diffraction from a nanostructured wafer. A grating structure for a gMOT operating with strontium atoms is optimized and fabricated. We trap $10^6$ $^{88}$Sr atoms on the $^1$S$_0$ $\rightarrow$ $^1$P$_1$ transition at $461\;\mathrm{nm}$ and transfer $25\;\%$ of these atoms to the second cooling stage on the narrower $^1$S$_0$ $\rightarrow$ $^3$P$_1$ inte…
We describe progress toward a precise measurement of the recoil energy of an atom measured using a perturbative grating-echo atom interferometer (AI) that involves three standing-wave (sw) pulses. With this technique, a perturbing sw pulse is used to shift the phase of excited momentum states---producing a modulation in the contrast of the interference pattern. The signal exhibits narrow fringes that revive periodically at twice the two-photon recoil frequency, $2ω_q$, as a function of the onset time of the pulse. Experiments are performed using samples of laser-cooled rubidium atoms with temp…
We report on the observation of emerging beam resonances, well known as Rayleigh-Wood anomalies and threshold resonances in photon and electron diffraction, respectively, in an atom-optical diffraction experiment. Diffraction of He atom beams reflected from a blazed ruled grating at grazing incidence has been investigated. The total reflectivity of the grating as well as the intensities of the diffracted beams reveal anomalies at the Rayleigh angles of incidence, i.e., when another diffracted beam merges parallel to the grating surface. The observed anomalies are discussed in terms of the clas…
We have studied the optical properties of gratings micro-fabricated into semiconductor wafers, which can be used for simplifying cold-atom experiments. The study entailed characterisation of diffraction efficiency as a function of coating, periodicity, duty cycle and geometry using over 100 distinct gratings. The critical parameters of experimental use, such as diffraction angle and wavelength are also discussed, with an outlook to achieving optimal ultracold experimental conditions.
Strontium ${}^{1}S_{0}\!\rightarrow\!{}^{1}P_{1}$ transition frequency measurements assisted by a photonic grating chip
Korea Research Institute of Standards and Science（韩国计量科学研究院）；Graduate School of Quantum Science and Technology, Korea Advanced Institute of Science and Technology（韩国科学技术院量子科学与技术研究生院）；Center for Next-Generation Platform Development, National NanoFab Center (NNFC)（国家纳米制造中心下一代平台开发中心）
We perform Raman spectroscopy of optically trapped non interacting \Rb atoms, and observe revivals of the atomic coherence at integer multiples of the trap period. The effect of coherence control methods such as echo and dynamical decoupling is investigated experimentally, analytically and numerically, along with the effect of the anharmonicity of the trapping potential. The latter is shown to be responsible for incompleteness of the revivals. Coherent Raman control of trapped atoms can be useful in the context of free-oscillation atom intefrerometry and spatial multi-mode quantum memory.
We consider photo ionization of an atom which, due to passing through a diffraction grating, is prepared in a multi-site state possessing a periodic space structure with alternating maxima and minima. It has been found that this process qualitatively differs from photo ionization of a 'normal' atom. In particular, the spectra of emitted electrons and recoil ions in this process display clear one- and two-particle interference effects. Moreover, there are also striking differences between the momentum distributions of these particles, which no longer mirror each other. The origin of all these f…
We present here an analysis of the influence of the frequency dependence of the Raman laser light shifts on the phase of a Raman-type atom gravimeter. Frequency chirps are applied to the Raman lasers in order to compensate gravity and ensure the resonance of the Raman pulses during the interferometer. We show that the change in the Raman light shift when this chirp is applied only to one of the two Raman lasers is enough to bias the gravity measurement by a fraction of $μ$Gal ($1~μ$Gal~=~$10^{-8}$~m/s$^2$). We also show that this effect is not compensated when averaging over the two directions…
We have laser cooled 3$\times10^6$ $^{87}$Rb atoms to 3$μ$K in a micro-fabricated grating magneto-optical trap (GMOT), enabling future mass-deployment in highly accurate compact quantum sensors. We magnetically trap the atoms, and use Larmor spin precession for magnetic sensing in the vicinity of the atomic sample. Finally, we demonstrate an array of magneto-optical traps with a single laser beam, which will be utilised for future cold atom gradiometry.
In 1995, Chapman et al. (1995 Phys. Rev. Lett. 75 2783) showed experimentally that the interference contrast in a three-grating atom interferometer does not vanish under the presence of scattering events with photons, as required by the complementarity principle. In this work we provide an analytical study of this experiment, determining the evolution of the atom wave function along the three-grating Mach-Zehnder interferometer under the assumption that the atom is hit by a photon after passing through the first grating. The consideration of a transverse wave function in momentum representatio…
Atom Optics for Multidimensional Raman Interferometry
A-Knows Lab, State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University（清华大学精密仪器系精密测量技术与仪器全国重点实验室A-Knows实验室）；The Key Laboratory of Quantum Precision Measurement of Zhejiang Province, School of Physcis and Optical Engineering, Zhejiang University of Technology（浙江工业大学物理与光学工程学院浙江省量子精密测量重点实验室）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）
We present an efficient method for subrecoil cooling of neutral atoms by applying Raman cooling in 2D to a four-level tripod-system. The atoms can be cooled simultaneously in two directions using only three laser beams. We describe the cooling process with a simple model showing that the momentum distribution can be rapidly narrowed to velocity spread down to $0.1v_\text{rec}$, corresponding to effective temperature equal to $0.01T_\text{rec}$. This method opens new possibilities for cooling of neutral atoms.
We investigate the effect of coherent population trapping (CPT) in an atom inter-ferometer gravimeter based on the use of stimulated Raman transitions. We find that CPT leads to significant phase shifts, of order of a few mrad, which may compromise the accuracy of inertial measurements. We show that this effect is rejected by the k-reversal technique, which consists in averaging inertial measurements performed with two opposite orientations of the Raman wavevector k, provided that internal states at the input of the interferometer are kept identical for both configurations.
We investigated the Raman pulse duration effect in a gravity gradiometer with two atom interferometers. Since the two atom clouds in the gradiometer experience different gravitational fields, it is hard to compensate the Doppler shifts of the two clouds simultaneously by chirping the frequency of a common Raman laser, which leads to an appreciable phase shift. When applied to an experiment measuring the Newtonian gravitational constant G, the effect contributes to a systematic offset as large as -49ppm in Nature 510, 518 (2014). Thus an underestimated value of G measured by atom interferometer…
IIn this paper we demonstrate a new scheme for Raman transitions which realize a symmetric momentum-space splitting of $4 \hbar k$, deflecting the atomic wave-packets into the same internal state. Combining the advantages of Raman and Bragg diffraction, we achieve a three pulse state labelled interferometer, intrinsically insensitive to the main systematics and applicable to all kind of atomic sources. This splitting scheme can be extended to $4N \hbar k$ momentum transfer by a multipulse sequence and is implemented on a $8 \hbar k$ interferometer. We demonstrate the area enhancement by measur…
A frequency doubled I/Q modulator based optical single-sideband (OSSB) laser system is demonstrated for atomic physics research, specifically for atom interferometry where the presence of additional sidebands causes parasitic transitions. The performance of the OSSB technique and the spectrum after second harmonic generation are measured and analyzed. The additional sidebands are removed with better than 20 dB suppression, and the influence of parasitic transitions upon stimulated Raman transitions at varying spatial positions is shown to be removed beneath experimental noise. This technique w…
We show theoretically that it is possible to form a cold molecular ion from a pair of colliding atom and ion at low energy by photoassociative two-photon Raman processes. We explore the possibility of stimulated Raman adiabatic passage (STIRAP) from the continuum of ion-atom scattering states to an ionic molecular state. We provide physical conditions under which coherent population transfer is possible in stimulated Raman photoassociation. Our results are important for experimental realization of PA in ion-atom cold collisions.
Atom interferometers in optical cavities benefit from strong laser intensities and high-quality wavefronts. The laser frequency pairs that are needed for driving Raman transitions (often generated by phase modulating a monochromatic beam) form multiple standing waves in the cavity, resulting in a periodic spatial variation of the properties of the atom-light interaction along the cavity axis. Here, we model this spatial dependence and calculate two-photon Rabi frequencies and ac Stark shifts. We compare the model to measurements performed with varying cavity and pulse parameters such as cavity…
We report improved precision measurements of the Van der Waals potential strength ($C_3$) for Na atoms and a silicon-nitride (SiN$_x$) surface. We studied diffraction from nano-fabricated gratings with a particular "magic" open-fraction that allows us to determine $C_3$ without the need for separate measurements of the width of the grating openings. Therefore, finding the magic open-fraction improves the precision of $C_3$ measurements. The same effect is demonstrated for a grating with an arbitrary open-fraction by rotating it to a particular "magic" angle, yielding $C_3=3.42\pm 0.19 \textrm{…
We derive an exact and analytical form for the cold-atom momentum distribution after a large number of one-dimensional (1D) Raman cooling cycles has been applied. Our result shows that one can select pulse profiles and lengths rather freely in order to obtain efficient cooling. Our approach takes into account optical pumping (resonant excitation followed by spontaneous emission) as an intergral part of the process, and it is noted that it does not affect the final momentum distribution. Thus subrecoil cooling is possible in general, and not just for carefully selected combinations of pulse for…
In this article we analyze the Casimir-Polder interaction of atoms with a solid grating and an additional repulsive interaction between the atoms and the grating in the presence of an external laser source. The combined potential landscape above the solid body is probed locally by diffraction of Bose-Einstein condensates. Measured diffraction efficiencies reveal information about the shape of the Casimir-Polder interaction and allow us to discern between models based on a pairwise-summation (Hamaker) approach and Lifshitz theory.
We demonstrate a compact magneto-optical trap (MOT) of alkaline-earth atoms using a nanofabricated diffraction grating chip. A single input laser beam, resonant with the broad $^1$S$_0\,\rightarrow \,^1$P$_1$ transition of strontium, forms the MOT in combination with three diffracted beams from the grating chip and a magnetic field produced by permanent magnets. A differential pumping tube limits the effect of the heated, effusive source on the background pressure in the trapping region. The system has a total volume of around 2.4 L. With our setup, we have trapped up to $5 \times 10^6$ $^{88}…
We demonstrate a compact (0.25 L) system for laser cooling and trapping atoms from a heated dispenser source. Our system uses a nanofabricated diffraction grating to generate a magneto-optical trap (MOT) using a single input laser beam. An aperture in the grating allows atoms from the dispenser to be loaded from behind the chip, increasing the interaction distance of atoms with the cooling light. To take full advantage of this increased distance, we extend the magnetic field gradient of the MOT to create a Zeeman slower. The MOT traps approximately $10^6$ $^7$Li atoms emitted from an effusive …
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 …
The laser spectroscopy with a narrow linewidth and high signal to noise ratio (S/N) is very important in the precise measurement of optical frequencies. Here, we present a novel high-resolution backward resonance Bragg-scattering (RBS) spectroscopy from a population difference grating (PDG). The PDG is formed by a standing-wave (SW) pump field in thermal 87Rb vapor, which periodically modulates the space population distribution of two levels in the 87Rb D1 line. A probe beam, having the identical frequency and the orthogonal polarization with the SW pump field, is Bragg-scattered by the PDG. S…
Interlaced Spin Grating is a scheme for the preparation of spectro-spatial periodic absorption gratings in a inhomogeneously broadened absorption profile. It relies on the optical pumping of atoms in a nearby long-lived ground state sublevel. The scheme takes advantage of the sublevel proximity to build large contrast gratings with unlimited bandwidth and preserved average optical depth. It is particularly suited to Tm-doped crystals in the context of classical and quantum signal processing. In this paper, we study the optical pumping dynamics at play in an Interlaced Spin Grating and describe…
The extreme miniaturization of a cold-atom interferometer accelerometer requires the development of novel technologies and architectures for the interferometer subsystems. Here we describe several component technologies and a laser system architecture to enable a path to such miniaturization. We developed a custom, compact titanium vacuum package containing a microfabricated grating chip for a tetrahedral grating magneto-optical trap (GMOT) using a single cooling beam. In addition, we designed a multi-channel photonic-integrated-circuit-compatible laser system implemented with a single seed la…
Low-phase-noise and pure-spectrum Raman light is vital for high-precision atom interferometry by two-photon Raman transition. A preferred and prevalent solution for Raman light generation is electro-optic phase modulation. However, phase modulation inherently brings in double sidebands, resulting in residual sideband effects of multiple laser pairs beside Raman light in atom interferometry. Based on a well-designed rectangular fiber Bragg grating and an electro-optic modulator, optical single-sideband modulation has been realized at 1560 nm with a stable suppression ratio better than -25 dB de…
A method for diffracting the weak probe beam into unidirectional and higher-order directions is proposed via a novel Rydberg electromagnetically induced grating, providing a new way for the implementations of quantum devices with cold Rydberg atoms. The proposed scheme utilizes a suitable and position-dependent adjustment to the two-photon detuning besides the modulation of the standing-wave coupling field, bringing a in-phase modulation which can change the parity of the dispersion. We observe that when the modulation amplitude is appropriate, a perfect unidirectional diffraction grating can …
