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Chinese Journal of Optics and Applied Optics

Calculation of AC Stark shift of 5S_(1/2) and 5P_(3/2) states of Rb atoms in optical dipole trap

Junmin Wang

Published Jan 1, 2010• 1 citation
OpenAlex

Abstract

Based on the two-level and multi-level models,the AC Stark shift of the 5S1/2 and 5P3/2 states of 87Rb atoms in an Optical Dipole Trap(ODT) formed by a strongly-focused single Gaussian laser beam is analyzed and calculated.For performance of molasses cooling of 87Rb atoms in the Far-off-resonance Trap(FORT) by 852 nm Gaussian laser beam,the AC Stark shift of 5S1/2F=2-5P3/2F′=3 cycling transition for cooling is also calculated,results show that the frequency shift has an important impact on the molasses cooling process.Furthermore,the AC Stark shift of 87Rb 5S1/2|F=2,mF=±2〉 and 5P3/2|F′=3,mF=±3〉 states versus the wavelength of the ODT laser is analyzed,which shows that there is no magic wavelength for 5S1/2-5P3/2 transition of 87Rb atoms in the red-off-resonance condition.

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Magic-wavelength optical dipole trap of cesium and rubidium atoms

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Optical dipole traps (ODT) with far-off-resonance laser are important tools in more and more present cold-atom experiments, which allow confinement of laser-cooled atoms with a long storage time. Particularly, the magic wavelength ODT can cancel the position-dependent spatially inhomogeneous light shift of desired atomic transition, which is introduced by the ODT laser beam. Now it plays an important role in the state-insensitive quantum engineering and the atomic optical clock. To verify the magic wavelength or the magic wavelength combination for D2 line transition of cesium (Cs) and rubidium (Rb) atoms, we calculated and analyzed the light shift of the 133Cs 6S1/2 - 6P3/2 transition for a monochromatic ODT, and also the 87Rb 5S1/2 - 5P3/2 transition for a dichromatic ODT with a laser frequency ratio of 2:1. Also a dichromatic magic-wavelength ODT laser system for 87Rb atoms is proposed and experimentally realized by employing the quasi-phase-matched frequency doubling technique with telecom laser and fiber amplifier.

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Magic wavelength optical-dipole trap (ODT) allows confinement of neutral atoms and cancellation of the position-dependent spatially inhomogeneous differential light shift for a desired atomic transition. The light shift of the 87 Rb 5P3/2 state can be expediently tailored to be equal to that of the 87 Rb 5S1/2 state by employing dicromatic (λ1 + λ2 (here λ2 = 2λ1 ∼ 1.5 μm)) linearly polarized ODT lasers. In our calculation, two sets of state-insensitive dichromatic (784.3 + 1568.6 nm and 806.4 + 1612.8 nm) are obtained for the 87 Rb 5S1/2 (F = 2) – 5P3/2 (F � = 3) transition. Further, 784.3 + 1568.6 nm dicromatic laser system with a moderate output power has been realized experimentally by marrying efficient second-harmonic generation using a PPMgO:LN bulk crystal with a fibre-amplified 1.5 μm telecom laser.

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Laser cooling and loading of Rb into a large period, quasi-electrostatic, optical lattice

Paul F. Griffin

This thesis reports on the design and construction of, and results from, an optical-dipole trapping apparatus developed to confine ultracold rubidium atoms in a conservative, large period, optical-dipole trap. An ultra-high vacuum system was designed and constructed to create a very low- background pressure. A new technique of viewport construction was developed, allowing for the fabrication of economical, high-quality windows for transmission of mid-infra-red laser radiation. The construction of a magneto-optical trap (MOT) and an optical molasses, and the subsequent characterisation, are discussed. A theory for the ac-Stark shift of atoms in a far-detuned laser field was developed. The nature of the scalar and tensorial light-shifts of the ground and first excited states of alkali atoms - the 5s(^2)S1/2 and 5p(^2)P3/2 states of Rb - has been examined. The effect of the differential light-shifts between these states on the operation of efficient laser cooling is discussed. A quasi-electrostatic dipole trap (QUEST) was formed from 50 W of CO2 laser power (٢ = 10.6 μm), focussed to <100 μm. The transfer of ultra-cold atoms from the MOT and optical molasses to the QUEST have been examined. Single beam and standing wave geometries of the QUEST have been implemented, with lifetimes of many seconds. The theory for the ac-Stark effect due to a single laser field has been further developed to consider orthogonally polarised fields with independent wavelengths. The use of an auxiliary laser field, a Nd:YAG laser at λ = 1.064 μm, to enhance the number and density of atoms loaded into the QUEST has been proposed and realised.

•Jan 1, 2005•9 citations
Based on the two-level and multi-level models,the AC Stark shift of the 5S1/2 and 5P3/2 states of 87Rb atoms in an Optical Dipole Trap(ODT) formed by a strongly-focused single Gaussian laser beam is analyzed and calculated.For performance of molasses cooling of 87Rb atoms in the Far-off-resonance Trap(FORT) by 852 nm Gaussian laser beam,the AC Stark shift of 5S1/2F=2-5P3/2F′=3 cycling transition for cooling is also calculated,results show that the frequency shift has an important impact on the molasses cooling process.Furthermore,the AC Stark shift of 87Rb 5S1/2|F=2,mF=±2〉 and 5P3/2|F′=3,mF=±3〉 states versus the wavelength of the ODT laser is analyzed,which shows that there is no magic wavelength for 5S1/2-5P3/2 transition of 87Rb atoms in the red-off-resonance condition.
Optical dipole traps (ODT) with far-off-resonance laser are important tools in more and more present cold-atom experiments, which allow confinement of laser-cooled atoms with a long storage time. Particularly, the magic wavelength ODT can cancel the position-dependent spatially inhomogeneous light shift of desired atomic transition, which is introduced by the ODT laser beam. Now it plays an important role in the state-insensitive quantum engineering and the atomic optical clock. To verify the magic wavelength or the magic wavelength combination for D2 line transition of cesium (Cs) and rubidium (Rb) atoms, we calculated and analyzed the light shift of the 133Cs 6S1/2 - 6P3/2 transition for a monochromatic ODT, and also the 87Rb 5S1/2 - 5P3/2 transition for a dichromatic ODT with a laser frequency ratio of 2:1. Also a dichromatic magic-wavelength ODT laser system for 87Rb atoms is proposed and experimentally realized by employing the quasi-phase-matched frequency doubling technique with telecom laser and fiber amplifier.
Laser cooling and trapping of neutral atoms is of great significance for studying the physical and chemical properties of atoms. To further realize the spatial localization of atoms, optical dipole trap (ODT) was proposed to manipulate individual atoms, ions or molecules and has become an increasingly important technique in the field of cold atomic physics and quantum optics. To eliminate the differential light shift of transitions between atomic states, ODT can be turned off during excitation/radiation. However, it will shorten the trap lifetime of the atom and reduce the repetition rate of the single photon. The AC stark shift can be eliminated experimentally by constructing blue-detuned dark ODT, but the micron-level dark ODT usually requires more complex experimental equipment and is not easy to operate. Therefore, magic-wavelength ODT was constructed to realize that the transition frequency of photons between atomic states is the same as in free space. When the trapping laser makes the differential light shift of the transition between the two atomic states zero, the laser wavelength is called the magic wavelength. The magic-wavelength ODT can eliminate the differential light shift of the transition between atoms, improve the repetition rate of the experimental sequence and weaken the atomic decoherence. In recent years, it has become a powerful tool for manipulating cold atoms, especially for coherently manipulating the atomic inner states. In the present work, with the theory of multi-level model, we calculate the dynamic electric polarizability of the 6S1/2 ground state and the 6P3/2 excited state connecting the D2 line of cesium atom in a range of 800–1000 nm, and obtain the magic wavelength of the optical trapping laser to trap the ground state and the excited state. Since the polarizability of atomic states with angular momentum greater than 0.5 is very sensitive to the polarization angle, the polarization-angle-dependent magic wavelength and the corresponding magic polarizability are analyzed by taking the linearly-polarized trapping laser for example. The magic polarization angle is 54.7° and the magic wavelength at this angle are 886.4315 and 934.0641 nm, respectively. The robustness of the magic conditions and the feasibility of the experimental operation are further analyzed.
Abstract In this work, the effect of AC-Stark shift of atomic energy levels in an optical dipole trap (ODT) on in situ absorption imaging of the trapped atoms has been investigated. The Stark shift of various energy levels of 87 Rb atoms relevant for trapping in the optical dipole trap (ODT) has been calculated. The spatially varying AC-Stark shift of energy levels due to ODT beam results in position dependent absorption cross-section of the atom at the absorption probe laser wavelength, which significantly modifies the measured optical density (OD) of the trapped atom cloud during the in situ absorption imaging. We have estimated the number of atoms trapped in the ODT taking AC-Stark shift into account. The estimated numbers are found to be higher at higher ODT beam power, making a qualitative agreement with larger trap depth at higher ODT beam power. This work can be particularly useful in estimating the in situ loss rate of atoms from the trap during the evaporative cooling of the trapped atom cloud.
For the trapped pre-cooled atoms in an optical dipole trap (ODT), the magic-wavelength ODT can eliminate the differential light shift of the transition between two atomic states, so that the transition frequency between the two states is the same as that of atoms in the free space, which is of great significance for improving the experimental repetition rate and reducing the atomic decoherence in the fields of cold atom physics, quantum optics, and precision measurement. Here we calculate the dynamic polarizabilities of cesium 6S ground state and 7P excited state by using the multi-level model for the ODT with laser wavelength from 1200 to 2000 nm. The magic wavelengths of ODT are obtained for the linearly and circularly polarized laser beams at the intersection of dynamic polarizabilities of two atomic states. Furthermore, we analyze the robustness of the magic trapping conditions and the feasibility of the experimental operation near the telecom C-band wavelength.
Magic wavelength optical-dipole trap (ODT) allows confinement of neutral atoms and cancellation of the position-dependent spatially inhomogeneous differential light shift for a desired atomic transition. The light shift of the 87 Rb 5P3/2 state can be expediently tailored to be equal to that of the 87 Rb 5S1/2 state by employing dicromatic (λ1 + λ2 (here λ2 = 2λ1 ∼ 1.5 μm)) linearly polarized ODT lasers. In our calculation, two sets of state-insensitive dichromatic (784.3 + 1568.6 nm and 806.4 + 1612.8 nm) are obtained for the 87 Rb 5S1/2 (F = 2) – 5P3/2 (F � = 3) transition. Further, 784.3 + 1568.6 nm dicromatic laser system with a moderate output power has been realized experimentally by marrying efficient second-harmonic generation using a PPMgO:LN bulk crystal with a fibre-amplified 1.5 μm telecom laser.
This thesis reports on the design and construction of, and results from, an optical-dipole trapping apparatus developed to confine ultracold rubidium atoms in a conservative, large period, optical-dipole trap. An ultra-high vacuum system was designed and constructed to create a very low- background pressure. A new technique of viewport construction was developed, allowing for the fabrication of economical, high-quality windows for transmission of mid-infra-red laser radiation. The construction of a magneto-optical trap (MOT) and an optical molasses, and the subsequent characterisation, are discussed. A theory for the ac-Stark shift of atoms in a far-detuned laser field was developed. The nature of the scalar and tensorial light-shifts of the ground and first excited states of alkali atoms - the 5s(^2)S1/2 and 5p(^2)P3/2 states of Rb - has been examined. The effect of the differential light-shifts between these states on the operation of efficient laser cooling is discussed. A quasi-electrostatic dipole trap (QUEST) was formed from 50 W of CO2 laser power (٢ = 10.6 μm), focussed to <100 μm. The transfer of ultra-cold atoms from the MOT and optical molasses to the QUEST have been examined. Single beam and standing wave geometries of the QUEST have been implemented, with lifetimes of many seconds. The theory for the ac-Stark effect due to a single laser field has been further developed to consider orthogonally polarised fields with independent wavelengths. The use of an auxiliary laser field, a Nd:YAG laser at λ = 1.064 μm, to enhance the number and density of atoms loaded into the QUEST has been proposed and realised.