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Investigation of cold collision in a Rb-Cs magneto-optical trap

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Investigation of cold collision in a Rb-Cs magneto-optical trap

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    Investigation of cold collision in a Rb-Cs magneto-optical

    trap

    JI Zhonghua, ZHAO Yanting

    5 (State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University,

    Taiyuan 030006)

    Abstract: We have measured the interspecies trap loss rate coefficient. The experiment was measured the rubidium atom trap loss rate coefficient as a function of Rb trapping laser intensity by loading process for rubidium atom in either presence or absence of cesium atomic cloud. The trap loss rate

    10 coefficient decreases as the Rb trapping laser intensity increases where the trap loss caused by hyperfine-state changing collision is suppressed due to the increasing Rb trap depth. The corresponding Rb trapping laser intensities are 7.8 mW/cm2, 12.1 mW/cm2 and 34.7 mW/cm2 respectively. The experimental results agree with the calculated critical intensity IC of Rb trapping laser by a simple Doppler model.

    15 Key words: atom-molecular physics; cold collision; magneto-optical trap

0 Introduction

    In this paper, we measured the rubidium atom trap loss rate coefficient as a function of Rb trapping laser intensity by loading process for rubidium atom in either presence or absence of cesium atomic cloud. The trap loss rate coefficient decreases as the Rb trapping laser intensity

    20 increases where the trap loss caused by hyperfine-state changing collision is suppressed due to the increasing Rb trap depth. The critical intensity Iof Rb trapping laser is calculated by a simple C

    Doppler model [1] to interpret the experimental results.

1 Experimental setup

    87133Our experiment uses a standard vapor-loaded Rb-Cs MOT in a stainless-steel, Kimball

    25 physics chamber attached to an extensive vacuum system. Rb and Cs sources are produced from commercial alkali-metal vapor dispensers. The quantities of Rb and Cs vapor can be controlled independently by current of Rb and Cs dispensers. So it is convenient to independently control the

    -7 -6 number of each species. The background pressure will increase from 10Pa to 10Pa when the

    atom vapors fill the vacuum chamber. A system of four tunable diode lasers generates trapping

    30 and repumping frequencies for the MOTs. We use saturated absorption spectroscopy as a reference for laser frequency lock. Two acousto-optic modulators are used to control the frequency detuning for Rb and Cs trapping lasers. All of the laser beams are expanded to about 10mm. A separate set of trapping and repumping lasers is used for each MOT. This scheme of independent optics has an advantage of permitting independent control of the placement of each

    35 MOT, allowing optimal overlap of the two clouds to be achieved, which is essential for atom collision and heteronuclear molecules. A pair of anti-Helmholtz configuration current-carrying coils provides a 15 G/cm magnetic field gradient. Three other pairs of current coils are placed in Helmholtz configuration around the vacuum chamber in order to compensate dc magnetic field at the site of the cold atomic cloud. The temperature of Rb and Cs atoms are typically around 150µK

     40 and 100µK. Three charge-coupled device (CCD) cameras are set at right angles to verify good

    Foundations: New Teacher Fund of Ministry of Education of China (200801081021);National Natural Science Foundation of China (No.60808009)

    Brief author introduction:JI Zhonghua(1983-),male,Phd student,Main research is ultrcold moleculars Correspondance author: ZHAO Yanting(1975-),male,associate professor,Main research is ultracold moleculars. E-mail: zhaoyt@sxu.edu.cn

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    spatial overlap of two atomic clouds and are used to measure each species dimension with two

    kinds of narrow band interference filters (=?5nm). Two calibrated photomultiplier tubes (PMT)

    with two filters are used to measure the numbers of both trapped atoms by detecting fluorescence.

    The Rb and Cs atomic densities are obtained from these parameters. The characteristic parameters 45 of our MOT are summarized in table 1, compared with several other related experiments. The total

    number and density of atoms listed here for each species represent values in the absence of the

    other species.

    Table 1. Summary of several related experimental parameters

     [2] [3] Parameters D. Ciamini et al M. E. Holmes This work

    Detuning from Rb resonance ?-2.1Γ-2.5Γ -1.4Γ Г,Rb87RbRbRb

    Detuning from Cs resonance ?-2.0Γ-1.3Γ-2.9Γ Г,CsCsCsCs222 10-45 mW/cm4-13 mW/cm8-37 mW/cmTotal Rb laser intensity I tot, Rb87222 40 mW/cm53 mW/cm40 mW/cmTotal Cs laser intensity I tot, Cs666 Rb atom number N2×103-9×100.8-2.6×10 Rb676 Cs atom number N5×101×101.2-6×10Cs 10-311 -310 -3 Rb atom intensity n1.5×10cm4-1×10cm1.3×10cmRb 9-311 -310 -37.2×10cm cm cm Cs atom intensity n3-4.5×101.7×10 Cs

    50

    2 Trap loss collision rate measurement

    The time evolution for the number of Rb atoms in the presence of Cs atoms is given by the

    following differential equation: dN 32 3Rb = Lnd r ? βn n d r (1)? γ N ? βRb Rb Rb Rb Rb Rb?Cs Rb Cs ? ? dt VV RbRb

    55 where Lis the Rb MOT loading rate, γis the loss rate coefficient caused by collision between Rb Rb

    Rb atoms and the hot background gas (which is mainly composed by thermal Cs and Rb atoms),

    βis the loss rate coefficient resulting from collision among the ultracold trapped Rb atoms, and Rb

    βis the loss rate coefficient due to cold collision between ultracold Rb atoms and ultracold Cs Rb-Cs

    atoms. Nis the number of trapped Rb atoms, nand nare the density profiles of cold Cs and Rb Cs Rb

    60 Rb atoms respectively, following the Gaussian distribution. The integral is taken over the whole

    volume of the trapped Rb atomic cloud. The time evolution for Cs atoms in the trap obeys an

    analogous equation, the ultracold collision measure methods below for Rb are also applicable for

    ultracold Cs collision. Strictly speaking, the atom density n is a function of time and space, usually

    -2(r/ω(t))^2written as n(r,t)=n(t)e, where nand ω are density peak and Gaussian radius respectively. 00

    65 Usually, the density distribution in MOT is either in a constant volume or constant density regime.

    In the constant volume regime, as the number of atoms increases in the trap, the density increases,

    but the atomic cloud size remains nearly constant. However, in the constant density regime, the

    radiation trapping effect becomes prominent and the density distribution is approximated to a

    constant value. Similar to previous treatments in the literature, we find that the constant density 70 approximation works well for our trapped atom number and density by measurement. In addition,

    we can use alkali-metal dispensers to control the quantities of Cs and Rb atoms, thence we can

    make the rubidium atom cloud totally immersed in the region of the cesium atomic cloud where

    cesium density could be treated as a constant value. In this case, the solution of equation (1) can

     be written as s s' 75 N = N {1 ? exp[?(γ + βn+ β n)t ]} = N {1 ? exp[?Pt ]} (2)Rb R b Rb Rb Rb Rb ? Cs Cs Rb R bSwhere Nis the number of the rubidium atoms corresponding to the steady-state solution of Rb

    equation (1) and exponential rate Prepresents the total loss rate of Rb atom immersed in Cs Rb

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     atomic cloud. . We firstly block the Cs repumping A two-step process is used in the determination of βRb-Cs

    laser, avoiding the formation of the cold Cs atomic cloud while leaving the Cs trapping laser on. In 80 S this situation, n=0 and βdrops out in equation (2). A logarithmic plot of (1-N/N) versus CsRb-Cs RbRb time determines the slope which is equal to (γ+βn), marked as P. Secondly, the Cs RbRbRbRb

     repumping laser is unblocked, allowing the complete formation of the Cs atomic cloud, and we again record the loading process for Rb atom in the presence of Cs atomic cloud. A similar

    85 processing method is used to get (γ+βn+βn), i.e. -P. An example of Rb loading in RbRbRbRb-CsCsRb the absence and the presence of Cs atomic cloud is shown in figure 1. The experimental parameters are listed in table 1. With Cs introduced, a reduction of as much as 18% is observed in

     the number of trapped Rb atoms in steady state. However, no obvious variety is observed in the The insert in figure 1 shows the Pand Pby fitting the two number of trapped Cs atoms. Rb Rb

    loading curves of trapped Rb atoms. These plots are indeed linear, which confirms that trap 90 itting the loading loading takes place within the regime of constant density as described above. In f

     curves we ignore the early times where the constant density regime has not yet been reached. 3 Experimental results and analysis Figure 2(a) shows Rb atom total trap loss rates Pand Pversus the total intensity of Rb Rb Rb

    trapping laser in the absence and the presence of Cs atoms while the Cs trapping laser intensity 95 2 keeps 40mW/cm. Background atom collisional loss rate γ, which is mainly dependent on Cs background pressure and temperature, can be considered as a constant value in the absence and the

     tom densities in the absence and the presence of Cs are presence of Cs atomic cloud. Rubidium a measured in order to derive homonuclear and heteronuclear collision loss rates, but we did not

    observe obvious difference. So the heteronuclear collision rate βcan be simply derived from 100 Rb-Cs the difference between total loss P divided by the density of cesium atom. Figure 2(b) and P RbRb βas a function of Rb trapping laser intensity. From this shows the trap loss rate coefficient Rb-Cs

     plot, we can see that the change of coefficient βcovers nearly one order of magnitude and Rb-Cs 2 2decreases in the range of 8~14mW/cmand 27~37mW/cm. Because of the weak fluorescence

    intensity at low trapping laser intensity and the trapping laser intensity limitation, collisional rate 105 2βis not measured exceed the range of 8~37mW/cm. The error bars in figure 2 correspond to Rb-Cs

    standard deviations in mean value, averaged over 5 repeated experimental measurements while

    keeping other parameters constant. Experimental errors mainly arise from the determination of the

     trapped atoms number and volume. In the influence of the added background Cs atoms, the error110 bars of P in the absence of Cs in the presence of Cs atomic cloud are bigger than the ones of P Rb Rb atomic cloud. In the low Rb trapping laser intensity, hyperfine-state changing collision mechanism has been [4] Both fine structure and radiative escape between a suggested in the Rb-Cs collision system. ground state Rb atom and an excited state Cs atom with smaller fraction only add a constant offset

    to the observed values βas the Cs trap parameters are kept constant. Let us firstly review the 115 Rb-Cs

     trap loss rate coefficient behavior at low trapping laser intensity in homonuclear Rb atom cold [5]collision. The collision rate decreases as the trapping laser intensity increases when trap depth is

     smaller than HFC exoergic energy, then reaches to a minimum value when trapping laser intensity is equal to the HFC exoergic energy. We mark this critical intensity as I. As the trapping laser C

    intensity increases, the number of excited state atom also will increase, thence the collision rate 120

    increases nearly linearly due to the domination by FSC and RE of ground-excited state collision

    where the HFC influence is relatively weak. Similar to homonuclear collisions at low trapping

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     laser intensity, HFC collision is also the main trap loss mechanism in heteronuclear case, however in heteronuclear collision is larger than the one in the trapping laser critical intensity IC

    homonuclear case, that is due to different properties between these two collisions. Firstly, the 125

    6 excited quasi-molecular states are much less attractive at long range due to the dominant C/R 6 3 behavior (compared to C/Rat the S + P asymptote of a homonuclear alkali molecule). Secondly, 3 energy released in the inelastic collision is equally distributed between the two collisional partners in a homonuclear two-body collision. However, the exoergic energy is distributed to atom A and

    atom B with the energy ?E?(m/ m+m) and ?E?(m/ m+m) in a heteronuclear case, where ?E 130 BABAAB exoergic energy, mand mare the mass of atom A and atom B respectively. represent the A B 87133 There are three types of HFC collision in Rb-Cs system: Rb (5S,F=2)+Cs (6S,F=4)?Rb (5S,F=1)+Cs (6S,F=4)+?E(3.1) 1/21/21/21/21 Rb (5S,F=2)+Cs (6S,F=4)?Rb (5S,F=2)+Cs (6S,F=3)+?E(3.2) 1/21/21/21/22 Rb (5S,F=2)+Cs (6S,F=4)?Rb (5S,F=1)+Cs (6S,F=3)+?E(3.3) 1/21/21/21/23 135 ?E(i=1,2,3) is HFC exoergic energy, which is 6.83GHz, 9.19GHz and 16.02GHz i respectively. Each Rb atom gains 0.6?E, i.e. 4.1GHz, 5.5GHz and 9.6GHz respectively in each i[1] collision process while each Cs atom gains 0.4?Eto calculate . We use a simple Doppler model i the trap depth of Rb atom as a function of total Rb trapping laser intensity (shown in Figure 3(b)).

     The three horizontal dashed lines mark the gained energies by the cold rubidium atom during

    140 processes (3.1?3.3), which are 4.1GHz, 5.5GHz and 9.6 GHz respectively. The three 22 corresponding rubidium trapping laser critical intensities are 7.8mW/cm, 12.1mW/cmand 2 34.7mW/cmrespectively. The trap loss rate coefficient decreases as the Rb trapping laser 2 2 intensity increases in the range of 8~14mW/cmand 27~37mW/cmwhere the trap loss caused by

     hyperfine-state changing collision is suppressed due to the increasing Rb trap depth. It is

    145 suggested that there should be three minimum values of βat these three trapping laser Rb-Cs 2 2intensities. The first two minimum values of βat 7.8mW/cmand 12.1mW/cm, which arises Rb-Cs

     from process (3.1) and (3.2), can not be distinguished in figure (2b) for the small energy difference 2 between them and large experimental error. The decrease of βin the range of 27~37mW/cmRb-Cs

    is considered to arise from the HFC collision in process (3.3). As the third process (3.3) release the 2 150 largest amount of energy, it cause more trap loss in the region of 27~37mW/cmthan the one in 2 the region of 8~14mW/cm. 4 Conclusion In summary, we have measured rubidium atom trap loss rate coefficient βas a function Rb-Cs of Rb trapping laser intensity under constant density approximation by loading process for

    155 rubidium atoms in the presence or the absence of the cesium atomic cloud. The change of coefficient βcovers nearly one order of magnitude and decreases in the range of Rb-Cs 2 2 8~14mW/cmand 27~37mW/cm, which are suggested to arise from Hyperfine-state changing collision. A simple Doppler model is used to calculate the Rb atom trap depth as atom trap depth

    and exoergic energy determine the behavior of collision trap loss rate coefficient. The three 22 160 corresponding calculated rubidium trapping laser critical intensities are 7.8mW/cm, 12.1mW/cm

    2 87133and 34.7mW/cmrespectively in the Rb-Cs hyperfine-state changing collision process. The

    calculated critical intensity agrees with the experimental results.

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     165 Figure 1. Typical loading curves of the Rb MOT in the absence and the presence of cold Cs atoms at the Rb trap 2Slaser intensity of 33mW/cm. Inset: Logarithmic plot [-ln(1-N/N)] vs time for the two loading curves. The Rb Rbcorresponding slopes P, Pare respectively 0.45 and 0.56 by linear fitting. RbRb

     170 Figure 2. (a) Total loss rates for trapped Rb atoms in the absence of trapped Cs atoms (P) and in the presence ofRb trapped Cs atoms (P). (b) Heteronuclear trap loss rate coefficient. The dashed vertical lines in (b) mark theRb predicted regions where the rate coefficient drops down. Both quantities are shown for a Cs trapping laser intensity 2 of 40mW/cmas a function of Rb trapping laser intensity. 175

     Figure 3. Calculated trap depth for cold Rb atom as a function of total Rb trapping laser intensity under our experimental condition (Table 1). The gained energy ?Eper atom (shown with three horizontal dashed lines) due i to hyperfine-state changing collision is 4.1GHz, 5.5GHz and 9.6GHz respectively. The corresponding Rb trapping 22 2 laser intensities are 7.8 mW/cm, 12.1 mW/cmand 34.7 mW/cmrespectively. 180

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     References [1] Shafer J P Ph.D. thesis 1999 university of Rochester (available from University of Rochester microfilms) [2] Telles G D, Garcia W, Marcassa L G, Bagnato V S, Ciampini D, Fazzi M, Müller J H, Wilkowski D and 185 Arimondo E,Trap loss in a two-species Rb-Cs magneto-optical trap[J].Phys. Rev. A,2001, 63(3): 033406 [3] M E, Tscherneck M, Quinto-Su P A and Bigelow N P,Isotopic difference in the heteronuclear loss rate in a two-species surface trap[J].Phys. Rev. A,2004, 69(6): 063408. [4] Telles G D, Garcia W, Marcassa L G, Bagnato V S, Ciampini D, Fazzi M, Muller J H, Wilkowski D and Arimondo E.Trap loss in a two-species Rb-Cs magneto-optical trap[J].Phys. Rev. A,2001,63(3): 033406 190 [5] Wallace C D, Dinneen T P, Tan K N, Grove T T and Gould P L.Isotopic difference in trap loss collisions of

    laser cooled rubidium atoms[J].Phys. Rev. Lett., 1992, 69(6):897900

     Rb-Cs 磁光阱中的超冷碰撞 195

     姬中华,赵延霆 ?山西大学量子光学与光量子器件国家重点实验室,太原,030006 摘要!文章报告了在 激光冷却和俘获中超冷 Rb Cs 不同原子间的碰撞损耗率。实验通过 测量在有和无 Cs 子时 Rb 冷原子团的装载特性测量了 Rb-Cs 碰撞系数与 Rb 俘获激光光强 的关系。同时观察 了超精细态转换的碰撞,相对应的 Rb 俘获激光强度分别为 7.8 mW/cm2, 200 12.1 mW/cm2 34.7 mW/cm2。实验结果与 Doppler 模型获得的结果有很好的一致。

     关键词!原子分子物理,冷碰撞,磁光阱

     中图分类号!O561.3

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