Elimination of degenerate trajectory of single atom strongly coupled to the tilted cavity TEM10 mode
Elimination of degenerate trajectory of single atom strongly coupled to the tilted cavity TEM10 mode
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DOI：
10.1103/physreva.83.031804
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发表时间：
2010-12
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影响因子：
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通讯作者：
Pengfei Zhang;Yanqiang Guo;Zhuoheng Li;Yanfeng Zhang;Jinjin Du;Gang Li;Junmin Wang;Tian-Cai Zhang-T
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文献类型：
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作者：
Pengfei Zhang;Yanqiang Guo;Zhuoheng Li;Yanfeng Zhang;Jinjin Du;Gang Li;Junmin Wang;Tian-Cai Zhang-T
我们利用高精细光学微腔实现了中性单原子轨道的确定性测量。单原子强耦合到高阶横真空TEM 10模，而不是通常的TEM 00模，系统的参数为10（，，）/2（20.5，2.6，2.6）g MHz单模.原子只是从磁光阱中自由下落到腔模中，单个原子的轨迹是线性的。用单光子计数器测量了原子通过TEM 10模的透射谱，并进行了拟合。由于倾斜腔横TEM 10模与垂直方向倾斜约45度，首次消除了单原子在腔中的简并轨迹，得到了唯一的原子轨迹。在离轴方向（y轴）上获得了0.1 μ m的高精度原子位置，并且在沿垂直方向（x轴）沿着10 μ s的时间内获得了5.6 μ m的空间分辨率。原子的平均速度也是从原子跃迁测量的，它决定了磁光阱中原子的温度，186 K ± 19 K。PACS编号：42.50.Pq，37.10.Jk操纵中性单原子，被称为量子光学和原子物理学的基本系统，自过去二十年以来，无论是在自由空间[1 - 6]还是在腔[7 - 10]中，都得到了广泛的研究。从早期的热原子束和随机原子束到冷原子束和单个原子的确定性控制，单原子现在是演示量子逻辑门[11]和量子寄存器[4，12]的良好系统。为了从单个原子中获得信息，在大多数实验中使用两种主要方法。一种是使用特殊设计的光收集系统和高效光学探测器直接检测原子的荧光;另一种是检测来自高精细光学腔的透射光，该腔通常与原子强耦合[13]。腔量子电动力学（CQED）系统已被用于检测单个原子以及原子轨迹[14]。单原子和腔之间的大耦合提供了通过腔的传输测量原子轨迹的能力[15，16]。在早期的实验中，原子束已经被用于CQED实验[17 - 19]，并且原子渡越的持续时间是如此之短，以至于不能在真实的时间内完成单个原子位置及其轨迹的检测。冷原子技术的发展和对单原子的操纵[20，21]为CQED实验提供了有效的工具。无论是原子自由下落还是发射到腔中，原子在腔模中的渡越时间都超过100 μ s [15，16]，并且可以测量单个原子的轨迹。2000年，Hood等人将单个原子困在微腔中数毫秒，并从腔传输中重建了垂直于腔轴的平面内的2D原子轨迹，他们在10 μ s的时间间隔内获得了2 μ m的空间分辨率[14]。但对于上述所有实验，原子都耦合到基本的厄米-高斯TEM 00模。虽然原子通过腔模中心时，原子与腔模TEM 00的耦合比其它模强，但由于TEM 00模的空间对称性导致原子轨迹的四重简并性，原子沿腔轴的位移或波腹与波腹之间的位移无法确定.高阶横模可以打破空间对称性，降低原子轨道的简并度。2003年，Puppe等人证明了高精细光学腔的高阶横模中的单原子轨道[22]。根据腔的透射谱得到了原子的运动轨迹。而TEM 01和TEM 10模的空间方向图几乎是水平取向的，原子轨道仍然是简并的，但从四重简并到双重简并。在这封信中，使用倾斜的空间横TEM 10模式，它打破了对称性，并允许完全消除原子轨道的简并性。我们利用强耦合的原子-腔系统来跟踪原子的运动轨迹，唯一地确定单个原子的运动轨迹。在沿垂直方向（x轴）沿着10 μ s的时间内实现了5.6 μ m的空间分辨率，而沿水平方向（y轴）沿着的原子位置可以以0.1 μ m的精度获得。借助高精细度腔的更高阶模和更小的模腰，基于原子腔显微镜（ACM）系统[14]的所谓原子万花筒[23，24]能够获得具有高空间分辨率的单个原子的轨迹。如图1所示，CQED系统包含一个腔和一个原子耦合到电磁场的单模。原子和单模场之间的相互作用由能量的振荡交换（拉比振荡）描述，其特征在于g。真实的实验系统是一个开放系统，必须同时考虑腔衰变率κ和原子衰变率γ。在强耦合区，TEM_（00）模的最佳耦合常数g_0远大于κ和γ。小激发态布居的弱场极限下的腔传输为[25]
We demonstrate the trajectory measurement of the single neutral atoms deterministically using a high-finesse optical micro-cavity. Single atom strongly couples to the high-order transverse vacuum TEM10 mode, instead of the usual TEM00 mode, and the parameter of the system is 10 ( , , ) / 2 (20.5,2.6,2.6) g MHz . The atoms simply fall down freely from the magneto-optic trap into the cavity modes and the trajectories of the single atoms are linear. The transmission spectrums of atoms passing through the TEM10 mode are detected by a single photon counting modules and well fitted. Thanks to the tilted cavity transverse TEM10 mode, which is inclined to the vertical direction about 45 degrees and it helps us, for the first time, to eliminate the degenerate trajectory of the single atom falling through the cavity and get the unique atom trajectory. Atom position with high precision of 0.1m in the off-axis direction (axis y) is obtained, and the spatial resolution of 5.6m is achieved in time of 10s along the vertical direction (axis x). The average velocity of the atoms is also measured from the atom transits, which determines the temperature of the atoms in magneto-optic trap, 186K±19K. PACS number(s): 42.50.Pq, 37.10.Jk Manipulation of neutral single atoms, known as the basic system of quantum optics and atomic physics, has been extensively studied since the last two decades, either in free space [1-6] or inside a cavity [7-10]. From the early hot and stochastic atom beam to the cold and deterministic control of individual atoms, single atom is now a good system to demonstrate quantum logic gate [11] and quantum register [4, 12]. In order to get information from a single atom two predominant methods are used in most experiments. One is to detect directly the fluorescence of the atoms using a special designed light collection system and high-efficiency optical detector; another is to detect the transmitted light from a high-finesse optical cavity, which is usually strongly coupled to the atoms [13]. The cavity quantum electrodynamics (CQED) system has been used to detect single atoms as well as the atom trajectory [14]. Large coupling between single atom and cavity provides the capability of measuring the atomic trajectory through the transmission of the cavity [15, 16]. In the earlier experiments, atom beam has been used in CQED experiments [17-19] and the duration of the atom transits was so short that the detection of individual atom positions and its trajectory could not be accomplished in real time. The development of the cold atoms technology and the manipulation of single atoms [20, 21] provide the effective tools for the CQED experiments. Either through the atom free falling down or launching up to the cavity, the transit time of atoms in the cavity mode lasted more than 100μs [15, 16] and the trajectories of single atom can be measured. In 2000, Hood et al trapped single atom inside a micro-cavity for milliseconds and the 2D atom trajectories in the plane perpendicular to the cavity axis were reconstructed from the cavity transmissions and they obtained 2m of the spatial resolution in a 10s of time interval [14]. But for all these experiments mentioned above, the atom was coupled to the fundamental Hermite-Gaussian TEM00 mode. Although the coupling between atom and cavity TEM00 mode is stronger than all the other modes when the atom passes in the centre of cavity mode, the displacements of the atom along the cavity axis, or between a node and antinode, can not be determined since the spatial symmetry of the TEM00 mode causes the quadruple degeneracy of the atom trajectories in principle. Higher order transverse modes may break the spatial symmetry and reduce the degeneracy of the atom trajectories. In 2003, Puppe et al. demonstrated the single-atom trajectories in high-order transverse modes of a high-finesse optical cavity [22]. The atom trajectories were obtained according to the transmission spectrum of the cavity. However, the spatial patterns of TEM01 and TEM10 modes were oriented nearly horizontally and the atom trajectories were still degenerate, but from quadruple degeneracy to duplicate degeneracy. In this letter, a tilted spatial transverse TEM10 mode is used, which breaks the symmetry and allows eliminating the degeneracy of the atom trajectories completely. We use the strong coupled atom-cavity system to track the atomic path and determine the ballistic trajectory of a single atom uniquely. The spatial resolution of 5.6m is achieved in the time of 10s along the vertical direction (axis x), while the atom position along the horizontal direction (axis y) can be obtained with precision of 0.1m. With the help of even higher order modes and smaller mode waist of the high-finesse cavity, it is capable to obtain the trajectory of the single atom with high spatial resolution by the so-called atomic kaleidoscope [23, 24] based on the atom-cavity microscope (ACM) system [14]. The CQED system contains a cavity and an atom couples to a single mode of the electromagnetic field as shown in Fig. 1. The interaction between the atom and the single-mode field is described by the oscillatory exchange of energy (Rabi Oscillation), characterized by g. Real experimental system is an open system and both of cavity decay rate κ and atom decay rate γ must be taken in account. In the strong coupling regimes the optimum coupling constant g0 in the TEM00 mode is much lager than κ and γ. The cavity transmission in the weak-field limit of small excited state population is [25]