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arXiv:1012.2156 · Physical Review A

Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM 10 cavity mode

Pengfei Zhang, Yanqiang Guo, Zhuoheng Li, Yuchi Zhang, Yanfeng Zhang, Jinjin Du, Gang Li, Junmin Wang, Tiancai Zhang

Published Mar 28, 2011• 23 citations
arXivHTMLPDF

Abstract

We demonstrate the trajectory measurement of the single neutral atoms deterministically using a high-finesse optical microcavity. The single atom strongly couples to the high-order transverse vacuum TEM${}_{10}$ mode, instead of the usual TEM${}_{00}$ mode, and the parameters of the system are $({g}_{10},\ensuremath{\kappa},\ensuremath{\gamma})=2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}(20.5,2.6,2.6) \text{MHz}$. The atoms simply fall down freely from the magneto-optical trap into the cavity modes, and the trajectories of the single atoms are linear. The transmission spectra of atoms passing through the TEM${}_{10}$ mode are detected by single-photon counting modules and are well fitted. Thanks to the tilted cavity transverse TEM${}_{10}$ mode, which is inclined to the vertical direction $~$${45}^{\ifmmode^\circ\else\textdegree\fi{}}$, it helps us to eliminate the degenerate trajectory of the single atom falling through the cavity and to obtain a unique atom trajectory. An atom position with a high precision of $0.1 \ensuremath{\mu}\text{m}$ in the off-axis direction (axis $y$) is obtained, and a spatial resolution of $5.6 \ensuremath{\mu}\text{m}$ is achieved in a time interval of $10 \ensuremath{\mu}\text{s}$ along the vertical direction (axis $x$). The average velocity of the atoms is also measured from the atom transits, which determines independently the temperature of the atoms in a magneto-optical trap, $186\ifmmode\pm\else\textpm\fi{}19 \ensuremath{\mu}\text{K}$.

DOI
10.1103/physreva.83.031804

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We demonstrate the trajectory measurement of the single neutral atoms deterministically using a high-finesse optical microcavity. The single atom strongly couples to the high-order transverse vacuum TEM10{}_{10}10​ mode, instead of the usual TEM00{}_{00}00​ mode, and the parameters of the system are (g10,\ensuremathκ,\ensuremathγ)=2\ensuremathπ\ifmmode×\else\texttimes\fi(20.5,2.6,2.6)MHz({g}_{10},\ensuremath{\kappa},\ensuremath{\gamma})=2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}(20.5,2.6,2.6) \text{MHz}(g10​,\ensuremathκ,\ensuremathγ)=2\ensuremathπ\ifmmode×\else\texttimes\fi(20.5,2.6,2.6)MHz. The atoms simply fall down freely from the magneto-optical trap into the cavity modes, and the trajectories of the single atoms are linear. The transmission spectra of atoms passing through the TEM10{}_{10}10​ mode are detected by single-photon counting modules and are well fitted. Thanks to the tilted cavity transverse TEM10{}_{10}10​ mode, which is inclined to the vertical direction ~$${45}^{\ifmmode^\circ\else\textdegree\fi{}}, it helps us to eliminate the degenerate trajectory of the single atom falling through the cavity and to obtain a unique atom trajectory. An atom position with a high precision of 0.1\ensuremathμm0.1 \ensuremath{\mu}\text{m}0.1\ensuremathμm in the off-axis direction (axis yyy) is obtained, and a spatial resolution of 5.6\ensuremathμm5.6 \ensuremath{\mu}\text{m}5.6\ensuremathμm is achieved in a time interval of 10\ensuremathμs10 \ensuremath{\mu}\text{s}10\ensuremathμs along the vertical direction (axis xxx). The average velocity of the atoms is also measured from the atom transits, which determines independently the temperature of the atoms in a magneto-optical trap, 186\ifmmode±\else\textpm\fi19\ensuremathμK186\ifmmode\pm\else\textpm\fi{}19 \ensuremath{\mu}\text{K}186\ifmmode±\else\textpm\fi19\ensuremathμK.
We present an alternative route to track the motion of a single atom traversing a high-finesse optical cavity by means of the coherence statistics of photon antibunching. Here the single atom strongly couples to the high-order transverse Laguerre-Gaussian (LG) mode (e.g., LG01{\text{LG}}_{01}LG01​) of optical cavity, instead of the high-order transverse Hermite-Gaussian (HG) mode, which is beneficial to the single-atom trajectory measurement utilizing such a photon antibunching effect. With this aim, we characterize the position-dependent quantum correlations of the transmitted light in such a cavity quantum electrodynamics (QED) system subject to various kinds of the LG modes, finding that the photon antibunching effect is closely related to the position of the atom in the transverse plane and therefore the degree of the antibunching carries the information about the position of the atom within the cavity. The numerical results of the second-order correlation function agree well with the analytical calculations. Thanks to the tilted transverse LG01{\text{LG}}_{01}LG01​ mode of the cavity, which is inclined to the vertical direction by an angle of $\ensuremath{\sim}{15}^{\ensuremath{\circ}}$, the LG-mode cavity QED architecture helps us to eliminate the degenerate trajectory of the single atom falling through the cavity and to obtain a unique atomic trajectory. In a $10\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{s}$-long time interval as an example, our in-depth analysis displays that the atomic position with the spatial resolution of $\ensuremath{\sim}4.0\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$ in the vertical direction (axis xxx) can be achieved. The present study is useful for well understanding and researching both the robust generation of single-photon source and the precision measurement of single-atom trajectory.
We have experimentally demonstrated the strong coupling between single atoms and the higher-order Hermite-Gaussian transverse modes in a high-finesse optical microcavity. Compared to the usual low-order symmetric transverse modes, multiple lobes and the asymmetric spatial pattern of the titled modes provide more information about the motion of single atoms in the cavity. The motional information can be extracted from the measured transmission spectra, which includes the velocities and the positions of the atoms in vertical and off-axis directions. The scheme has great potential in time-resolved atom-cavity microscopy and in tracking the three-dimensional single atom trajectory in real time.
Strong coupling of single cesium atoms with a high-finesse optical micro-cavity (the finesse of our Fabry-Perot-type micro-cavity is F = 3.3 x 105 and the cavity length is lc = 86 μm) has been realized for the both cases of TEM00 and TEM10 cavity modes in our experiments. The typical parameters are (g00, κ, Υ) = 2π x (23.9, 2.6, 2.6) MHz and (g10, κ, Υ) = 2π x (20.5, 2.6, 2.6) MHz for these two cases, respectively. Obviously our system reaches the strong coupling regime. The first application is to adopt strong coupling of free-fall individual atoms with the TEM00 cavity mode for determining the effective temperature of laser-cooled atoms prepared in a magneto-optical trap located just above the micro-cavity. The second application is to employ strong coupling of free-fall individual atoms with the tilted TEM10 cavity mode, in stead of TEM00 mode, for more precisely tracking the trajectories of atoms passing through the cavity mode.
Summary form only given. The strong atom-photon coupling generated inside high-finesse optical micro cavity lets us detect a single atom trajectory in real time. Such a strong coupling is a candidate for trapping a single atom with a single photon. Dynamics of trapped atoms can be observed in situ and in real time by detecting intensity change on the transmission of a blue-shifted laser beam. We cooled down and trapped rubidium atoms by using conventional cell magneto optical trap (MOT) and launched them into the micro optical cavity which locates 35 mm above the MOT. By using this signal as trigger and changing the laser frequency, it is, in principle, possible to trap the atom in the cavity.
We experimentally demonstrate real-time detection of individual cesium atoms by using a high-finesse optical micro-cavity in a strong coupling regime. A cloud of cesium atoms is trapped in a magneto-optical trap positioned at 5 mm above the micro-cavity center. The atoms fall down freely in gravitation after shutting off the magneto-optical trap and pass through the cavity. The cavity transmission is strongly affected by the atoms in the cavity, which enables the micro-cavity to sense the atoms individually. We detect the single atom transits either in the resonance or various detunings. The single atom vacuum-Rabi splitting is directly measured to be Ω = 2π × 23.9 MHz. The average duration of atom-cavity coupling of about 110 μs is obtained according to the probability distribution of the atom transits.
A coupled quantum system composed of cavity field and atoms is one of the main research contents of cavity quantum electrodynamics. It can be used to realize single atom manipulation and measurement, and has important significance for studying the interaction between light and the atom, preparing quantum states and quantum entanglement. Current research work mainly focuses on two aspects. One is to achieve the atom trapping via the feedback control of the trapping laser intensity. The other is to measure the single atomic motion in a Fabry-Perot cavity by using Hermite-Gaussian transverse modes. The detection of the atomic trajectories has been realized via the observation of transmission spectra of the strong coupling system composed of cold atoms and Hermite-Gaussian transverse modes in a Fabry-Perot cavity. In order to observe the atomic motion trajectories in the cavity, we theoretically study the transmission spectrum of a strong coupling system composed of cold atoms and Laguerre-Gaussian transverse modes in a Fabry-Perot cavity in this paper. We calculate the relationship between the coupling coefficient and the mode number of Laguerre-Gaussian transverse modes. The result shows that with the increase of Laguerre-Gaussian transverse mode number, the maximum coupling coefficient between the atoms and cavity fields is almost unchanged, so the contrast of the detected spectrum is nearly independent of the mode number. Analysis shows that Laguerre-Gaussian transverse mode provides more abundant information about atomic motion trajectory than Hermite-Gaussian transverse mode. The field distribution of Laguerre-Gaussian transverse mode is ring-shaped. Owing to the ring shape, the atoms dropped at different positions experience different electric field intensities, and the detected transmission spectra are changed. Therefore, we can implement the high precision distinguishment of the atomic trajectories by observing the features of the transmission spectra such as the number of the transmission peaks and their positions. Furthermore, a small deviation of the atomic motion trajectories, on the edges of the rings of the electric field, may induce great change in transmission spectrum, and then we can very accurately detect the atomic motion around these positions.