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We demonstrate a direct, fluorescence-free measurement of the oscillation frequency of cold atoms in an optical dipole trap based on a high-finesse optical cavity strongly coupled to atoms. The parametric heating spectra of the trapped atoms are obtained by recording the transmitted photons from the cavity with the trap depth is modulated by different frequency. Moreover, in our method the oscillation can be observed directly in the time scale. Being compared to the conventional fluorescence-dependent method, our approach avoids uncertainties associated with the illuminating light and auxiliary imaging optics. This method has the potential application of determining the motion of atoms with stored quantum bits or degenerate gases without destroying them.
Optical dipole traps (ODT) have become practical tools in experimental realization of qubit manipulation between single photons and single atoms, which can be used to store and process the quantum information locally for quantum computation.[1] In a far-off-resonance optical trap (FORT), where the heating due to spontaneous scattering forces is strongly suppressed,[2] one can not only realize a long-time trapping of atoms but also manipulate the atomic internal state[3] with long coherent time,[4] and characterize the quantum state of a single atom[5] that is treated as a well-prepared quantum qubit. In particular, by using a tightly focused FORT, degenerate Raman sideband cooling of trapped atoms[6] and transfer of ultra-cold atoms[7–10] over macroscopic distances have been carried out. During the transfer, specific discrete transport durations are exhibited that are largely dependent on oscillation frequency of atomic ensembles in an ODT with no excitation of the vibration and no losses after transport.[10] To this end, researchers attempted to determine the trapping frequency in the experiment and clarified the dynamics of cold atoms in an ODT. The vibration mode of cold atoms inside ODT or lattices has been investigated[11–14] with an auxiliary probe beam applied to measure the fluorescence. However, this approach must induce some extra uncertainties, such as the spatial profile of the probe beam, and the intensity and the pointing fluctuations of the probe beam.[15] In addition, in some situations where a finite interspace exists, such as a cavity quantum electrodynamics (QED) system, imaging optics with a large numerical aperture to collect the fluorescence usually make the system complex.
A strongly coupled cavity QED system, even in the intermediate coupling regime, is very sensitive to atoms on the single-particle level. Such a system enables not only a succession of experiments of quantum information processing[16–18] and a nonlinear process[19] with single atoms, but also atomic sensing.[15,20–23] In a cavity QED system, the vacuum Rabi splitting is approximately proportional to the square root of the effective average number (
Figure
The atomic sample is prepared in 6S1/2F = 4 before the transportation. However, a second state preparing process after the transportation is necessary to pump atoms which decayed into the 6S1/2F = 3 state during the transporting back to 6S1/2F = 4 state. From the transmitting spectra, we can get the effective number of atoms which are strongly coupled to the cavity. Figure
The ODT can be approximately considered a harmonic potential. The oscillation frequencies of trapped atoms in both radial and axial directions are given[26]
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In our experiment the amplitude modulation is realized by an acousto-optic modulator (AOM) and the cavity is tuned and resonant to the transition of the trapped atoms, i.e., the ac Stark shift due to the trap is considered. The observations of both radial and axial excitation are presented in Fig.
Similarly, we obtain parametric heating spectra for axial atomic oscillation, as shown in Fig.
The measured oscillation frequencies 2.76 ± 0.01 kHz and 33.0 ± 0.8 Hz are a little smaller than the theoretical expectations 3.4 kHz and 40.8 Hz. The discrepancy mainly results from the following facts. The presumption of a harmonic potential trap is not perfectly reasonable in our case, because the presumption of a harmonic potential trap is valid only under the condition when the atom temperature much lower than the trap depth. In our experiment the temperature of the atom is
Benefiting from the fluorescence-free process, the atom number and state do not change in principle when interacting with cavity. The coupling strength g is position-dependent due to the cavity mode distribution, so the system provides a good way to measure the motion of the atom. The respond time of the cavity probe beam to the coupled atom is much faster than the conventional fluorescence-dependent detection method. The cavity QED system can also be used to continuous observe the atom movement in the cavity mode. Thus, the oscillation of the atom in the ODT in our experiment can be directly measured. The shape of cold atoms in our running wave ODT is known as a “cigar-shaped” cloud. A near-resonant intense pulse laser (x direction in Fig.
Utilizing the proposed fluorescence-free detection method on the single atom level, we provided a method to determine the trap frequency of the cold atoms in an optical trap. The method avoids uncertainties in the usual measurement in which the fluorescence light is scattered by the atoms. Compared to these methods, the cavity-enhanced approach is extremely sensitive to atoms. One does not have to repeat the measurement many times, especially if the number of atoms in the ODT is small, even on the single-particle level. When the confinement is weak, or the trap frequency is low, such as several hertz, the traditional approach becomes ineffective owing to the tremendous loss of atoms during a long-playing AM procedure.[13] However, for a lower frequency in the axial direction, the advantage of the proposed system makes it easy to obtain the oscillation signal, as shown in Fig.
In conclusion, we have presented a new cavity-enhanced method to measure the oscillation frequency of cold atoms in an ODT based on a strongly coupled cavity QED system. By modulating the intensity of the ODT beam and recording the transmission spectra of the cavity we get the oscillation frequencies of the trapped atoms with 2.76 ± 0.01 kHz and 33.0 ± 0.8 Hz, which correspond to the oscillation frequencies in the radial and axial directions of the ODT beam, respectively. We also provide a direct observation method for the motion of cold atoms in an ODT. By splitting the atom cloud, we get a transmission spectrum with an oscillation frequency of 73.5 ± 0.6 Hz that corresponds to twice the trap frequency in the axial direction. Although it is difficult to eliminate the fluctuation of the average number of atoms for each transport, only the widths of the spectra are affected, while the frequencies of both resonant and parametric excitation are closely intensity dependent, and, in principle, the drift of which can be eliminated by using a servo technique.[37] Being compared to the conventional fluorescence detection, our approach avoids uncertainties associated with the illuminating light and auxiliary imaging optics. At the same time, this method enables us, simply and quickly, to obtain the most promising parameters for optimally transporting cold atoms and trapping atoms in cavity mode,[38] to determine the temperature of a single atom,[39] and to control the motion of cold atoms.
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