Light-shift Effect Research Articles

Impact of the frequency error of direct digital synthesizers on the evaluation of two-photon light shift in atom gravimeters

One major systematic error for free-fall atom gravimeters is the effect of two-photon light shift (LS2). In the process of evaluating LS2, the results can be affected by the residual frequency error of direct digital synthesizers due to necessary experimental parameter changes. In this paper, the impact of the coupling effect between the frequency error and LS2 has been investigated and analyzed, along with the related physical mechanisms. The parameters of the frequency error sequence, such as the time step of δt and the time delay of Δt, significantly affect the bias and uncertainty of LS2. Notably, when these parameters are significantly altered or misaligned, the impact can reach several tens of µGal. Conversely, when they remain within the optimal ranges, the impact can be minimal. Specifically, when δt is less than or equal to 10 µs, the impact on the LS2 bias is less than 0.3 µGal, with the contribution to the total uncertainty of the gravity value being approximately 0.1 µGal. Furthermore, after correcting the phase shift introduced by the frequency error, the evaluation results have a similar improvement effect on the whole. Compared to the LS2 theoretical value, the residual is generally on the order of µGal. Through the comprehensive analysis and optimization, as well as related experiments, this cross-effect is managed and decoupled, leading to accurate LS2 evaluation results. This improvement ensures a better accuracy in the obtained absolute gravity values. The analysis methods discussed can provide an effective strategy for enhancing the performance of atom gravimeters.

Pulsed-CPT Cs-Ne microcell atomic clock with frequency stability below 2 × 10-12 at 105 s.

We report on the mid-term stability progress of a table-top coherent population trapping (CPT) microcell atomic clock, previously limited by light-shift effects and variations of the cell's inner atmosphere. The light-shift contribution is now mitigated through the use of a pulsed symmetric auto-balanced Ramsey (SABR) interrogation technique, combined with setup temperature, laser power, and microwave power stabilization. In addition, Ne buffer gas pressure variations in the cell are now greatly reduced through the use of a micro-fabricated cell built with low permeation alumino-silicate glass (ASG) windows. Combining these approaches, the clock Allan deviation is measured to be 1.4 × 10-12 at 105 s. This stability level at one day is competitive with the best current microwave microcell-based atomic clocks.

An optically pumped atomic clock based on a continuous slow cesium beam

Herein, we report the scheme of an optically pumped atomic clock based on a cold cesium atomic beam source. We propose the laser system and physical mechanism of this atomic clock, wherein the atomic beam travels in an upper parabolic trajectory, thereby eliminating the light shift effect. In the experiments, when the length of the free evolution region was 167 mm, the line width of the Ramsey fringe was 37 Hz. When the expected signal-to-noise ratio of the Ramsey fringe that can be achieved is 36,000, the expected short-term frequency stability is about 3.6 × 10–14/√τ, which is significantly higher than that of a conventional optically pumped cesium clock of similar volume.

Effect of light and dark shift on primary follicles diameter during post natal development in ovary of rabbit (Oryctolagus cuniculus)

Effect of light and dark shift on primary follicles diameter during post natal development in ovary of rabbit (Oryctolagus cuniculus)

μ POP Clock: A Microcell Atomic Clock Based on a Double-Resonance Ramsey Scheme

We demonstrate and study a microcell microwave atomic clock based on optical-microwave double resonance (DR) interrogation operated in a pulsed Ramsey scheme, called the \ensuremath{\mu}POP clock, based on a microfabricated Rb vapor cell and a micro-loop-gap microwave resonator. For the mm-scale dimensions of this cell, the population and coherence relaxation rates of the Rb clock transition are on the order of 4--5 kHz, which puts constraints on the useful Ramsey times and overall pulse sequence in view of optimized clock performance. Our proof-of-principle demonstration of the \ensuremath{\mu}POP clock shows that the pulsed DR approach is nevertheless feasible and results in a short-term clock stability of 1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ \ensuremath{\tau}${}^{\ensuremath{-}1/2}$ and reaching the \ensuremath{\le}2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}12}$ level at timescales of 1000 s to one day. The short-term instability budget established for the \ensuremath{\mu}POP clock shows that the main limitation to the short-term stability arises from the detection noise. Thanks to the pulsed Ramsey scheme, light-shift effects are strongly reduced in the \ensuremath{\mu}POP clock, which opens perspectives for further improvements of long-term clock stability, in view of future generations of miniature vapor-cell clocks with enhanced performances based on the DR scheme.

Light-Shift-Free and Dead-Zone-Free Atomic-Orientation-Based Scalar Magnetometry Using a Single Amplitude-Modulated Beam

The detection dead zones and heading errors induced by light shifts are two important problems in optically pumped scalar magnetometry. We introduce an atomic-orientation-based single-beam magnetometry scheme to simultaneously solve these problems, using a polarization-reversing and path-bending Herriott cavity. Here, a reflection mirror is inserted into the cavity to bend the optical paths in the middle and divide them into two separated orthogonal regions to avoid the detection dead zone. Moreover, half-wave plates are added in the center of each optical region, so that the light polarization is flipped each time it passes the wave plates and the light-shift effects are spatially averaged out. This operation is demonstrated to eliminate the unnoticed heading errors induced by ac light shifts. The methods developed in this paper are robust to use and easy to apply other atomic devices.

Light-shift mitigation in a microcell-based atomic clock with symmetric auto-balanced Ramsey spectroscopy

The mid-term fractional frequency stability of miniaturized atomic clocks can be limited by light-shift effects. In this Letter, we demonstrate the implementation of a symmetric auto-balanced Ramsey (SABR) interrogation sequence in a microcell-based atomic clock based on coherent population trapping. Using this advanced protocol, the sensitivity of the clock frequency to laser power, microwave power, and laser frequency variations is reduced, at least by one order of magnitude, in comparison with continuous-wave or Ramsey interrogation schemes. Light-shift mitigation obtained with the SABR sequence benefits greatly to the clock Allan deviation for integration times between 102 and 105 s. These results demonstrate that such interrogation techniques are of interest to enhance the timekeeping performance of chip-scale atomic clocks.

Chirping removes recoil effect on fluorescence signal of optical pumping by synchronous frequency modulation

Recoil effect is one of the limiting factors of signal amplitude in many spectroscopic applications due to creating light shift or AC Stark effect. Doppler shift of the Recoil velocity of the pumped atoms reduces their absorption efficiency. Synchronous Frequency Modulation or chirping of the pump laser enhances optical pumping and amplitude of the fluorescence signal. Results of this paper demonstrate significant enhancement of the fluorescence signal and the symmetry of the signal.

Exploring the Use of Ramsey-CPT Spectroscopy for a Microcell-Based Atomic Clock.

We investigate the application of Ramsey spectroscopy for the development of a microcell atomic clock based on coherent population trapping (CPT). The dependence of the central Ramsey-CPT fringe properties on key experimental parameters is first studied for optimization of the clock's short-term frequency stability. The sensitivity of the clock frequency to light-shift effects is then studied. In comparison with the continuous-wave (CW) regime case, the sensitivity of the clock frequency to laser power variations is reduced by a factor up to 14 and 40.3 for dark times of 150 and [Formula: see text], respectively, at the expense of intensity 3.75 times higher for short-term stability optimization. The dependence of the clock frequency on the microwave power is also reduced in the Ramsey case. We demonstrate that the Ramsey-CPT interrogation improves the clock Allan deviation for averaging times higher than 100 s. With a dark time of [Formula: see text], a clock fractional frequency stability of 3.8 ×10-12 at 104 s is obtained, in comparison with the level of 8×10-11 obtained in the standard CW case, in similar environmental conditions. These results demonstrate that Ramsey-based interrogation protocols might be an attractive approach for the development of chip-scale atomic clocks (CSACs) with enhanced mid- and long-term stability.

A new method for high-bandwidth servo control of the power ratio between two Raman beams for cold atom interferometer.

Light shift produced by the AC Stark effect is one of the major factors limiting the accuracy and long-term stability of a cold atom interferometer. The first order light shift can be canceled by fixing the power ratio of the Raman beams at a specified value. We report here a new method to stabilize the power ratio of the two Raman lasers with ∼100 kHz locking bandwidth, suppressing the effect of the first order light shift. We first mixed the two Raman lasers (at different optical frequencies) with a reference beam and then used two Schottky diode detectors to extract the corresponding beat note signals for each beam, which are much easier to be manipulated and processed as they are in the microwave band. The stability of the power ratio is improved by three orders of magnitude from 5.84 × 10-3 to 3.51 × 10-6 at 1 s averaging time and reaches 1.59 × 10-7 at 10 000 s integrating time when the servo loop is engaged. This method can be used in other precise quantum measurement based on the stimulated Raman transition and can be applied to compact inertial sensors.

Dependence on sensitivity patterns of bias fields for vector measurements using optically pumped vapor magnetometers

The optical light shift effect is an all-optical technique to create magnetic bias fields to determine the vector components of the magnetic field using a scalar optically pumped magnetometer. We show that the measurement of the induced bias fields is affected by the response pattern of the scalar magnetometer. The sensitivity of the magnetometer affects the minimum total field resolution as well as the angular resolution of the vector measurement. Three configurations of multiple-laser, optically pumped cesium vapor vector magnetometers are characterized for their spatial sensitivity patterns. Each configuration has a unique response level as a function of the relative magnetic field orientation. Thus, the formulations used for angular determination are dependent on the magnetometer configuration, and the angular resolution of the vector measurement is dependent on the relative angle between the magnetic field and the optical probe beam. The spatial dependence of the light shift signals is measured, and the equations describing their responses are presented for each configuration. Equations for determining the field angles from the bias field responses are derived.

The effect of tensor light shift on residual magnetic field compensation in a nuclear spin co-magnetometer

In a nuclear spin co-magnetometer, it was found that the probe light parameters have a significant impact on the transverse residual magnetic field compensation. In this paper, we demonstrated that this effect is caused by the tensor light shifts of the linearly polarized probe light. This effect can be suppressed at a certain probe light polarization. We obtained this probe light polarization experimentally and reduced the impact of probe power on magnetic field compensation by 35 times. The impact of probe light frequency is also suppressed. Furthermore, the influence of the pump power, the static magnetic field, and the cell temperature on this optimized polarization was investigated. The tensor light shift can be suppressed at about 17° polarization under different conditions in our system. Moreover, the actual residual magnetic field in the magnetic shields can be obtained, which is useful for the magnetic field design of the co-magnetometer, and this method can also be extended to other atomic devices to suppress the tensor light shift.

Optical frequency dependence of the light shift effect for vector magnetometry with cesium.

Atomic vapor magnetometers have demonstrated very high sensitivity to the magnitude of the magnetic field. Vector field measurements are possible using bias fields applied to the vapor. For remote operation, the bias field can be generated using the optical light shift (LS) effect created with an optical beam delivered through optical fiber. Here, it is shown that the optical frequency of the LS effect for an optically pumped vapor vector magnetometer causes an angular error in the measured field orientation when it is tuned near the absorption resonances, countering the benefit of higher response. This angle-shifting effect is dependent on the LS beam power. The LS response, normalized to the LS power, is higher for lower powers due to a saturation effect but also shows a dependence on the LS optical frequency. We show that it is necessary to carefully choose the LS optical frequency and power to maximize the LS effect while avoiding potential angular error.

Long-Term Stability Analysis Toward

Long-term frequency instabilities in vapor-cell clocks mainly arise from fluctuations of the experimental and environmental parameters that are converted to clock frequency fluctuations via various physical processes. Here, we discuss the frequency sensitivities and the resulting stability limitations at one-day timescale for a rubidium vapor-cell clock based on a compact magnetron-type cavity operated in air (no vacuum environment). Under ambient laboratory conditions, the external atmospheric pressure fluctuations may dominantly limit the clock stability via the barometric effect. We establish a complete long-term instability budget for our clock operated under stable pressure conditions. Where possible, the fluctuations of experimental parameters are measured via the atomic response. The measured clock instability of at one day is limited by the intensity light-shift effect, which could further be reduced by active stabilization of the laser intensity or stronger optical pumping. The analyses reported here show the way toward simple, compact, and low-power vapor-cell atomic clocks with excellent long-term stabilities ≤ 10-14 at one day when operated in ambient laboratory conditions.

Mitigation of Temperature-Induced Light-Shift Effects in Miniaturized Atomic Clocks.

The demonstration of miniature atomic clocks (MACs) based on coherent population trapping (CPT) with improved mid- and long-term frequency stability benefits from the implementation of additional stabilization loops to reduce temperature-induced light-shift effects. In this article, we report and highlight the individual and combined benefits of such servo loops on the frequency stability of a CPT-based MAC. The first loop stabilizes the actual temperature of the vertical-cavity surface-emitting laser (VCSEL) chip using a compensation method in which the reading of external temperature variations is derived from the atomic vapor output signal. The second loop maintains the total microwave power absorbed by the laser to a value that maximizes the optical absorption and significantly reduces the laser power dependence of the clock frequency. Experimental tests are performed onto a miniaturized CPT-clock physics package using a chip-VCSEL tuned on the Cs D1 line ( λ = 895 nm). The VCSEL temperature compensation technique improves, by a factor of 4, the Allan deviation of the clock at 104 s. The simultaneous operation of both servo loops improves, by a factor of 7, the clock fractional frequency stability at 104 s. The clock demonstrates a fractional frequency stability of 7.5×10 -11 at 1 s and better than 2×10-11 at 1 day.

Lamplight Stabilization for GPS Rb Atomic Clocks via RF-Power Control.

Recent evidence indicates that the signal-in-space user-range-error (SIS-URE) for GPS is strongly influenced by the satellite atomic clock's rubidium (Rb) lamplight intensity jumps. Following a proposal by Bloom and Bell, we have implemented RF-power control of an RF-discharge lamp of the type employed in Rb atomic frequency standards (RAFS). Since Rb lamplight intensity jumps are mapped onto the clock's output frequency via the light-shift effect, stabilization of the Rb light emitted by the lamp has the potential to significantly improve the RAFS' long-term frequency stability, and hence the GPS SIS-URE. Here, we not only demonstrate that RF-power control of the discharge lamp is possible, but also that by employing such control the fluctuations in Rb lamplight intensity can be reduced by orders of magnitude, providing a pathway for significant improvement in global navigation satellite systems.

Demonstration of the mass-producible feature of a Cs vapor microcell technology for miniature atomic clocks

We report on the characterization of Cs vapor microcells based on pill dispensers and fabricated in a MEMS foundry according to a process compatible with mass-production. More than three quarters of cells from 6-inch wafers are successfully filled with Cs vapor. Various cells of a given wafer have been characterized using coherent population trapping (CPT) spectroscopy, demonstrating similar buffer gas (Ne) pressure with a standard deviation of about 2.5% and CPT resonances with similar linewidth and contrast properties. In addition, frequency drifts mainly attributed to cell inner atmosphere variations have been investigated onto several cells over 250–500 h measurements. The corresponding contribution at 1 day averaging time to a clock fractional frequency stability is estimated to be about 10−11 or lower. In a last section, the fractional frequency stability of a clock prototype using one fabricated Cs-Ne microcell is measured to be 2.5 × 10−11 τ−1/2 up to 200 s averaging time and better than 2 × 10−11 at 105 s. The clock frequency stability is mainly limited at short-term by the frequency-to-amplitude (FM-AM) noise conversion process and the laser amplitude (AM) noise. The mid-term stability is mainly affected by temperature-induced light shift effects. These performances tend to demonstrate that this vapor cell technology, compatible with mass-production, is suitable for miniature quantum clocks or sensors.

Mitigation of Lamplight-Induced Frequency Jumps in Space Rubidium Clocks.

Rubidium clocks are currently the most common atomic clocks for space applications, playing a fundamental role in global navigation satellite systems. Their stability is affected by the light-shift effect, turning lamplight variations into frequency variations, e.g., lamplight intensity jumps into frequency jumps. In our previous work, analyzing data from GPS rubidium clocks, we uncovered the impact of the lamp on the in-orbit clock's performance. Specifically, the rubidium clock's random walk of frequency seems to be driven by a compound Poisson process associated with lamplight intensity jumps. Most important, large lamplight-induced frequency jumps could affect the validity of the navigation message. Here, we propose and test on simulated data, a software compensation scheme for lamplight-induced rubidium clock frequency jumps. We show how this could be implemented as an automated onboard process, and the potential improvements this scheme might yield in timekeeping and navigation performance. In particular, we demonstrate the possibility to correct large lamplight-induced frequency jumps in a time smaller than the interval between consecutive navigation message upgrades, thus improving the quality of the navigation message.

Characterization of Frequency-Doubled 1.5- m Lasers for High-Performance Rb Clocks.

We report on the characterization of two fiber-coupled 1.5- diode lasers, frequency-doubled and stabilized to Rubidium (Rb) atomic resonances at 780 nm. Such laser systems are of interest in view of their implementation in Rb vapor-cell atomic clocks, as an alternative to lasers emitting directly at 780 nm. The spectral properties and the instabilities of the frequency-doubled lasers are evaluated against a state-of-the-art compact Rb-stabilized laser system based on a distributed-feedback laser diode emitting at 780 nm. All three lasers are frequency stabilized using essentially identical Doppler-free spectroscopy schemes. The long-term optical power fluctuations at 780 nm are measured, simultaneously with the frequency instability measurements done by three beat notes established between the three lasers. One of the frequency-doubled laser systems shows at 780 nm excellent spectral properties. Its relative intensity noise <10-12 Hz-1 is one order of magnitude lower than the reference 780-nm laser, and the frequency noise <106 Hz2/Hz is limited by the laser current source. Its optical frequency instability is at s, limited by the reference laser, and better than at all timescales up to one day. We also evaluate the impact of the laser spectral properties and instabilities on the Rb atomic clock performance, in particular taking into account the light-shift effect. Optical power instabilities on long-term timescales, largely originating from the frequency-doubling stage, are identified as a limitation in view of high-performance Rb atomic clocks.

Hybrid optical pumping of K and Rb atoms in a paraffin coated vapor cell.

Dynamic hybrid optical pumping effects with a radio-frequency field-driven nonlinear magneto-optical rotation scheme are studied in a dual-species paraffin coated vapor cell. By pumping K atoms and probing Rb87 atoms, we achieve an intrinsic magnetic resonance linewidth of 3Hz, and the observed resonance is immune to power broadening and light-shift effects. Such an operation scheme shows favorable prospects for atomic magnetometry applications.