Generalised Ramsey methods for suppressing light shifts in atomic clocks based on the coherent population trapping effect

We examine experimentally and theoretically the Ramsey effects on the coherent population trapping (CPT) resonance in a paraffin-coated Rb vapor cell. The observed CPT spectrum in the Hanle configuration of the 5S1/2(F = 2)−5P1/2(F′ = 1) transition of 87Rb atoms consists of a narrow structure with a spectral width of 0.10 mG due to the wall-induced Ramsey effect and a broad structure with a spectral width of 23 mG due to the transit effect. Considering the velocity distribution of atoms and the number of wall-atom collisions, we numerically calculated the transmittance of the laser beam as a function of the longitudinal magnetic field. The experimental results of the CPT Ramsey interference were in good agreement with the theoretical results, and the dependences of the CPT Ramsey effects on the atom-laser interaction time were investigated in detail.

We studied the relationship between the frequency shift of coherent population trapping resonance and the cell temperature of (85)Rb. Results show that the temperature coefficient of the frequency shift can be reduced by buffer gas pressure adjustment and light shift optimization. When the contribution of buffer gas collision to temperature coefficient of frequency shift is less than 0.3 Hz/K, the contribution of light shift to the temperature coefficient of frequency shift becomes obvious. Under this cancelling effect, we can reduce the rate of total frequency shift to near zero.

To achieve high degree of quantum noise squeezing, an optical cavity is often employed to enhance the interaction time between light and matter. Here, we propose to utilize the effect of coherent population trapping (CPT) to directly generate squeezed light without any optical cavity. Combined with the slow propagation speed of light in a CPT medium, a coherent state passing through an atomic ensemble with a high optical density (OD) can evolve into a highly squeezed state even in a single passage. Our study reveals that noise squeezing of more than $10$ dB can be achieved with an OD of 1,000, which is currently available in experiments. A larger OD can further increase the degree of squeezing. As the light intensity and two-photon detuning are key factors in the CPT interaction, we also demonstrate that the minimum variance at a given OD can be reached for a wide range of these two factors, showing the proposed scheme is flexible and robust. Furthermore, there is no need to consider the phase-matching condition in the CPT scheme. Our introduction of high OD in atomic media not only brings a long light-matter interaction time comparable to optical cavities, but also opens new avenue in the generation of squeezed light for quantum interface.

In the atomic frequency standard, the light shift inevitably affects the long-term stability of the atomic clock. In this work, we accurately calculated the light shifts of electromagnetically induced transparency (EIT) and coherent population trapping (CPT) clocks operating under continuum and pulse sequence regimes by numerically solving the Liouville density matrix equation, including all the relaxation terms of a three-level system. The results show that the light shifts under pulse excitation are smaller than those under continuous excitation and the light shifts of the CPT process are much smaller than those of the EIT process under both excitations. It is also found that the light shifts in the continuous excitation increase and those in the pulse excitation decrease with an increase in the Rabi frequency. The light shifts will increase with an increase of the relaxations of the ground states for both the processes under both regimes. Compared to all process atomic clocks, the light shift of pulse-excited atomic clocks is the smallest, which will be suitable for many applications.

The article presents the results of the development, fabrication and investigation of miniature cesium vapor cells for quantum frequency standards with optical pumping, working on the effect of coherent population trapping. Microelectromechanical systems technologies were used in the manufacture of cells. For the first time, the dry silicon etching in inductively coupled plasma of sulfur hexafluoride and freon gas in a mixed mode was used to form internal cavities of cells with a thickness of 1.5 mm. Vacuum-tight sealing of cells containing a solid-state source of cesium vapor and buffer gas was carried out by anodic bonding of glass and silicon in a neon atmosphere. The coherent population trapping signal with a linewidth of 750 Hz and a signal-to-noise ratio of 1190 in the 1-Hz bandwidth was observed. Experimental results show that these microcells are appropriate for applications to atomic clock with a relative frequency stability of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$6\cdot 10^{-11}$</tex> at 1 s.

Stability and precision of atomic devices are closely tied to the quality and stability of the internal atmosphere of the atomic vapor cells on which they rely. Such an atmosphere can be stabilized by building the cell with low permeation materials such as sapphire or aluminosilicate glass in microfabricated devices. Recently, we have shown that permeation barriers made of Al2O3 thin-film coatings deposited on standard borosilicate glass could be an alternative for buffer gas pressure stabilization. In this study, we, hence, investigate how helium permeation is influenced by the thickness, ranging from 5 to 40 nm, of such Al2O3 thin films coated by atomic layer deposition. Permeation rates are derived from long-term measurements of the pressure-shifted transition frequency of a coherent population trapping (CPT) atomic clock. From thicknesses of 20 nm onward, a significant enhancement of the cell hermeticity is experienced, corresponding to two orders of magnitude lower helium permeation rate. In addition, we test cesium vapor cells filled with neon as a buffer gas and whose windows are coated with 20 nm of Al2O3. As for helium, the permeation rate of neon is significantly reduced, thanks to alumina coatings, leading to a fractional frequency stability of 4×10−12 at 1 day when the cell is used in a CPT clock. These features outperform the typical performances of uncoated Cs–Ne borosilicate cells and highlight the significance of Al2O3 coatings for buffer gas pressure stabilization.

Coherent population trapping (CPT) is extensively studied for future vapor cell clocks of high frequency stability. In the constructive polarization modulation CPT scheme, a bichromatic laser field with polarization and phase synchronously modulated is applied on an atomic medium. A high contrast CPT signal is observed in this so-called double-modulation configuration, due to the fact that the atomic population does not leak to the extreme Zeeman states, and that the two CPT dark states, which are produced successively by the alternate polarizations, add constructively. Here, we experimentally investigate CPT signal dynamics first in the usual configuration, a single circular polarization. The double-modulation scheme is then addressed in both cases: one pulse Rabi interaction and two pulses Ramsey interaction. The impact and the optimization of the experimental parameters involved in the time sequence are reviewed. We show that a simple seven-level model explains the experimental observations. The double-modulation scheme yields a high contrast similar to the one of other high contrast configurations like push-pull optical pumping or crossed linear polarization scheme, with a setup allowing a higher compactness. The constructive polarization modulation is attractive for atomic clock, atomic magnetometer, and high precision spectroscopy applications.

We experimentally investigated the characteristics of two-photon transmission resonances in Rb vapor cells with different amount of buffer gas under the conditions of steady-state coherent population trapping (CPT) and pulsed Raman-Ramsey (RR-) CPT interrogation scheme. We particularly focused on the influence of the Rb atoms diffusing in and out of the laser beam. We showed that this effect modifies the shape of both CPT and Raman-Ramsey resonances, as well as their projected performance for CPT clock applications. In particular we found that at moderate buffer gas pressures RR-CPT did not improved the projected atomic clock stability compare to the regular steady-state CPT resonance.

Light shift is important and inevitably affects the long-term stability of an atomic clock. In this work, considering two unbalanced branches of the spontaneous decay rate in a three-level system, we studied the frequency shifts of electromagnetically induced transparency (EIT) and coherent population trapping (CPT) clocks operating under the pulse sequence regime by numerically solving the Liouville density matrix equations. The results show that the frequency shifts are larger when the two branches of spontaneous emission rate are not equal compared to the equal case. In addition, in EIT-Ramsey, the effect of the unbalanced branches of the spontaneous decay rate and relaxations of low-energy states on the frequency shift is greater than that of Rabi frequency. In CPT-Ramsey, the relaxations of low-energy states play a dominant role in frequency shift.

The utilization of Ramsey interferometry via coherent population trapping (CPT), which enables the optical interrogation of microwave transitions without the reliance on microwave cavities, plays a crucial role in the advancement of compact and low-power quantum sensors. Particularly, high-resolution CPT-Ramsey spectroscopy of alkali-metal atoms has found extensive application in constructing miniaturized quantum sensors like atomic magnetometers and atomic clocks. Due to their well-defined environment and extended coherence time, cold atoms offer enhanced sensitivity and precision in CPT-Ramsey interferometry. This review comprehensively examines CPT-Ramsey interferometry with cold atoms, encompassing both conventional and multi-pulse techniques, and explores their potential applications in practical quantum sensors.

We propose a constructive polarization modulation scheme for atomic clocks based on coherent population trapping (CPT). In this scheme, the polarization of a bichromatic laser beam is modulated between two opposite circular polarizations to avoid trapping the atomic populations in the extreme Zeeman sublevels. We show that if an appropriate phase modulation between the two optical components of the bichromatic laser is applied synchronously, the two CPT dark states which are produced successively by the alternate polarizations add constructively. Measured CPT resonance contrasts up to 20% in one-pulse CPT and 12% in two-pulse Ramsey-CPT experiments are reported, demonstrating the potential of this scheme for applications to high performance atomic clocks.

Three-dimensional velocity-selective coherent population trapping of a (3+3)-level atom

We report on Doppler-free laser spectroscopy in a Cs vapor cell using a dual-frequency laser system tuned on the Cs D1 line. Using counter-propagating beams with crossed linear polarizations, an original sign reversal of the usual saturated absorption dip and large increase in Doppler-free atomic absorption is observed. This phenomenon is explained by coherent population trapping (CPT) effects. The impact of laser intensity and light polarization on absorption profiles is reported in both single-frequency and dual-frequency regimes. In the latter, frequency stabilization of two diode lasers was performed, yielding a beat note fractional frequency stability at the level of 3×10-12 at 1 s averaging time. These performances are about an order of magnitude better than those obtained using a conventional single-frequency saturated absorption scheme.

A frequency-hopping communication receiver based on Rydberg atoms, whose carrier frequency changes in accordance with a predetermined sequence, is proposed for what we believe to be the first time and experimentally verified. Based on the coherent population trapping (CPT) effect of atoms, a five-level system is built under the assumption of a constant laser wavelength, where the carrier is the resonance band corresponding to different separated quantum states. Pseudo-random binary sequence (PRBS) and complex image signals undergo keying modulation to achieve frequency-domain hopping reception. In the experiment, a dynamic range of 62 dB is demonstrated. The digital transmission with a data rate of 1 Mbps is performed reliably, within a tunable bandwidth of 50 MHz, an instantaneous bandwidth of 700 kHz and a max hopping rate of 20000 hop/s. The proposed atom-based frequency-hopping receiver is suitable for secure communications, satellite uplinks, quantum cryptography, and high-precision scientific research.

The combination of unmanned aerial vehicles and atomic magnetometers can be used for detection applications such as mineral resource exploration, environmental protection, and earthquake monitoring, as well as the detection of sunken ships and unexploded ordnance. A dark-resonance atomic magnetometer offers the significant advantages of a fully optical probe and omnidirectional measurement with no dead zones, making it an ideal choice for airborne applications on unmanned aerial vehicles. Enhancing the sensitivity of such atomic magnetometers is an essential task. In this study, we sought to enhance the sensitivity of a dark-state resonance atomic magnetometer. Initially, through theoretical analysis, we compared the excitation effects of coherent population trapping (CPT) resonance on the D1 and D2 transitions of 133Cs thermal vapor. The results indicate that excitation via the D1 line yields an increase in resonance contrast and a reduction in linewidth when compared with excitation through the D2 line, aligning with theoretical predictions. Subsequently, considering the impact of various quantum system parameters on sensitivity, as well as their interdependent characteristics, two experimental setups were developed for empirical investigation. One setup focused on parameter optimization experiments, where we compared the linewidth and contrast of CPT resonances excited by both D1 and D2 transitions; this led to an optimization of atomic cell size, buffer gas pressure, and operating temperature, resulting in an ideal parameter range. The second setup was employed to validate these optimized parameters using a coupled dark-state atom magnetometer experiment, achieving approximately a 10-fold improvement in sensitivity.