Population Trapping Research Articles

Inhomogeneous light shifts of coherent population trapping resonances

Coherent population trapping (CPT) in atomic vapors using all-optical interrogation has enabled the miniaturization of microwave atomic clocks. Light shifts induced by the CPT driving fields can impact the spectral profile of CPT resonances and are a common limit to the long-term stability of CPT clocks. Nonlinear light shifts have been observed in several CPT systems and have not been explored in detail. In this Letter, we demonstrate that nonlinear light shifts in CPT clocks can arise from spatially inhomogeneous CPT driving fields. We measure this effect using Gaussian laser beams in a buffer gas cell and show strong agreement with a four-level model describing the CPT Λ-system with a noninteracting “trap” state. We estimate the effect of this nonlinearity on recently developed light shift mitigation techniques and suggest improvements to existing techniques.

Wafer-Level Assembly of Physics Package for Chip-Scale Atomic Clocks

Chip-scale atomic clocks (CSACs) have been extensively investigated and many prototypes or products have been realized as time sensors. Researchers focus on improving the frequency stability performance, reducing the volume and the power consumption of CSACs. To the best of our knowledge, the physics packages reported until now are all assembled from discrete components. This traditional assembly method has a very low efficiency and causes variations among different physics packages. In this article, we propose a wafer-level assembled physics package for CSACs based on three dimensional (3-D) wafer-level packaging (WLP) and microelectromechanical system (MEMS) technologies. The components of the physics package are all fabricated on wafers. These wafers are integrated together vertically and then diced into separate physics packages. The proposed method has the advantages of high uniformity among different physics packages and high efficiency. And it improves the utilization rate of wafers by reducing the unused area. Thus, the production cost is reduced considerably. The volume of the proposed functional physics package is less than 8 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . The prototype chip-scale atomic clock incorporating the proposed physics package reveals the coherent population trapping (CPT) linewidth of 1.8 kHz and the total power consumption of about 20mW. The frequency stability is about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6.1 \times 10^{-12}$ </tex-math></inline-formula> @1000s. The observed results demonstrate promising performance of the wafer-level assembled physics package. The approach described in this article reveals a viable method for batch production for its low cost, high efficiency and high product uniformity.

Comparison of field shifts in an atomic clock based on the effect of coherent population trapping in 87Rb atoms under modulation of laser pump current at frequencies of 3.4 and 6.8 GHz

Experimental parameters of the resonance of coherent population trapping (CTP) on D1 line in 87Rb and light shifts are compared under modulation of the laser pump current at frequencies of 3.4 and 6.8 GHz. Reproducibility of the parameters of a laser with a vertical cavity needed for long-term stability of an atomic clock is considered. The instabilities of atomic CPT-clock obtained for 1 s are 1.2 × 10−11 and 3 × 10−12 for frequencies of 3.4 GHz and 6.8 GHz, respectively.

Microwave phase detection of coherent population trapping resonance in a Cs vapor cell

We report a phase-sensitive microwave detection setup for spectroscopy of coherent population trapping (CPT) resonance in a Cs vapor cell. In this scheme, the optically carried microwave interrogation signal that interacts with atoms is detected by a fast photodiode at the cell output and is then mixed with the local oscillator microwave signal itself. This detection scheme produces at the output of the microwave mixer a dispersive CPT signal that can be directly used for correction of the local oscillator frequency onto the atomic resonance. The evolution of the dispersive CPT resonance signal with the laser power is briefly reported. With this detection scheme, we demonstrate the operation of a CPT atomic clock with a short-term fractional frequency stability of 1 × 10 − 11 at 1 s, which is in good agreement with the slope of the frequency discriminator and the residual microwave phase noise of the setup.

Optimization of a quantum control sequence for initializing a nitrogen-vacancy spin register

Implementation of many quantum information protocols requires an efficient initialization of the quantum register. In the present paper, we optimize a population trapping protocol for initializing a hybrid spin register associated with a single nitrogen-vacancy (NV) center in diamond. We initialize the quantum register by polarizing the electronic and nuclear spins of the NV with a sequence of microwave, radio-frequency, and optical pulses. We use a rate equation model to explain the distribution of population under the effect of the optical pulses. The model is compared to the experimental data obtained by performing partial quantum state tomography. To further increase the spin polarization, we propose a recursive protocol with optimized optical pulses. We also discuss the role of the relative values of the nuclear- and electronic-spin pumping rate in achieving the maximum degree of spin polarization.

A vertical cavity surface emitting laser for CPT atomic clock

A polarization-stabilized fundamental mode vertical cavity surface emitting laser (VCSEL) was developed for a coherent population trapping (CPT) Cs atomic clock. The VCSEL achieved a single stabilized polarization state through a directly-etched surface grating structure on the surface. The device polarization characteristics of different surface grating parameters were analysed using the finite-difference time-domain (FDTD) method. For the fundamental transverse mode condition, the lasing wavelength corresponded to the Cs atom’s D1 line. Owing to the polarization-dependent reflectivity of surface gratings, the VCSEL’s orthogonal polarization suppression ratio (OPSR) exceeded 20 dB. Since the surface grating eliminated the degeneracy of the two orthogonal linear polarization fundamental modes, a linewidth of approximately 53 MHz for the VCSEL could be obtained using the delayed self-homodyne method. A 7.6 GHz modulation bandwidth satisfied the atomic clock’s bandwidth requirement. We introduced the directly-etched surface grating VCSEL to the Cs atomic clock, and measured the CPT resonance signal.

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.

Coherent Spin Preparation of Indium Donor Qubits in Single ZnO Nanowires.

Shallow donors in ZnO are promising candidates for photon-mediated quantum technologies. Utilizing the indium donor, we show that favorable donor-bound exciton optical and electron spin properties are retained in isolated ZnO nanowires. The inhomogeneous optical line width of single nanowires (60 GHz) is within a factor of 2 of bulk single-crystalline ZnO. Spin initialization via optical pumping is demonstrated and coherent population trapping is observed. The two-photon absorption width approaches the theoretical limit expected due to the hyperfine interaction between the indium nuclear spin and the donor-bound electron.

Line shape of the coherent population trapping resonance in the case of a Gaussian spatial profile of a light beam

For coherent population trapping (CPT) resonance excited by a bichromatic field in a closed Λ-system, we have obtained an analytical expression for the line shape in the case of a Gaussian profile of the radiation intensity distribution, taking into account the light shift of the reference transition frequency. Due to the spatial inhomogeneity of the light shift, the line shape is asymmetric. The dependence of the shift of the resonance peak position on the light intenisty is investigated.

Line shape and light shift of coherent population trapping resonance under Ramsey interrogation in ‘hot’ atoms in an optically dense medium

A theory is developed for the effect of coherent population trapping (CPT) in ‘hot’ atoms under pulsed pumping in an optically dense medium with a buffer gas. The case is considered when the excited level is not degenerate. Based on an analysis of the shape of Ramsey resonances, we show that with increasing optical density of the medium, the dependence of the light shifts of the CPT resonance becomes more and more nontrivial. The dependence of the light shifts of the CPT resonance on the magnitude of the hyperfine splitting of the excited level, concentration of active atoms, temperature, and duration of the dark pause is constructed.

CPT resonances under multifrequency pumping

The possibility of detecting coherent population trapping (CPT) resonances with combined microwave and HF modulation of the injection current of a diode laser has been demonstrated for the first time. A series of resonances is observed, separated from each other by half the RF modulation frequency.

Wafer-Level Filling of MEMS Vapor Cells Based on Chemical Reaction and Evaporation.

Micro-electro-mechanical system (MEMS) vapor cells are key components for sensors such as chip-scale atomic clocks (CSACs) and magnetometers (CSAMs). Many approaches have been proposed to fabricate MEMS vapor cells. In this article, we propose a new method to fabricate wafer-level filling of MEMS vapor cells based on chemical reaction and evaporation. The Cs metals are firstly obtained through the chemical reaction between cesium chloride and barium azide in a reservoir baseplate. Then, the Cs metals are evaporated to the preform through the microchannel plate and condensed on the inner glass surface of the preform. Lastly, the MEMS vapor cells are filled with buffer gas, sealed by anodic bonding, and mechanically diced into three dimensions: 5 mm × 5 mm × 1.2 mm, 4 mm × 4 mm × 1.2 mm, and 3 mm × 3 mm × 1.2 mm. The full width at half maximum (FWHM) linewidth of the coherent population trapping (CPT) signal of the MEMS vapor cells is found to be 4.33 kHz. The intrinsic linewidth is about 1638 Hz. Based on the CPT signal, the frequency stability is 4.41 × 10−12@1000 s. The results demonstrate that the presented method of the wafer-level filling of MEMS vapor cells fulfills the requirements of sensors such as CSACs.

All-optical microwave feedback oscillator with atomic cell resonator

We report the demonstration of an all-optical self-sustained cell-based microwave feedback oscillator. In this scheme, a microwave resonance, optically induced in a buffer-gas filled vapor cell resonator through coherent population trapping (CPT), is detected by a fast photodiode, amplified, and used to drive back, through a frequency divider, a Mach–Zehnder electro-optic modulator in a sustaining loop configuration. The total gain and phase of the system was measured in an open-loop configuration with a network analyzer. In good agreement with values predicted by the Leeson effect, the CPT feedback oscillator demonstrates an absolute phase noise of −24 dB rad2/Hz at 1 Hz offset frequency, compatible with a fractional frequency stability of 8 × 10−12 at 1 s, and a phase noise floor of −112 dB rad2/Hz, limited by the low microwave power available at the photodiode output. The amplitude noise of the oscillator shows a comparable noise floor and, for offset frequencies lower than 200 Hz, a 1/f dependence, due to the presence of the frequency divider in the loop.

Real-time magnetometry with coherent population trapping in a nitrogen-vacancy center

We demonstrate real-time magnetometry by detecting fluorescence from a nitrogen-vacancy center in the setting of coherent population trapping and by estimating the magnetic field from the time series of the observed photon counts, which are correlated with the underlying field variation. The proof-of-principle experiment uses an external time-varying magnetic field that follows an Ornstein-Uhlenbeck (OU) process. A conventional estimator based on the use of average photon counts per relevant time interval is susceptible to photon number shot noise and performs poorly at relatively low average photon counts. In comparison, by taking into consideration the statistical properties of the OU process, a Bayesian inference-based estimator can effectively update dynamical information of the field in real time with the detection of just a single photon.

Effect of radiation physics on inherent statistics of glow curves from small samples or low doses

A theory is developed to predict statistical noise in the trap populations of small samples or single grains subjected to high-energy ionizing irradiation. Using a model of the radiation process and a one-trap one-center model of a thermoluminescent (TL) material, the statistical behavior of the number of occupied traps during irradiation is predicted. The model focuses on the inherent physics of the process. Experimental sources of error are not considered. The interaction of radiation with the TL material is modeled in a simple way using the Bethe equation. The trap and center populations in the TL material are modeled both with the conventional phenomenological equations and also the more general Master Equation approach. The theory predicts, as the irradiation process proceeds, the mean, standard deviation, dispersion, skewness, and kurtosis of the probability distribution of occupied traps in the TL material. For the same applied dose, the standard deviation and dispersion of the trap population depend strongly on the type of radiation as well as the shape and orientation of the material. High-energy radiation sources, such as alpha, beta, or gamma rays, are found to produce standard deviations and dispersion much larger than low-energy sources, such as UV radiation. The results are summarized in tables which enable, for useful limiting cases, easy calculation of not just standard deviation but also skewness and kurtosis for various radiation sources and geometries.

Multiplexed Sensing of Magnetic Field and Temperature in Real Time Using a Nitrogen-Vacancy Ensemble in Diamond

Nitrogen-Vacancy (NV) spin in diamond is a versatile quantum sensor, being able to measure physical quantities such as magnetic field, electric field, temperature, and pressure. In the present work, we demonstrate a multiplexed sensing of magnetic field and temperature. The dual frequency driving technique we employ here is based on frequency-division multiplexing, which enables sensing both measurables in real time. The pair of NV resonance frequencies for dual frequency driving must be selected to avoid coherent population trapping of NV spin states. With an enhanced optical collection efficiency higher than 50 $\%$ and a type 1b diamond crystal with natural abundance $^{13}$C spins, we achieve sensitivities of about 70 pT/$\sqrt{\mathrm{Hz}}$ and 25 $\mu$K/$\sqrt{\mathrm{Hz}}$ simultaneously. A high isolation factor of 34 dB in NV thermometry signal against magnetic field was obtained, and we provide a theoretical description for the isolation factor. This work paves the way for extending the application of NV quantum diamond sensors into more demanding conditions.

The Microfabricated Alkali Vapor Cell with High Hermeticity for Chip-Scale Atomic Clock

Herein, a microfabricated millimeter-level vapor alkali cell with a high hermeticity is fabricated through a wet etching and single-chip anodic bonding process. The vapor cell, containing Rb and N2, was investigated in a coherent population trapping (CPT) setup for the application of a chip-scale atomic clock (CSAC). The contrast of CPT resonance is up to 1.1% within the only 1 mm length of light interacting with atom. The effects of some critical external parameters on the CPT resonance, such as laser intensity, cell temperature, and buffer gas pressure, are thoroughly studied and optimized. The improved microfabricated vapor cell also exhibited great potential for other chip-scale atomic devices.

Microwave Synthesizer and Self-Adaption System for High Performance Coherent Population Trapping Atomic Clocks

Microwave Synthesizer and Self-Adaption System for High Performance Coherent Population Trapping Atomic Clocks

Autobalanced spectroscopy of CPT resonance in an optically dense atomic ensemble

We investigate the influence of optical thickness on the coherent population trapping (CPT) resonance interrogated by the autobalanced Ramsey method as well as by the method of combined error signals (CESs). We analyze sensitivity of the CPT resonance to the light shift of the etalon transition for the microwave quantum frequency standards based on cold or hot atomic ensembles. When the CPT resonance is excited, two-frequency laser radiation can be significantly absorbed at the atomic transitions of the optical range. The effects of absorption and phase incursion lead to additional shift of the reference resonance. This is an additional factor that degrades the accuracy of the frequency standards because this additional shift can vary with intensity and temperature fluctuations. It was shown that the CES method is more robust in an optically dense medium than is the autobalanced Ramsey method, but it also undergoes the light shift. We found that by choosing the normalization factor of the CES method it is possible to suppress the light shift for a certain density of the medium or suppress its sensitivity to temperature fluctuations.

Quantum Control of the Tin-Vacancy Spin Qubit in Diamond

Group-IV color centers in diamond are a promising light-matter interface for quantum networking devices. The negatively charged tin-vacancy center (SnV) is particularly interesting, as its large spin-orbit coupling offers strong protection against phonon dephasing and robust cyclicity of its optical transitions towards spin-photon entanglement schemes. Here, we demonstrate multi-axis coherent control of the SnV spin qubit via an all-optical stimulated Raman drive between the ground and excited states. We use coherent population trapping and optically driven electronic spin resonance to confirm coherent access to the qubit at 1.7 K, and obtain spin Rabi oscillations at a rate of $\Omega/2\pi$=3.6(1) MHz. All-optical Ramsey interferometry reveals a spin dephasing time of $T_2^*$=1.3(3)$\mu$s and two-pulse dynamical decoupling already extends the spin coherence time to $T_2$=0.33(14) ms. Combined with transform-limited photons and integration into photonic nanostructures, our results make the SnV a competitive spin-photon building block for quantum networks.