Review of chip-scale atomic clocks based on coherent population trapping

Research on chip-scale atomic clocks （CSACs） based on coherent population trapping （CPT） is reviewed. The back- ground and the inspiration for the research are described, including the important schemes proposed to improve the CPT signal quality, the selection of atoms and buffer gases, and the development of micro-cell fabrication. With regard to the re- liability, stability, and service life of the CSACs, the research regarding the sensitivity of the CPT resonance to temperature and laser power changes is also reviewed, as well as the CPT resonance＇s collision and light of frequency shifts. The first generation CSACs have already been developed but its characters are still far from our expectations. Our conclusion is that miniaturization and power reduction are the most important aspects calling for further research.

High-performance coherent population trapping clock based on laser-cooled atoms

We present a coherent population trapping clock system based on laser-cooled^(87)Rb atoms.The clock consists of a frequency-stabilized CPT interrogation laser and a cooling laser as well as a compact magneto-optical trap,a highperformance microwave synthesizer,and a signal detection system.The resonance signal in the continuous wave regime exhibits an absorption contrast of~50%.In the Ramsey interrogation method,the linewidth of the central fringe is31.25 Hz.The system achieves fractional frequency stability of 2.4×10^(-11)/(√τ),which goes down to 1.8×10^(-13)at 20000 s.The results validate that cold atom interrogation can improve the long-term frequency stability of coherent population trapping clocks and holds the potential for developing compact/miniature cold atoms clocks.

High contrast atomic magnetometer based on coherent population trapping

We present an experimental and theoretical investigation of the coherent population trapping （CPT） resonance excited on the D1 line of 87Rb atoms by bichromatic linearly polarized laser light. The experimental results show that a lin｜｜lin tran- sition scheme is a promising alternative to the conventional circular-circular transition scheme for an atomic magnetometer. Compared with the circular light transition scheme, linear light accounts for high-contrast transmission resonances, which makes this excitation scheme promising for high-sensitivity magnetometers. We also use linear light and circular light to detect changes of a standard magnetic field, separately.

Characterizing passive coherent population trapping resonance in a cesium vapor cell filled with neon buffer gas

We present a pair of phase-locked lasers with a 9.2-GHz frequency difference through the injection locking of a master laser to the RF-modulation sideband of a slave diode laser. Using this laser system, a coherent population trapping （CPT） signal with a typical linewidth of ～ 182 Hz is obtained in a cesium vapor cell filled with 30 Torr （4kPa） of neon as the buffer gas. We investigate the influence of the partial pressure of the neon buffer gas on the CPT linewidth, amplitude, and frequency shift. The results may offer some references for CPT atomic clocks and CPT atomic magnetometers.

Dependence of the ^(85)Rb coherent population trapping resonance characteristic on the pressure of N_2 buffer gas

In order to exploit its potential applications, we experimentally study the dependence of ^85 Rb-based coherent population trapping （CPTi resonance on N2 buffer gas with 6 vapor cells filled with natural rubidium and N2. The experiments are carried out at different pressures and temperatures, and the results reveal that higher cell temperature makes the resonance more sensitive to N2 pressure. Thus, it is importmlt to choose a proper buffer gas pressure at a given cell temperature. This work provides valuable data for the application of 85Rb CPT resonance with a buffer gas of N2.

Coherent population trapping magnetometer by differential detecting magneto–optic rotation effect

A pocket coherent population trapping（CPT） atomic magnetometer scheme that uses a vertical cavity surface emitting laser as a light source is proposed and experimentally investigated.Using the differential detecting magneto–optic rotation effect,a CPT spectrum with the background canceled and a high signal-to-noise ratio is obtained.The experimental results reveal that the sensitivity of the proposed scheme can be improved by half an order,and the ability to detect weak magnetic fields is extended one-fold.Therefore,the proposed scheme is suited to realize a pocket-size CPT magnetometer.

Atomic magnetometer with microfabricated vapor cells based on coherent population trapping

An atomic magnetometer based on coherent population trapping(CPT) resonances in microfabricated vapor cells is demonstrated. Fabricated by the micro-electro-mechanical-system(MEMS) technology, the cells are filled with Rb and Ne at a controlled pressure. An experimental apparatus is built for characterizing properties of microfabricated vapor cells via the CPT effects. The typical CPT linewidth is measured to be about 3 k Hz(1.46 k Hz with approximately zero laser intensity) for the rubidium D1 line at about 90℃. The effects of pressure, temperature and laser intensity on CPT linewidth are studied experimentally. A closed-loop atomic magnetometer is finally finished with a sensitivity of 210.5 p T/Hz1/2 at 1 Hz bandwidth. This work paves the way for developing an integrated chip-scale atomic magnetometer in the future.

Phase-controlled coherent population trapping in superconducting quantum circuits

We investigate the influences of the-applied-field phases and amplitudes on the coherent population trapping behavior in superconducting quantum circuits. Based on the interactions of the microwave fields with a single A-type three-level fluxonium qubit, the coherent population trapping could be obtainable and it is very sensitive to the relative phase and amplitudes of the applied fields. When the relative phase is tuned to 0 or π, the maximal atomic coherence is present and coherent population trapping occurs. While for the choice of π/2, the atomic coherence becomes weak. Meanwhile, for the fixed relative phase π/2, the value of coherence would decrease with the increase of Rabi frequency of the external field coupled with two lower levels. The responsible physical mechanism is quantum interference induced by the control fields, which is indicated in the dressed-state representation. The microwave coherent phenomenon is present in our scheme, which will have potential applications in optical communication and nonlinear optics in solid-state devices.

Image transfer through coherent population trapping based on an atomic ensemble

We report on an experiment on transferring an image through coherent population trapping （CPT） effect in a hot rubidium vapor. We demonstrate experimentally that an image can be transferred from a control light to a probe light. Moreover, we describe the demonstration that the image can be transferred from a control light to two different probes showing a feasibility of transferring an image onto multiple probes. We believe that this effect definitely has important applications in image metrology, high dimensional information transfer in quantum information field, etc.

VIPA-based two-component detection for a coherent population trapping experiment

We demonstrate a two-component detection of a coherent population trapping(CPT)resonance based on virtually imaged phased array(VIPA).After passing through a VIPA,the two coupling lights with different frequencies in the CPT experiment are separated in space and detected individually.The asymmetric lineshape is observed experimentally in the CPT signal for each component,and the comparison with the conventional detection is presented.The shift of the CPT resonant frequency is studied with both the two-component and one-component detections.Our scheme provides a convenient way to further study the CPT phenomenon for each frequency component.

Atomic Coherent Trapping and Properties of Trapped Atom

Based on the theory of velocity-selective coherent population trapping, we investigate an atom-laser system where a pair of counterpropagating laser fields interact with a three-level atom. The influence of the parametric condition on the properties of the system such as velocity at which the atom is selected to be trapped, time needed for finishing the coherent trapping process, and possible electromagnetically induced transparency of an altrocold atomic medium, etc., is studied.

Coherent Assembly of Ultracold Polyatomic Molecules: Two-Channel Interference

The evidences of three-body and four-body bound states have been reported in a series of very recent experiments with ultracold atoms.Here we study coherent creation of polyatomic molecules via a generalized atom-molecule dark-state technique.By keeping the intermediate trimer or tetramer state essentially unpopulated,the constructive quantum two-channel interference is shown to play an important role in,e.g.coherent atom-pentamer conversion at ultracold temperature.

Coherent spectroscopy of the ^87Rb Fg = 1→ Fe = 0 closed transition

This paper has observed linewidth narrowing of dark states in rubidium cell by using the Hanle configuration. The reduction of the coherent resonance width under the transition of ^87Rb Fg = 1 → Fe = 0 is observed and the qualitative explanation about its mechanism is presented. Multiple subnatural width dips are obtained with a linearly polarized laser beam for the transitions of ^87Rb Fg = 1→Fe = 0, 1, 2. The feature of negative and positive slope, namely dispersionlike feature, is observed in the transmitted light.

Integrated physics package of a chip-scale atomic clock

The physics package of a chip-scale atomic clock （CSAC） has been successfully realized by integrating vertical cavity surface emitting laser （VCSEL）, neutral density （ND） filter, λ/4 wave plate, 87Rb vapor cell, photodiode （PD）, and magnetic coil into a cuboid metal package with a volume of about 2.8 cm3. In this physics package, the critical component, 87Rb vapor cell, is batch-fabricated based on MEMS technology and in-situ chemical reaction method. Pt heater and thermistors are integrated in the physics package. A PTFE pillar is used to support the optical elements in the physics package, in order to reduce the power dissipation. The optical absorption spectrum of 87Rb D1 line and the microwave frequency correction signal are successfully observed while connecting the package with the servo circuit system. Using the above mentioned packaging solution, a CSAC with short-term frequency stability of about 7 × 10^-10τ-1/2 has been successfully achieved, which demonstrates that this physics package would become one promising solution for the CSAC.

Stable ^(85)Rb micro vapour cells:fabrication based on anodic bonding and application in chip-scale atomic clocks

We describe the microfabrication of ^85Rb vapour cells using a glass-silicon anodic bonding technique and in situ chemical reaction between rubidium chloride and barium azide to produce Rb. Under controlled conditions, the pure metallic Rb drops and buffer gases were obtained in the cells with a few mm^3 internal volumes during the cell sealing process. At an ambient temperature of 90 ℃ the optical absorption resonance of ^85Rb D1 transition with proper broadening and the corresponding coherent population trapping （CPT） resonance, with a signal contrast of 1.5% and linewidth of about 1.7 kHz, have been detected. The sealing quality and the stability of the cells have also been demonstrated experimentally by using the helium leaking detection and the after-9-month optoelectronics measurement which shows a similar CPT signal as its original status. In addition, the physics package of chip-scale atomic clock （CSAC） based on the cell was realized. The measured frequency stability of the physics package can reach to 2.1 × 10^-10 at one second when the cell was heated to 100 ℃ which proved that the cell has the quality to be used in portable and battery-operated devices.

Theoretical analysis of suppressing Dick effect in Ramsey-CPT atomic clock by interleaving lock

For most pulsed atomic clocks, the Dick effect is one of the main limits to reach its frequency stability limitation due to quantum projection noise. In this paper, we measure the phase noise of the local oscillator in the Ramsey-CPT atomic clock and calculate the Dick effect induced Allan deviation based on a three-level atomic model, which is quite different from typical atomic clocks. We further present a detailed analysis of optimizing the sensitivity function and minimizing the Dick effect by interleaving lock. By optimizing the duty circle of laser pulses, average time during detection and optical intensity of laser beam, the Dick effect induced Allan deviation can be reduced to the level of 10 14.

Transient responses of transparency in a far-off resonant atomic system

Transient coherent oscillations in a closed A system under far-off resonant Raman fields were investigated theoreti- cally. It has been found that the coherent superposition of the ground states can be formed due to the absorption even for initial maximal mixed ground states. The absorption oscillates with a period depending on the two-photon detuning when the system is initially in a transparent state and the two-photon Raman detuning is suddenly changed. The amplitude of the absorption decays with the decay rate of the ground states, which is different from the case when the lasers are applied resonantly. These transient coherent oscillations can be used to measure the relaxation rate of the ground states.

Investigation of the nonlinear CPT spectrum of ^87Rb and its application for large dynamic magnetic measurement

The coherent population trapping（CPT） phenomenon has found widespread application in quantum precision measurements. Various designs based on the narrow resonant spectrum corresponding to the linear Zeeman effect have been demonstrated to achieve high performance. In this article, the nonlinear Zeeman split of the CPT spectrum of ^87Rb in the lin｜｜lin setup is investigated. We observe re-split phenomenon for both magnetic sensitive and magnetic insensitive CPT resonant lines at a large magnetic field. The re-split in the magnetic sensitive lines raises a practical problem to magnetometers worked in the lin｜｜lin setup while the other one shows a good potential for applications in large magnetic field. We propose a design based on the nonlinear split of the magnetic insensitive lines and test its performance. It provides a much larger measurement range compared to the linear one, offering an option for atomic magnetometers where a large dynamic range is preferred.

Optical nuclear spin polarization in quantum dots

Hyperfine interaction between electron spin and randomly oriented nuclear spins is a key issue of electron coherence for quantum information/computation. We propose an efficient way to establish high polarization of nuclear spins and reduce the intrinsic nuclear spin fluctuations. Here, we polarize the nuclear spins in semiconductor quantum dot(QD) by the coherent population trapping(CPT) and the electric dipole spin resonance(EDSR) induced by optical fields and ac electric fields. By tuning the optical fields, we can obtain a powerful cooling background based on CPT for nuclear spin polarization. The EDSR can enhance the spin flip–flop rate which may increase the cooling efficiency. With the help of CPT and EDSR, an enhancement of 1300 times of the electron coherence time can be obtained after a 10-ns preparation time.

Coherent effects in a three-photon CPT process of Ca＋

Linewidth narrowing and other quantum coherent effects based on three-photon coherent population trapping （CPT） in Ca＋ ions are investigated. If the propagation directions of the three lasers obey the phase matching condition, the dark linewidth resulting from the CPT can be very narrow, and it can be controlled by adjusting the parameters of the lasers.