Active Optical Clock Research Articles

Prospects for an Active Optical Clock Based on Cavityless Lasing

AbstractActive optical clocks take advantage of the substantial suppression of cavity pulling in the bad‐cavity lasing regime and feature the simple structure and excellent portability. In the extreme case, where the cavity mirror reflection approaches zero and cannot support any quasi‐bound modes for light waves, conventional bad‐cavity lasers become the cavityless lasing and the cavity pulling vanishes. Consequently, the laser frequency is determined entirely by the atomic transition. This work is dedicated to theoretically explore the potential application of the cavityless lasing in active optical clocks. Without loss of generality, Cs atoms with well‐established quantum control techniques are employed as the gain medium that is pumped by a 459‐nm laser. The clock laser wavelength is 1470 nm. The simulation shows that the frequency stability of the clock laser with feasible physical quantities reaches at 1 s of averaging time, one order of magnitude better than the recently demonstrated compact passive optical clocks that are built upon a two‐photon transition in a hot Rb vapor and upon the modulation transfer spectroscopy of thermal Cs atoms. Such compact cavityless lasing‐based active optical clocks have the broad application prospect in satellite navigation and communications and promise an architecture for the integrated photonic metrology.

Active whispering-gallery microclock in pulsed-operation mode

A whispering-gallery-mode microlaser in the bad-cavity limit serves as an active optical clock. In this clock scheme, an ensemble of two-level atoms is trapped in a two-color ring-shaped optical lattice, i.e., Lamb-Dicke regime, and evanescently interacts with an optical microcavity. The microclock is operated in the pulsed mode, where the atoms are periodically pumped into the upper state of the electric-dipole-forbidden clock transition, providing the optical gain. The numerical simulation shows that the fractional frequency instability of the microclock reaches $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ at ${10}^{3}$ s of averaging, mainly limited by the lattice-induced frequency shifts. This miniature optical clock owns the high integration and can be potentially used to supply the time standard in a photonic network, paving the way towards the on-chip metrology.

Antiresonant Fabry-Pérot cavity with ultralow finesse

The exact expressions of finesse and full width at half maximum (FWHM) of the Airy distribution of a Fabry-P\'erot (FP) resonator are derived, which solves the breakdown problem at ultralow reflectivity in traditional formulas. We demonstrate that, when the cavity-mirror reflectivity $R\ensuremath{\rightarrow}0$, the FWHM approaches half of the free spectral range rather than infinity; moreover, the cavity finesse $\mathcal{F}$ approaches 2 rather than zero. These expressions are useful for the development of bad-cavity lasers, such as the four-level active optical clock based on the strong atomic transition of cesium. Also, the exact expressions of the FWHM and finesse of the reflection distribution composed of reflected mode profiles are derived, which separately intersect with that of the Airy one at $R=0$. In addition, the characteristics of an antiresonant cavity, the frequency of which is exactly at the center of two adjacent resonant cavity modes, are analyzed. It is demonstrated that at the resonant and antiresonant frequencies the enhancement and inhibition of intracavity light intensity caused by the FP cavity are symmetrical in the logarithmic view. Furthermore, we provide a universal expression of the cavity-enhancement factor rather than the classical representation of ``$\text{2}\mathcal{F}/\phantom{\text{2}\mathcal{F}\ensuremath{\pi}}\phantom{\rule{0.0pt}{0ex}}\ensuremath{\pi}$,'' which is inadequate for the high-loss cavity because the cavity-enhancement factor should naturally reach 1 when $R\ensuremath{\rightarrow}0$. Finally, we extend the application of the antiresonant cavity to an inhibited laser, the frequency of which has a stronger suppression effect on the cavity-length thermal noise than the traditional resonant laser.

Proposal for a hybrid clock system consisting of passive and active optical clocks and a fully stabilized microcomb.

Optical atomic clocks produce highly stable frequency standards and frequency combs bridge clock frequencies with hundreds of terahertz difference. In this paper, we propose a hybrid clock scheme, where a light source pumps an active optical clock through a microresonator-based nonlinear third harmonic process, serves as a passive optical clock via indirectly locking its frequency to an atomic transition, and drives a chip-scale microcomb whose mode spacing is stabilized using the active optical clock. The operation of the whole hybrid system is investigated through simulation analysis. The numerical results show: (i) The short-term frequency stability of the passive optical clock follows an Allan deviation of σy(τ) = 9.3 × 10-14τ-1/2 with the averaging time τ, limited by the population fluctuations of interrogated atoms. (ii) The frequency stability of the active optical clock reaches σy(τ) = 6.2 × 10-15τ-1/2, which is close to the quantum noise limit. (iii) The mode spacing of the stabilized microcomb has a shot-noise-limited Allan deviation of σy(τ) = 1.9 × 10-11τ-1/2. Our hybrid scheme may be realized using recently developed technologies in (micro)photonics and atomic physics, paving the way towards on-chip optical frequency comparison, synthesis, and synchronization.

Cold-atom optical filtering enhanced by optical pumping

Atomic optical filters such as Faraday anomalous dispersion optical filters (FADOFs) or similar technologies can achieve very narrow optical bandwidth close to the scale of atomic linewidth, which can be greatly reduced in cold atoms. However, limited by the number of cold atoms and the size of the cold atomic cloud, the number of atoms interacting with the laser is reduced, and the transmission remains as low as 2%. In this work, we introduce the optical pumping into the cold atomic optical filter to solve this problem. Circular polarized optical pumping can produce polarization of the atomic ensemble and induce dichromatic as well as the Faraday rotation. We demonstrate a cold-atom optical filter which operates on the 87Rb 52S1/2 (F=2) to 52P3/2 (F′=2) transition at 780 nm. The filter achieves an ultranarrow bandwidth of 6.6(4) MHz, and its peak transmission is 15.6%, which is nearly 14 times higher than that of the cold-atom optical filter realized by Faraday magneto-optic effect. This scheme can be extended to almost all kinds of atomic optical filters and may find applications in self-stabilizing laser and active optical clock.

Corrigendum: Active optical clock lasing on the Cs 7S1/2-6P3/2 transition under a weak magnetic field

Corrigendum: Active optical clock lasing on the Cs 7S1/2-6P3/2 transition under a weak magnetic field

An inhibited laser

Traditional lasers function using resonant cavities, in which the round-trip optical path is equal to an integer multiple of the intracavity wavelengths to constructively enhance the spontaneous emission rate. Taking advantage of the cavity enhancement effect, the narrowest sub-10-mHz-linewidth laser and a 10−16-fractional-frequency-stability superradiant active optical clock (AOC) have been achieved. However, a laser with atomic spontaneous radiation being destructively inhibited in an anti-resonant cavity, where the atomic resonance is exactly between two adjacent cavity resonances, has not been reported. Herein, we experimentally demonstrate the inhibited laser. Compared with traditional AOCs, which exhibit superiority in terms of the high suppression of cavity noise, the suppression of the cavity-pulling effect of an inhibited laser can be further improved by a factor of {left(2{{{{{{{mathcal{F}}}}}}}}/pi right)}^{2}, which is improved from 26 to 53 times. This study will guide further development of AOCs with better stability, and thus, it is significant for quantum metrology and may lead to new research in the laser physics and cavity quantum electrodynamics fields.

Active optical clock lasing on the Cs 7S1/2-6P3/2 transition under a weak magnetic field

In the bad-cavity limit, the collective atomic dipole is highly coherent, resulting in the phase information of an active optical clock (AOC) laser primarily stored in the atomic gain medium. Therefore, compared with the good-cavity laser, the sensitivity of an AOC laser to cavity fluctuations is greatly reduced, as characterized by the suppressed cavity-pulling effect. In this work, the AOC lasing on the cesium 7S1/2-6P3/2 clock transition with a natural linewidth of 1.81 MHz under a weak magnetic field is achieved. We calculate the Zeeman spectra of upper and lower states of clock transition, and measure the beat-note spectrum between different Zeeman-sublevel transitions of 7S1/2-6P3/2. Moreover, the cavity-pulling, temperature, power, and linewidth characteristics of the AOC laser are demonstrated under a weak magnetic field. Such an emerging laser can be applied as a narrow-linewidth local oscillator, as well as an active optical frequency standard, which is promising for the field of precision measurement.

Continuous multi-step pumping of the optical clock transition in alkaline-earth atoms with minimal perturbation.

A suitable scheme to continuously create inversion on an optical clock transition with negligible perturbation is a key missing ingredient required to build an active optical atomic clock. Repumping of the atoms on the narrow transition typically needs several pump lasers in a multi step process involving several auxiliary levels. In general this creates large effective level shifts and a line broadening, strongly limiting clock accuracy. Here we present an extensive theoretical study for a realistic multi-level implementation in search of parameter regimes where a sufficient inversion can be achieved with minimal perturbations. Fortunately we are able to identify a useful operating regime, where the frequency shifts remain small and controllable, only weakly perturbing the clock transition for useful pumping rates. For practical estimates of the corresponding clock performance, we introduce a straightforward mapping of the multilevel pump scheme to an effective energy shift and broadening of parameters for the reduced two-level laser model system. This allows us to evaluate the resulting laser power and spectrum using well-known methods.

Realization of phase locking in good-bad-cavity active optical clock.

The residual cavity-pulling effect limits further narrowing of linewidth in dual-wavelength (DW) good-bad-cavity active optical clocks (AOCs). In this paper, we for the first time experimentally realize the cavity-length stabilization of the 1064/1470 nm DW-AOCs by utilizing the phase locking technique of two independent 1064 nm good-cavity lasers. The frequency tracking accuracy between the two main-cavities of DW-AOCs is better than 3 × 10-16 at 1 s, and can reach 1 × 10-17 at 1000 s. Each 1470 nm bad-cavity laser achieves a most probable linewidth of 53 Hz, which is about a quarter of that without phase locking. The influence of the asynchronous cavity-lengths variation between two DW laser systems is suppressed.

Dual-Wavelength Good-Bad-Cavity Laser System for Cavity-Stabilized Active Optical Clock.

Active optical clocks (AOCs) have the intrinsic suppression of the influence of the cavity's noise on the output frequency, giving rise to the potentially ultranarrow linewidth. To break the cavity's thermal noise limitation by taking full advantage of the AOC's principle, as well as to achieve a long-term instability, we propose a scheme of cavity-stabilized active optical clock. The system consists of two key procedures. The dual-wavelength (DW) output signals share the same cavity and work in the good- and the bad-cavity regime, respectively. Then, the good-cavity signal is locked to a reference cavity by the Pound-Drever-Hall (PDH) technique to stabilize the main-cavity length. By doing this, the main-cavity's noise is expected to be reduced to the thermal noise floor of the reference cavity. Hence, the frequency stability of the bad-cavity signal will break this noise floor due to the suppression of the cavity-pulling effect. Experimentally, we realize the DW good-bad-cavity laser system by taking the Nd:YAG 1064 nm and Cs 1470 nm transitions as the good- and bad-cavity gain medium. The power and linewidth characteristics of the DW output are studied. Limitation factors of the clock frequency as well as the feasibility of the PDH cavity stabilization are analyzed.

A highly integrated single-mode 1064 nm laser with 8.5 kHz linewidth for dual-wavelength active optical clock.

Without exploiting any frequency selective elements, we have realized a highly integrated, single-mode, narrow-linewidth Nd:YAG 1064 nm laser, which is end-pumped by the 808.6 nm diode laser in an integrated invar cavity. It turns out that each 1064 nm laser achieves a most probable linewidth of 8.5 kHz by beating between two identical laser systems. The output power of the 1064 nm laser increases steadily as the 808.6 nm pump power is raised, which can be up to 350 mW. Moreover, the resonant wavelength of cavity grows continuously in a certain crystal temperature range. Such a 1064 nm laser will be frequency stabilized to an ultrastable cavity by using the Pound-Drever-Hall technique and used as the good cavity laser to lock the main cavity length of 1064/1470 nm good-bad cavity dual-wavelength active optical clock.

Ultra-narrow linewidth optical filter based on Faraday effect at isotope 87Rb 420 nm transitions

An ultra-narrow linewidth optical filter with isotope 87Rb vapor at 420 nm, within the best waveband 400–500 nm for deep sea communication is achieved for the first time. The Faraday effect, circular dichroism, and nonlinear saturation techniques are utilized to narrow the bandwidth from previous 2.5 GHz to about 15 MHz level on the energy transition 5S1/2→6P3/2. By changing the temperature and magnetic field, the maximum transmission is obtained when the temperature and the magnetic field of the 87Rb cell are at 100 °C and 12 G. We discuss the varying influences of temperature, magnetic field, and pump power on the transmission of the atomic filter. The maximum single peak transmission at 5S1/2, F=2→6P3/2, F′=3 transition is 2.1% with a bandwidth of 17.8 MHz, and 1.9% at the 5S1/2, F=2→6P3/2, F′=2,3 (cross-over) transition with that of 14.2 MHz. The calculated equivalent noise bandwidth of this system is 32.5 MHz. Compared with the conventional Faraday anomalous dispersion optical filter, the bandwidth of our system is narrowed at least two orders of magnitude and is closer to the natural linewidth. This ultra-narrow linewidth filter has the potential to be applied to submarine communication or the pump laser in a four-level Rb-based active optical clock.

Different ways to active optical frequency standards

Active optical frequency standard, or active optical clock, is a new concept of optical frequency standard, where a weak feedback with phase coherence information in optical bad-cavity limitation is formed, and the continuous self-sustained coherent stimulated emission between two atomic transition levels with population inversion is realized. Through ten years of both theoretical and experimental exploration, the narrow linewidth and suppression of cavity pulling effect of active optical frequency standard have been initially proved. In this paper, after a simple review, we will mainly present the most recent experimental progresses of active optical frequency standards in Peking University, including 4-level cesium active optical frequency standards and active Faraday optical frequency standards. The future development of active optical frequency standards is also discussed.

Experimental Scheme of 633 nm and 1359 nm Good-Bad Cavity Dual-Wavelength Active Optical Frequency Standard**Supported by the National Natural Science Foundation of China under Grant Nos 10874009, 11074011 and 91436210, and the International Science & Technology Cooperation Program of China under Grant No 2010DFR10900.

The experimental scheme of 633 nm and 1359 nm good-bad cavity dual-wavelength active optical frequency standard is proposed, where He-Ne 633 nm and Cs 1359 nm stimulated emissions are working at good-cavity and bad-cavity regimes, respectively. The cavity length is stabilized by locking the 633 nm output frequency to a super-cavity with the Pound–Drever–Hall (PDH) technique. The frequency stability of 1359 nm bad-cavity stimulated emission output is then expected to be further improved by at least 1 order of magnitude than the 633 nm PDH system due to the suppressed cavity pulling effect of active optical clock, and the quantum limited linewidth of 1359 nm output is estimated to be 72.5 mHz.

Research progress on active optical clocks

Active optical clocks, a new class of optical atomic clocks, work through stimulated emission lasing, a unique mechanism that is distinct from laser absorption spectroscopy of conventional optical clocks. With coherent weak optical feedback from a Fabry-Perot resonator operating in the bad-cavity regime, active optical clocks sustain a lasing oscillation at an atomic transition frequency. They are used directly as quantum optical frequency standards with expected stability better by about two orders of magnitude than that of the best clocks. This review starts with a simplified account of historical developments and the limitations of critical techniques in optical atomic clocks. After an introduction of the basic mechanism underlying active optical clocks, we discuss the most recent experimental results for several configurations and experimental set-ups of active optical clocks. These include those based on a 2-level atomic beam and 3-level laser-cooled trapped-atom system, those based on a 4-level atom scheme, and the Faraday active optical clock. Moreover, following the successful lasing and preliminary results on a Faraday active optical frequency standard with Faraday atomic filter using thermal Cs cell, we describe an experimental scheme of a Faraday active optical clock with a Faraday atomic filter using magic-lattice-trapped Sr atoms at the 689-nm transition, and Faraday optical clocks operating in the good-cavity regime. We conclude with a comprehensive comparison of the different active optical clocks, prospects for active Faraday optical clocks, and potential applications of active optical clocks.

Cs 728 nm Laser Spectroscopy and Faraday Atomic Filter

We mainly present the 728 nm laser spectroscopy and Faraday atomic filter of Cs atoms with 650 MHz linewidth and 2.6% transmission based on an electrodeless discharge vapor lamp, compared with Rb 728 nm laser spectroscopy. Accidentally, this remarkably strong Cs 728 nm transition from the 6F7/2 state to the 5D5/2 state is only about 2.5 GHz away from the Rb 728 nm transition of the future potential four-level active optical clock, once laser cooled and trapped from the 7S1/2 state to the 5P1/2 state, as we proposed previously. A Faraday atomic filter stabilized 728 nm laser using a Cs electrodeless discharge vapor lamp with a power of 10mW will provide a frequency reference to evaluate the performance of the potential Rb four-level active optical clock at 728 nm with power less than 1 nW by 2.5 GHz heterodyne measurements.

Laser 728 nm Spectroscopy of Electrodeless Discharge Rb Lamp

We mainly report the 728.0 nm transition between 7S1/2 and 5P1/2 laser spectroscopy of an electrodeless discharge Rb vapor lamp, which is the clock transition of a potential four-level active optical clock, once laser cooled and trapped Rb atoms are pumped by 359.2 nm laser. To realize this proposition, we study the linewidth and absorption characteristics of the 728.0 nm laser absorption spectrum of a rubidium electrodeless discharge vapor lamp with varying lamp temperature and rf driving power respectively, measured by an external cavity diode laser in a Littrow configuration. The measured 728.0 nm spectrum of a glass cell filled with Rb and Ar buffer gases in the electrodeless discharge Rb lamp based Faraday filter stabilized laser can be a heterodyne comparison reference for the weak power output of a possible cold Rb four-level active optical clock at 728.0 nm clock transition with laser cooled and trapped atoms. To the best of our knowledge, there has not been any research reported on Rb 728.0 nm laser spectroscopy in detail.

Active Faraday optical frequency standard.

We propose the mechanism of an active Faraday optical clock, and experimentally demonstrate an active Faraday optical frequency standard based on narrow bandwidth Faraday atomic filter by the method of velocity-selective optical pumping of cesium vapor. The center frequency of the active Faraday optical frequency standard is determined by the cesium 6 (2)S(1/2) F=4 to 6 (2)P(3/2) F'=4 and 5 crossover transition line. The optical heterodyne beat between two similar independent setups shows that the frequency linewidth reaches 281(23) Hz, which is 1.9×10(4) times smaller than the natural linewidth of the cesium 852-nm transition line. The maximum emitted light power reaches 75 μW. The active Faraday optical frequency standard reported here has advantages of narrow linewidth and reduced cavity pulling, which can readily be extended to other atomic transition lines of alkali and alkaline-earth metal atoms trapped in optical lattices at magic wavelengths, making it useful for new generation of optical atomic clocks.

An Active Ion Optical Clock

We propose a scheme for an active ion optical clock with a detailed description of the pumping method, lasing states, output power, linewidth and light shift. Considering 171Yb+ ions in a Paul trap, we propose utilizing a Fabry—Perot resonator to realize the lasing of active optical frequency standards. The quantum-limited linewidth of an active 171Yb+ ion optical clock is narrower than 1 mHz. Based on the mechanism and the advantages of an active optical clock at the ion optical clock transition frequency, this new laser light source as a stable local oscillator will be beneficial to the single-ion optical clock, which currently is one of the most accurate clocks.