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(a) The energy level of Cs four-level active optical clock system. (b) The relation between the temperature of the Cs atomic vapor cell and the power of output lasers in the Cs four-level AOC. The black square-dots and the red square-dots represent the output power of 1470 nm laser and 1359 nm laser, respectively.
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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....
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... In addition, a number of techniques have been reported on the development of extremely coherent light sources. For example, the most widely used ones include the Pound-Drever-Hall method wherein the laser frequency is stabilized to an optical stable cavity to narrow the laser linewidth [23,24], the active optical clock technique [25][26][27][28][29] in which the stimulated emission from the atomic gain medium is used to generate narrow linewidth lasers [30,31], and the SHB phenomenon in cryogenically cooled crystals [32,33] which is the focus of interest of this paper. ...
In limit of saturation spectroscopy, we theoretically study the spectral hole burning (SHB) in the absorption spectrum of a probe field through a tripod atomic system. The response function for the probe field is calculated in a Doppler-broadened medium. Burning of spectral holes is observed only for the counter propagation of either one or both the coupling fields in the medium. The SHB is not observed below some critical temperature which is a condition for the electromagnetically induced transparency (EIT) in the medium. The most interesting and significant feature is that the Doppler broadening acts as a decoherence effect in case of EIT, however, the Doppler broadening acts inversely in case of SHB, and consequently the burning effect enhances. The SHB is further enhanced and controlled by classes of the average velocity of atoms. The classes of high average atomic velocity in the medium increase the number of spectral hole burns (HBs). The widths of HBs can be controlled by the intensity of the driving fields. A single HB can be switched to multiple HBs in a well-controlled manner using different classes of high average atomic velocity. The various switchable holes can be burned in a desired position of the absorption spectrum which in turn simultaneously slows down multiple probe fields. The phenomenon of SHB may be useful in the construction of multichannel optical switching and storage devices.
... Thus far, active optical clocks with the gain of thermal alkali-metal atoms have shown a spectral linewidth of ∼ 50 Hz, corresponding to a potential fractional frequency stability of 1.4 × 10 −14 at 1 s of averaging. [18,19] In contrast, a superradiant active clock, which makes use of the forbidden electricdipole transition in lattice-trapped Sr atoms, has achieved an Allan deviation of 6.7 × 10 −16 ∕ √ with the averaging time . [20] Nevertheless, this clock is operated in pulsed mode and suffers from the Dick effect [21] and large photon shot noise. ...
... According to this, active optical clocks were proposed [15] and have been demonstrated. [18,28,29] Employing the ultranarrow-linewidth clock transition in Sr as the laser transition leads to ( ∕2Γ) of the order of 10 6 . [20] In addition, lasing in the bad-cavity regime benefits from a spectral linewidth Δ l that overcomes the usual Schawlow-Townes limit Δ ST , ...
Active 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 3.4×10−14$3.4\times 10^{-14}$ 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.
... Atomic clocks also can be divided into two categories according to their working mode, namely passive clocks and active clocks International Frequency Control Symposium (IFCS), the AOC was listed as one of the three most emerging technologies receiving the most attention in this field. Currently, there are research groups across the globe such as JILA [41][42][43], NIST, University of Colorado, Vienna University of Technology (TU Wien) [44,45], University of Copenhagen [46], University of Amsterdam [47,48], Aarhus University [49,50], Zhengzhou University [51,52], Physical Research Laboratory (India) [53], University of Hamburg [54], University of Innsbruck [55,56], Leibniz University Hannover [57], Nicolaus Copernicus University [58], Academia Sinica [59], Guru Nanak Dev University [60], Université Sorbonne Paris Nord [61], and Peking University [53,62] conducting research on bad-cavity superradiant laser based on various atomic systems. Currently, the JILA research group achieves a superradiant pulsed lasing based on the ultra-narrow transition linewidth of 87 Sr atoms with a frequency stability of 6.7 × 10 −16 at 1 s and an accuracy of 4 × 10 −15 [43]. ...
... The Aarhus University realizes superradiant pulsed laser with linewidth less than 2 Hz [49]. The Peking University achieves a continuous-wave (CW) 1470 nm active light field based on Cs thermal atoms with a linewidth of 53 Hz and demonstrate its superior cavity-pulling suppression property [62]. ...
... In a four-level AOC scheme, the quantum system can select alkali metal atoms such as K [92], Rb [93,94], and Cs [62,[95][96][97][98]. Taking Cs atom as an example, the Cs atomic gas cell is placed in a low-finesse optical cavity to make cavity-mode linewidth larger than gain linewidth to satisfy bad-cavity condition. ...
The atomic clocks, whether operating at optical or microwave region, can be divided into two categories according to their working mode, namely the passive clocks and active clocks. The passive clocks, whose standard frequency is locked to an ultra-narrow atomic spectral line, such as laser cooled Cs beam or lattice trapped Sr atoms, depend on the spontaneous emission line. On the contrary, the active clocks, in which the atoms are used as the gain medium, are based on the stimulated emission radiation, their spectrum can be directly used as the frequency standard. Up to now, the active hydrogen maser has been the most stable microwave atomic clocks. Also, the Sr superradiant active atomic clock is prospects for a millihertz-linewidth laser. Moreover, the optical clocks are expected to surpass the performance of microwave clocks both in stability and uncertainty, since their higher working frequency. The active optical clock has the potential to improve the stability of the best clocks by 2 orders of magnitude. In this work, we introduce the development of active optical clocks, and their types is classified according to the energy-level structure of atoms for stimulated radiation.
... Alternatively, by using a cavity with ultralow finesse, the above problems will be solved. A typical application is an active optical clock (AOC) [13][14][15][16][17][18][19][20][21][22] based on strong atomic transition of cesium [20,23]. Working in the bad-cavity limit [13,15,16,[18][19][20]22], where the atomic decay rate gain is much smaller than the cavity dissipation rate c , only weak cavity-induced feedback occurs on the atomic dipole, resulting in the collective atomic dipole being highly coherent, and the phase information of an AOC laser is primarily stored in the atomic gain medium. ...
... Alternatively, by using a cavity with ultralow finesse, the above problems will be solved. A typical application is an active optical clock (AOC) [13][14][15][16][17][18][19][20][21][22] based on strong atomic transition of cesium [20,23]. Working in the bad-cavity limit [13,15,16,[18][19][20]22], where the atomic decay rate gain is much smaller than the cavity dissipation rate c , only weak cavity-induced feedback occurs on the atomic dipole, resulting in the collective atomic dipole being highly coherent, and the phase information of an AOC laser is primarily stored in the atomic gain medium. ...
... A typical application is an active optical clock (AOC) [13][14][15][16][17][18][19][20][21][22] based on strong atomic transition of cesium [20,23]. Working in the bad-cavity limit [13,15,16,[18][19][20]22], where the atomic decay rate gain is much smaller than the cavity dissipation rate c , only weak cavity-induced feedback occurs on the atomic dipole, resulting in the collective atomic dipole being highly coherent, and the phase information of an AOC laser is primarily stored in the atomic gain medium. Therefore, compared with the good-cavity laser using an ultrahigh-finesse optical cavity as a reference, the sensitivity of an AOC laser to cavity fluctuations is greatly reduced, as characterized by the suppressed cavity-pulling effect. ...
The exact expressions of finesse and full width at half maximum (FWHM) of the Airy distribution of a Fabry-Pérot (FP) resonator are derived, which solves the breakdown problem at ultralow reflectivity in traditional formulas. We demonstrate that, when the cavity-mirror reflectivity R→0, the FWHM approaches half of the free spectral range rather than infinity; moreover, the cavity finesse 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 “2F/2Fππ,” which is inadequate for the high-loss cavity because the cavity-enhancement factor should naturally reach 1 when R→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.
... In addition, the active optical clock scheme is applicable to rubidium atoms with clock 5p 2 P 1/2,3/2 − 6s 2 S 1/2 (wavelengths of 1323 and 1366 nm) and pump 5s 2 S 1/2 − 6p 2 P 1/2 (wavelength of 421 nm) transitions. Despite the absence of the Allan deviation measurement, active optical clocks have been demonstrated in [44,45] with thermal atoms. Employing cold atoms as the gain medium potentially improves the clock stability [46]. ...
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 σ y (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 σ y (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 σ y (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.
... Recently, active optical clocks based upon the laser oscillation in the bad-cavity limit have been proposed [12] and demonstrated [13]. As illustrated in [14,15], the quantum-limited spectral linewidth of a single-mode laser takes the form: ...
... The lasing action occurs when the pump rate Γ exceeds the energy loss rate of the system. Unlike the four-level active optical clocks based upon alkali metal atoms [13], our system is a three-level scheme, where the zero nuclear spin of 88 Sr much simplifies the atom-microcavity interaction. In comparison to the laser system based upon the ultranarrow (5s 2 ) 1 S 0 −(5s5p) 3 P 0 transition of fermionic strontium [37], the relatively strong (5s 2 ) 1 S 0 −(5s5p) 3 P 1 transition potentially enhances the laser output power by three orders of magnitude, although the resulting frequency stability of clock lasers degrades. ...
... Employing a four-level laser system, where the pump beam is far-detuned to any atomic transitions associated with two clock states, may strongly reduce the pump-induced light shifts. As it has been demonstrated in [13], the pump beam at 459 nm (corresponding to the (6s) 2 S 1/2 −(7p) 2 P 1/2 transition) is far-off resonant to the |e⟩ ≡ (6p) 2 P 1/2.3/2 −|g⟩ ≡ (7s) 2 S 1/2 clock transitions (wavelengths of 1359 and 1470 nm, respectively) in 133 Cs. ...
Optical atomic clocks with compact size, reduced weight and low power consumption have broad out-of-the-lab applications such as satellite-based geo-positioning and communication engineering. Here, we propose an active optical microclock based on the lattice-trapped atoms evanescently interacting with a whispering-gallery-mode microcavity. Unlike the conventional passive clock scheme, the active operation directly produces the optical frequency standard without the need of extra laser stabilization, substantially simplifying the clock configuration. The numerical simulation illustrates that the microclock’s frequency stability reaches 1.5×〖10〗^(-14) at 1 s of averaging, over one order of magnitude better than the recently demonstrated chip-scale optical clock that is built upon rubidium vapour cell and also more stable than current cesium fountain clocks and hydrogen masers. Our work extends the chip-scale clocks to the active fashion, paving the way towards the on-chip quantum micro-metrology, for example, the optical frequency comparison and synchronization between multiple microclocks through frequency microcombs.
... The development of new laser mechanisms has continually expanded the technological range of laser applications. An intriguing class of laser mechanisms is superradiant lasing, which is based on collective coherent spontaneous emission of identical atomic transitions, i.e. superradiance, which is a transient phenomenon that can be engineered into continuous operation to achieve ultra narrow linewidths [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. This laser operation is characterized by the coherence that is stored in the two-level systems (TLS) rather than the photon state in the cavity, in contrast to conventional lasing. ...
... We then identify the cavity loss rate as the most sensitive parameter, as the FSP vanishes comparatively rapidly as a function of cavity losses. This establishes the FSP as a 'good-cavity'-regime laser mechanism, in contrast to superradiant lasers which operate in the 'bad-cavity'-regime [2][3][4][5][6][7]. Overall, our model suggests the possibility of laser operation in a solid state system, such as a two-band material, due to the form of the dissipative processes, the magnitude of the dissipation that we consider, and the robustness against inhomogeneous broadening. ...
We demonstrate the feasibility of utilizing the recently established Floquet-assisted superradiance for laser operation. In particular, we show the robustness of this state against key imperfections. We consider the effect of a finite linewidth of the driving field, modelled via phase diffusion. We find that the linewidth of the light field in the cavity narrows drastically across the FSP transition, reminiscent of a line narrowing at the laser transition. Next, we demonstrate that the FSP is robust against inhomogeneous broadening, while displaying a reduction of light intensity. We show that the depleted population inversion of near-resonant Floquet states leads to hole burning in the inhomogeneously broadened Floquet spectra. Finally, we show that the FSP is robust against dissipation processes, with coefficients up to values that are experimentally available. We conclude that the FSP presents a robust mechanism that is capable of realistic laser operation.
... Here, we report an experimental demonstration of an inhibited laser. The energy level scheme and general setup are depicted schematically in Fig. 1a, b, respectively, sharing similarities with the proposed superradiant AOC based on thermal atoms 23 . N ≈ 1.8 × 10 11 pure cesium (Cs) atoms are confined to the TEM 00 mode of a low-finesse optical cavity (F ¼ 3:07), whose dissipation rate is κ 0 = 2π × 257 MHz. ...
... To analyze the impact of collision broadening on the laser linewidth caused by temperature fluctuations individually, we stabilized the cavity length by the optical phase loop locking (OPLL) technique in the system of the dualwavelength AOC, whose experimental details are shown in Ref. 23 . After cavitylength stabilization, the slope of the frequency shift of the 1470 nm laser with the change of the temperature fluctuations was below 45 ± 1.2 kHz ∘ C −1 . ...
... The linewidth of the 1470 nm laser was also influenced by the power stability of the pumping laser. To further evaluate the influence of the power stability of the pumping laser on the laser linewidth, we measured the laser frequency variations with the power of the pumping laser, as shown in Ref. 23 . An approximately linear relationship was obtained, with a slope of −36.1 ± 0.94 kHz mW −1 . ...
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 2F/π2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\left(2{{{{{{{\mathcal{F}}}}}}}}/\pi \right)}^{2}$$\end{document}, 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.
... Consequently, great efforts have been put into the development of extremely coherent light sources. Three of the most widely used techniques include the Pound-Drever-Hall (PDH) technique using highly stable optical Fabry-Pérot (F-P) resonators [8,9], the spectral-hole burning in cryogenic crystals [10,11], and the stimulated emission of radiation from the atomic gain medium of the active optical clock (AOC) technique to realize mHz-linewidth superradiant lasers [12][13][14][15][16][17][18] and frequency stabilized bad-cavity lasers [19,20]. In the first approach, the laser frequency is stabilized to an optical reference cavity with the ultra-stable length to narrow the laser linewidth, which has realized the most-coherent oscillator with the narrowest linewidth of 10 mHz [9]. ...
... Liu et al. proposed a superradiant laser based on the hot atomic-beam method, which has advantages of continuous-wave operation [18]. Moreover, using the thermal cesium ensemble as a gain medium, Chen [20] experimentally realized a continuouswave active optical frequency standard with power of 100 μW, based on the experimental scheme proposed in 2010 [23]. ...
... The smaller slope is owing to the lasers sharing one cavity, which will reduce the influence of temperature change in the beat-note frequency. In addition, this result is similar to the experimental value reported in [20], where the cavity length is stabilized by the optical phase-locking loop technique. ...
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 red cavity fluctuations is greatly reduced, as characterized by the suppressed cavity-pulling effect. In this work, the AOC lasing on the cesium 7S 1/2 -6P 3/2 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 7S 1/2 -6P 3/2 . 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.
... This limitation can be partially circumvented in an active reference, in which the system could consist of an atomic ensemble within an optical cavity [14][15][16][17][18][19]. Here the idea is to pump the atoms to an excited state with a long lifetime relative to the decay of the cavity field, thus operating in the bad cavity regime [20]. In this regime the cavity will enhance the emission rate by the atoms without pulling the frequency strongly to the cavity resonance, as the phase information is primarily stored in the atoms. ...
Lasing in the bad cavity regime has promising applications in precision metrology due to the reduced sensitivity to cavity noise originating from cavity length fluctuations. Here we investigate the spectral properties and phase behavior of pulsed lasing on the S01−P13 line of Sr88 in a mK thermal ensemble, as first described by S. A. Schäffer et al. [Phys. Rev. A 101, 013819 (2020)]. The system operates in a regime where the Doppler-broadened atomic transition linewidth is several times larger than the cavity linewidth. We find that for some detunings of the cavity resonance, the influence of the cavity noise on the peak lasing frequency can be eliminated to first order despite the system not being deep in the bad cavity regime. Experimental results are compared to a model based on a Tavis-Cummings Hamiltonian, which enables us to investigate the interplay between different thermal velocity classes as the underlying mechanism for the reduction in cavity noise. These velocity-dependent dynamics can occur in pulsed lasing and during the turn-on behavior of lasers in the superradiant crossover regime.
