3 ˜ N$_{bss}$ = R τ 2 [ 1 − C$_{0}$ − C$_{1}$ + C$_{2}$ g τ √ κ R ( B$_{0}$ − B$_{1}$ + B$_{2}$ ) ] . D = γ 2 ab ( κ/ 2 + γ$_{ab}$ ) 2 { D$_{ST}$ + D$_{Ram}$ [2 − p sin$^{2}$( Ω$_{R}$ τ ) sin$^{2}$( Δ$_{2}$ T $^{)]}$} . (11) ( δϕ $^{2}$)$_{ω}$ = 1 I$_{0}$ ( δ Y $^{2}$)$_{ω}$ . ( δϕ $^{2}$)$_{ω}$ ≈ ( κ/ 2 + γ$_{ab}$ ) 2 I$_{0}$ ω $^{2}$[( κ/ 2 + γ$_{ab}$ ) 2 + ω $^{2}$] g 2 4( κ/ 2 + γ$_{ab}$ ) 2 { 4 γ$_{ab}$ ˜ N$_{ass}$ + 2 R [( A$_{0}$ + B$_{0}$ ) + ( A$_{2}$ + B$_{2}$ )] + Rp [( C$_{0}$ − C ∗ $_{0}$) 2 + ( C$_{1}$ − C ∗ $_{1}$) 2 + ( C$_{2}$ − C ∗ $_{2}$) $^{$^{2}$]}$} . (9) A$_{0}$ = cos 2 ( Ω$_{R}$ 2 τ ) , A$_{1}$ = cos 2 ( Ω$_{R}$ 2 τ ) , A$_{2}$ = 1 − sin 2 ( Ω$_{R}$ τ ) cos 2 ( Δ$_{2}$ 2 T ) , B$_{0}$ = sin 2 ( Ω$_{R}$ 2 τ ) , B$_{1}$ = sin 2 ( Ω$_{R}$ 2 τ ) , B$_{2}$ = sin 2 ( Ω$_{R}$ τ ) cos 2 ( Δ$_{2}$ T 2 ) , ( C$_{0}$ − C ∗ $_{0}$) 2 = 0 , ( C$_{1}$ − C ∗ $_{1}$) 2 = − sin 2 ( Ω$_{R}$ τ ) sin 2 ( Δ$_{2}$ T ) , ( C$_{2}$ − C ∗ $_{2}$) 2 = − sin 2 ( Ω$_{R}$ τ ) sin 2 ( Δ$_{2}$ T ) , ( δϕ $^{2}$)$_{ω}$ = ( κ/ 2 + γ$_{ab}$ ) 2 ω $^{2}$[( κ/ 2 + γ$_{ab}$ ) 2 + ω $^{2}$)] γ 2 ab ( κ/ 2 + γ$_{ab}$ ) 2 { D$_{ST}$ + D$_{Ram}$ [2 − p sin$^{2}$( Ω$_{R}$ τ ) sin$^{2}$( Δ$_{2}$ T $^{)]}$} , (10) D ≈ 2 g 2 κ [2 − p sin$^{2}$( Ω$_{R}$ τ ) sin$^{2}$( Δ$_{2}$ T )] . (12) A detailed analysis about the stability of the steady-state can be found such as in [28]. In this paper, we assume the steady- state solution is stable. Laser linwidth: Suppose the quantum fluctuation is small, the evolution of the fluctuations can be obtained by making a linearization of the c-number Langevin equations around the steady-state solution. Then the measured spectra of field flu c- tuations will be directly related to these quantities. By Fourier transformations of the linearized equation, we get the ampli- tude and phase quadrature components δ X ( ω ) and δ Y ( ω ) [26]. Well above threshold, one can neglect the amplitude fluctu- ations, and the linewidth inside the cavity is related to the phase-di ff usion coe ffi cient [25]. For small fluctuation of laser phase, the spectrum of phase fluctuations is simply related t o the spectrum of the phase quadrature component of the field fluctuations, namely, In the region γ$_{ab}$ ≪ T − 1 ≪ τ − 1 ≪ κ/ 2, as in the recently proposed active optical clock [15] with atomic beam. The phase quadrature component of the field fluctuations can be expressed as Since the time τ and T is much shorter than the time scale of the atomic dampings, we can neglect the dampings when calculate A$_{i}$ , B$_{i}$ , C$_{i}$ . By using we get Since D$_{ST}$ / D$_{Ram}$ ≪ 1 in our situation, and in the case of max- imal photon number, the steady state value of ˜ N$_{ass}$ is about R τ/ 2. Then we get the where Ω$_{R}$ is the Rabi frequency on resonance, D$_{ST}$ = g 2 ˜ N$_{ass}$ / I$_{0}$ γ$_{ab}$ , D$_{Ram}$ = g $^{2}$R / 2 I$_{0}$ γ 2 $_{ab}$, and Δ$_{2}$ = ω − ( ω$_{a}$$_{2}$ − ω$_{b}$$_{2}$ ) presents the detuning in the free drift region. p is a parameter, which characterizes the pump- ing statistics: a Poissonian excitation statistics corresponds to p = 0 , and for a regular statistics we have p = 1. Then the linewidth of Ramsey laser with bad cavity is given by From the expression above, we find that the pumping statis- tic can influence the linewidth. For regular injection ( p = 1), the linewidth is the narrowest, while for Poissonian injection ( p = 0), the linewidth is the broadest. But even for regular injection, the linewidth is larger than the case of one cavity. That means the mechanism of separated-field does not play the role in reducing the linewidth as in the conventional opti- cal Ramsey method, which is counter-intuitive. However, the separated fields are indispensable for any phase detection l ike atom interferometry. The details about the method of active atom interferometry will appear elsewhere. Our method of Ramsey laser is suitable for any atoms with metastable energy level, as an example, we choose the tran- sition from the metastable state 4 s 4 p $^{3}$P$_{1}$ to the ground state 4 s $^{2 1}$S$_{0}$ of $^{40}$Ca to check the striking feature of this laser: sub- natural linewidth. As mentioned in [29], the corresponding natural linewidth of the metastable state 4 s 4 p $^{3}$P$_{1}$ is 320Hz. As in the recently proposed active optical clock with atomic beam [15], the velocity of the atoms in thermal atomic beam is about 500m / s, and the length of the interaction region is about 1mm, then the time for the atom to traverse each coherent- interaction region is on the order of magnitude of 1 µ s. If a bad cavity with κ is on the order of 10$^{7}$Hz, the relation κ/ 2 ≫ τ − 1 is satisfied. Then when g is on the order of the magnitude of kHz, which can be easily achieved for current technique [30], from the linewidth expression of Eq.(16) the order of magnitude of linewidth is below 1 Hz. This means the linewidth of a Ramsey laser can be more than two or- ders of magnitude narrower than the atomic natural linewidth, therefore our Ramsey method provides a new subnatural spec- troscopy technique. And since it is stimulated-emission spec- trum, it overcomes the di ffi culty in other subnatural linewidth spectroscopy schemes where the quick reduction of signal to noise ratio is a formidable limit. We should point out that this Ramsey laser does not escape the limitation of all active optical clock: in order to pump atoms to the excited state ef- fectively and to be stimulated emit photon during the lifetime of a metastable state, this new method will only be applicable to some special transitions [17].