Quantum noise limits to simultaneous quadrature amplitude and phase stabilization of solid-state lasers

A quantum mechanical model is formulated to describe the coupling between pump intensity noise and laser frequency noise in a solid-state laser. The model allows us to investigate the limiting effects of closed-loop stabilization schemes that utilize this coupling. Two schemes are considered: active control of the quadrature phase noise of the laser and active control of the amplitude noise of the laser. We show that the noise of the laser in the actively stabilized quadrature is ultimately limited by the vacuum noise introduced by the feedback beamsplitter in both schemes. In the case of active control of the quadrature phase noise, the noise is also limited by the intensity noise floor of the detection scheme. We also show that some sources of noise in the passively stabilized quadrature can be suppressed and that it is possible to achieve simultaneous quadrature amplitude and phase stabilization of a solid-state laser. However, the quantum mechanically driven noise in the passively stabilized quadrature cannot be suppressed. While this poses the ultimate limit to the noise in the passively stabilized quadrature, we show that it is experimentally feasible to observe squeezing directly generated by a solid-state laser using this technique.

Figure 1

(a) A schematic diagram of frequency stabilization scheme using current lock. (b) A schematic diagram of the intensity stabilization scheme (noise-eater).

Figure 2

Plots of the quadrature amplitude and phase noise of the laser when $V_p^{+}=0\mathrm{dB}$ and when $V_p^{+}=60\mathrm{dB}$. The laser parameters used to generate these traces are $P_p=70\mathrm{mW}$, ${\eta }_p=0.552$ (pump quantum efficiency), ${\lambda }_p=0.813\mathrm{\mu }\mathrm{m}$ [13], ${\lambda }_l=1.064\mathrm{\mu }\mathrm{m}$, ${\kappa }_m=4.28\times {10}^7{\mathrm{s}}^{-1}$, ${\kappa }_l=1.74\times {10}^7{\mathrm{s}}^{-1}$, $l=26\mathrm{mm}$, and ${\tau }_T=0.032\mathrm{s}$. The $\mathrm{Nd}:\mathrm{YAG}$ parameters are: $n=1.82$, ${\gamma }_t=4.3\times {10}^3{\mathrm{s}}^{-1}$, $K=6.6\times {10}^{11}{\mathrm{s}}^{-1}$, ${\zeta }_T=1$, $\rho =4.55\times {10}^3\mathrm{kg}{\mathrm{m}}^{-1}$, $\sigma =0.25$, $\alpha =7.2\times {10}^{-6}{\mathrm{K}}^{-1}$, ${\alpha }_n=7.3\times {10}^{-6}{\mathrm{K}}^{-1}$, $C=100{\mathrm{JK}}^{-1}{\mathrm{m}}^{-1}$, and $C_{t,\varphi }=-0.0025$ $V_{\mathrm{cav}}=0$.

Figure 3

Plots of the quadrature amplitude and phase noise of the laser when the current lock stabilization loop is active and inactive. The parameters used to generate these traces are the same as for Fig. 2. We also set $\beta =0.5$, $\mid {\gamma }_F{\mid }^2=20\mathrm{dB}$, and $ϵ=0.5$.

Figure 4

Plots of the quadrature amplitude and phase noise of the laser when the noise-eater loop is active and inactive. The parameters used to generate these traces are the same as for Fig. 2. We also set $\mid {\gamma }_F{\mid }^2=20\mathrm{dB}$ and $ϵ=0.5$.