Quantum correlations and nonclassicality in a system of two coupled vertical external cavity surface emitting lasers

Here we demonstrate that photocurrent noise reduction below the standard quantum limit and modal anticorrelation can arise in a two-mode coupled vertical external cavity surface emitting laser system with a common pump. This effect occurs due to correlated loss of laser modes. It is possible to suppress noise below the standard quantum limit even for Poissonian coherent pumping, whereas the regularity of the pump can be harmful for nonclassicality.

Figure 1

(a) An illustration of the active media regions generating lasing modes. Emitters of region 1 (denoted as R1) interact only with modes denoted as “a,” emitters of region 2 (denoted as R2) interact only with modes denoted as “b,” and emitters of region 3 (denoted as R3) interact with both groups of modes. (b) A scheme of levels of the $j\mathrm{th}$ emitter of region $\mathrm{R}x$.

Figure 2

Spectra of the mode $a$ photocurrent, $C_{aa}\left(\Omega \right)$, for values of system parameters given by Eq. (47). (a) Spectra for different values of pumping rate. Thick solid, dashed, and dash-dotted lines correspond to $R_a=R_b=1.001{\overline{R}}_a,1.01{\overline{R}}_a,1.011{\overline{R}}_a$ for the coherent pumping, $p=0$; dotted and thin solid lines correspond to $R_a=R_b=1.01{\overline{R}}_a,1.011{\overline{R}}_a$ for the regular pumping, $p=1$; the overlap is ${\xi }_a={\xi }_b=0.8$. (b) Spectra for larger overlaps of VECSEL active zones; solid, dashed, dash-dotted, dotted lines correspond to ${\xi }_a={\xi }_b=0.5,0.6,0.7,0.8$; the pumping is the coherent one, $p=0$; $R_a=R_b=1.01{\overline{R}}_a$. (c) Spectra for smaller overlaps of VECSEL active zones; solid, dashed, dash-dotted, dotted lines correspond to ${\xi }_a={\xi }_b=0.1,0.2,0.3,0.4$; other parameters are as in (b); the inset shows spectra for small frequencies for the same parameters as in the main panel. (d) Spectra for different values of the interaction constant; solid, dashed, and dash-dotted lines correspond to $g=0.01{\kappa }_a,0.05{\kappa }_a,0.1{\kappa }_a$; the pumping is the coherent one, $p=0$; the overlap is ${\xi }_a={\xi }_b=0.8$; $R_a=R_b=1.01{\overline{R}}_a$. For all figures birefringence and the detuning between modal frequencies and the emitter transition frequency are taken to be zero, ${\omega }_{ap}={\omega }_{bp}=0$, ${\omega }_a=w$; $\Omega$ is given in units of $\kappa$.

Figure 3

Spectra of the mode $b$ photocurrent, $C_{bb}\left(\Omega \right)$, for values of system parameters given by Eq. (47). (a) Spectra for different values of pumping rate. Solid, dashed, dash-dotted, and dotted lines correspond to $R_a=R_b=1.001{\overline{R}}_a,1.005{\overline{R}}_a,1.01{\overline{R}}_a,1.011{\overline{R}}_a$; the overlap is ${\xi }_a={\xi }_b=0.8$, $p=0$ [the parameters are as in Fig. 2, coherent pumping]. (b) Spectra for larger overlaps of VECSEL active zones; solid, dashed, dash-dotted, dotted lines correspond to ${\xi }_a={\xi }_b=0.5,0.6,0.7,0.8$; other parameters are as in Fig. 2. (c) Spectra for smaller overlaps of VECSEL active zones; solid, dashed, dash-dotted, dotted lines correspond to ${\xi }_a={\xi }_b=0.1,0.2,0.3,0.4$; other parameters are as in (b). (d) Spectra for different values of the interaction constant; solid, dashed, and dash-dotted lines correspond to $g=0.01{\kappa }_a,0.05{\kappa }_a,0.1{\kappa }_a$; other parameters are as in Fig. 2. For all figures the pumping is the coherent one, $p=0$.

Figure 4

Cross-correlation function $C_{ab}\left(\Omega \right)$, for values of system parameters close to ones given by Eq. (47). (a) Cross-correlation function for different values of pumping rate. Solid, dashed, dash-dotted, and dotted lines correspond to $R_a=R_b=1.001{\overline{R}}_a,1.005{\overline{R}}_a,1.01{\overline{R}}_a,1.011{\overline{R}}_a$; other parameters are as in Fig. 3. (b) Cross-correlation function for larger overlaps of VECSEL active zones; solid, dashed, dash-dotted, dotted lines correspond to ${\xi }_a={\xi }_b=0.5,0.6,0.7,0.8$; other parameters are as in Fig. 3. (c) Cross-correlation function for smaller overlaps of VECSEL active zones; solid, dashed, dash-dotted, dotted lines correspond to ${\xi }_a={\xi }_b=0.1,0.2,0.3,0.4$; other parameters are as in (b). (d) Cross-correlation function for different values of the interaction constant; solid, dashed, and dash-dotted lines correspond to $g=0.01{\kappa }_a,0.05{\kappa }_a,0.1{\kappa }_a$; other parameters are as in Fig. 2.