Controlled Asymmetry of Einstein-Podolsky-Rosen Steering with an Injected Nondegenerate Optical Parametric Oscillator

We propose and analyze a nonlinear optical apparatus in which the direction of asymmetric steering is controllable within the apparatus, rather than by adding noise to measurements. Using a nondegenerate parametric oscillator with an injected signal field, we show how the directionality and extent of the steering can be readily controlled for output modes that can be up to one octave apart. The two down-converted modes, which exhibit the greater violations of the steering inequalities, can also be controlled to exhibit asymmetric steering in some regimes.

Figure 1

The minima of the spectral ${\mathrm{EPR}}_{ij}$ output correlations between the modes 0 and 1, and 1 and 2, as a function of the ratio of the injected signal to the pump amplitude at ${\omega }_0$. ${\gamma }_0={\gamma }_1={\gamma }_2=1$ for this result, $\kappa ={10}^{-2}$, and ${\epsilon }_0=100$. All quantities plotted in this Letter are dimensionless.

Figure 2

The minima of the spectral ${\mathrm{EPR}}_{ij}$ output correlations between the modes 0 and 1, and 1 and 2, as a function of the ratio of the injected signal to the pump amplitude at ${\omega }_0$. ${\gamma }_1={\gamma }_2=2=2{\gamma }_0$ for this result, $\kappa ={10}^{-2}$, and ${\epsilon }_0=100$.

Figure 3

The minima of the spectral ${\mathrm{EPR}}_{ij}$ output correlations between the modes 0 and 1, and 1 and 2, as a function of the ratio of the injected signal to the pump amplitude at ${\omega }_0$. ${\gamma }_2={\gamma }_0=1=2{\gamma }_1$ for this result, $\kappa ={10}^{-2}$, and ${\epsilon }_0=100$.

Figure 4

The positive frequency spectral ${\mathrm{EPR}}_{ij}$ output correlations between the modes 0 and 1, and 1 and 2, for ${\epsilon }_1=50$. ${\gamma }_2={\gamma }_0=1=2{\gamma }_1$ for this result, $\kappa ={10}^{-2}$, and ${\epsilon }_0=100$.

Figure 5

The steady-state mode amplitudes as a function of the ratio of the injected signal to the pump amplitude. ${\gamma }_2={\gamma }_0=1=2{\gamma }_1$ for this result, $\kappa ={10}^{-2}$, and ${\epsilon }_0=100$.