Large enhancement of fully resonant sum-frequency generation through quantum control via continuum states

A theory of quantum control of short-wavelength sum-frequency generation, which employs the continuum states, is developed. The proposed scheme employs all-resonant coupling and trade-off optimization of the accompanying constructive and destructive quantum interference effects in the lower-order and higher-order polarizations controlled by the overlap of two autoionizinglike laser-induced continuum structures. The scheme does not rely on adiabatic passage, coherent population trapping or maximum atomic coherence as a means to facilitate maximum output. The opportunities for manipulating transparency of the medium and refractive index for the fundamental and generated radiations, as well as nonlinear polarization in the multiple-resonant medium, are shown. This opens the feasibility of creating frequency-tunable narrowband filters, polarization rotators, and dispersive elements for vacuum ultraviolet radiation. The features specific for quantum interference in Doppler-broadened media are investigated. The feasibility of almost complete conversion of long-wavelength fundamental radiation into generated short-wavelength radiation, and of a dramatic decrease in the intensity of required fundamental radiations, is shown.

Figure 1

LICS-based coherent quantum control in ladder schemes.

Figure 2

Absorption index at ${\omega }_1$ reduced by its resonant value in the absence of all strong fields, $\alpha \left({\omega }_1\right)∕{\alpha }_{10}$, vs scaled one-photon detuning ${\Omega }_1∕{\Gamma }_{gm}=({\Omega }_1={\omega }_1-{\omega }_{gm})∕{\Gamma }_{gm}$. Here, $q_{ff}=0.9$, $q_{nn}=0.5$, ${\Gamma }_{gm}∕{\Gamma }_{gf}=100$, and ${\Gamma }_{gm}∕{\Gamma }_{gn}=10$. (a,b): ${\Omega }_2=0$, $q_{fn}=1.5$, $g_{mn}=7$, $g_{ff}=2$. (a): $g_{nn}=0$ (1), $g_{nn}=5$, ${\Omega }_L∕{\Gamma }_{gm}=0.8$ (2). (b): $g_{nn}=5$, ${\Omega }_L=0$. (c,d): ${\Omega }_2∕{\Gamma }_{mn}=0.3$, $g_{mn}=70$, $g_{ff}=10$, ${\Omega }_L∕{\Gamma }_{gm}=-1.1$, $g_{nn}=0$ (1), $g_{nn}=50$ (2). (c): $q_{fn}=15$. (d): $q_{fn}=1.5$.

Figure 3

Absorption index at ${\omega }_S$ reduced by its value in the absence of all strong fields, $\alpha \left({\omega }_S\right)∕{\alpha }_{S0}$, vs detunings $\Omega ∕{\Gamma }_{fg}=({\omega }_S-\omega -{\omega }_{fg})∕{\Gamma }_{fg}$ (a–c). The insets are the interference contributions to the corresponding curves vs detuning, the detuning interval is the same as for the main curves. Here, ${\Gamma }_{gm}∕{\Gamma }_{gf}=100$, ${\Gamma }_{gm}∕{\Gamma }_{gn}=10$. (a,b): $q_{ff}=0.9$, $q_{nn}=0.9$, ${\Omega }_L∕{\Gamma }_{gf}=-110$, ${\Omega }_2∕{\Gamma }_{gf}=30$. (a): $q_{gf}=-0.5$, $q_{gn}=-0.95$, $q_{fn}=15$. (1) $E_2=E_3=0$, ${\gamma }_{ff}∕{\Gamma }_{gf}=10$. (2–3) $g_{mn}=70$, ${\gamma }_{nn}∕{\Gamma }_{gn}=50$. (2) ${\gamma }_{ff}=0$. (3) ${\gamma }_{ff}=10$. (b): $q_{gf}=-0.95$, $q_{gn}=-0.5$, $q_{fn}=15$ (2,3), $q_{fn}=150$ (4). (1) $E_2=E_3=0$, ${\gamma }_{ff}∕{\Gamma }_{gf}=10$. (2–4) $g_{mn}=7$, ${\gamma }_{nn}∕{\Gamma }_{gn}=5$. (2) ${\gamma }_{ff}=0$. (3,4) ${\gamma }_{ff}∕{\Gamma }_{gf}=10$. (c): $q_{gf}=0.95$, $q_{gn}=0.01$, $q_{ff}=0.01$, $q_{nn}=-5$, $q_{fn}=1.5$, ${\Omega }_2∕{\Gamma }_{gf}=0$, ${\gamma }_{ff}∕{\Gamma }_{gf}=10$, $g_{mn}=7$. (1) ${\gamma }_{nn}∕{\Gamma }_{gn}=30$, ${\Omega }_L∕{\Gamma }_{gl}=-1530$. (2,3) ${\gamma }_{nn}∕{\Gamma }_{gn}=5$. (2) ${\Omega }_L∕{\Gamma }_{gf}=-110$. (3) ${\Omega }_L∕{\Gamma }_{gf}=-405$.

Figure 4

Scaled laser-induced change of the dispersive part of the refractive index at ${\omega }_S$ in the vicinity of LICS vs $\Omega ∕{\Gamma }_{fg}=({\omega }_S-\omega -{\omega }_{fg})∕{\Gamma }_{fg}$. All parameters are the same as for the corresponding plots (a–c) in Fig. 3.

Figure 5

Velocity averaged absorption index, $⟨\alpha \left({\omega }_1\right)⟩∕⟨{\alpha }_{10}⟩$, (solid) and dispersion part of the refractive index (dash) at ${\omega }_1$ reduced by their maximum values in the absence of all strong fields in a Doppler-broadened medium vs ${\Omega }_1∕\Delta {\omega }_{1D}$. Here, the Doppler HWHM $\Delta {\omega }_{1D}=16.65{\Gamma }_{gm}$, the wave vector orientations are $\mathbf{k}\uparrow \uparrow {\mathbf{k}}_1$, ${\mathbf{k}}_2\uparrow \uparrow {\mathbf{k}}_3\uparrow \downarrow {\mathbf{k}}_1$, and $k_2∕k_1=0.9$, $k_3∕k_1=0.5$, $k∕k_1=0.6$ (${\mathbf{k}}_i$ is wave vector corresponding to the frequency ${\omega }_i$), ${\Gamma }_{gm}∕{\Gamma }_{gf}=100$, ${\Gamma }_{gm}∕{\Gamma }_{gn}=10$; ${\mid G_{mn}\mid }^2∕{\left(\Delta {\omega }_{1D}\right)}^2=1$, $q_{nn}=0.5$, $q_{ff}=0.9$, ${\Omega }_2∕\Delta {\omega }_{1D}=-0.9$. (a,b): ${\gamma }_{nn}∕\Delta {\omega }_{1D}=0.1$, ${\gamma }_{ff}∕\Delta {\omega }_{1D}=0.2$, $q_{fn}=0.5$. (a): ${\Omega }_L=0$. (b–d): ${\Omega }_L∕\Delta {\omega }_{1D}=-0.8$. (c): ${\gamma }_{nn}∕\Delta {\omega }_{1D}=0.8$, ${\gamma }_{ff}∕\Delta {\omega }_{1D}=0.3$, $q_{fn}=-1.5$. (d): ${\gamma }_{nn}∕\Delta {\omega }_{1D}=0.2$, ${\gamma }_{ff}∕\Delta {\omega }_{1D}=0.8$, $q_{fn}=1.5$.

Figure 6

Velocity-averaged absorption index, $⟨\alpha \left({\omega }_S\right)⟩∕⟨{\alpha }_{S0}⟩$, (solid) and dispersion part of the refractive index (dash) at ${\omega }_S$ reduced by their values in the absence of all strong fields in a Doppler-broadened medium vs detuning $\Omega ∕\Delta {\omega }_{SD}=({\omega }_S-\omega -{\omega }_{fg})∕\Delta {\omega }_{SD}$. Here, the Doppler HWHM $\Delta {\omega }_{SD}=5\times {10}^3{\Gamma }_{gf}$; the wave vector orientations are the same $\mathbf{k}\uparrow \uparrow {\mathbf{k}}_3\uparrow \uparrow {\mathbf{k}}_2\uparrow \uparrow {\mathbf{k}}_S$, and $k∕k_S=0.8$, $k_3∕k_S=0.3$, $k_2∕k_S=0.37$, ${\Gamma }_{gm}∕{\Gamma }_{gf}=100$, ${\Gamma }_{gm}∕{\Gamma }_{gn}=10$; ${\mid G_{mn}\mid }^2∕{\left(\Delta {\omega }_{SD}\right)}^2=1$, ${\gamma }_{nn}∕\Delta {\omega }_{SD}=0.4$, ${\gamma }_{ff}∕\Delta {\omega }_{SD}=0.8$, $q_{gf}=0.95$, $q_{gn}=0.01$, $q_{ff}=0.01$, $q_{nn}=-5$. (a): $q_{fn}=1.5$, ${\Omega }_L∕\Delta {\omega }_{SD}=1.5$, ${\Omega }_2∕\Delta {\omega }_{SD}=2.2$. (b–d): ${\Omega }_2=0$. (b): $q_{fn}=15$, ${\Omega }_L∕\Delta {\omega }_{SD}=1.5$. (c): $q_{fn}=-1.5$, ${\Omega }_L∕\Delta {\omega }_{SD}=15$. (d): $q_{fn}=-1.5$, ${\Omega }_L∕\Delta {\omega }_{SD}=-0.5$.

Figure 7

Reduced absorption indices ${\alpha }_1∕{\alpha }_{10}$ and ${\alpha }_S∕{\alpha }_{10}$; reduced squared modulus of the FWM polarization, ${\overline{\eta }}_{q0}$; and reduced difference of the conversion and absorption rates, $\overline{b}$ vs detuning ${\Omega }_L$ (a). Dependence of the quantum conversion efficiency ${\eta }_q$ on ${\Omega }_L$ for $z{\alpha }_{10}=8.5\times {10}^3$ (1), $z{\alpha }_{10}=1\times {10}^4$ (2), and $z{\alpha }_{10}=2\times {10}^4$ (3) (b). Quantum conversion efficiency ${\eta }_q$ vs optical thickness and ${\Omega }_L$ (c). Here, $C={10}^{-5}$, $g_{ff}=150$, $g_{nn}=200$, $g_{mn}=9000$, ${\Omega }_1∕{\Gamma }_{gf}=5000$, ${\Omega }_2∕{\Gamma }_{gf}=-5100$, $q_{fg}=0.95$, $q_{gn}=-2$, $q_{ff}=0.01$, $q_{nn}=-5$, $q_{fn}=0$, ${\Gamma }_{gm}∕{\Gamma }_{gf}=100$, ${\Gamma }_{gm}∕{\Gamma }_{gn}=10$ (a–c).

Figure 8

Reduced absorption indices ${\alpha }_1∕{\alpha }_{10}$ and ${\alpha }_S∕{\alpha }_{10}$; reduced squared modulus of FWM polarization, ${\overline{\eta }}_{q0}$; and reduced difference of conversion and absorption rates, $\overline{b}$ vs detuning ${\Omega }_L$ (a). Quantum conversion efficiency ${\eta }_q$ vs ${\Omega }_L$ along the medium computed for $z{\alpha }_{10}=4.5\times {10}^2$ (1), $z{\alpha }_{10}=5\times {10}^2$ (2), and $z{\alpha }_{10}=5.5\times {10}^2$ (3) (b). Dependence of ${\eta }_{\mathrm{q}}$ on the optical thickness and on ${\Omega }_L$ (c). Here, $C=3\times {10}^{-2}$, $g_{nn}=500$, $g_{mn}=8000$ (a–c). The other parameters are the same as in Fig. 7.

Figure 9

Reduced absorption indices ${\alpha }_1∕{\alpha }_{10}$ and ${\alpha }_S∕{\alpha }_{10}$; reduced squared modulus of FWM polarization, ${\overline{\eta }}_{q0}$; and reduced difference of conversion and absorption rates, $\overline{b}$ vs detuning ${\Omega }_L$ (a). Quantum conversion efficiency ${\eta }_q$ vs optical thickness for ${\Omega }_L∕{\Gamma }_{gf}=0$ (1), ${\Omega }_L∕{\Gamma }_{gf}=-250$ (2), ${\Omega }_L∕{\Gamma }_{gf}=-400$ (3) (b). Dependence of the quantum conversion efficiency ${\eta }_q$ on the optical thickness and on ${\Omega }_L$ (c). Here, $g_{ff}=100$, $g_{nn}=5$, $g_{mn}=7$, ${\Omega }_1=0$, ${\Omega }_2∕{\Gamma }_{gf}=-250$ (a–c). The other parameters are the same as in Fig. 8.