Inducing quantum coherence via decays and incoherent pumping with application to population trapping, lasing without inversion, and quenching of spontaneous emission

Quantum interference in a decaying three-level system of V type with degenerate upper levels driven by a single incoherent field is shown to lead to a coherent population-trapping state and more generally to a population-locked state. The latter is a state with half the population locked in two upper states regardless of the strength of incoherent pumping and decay rates. We reveal the mechanism by which half the population is pumped to the upper states no matter how weak is the incoherent pumping. Transient regimes of gain without inversion and inversion without gain are demonstrated. Quenching of spontaneous emission due to electron collisions is also discussed in support of the experiments and ideas of Suckewer and [Phys. Rev. Lett. 60, 1122 (1988)].

Figure 1

Sketch of the three-level V-type system with closely spaced upper states. $r_a$ and $r_b$ are pump rates; ${\gamma }_a$ and ${\gamma }_b$ are decay rates.

Figure 2

Population inversions ${\rho }_{aa}-{\rho }_{cc}$ and ${\rho }_{bb}-{\rho }_{cc}$ and two-photon polarization ${\rho }_{ab}$ as function of time. Initial conditions are ${\rho }_{aa}\left(0\right)=1$, ${\rho }_{cc}\left(0\right)={\rho }_{bb}\left(0\right)={\rho }_{ab}\left(0\right)=0$. Parameters are $r_a=r_b\equiv r$, ${\gamma }_a={\gamma }_b\equiv \gamma$. Time is measured in units of $\gamma$. (a) No population inversion in the steady state, $r=0.5\gamma$; (b) population inversion in the steady state, $r=2.5\gamma$.

Figure 3

Transient dynamics of the system in the dressed-state basis for the case of a slow pump process and rapid relaxation, $r_a=0.1\gamma$ $({\gamma }_a={\gamma }_b)$. Initial conditions: all population is in $\mid c⟩$ state, ${\rho }_{cc}\left(0\right)=1$. Dark state is slowly populating toward the steady-state value of approximately $1∕2$, while the population of the bright state ${\rho }_{BB}$ and the dark-bright polarization ${\rho }_{DB}$ rapidly reach their small steady-state values. Note that in steady state ${\rho }_{BB}={\rho }_{DB}$, which follows from Eqs. (31, 32, 33).

Figure 4

Generic level scheme demonstrating the asymmetry of the emission processes in plasmas. Two closely spaced (degenerate) optical transitions $\mid a⟩\leftrightarrow \mid c⟩$ and $\mid b⟩\leftrightarrow \mid c⟩$ are driven by collisions with electrons. However, the electrons are not energetic enough to efficiently pump $\mid a⟩\leftrightarrow \mid d⟩$ and $\mid b⟩\leftrightarrow \mid d⟩$ vacuum ultraviolet transitions. The two upper states $\mid a⟩$ and $\mid b⟩$ (say, $P$ and $S$ states) radiatively decay at rates ${\gamma }_a$ and ${\gamma }_b$ to state $\mid c⟩$ (with mixed parity). The $\mid a⟩$ state decays also to the low-lying $D$-like state $\mid d⟩$. The state classification is solely for illustrative purposes.