Multilevel Interference Resonances in Strongly Driven Three-Level Systems

We study multiphoton resonances in a strongly driven three-level quantum system, where one level is periodically swept through a pair of levels with constant energy separation $E$. Near the multiphoton resonance condition $n\hslash \omega =E$, where $n$ is an integer, we find qualitatively different behavior for $n$ even or odd. We explain this phenomenon in terms of families of interfering trajectories of the multilevel system. Remarkably, the behavior is insensitive to fluctuations of the energy of the driven level, and survives deep into the strong dephasing regime. The setup can be relevant for a variety of solid state and atomic or molecular systems. In particular, it provides a clear mechanism to explain recent puzzling experimental observations in strongly driven double quantum dots.

Figure 1

Spectrum of (a),(b) the two-level Hamiltonian (1) and (c),(d) the three-level Hamiltonian (2). In (a),(c) the energy levels are plotted as a function of detuning and in (b),(d) as a function of time assuming strong driving (thin blue lines). We have set $A\gg q,q_{1,2}$. In (b),(d) we show interfering paths which bring the system from $|1⟩$ to $|S⟩$ (thick red lines).

Figure 2

The rate $W_{1\to S}^{(4)}$ at (a) zero detuning as a function of $n=E/\omega$, and (b) for integer $n=1,2,3$ as a function of $\delta$. (c),(d) The same for the rate $W_{1\to 2}^{(4)}$. In all plots we used ${\mathrm{\Gamma }}^{\prime }/\pi =0.3$. In (d) the curves are offset in steps of $\frac{3}{2}$.

Figure 3

Calculated current through a driven double quantum dot in spin blockade, normalized to the background current $I_{\text{bg}}$. (a) The current at $\delta =0$ as a function of $\omega$ and $E$. (b) Slow modulation of the resonances: the current as a function of $\delta$ for fixed $n=1,2,3$. In all plots we used $q_1^2/A=0.05\mu \mathrm{eV}$, $q_2^2/A=0.5\mu \mathrm{eV}$, and ${\mathrm{\Gamma }}_{1,2}=1\mu \mathrm{eV}$.