Relaxed parameter sensitivity for multiphoton quantum resonances

Abstract

Multiphoton resonances demonstrate the physical significance of counter-rotating wave terms in light-matter interactions. These resonances, however, are sensitive to detuning errors, making the phenomena challenging to experimentally observe. In this manuscript, we introduce an optimization strategy to address this problem. By using an optimized parameter segmented sequence (OPSS), the robustness against detuning errors of the high-order quantum state transfers can be substantially improved. We prove the versatility of our strategy against frequency detunings by demonstrating the evolution of two specific models. In both cases, the parameter window for maintaining a high state-transfer fidelity is substantially expanded. We further analyze the output photon flux of the optimized system and, taking the three-photon resonance as an example, demonstrate that the system remains capable of generating a stable output photon flux even in the presence of detuning errors.

Figures (10)

• Figure 1: Schematic comparison of the robustness against detuning frequency errors for the three-photon resonance. (a) The unoptimized case. The resonance is observable only under stringent parameter conditions. The fidelity decreases to zero at a detuning error of $\varepsilon = \pm 0.5\%$. Specifically, the fidelity reduces to $0.9$ with a minute deviation of $\epsilon = 0.05\%$. (b) The optimized case (OPSS). The system maintains the observability of the resonance over a significantly broader error range, with fidelity degradation occurring only beyond $\varepsilon = \pm 1\%$. Within this interval, the rapid oscillations maintain the fidelity in the range $[0.8, 0.9]$, ensuring the experimental visibility of the resonance.
• Figure 2: Eigenvalues of the third ($\ket{\phi_3}$) and fourth ($\ket{\phi_4}$) eigenstates are plotted as a function of the frequency ratio $\omega_c/\omega_a$. An avoided crossing is observed at $\omega_c/\omega_a \approx 0.334$ between the bare states $\ket{e,0}$ and $\ket{g,3}$. The simulation uses a coupling strength of $\lambda = 0.06\,\omega_a$.
• Figure 3: Eigenvalues of the fifth ($\ket{\phi_5}$) and sixth ($\ket{\phi_6}$) eigenstates are plotted as a function of the frequency ratio $\omega_c/\omega_m$. An avoided crossing is observed at $\omega_c/\omega_m \approx 1.5$ between the bare states $\ket{2,0}$ and $\ket{0,3}$. The minimum energy splitting is found at $\omega_c/\omega_m \approx 1.5000105$. The simulation uses a weak coupling strength of $g = 0.001\,\omega_m$.
• Figure 4: Schematic illustration of a set of optimizable parameters with different frequencies.
• Figure 5: Schematic of the optimization workflow. The DE algorithm generates a population of $P=100$ candidate sequences $\{\Delta_{i,N}\}$ ($i=1,\dots,P$), where $N$ denotes the segment number. Each sequence constructs a Hamiltonian $H_i$ subject to detuning errors $\varepsilon$. The resulting fidelities $\{F_{i,k}\}$ are calculated across $M=51$ error sample points ($k$) to evaluate the cost score $C_i$. Finally, the top-performing candidates are refined by GRAPE to yield the final optimized sequence $\{\Delta_{\text{final}}\}$. (Parameters: $w_b=1, w_f=500, w_r=5$; max iterations: 1500 for DE, 3000 for GRAPE).