# Robustness of STIRAP Shortcuts under Ornstein-Uhlenbeck Noise in the Energy Levels
## 1 Introduction  
Stimulated Raman adiabatic passage (STIRAP) is a widely used quantum control method for the efficient transfer of a population in a three-level \(\Lambda\)-type system [1; 2; 3; 4], which has also been exploited in multi-level systems [5]. The population is transferred from level \(\left|1\right>\) to level \(\left|3\right>\) through the intermediate level \(\left|2\right>\) by applying two laser pulses in a counterintuitive order, the Stokes pulse connecting levels \(\left|2\right>-\left|3\right>\) and the pump pulse connecting levels \(\left|1\right>-\left|2\right>\). During the application of STIRAP pulses, the intermediate level \(\left|2\right>\) is hardly populated, while states \(\left|1\right>\) and \(\left|3\right>\) form a coherent superposition, which is adiabatically transformed from state \(\left|1\right>\) at the beginning to state \(\left|3\right>\) at the end. The method has found a broad spectrum of applications in current quantum technologies, ranging from optical waveguides [6] and matter waves [7] to diamond nitrogen vacancy centers [8] and superconducting quantum circuits [9]; for more details, see the recently published roadmap [4]. The major advantage of STIRAP is its robustness against moderate variations of system parameters. Its drawback is the long time required for the adiabatic transfer, which in general leads to a degraded performance in the presence of undesirable interactions with the environment. In order to reduce the necessary time and thus improve the efficiency of quantum adiabatic evolution, several methods have been suggested, collectively referred as shortcuts to adiabaticity [10; 11; 12; 13; 14; 15; 16; 17; 18]. As their name indicates, the main concept behind them is to bring the system to the same final state in shorter time; some of these methods simply bypass the intermediate adiabatic states, while in others, an extra term is added in the system Hamiltonian, which cancels the diabatic transitions and allows the system to evolve along the adiabatic trajectory of the original Hamiltonian. The latter procedure is usually referred to as the transitionless tracking algorithm or assisted adiabaticpassage. Both techniques have found a wide range of applications across various disciplines of modern quantum science; see the recent review [10]. They have also been exploited to improve the performance of the STIRAP system; see for example [19; 20; 21; 22; 23] for the first method and [12; 24; 25; 26; 27; 28; 29; 30; 31] for the second. We should nevertheless point out that in the transitionless tracking methods, the extra counterdiabatic term usually corresponds to a third laser pulse coupling directly levels \(|1\rangle\) and \(|3\rangle\), deviating thus from the classical STIRAP framework. Several works have been devoted to study the effect of noise on STIRAP. In [32], the efficiency of STIRAP in the presence of classical Ornstein-Uhlenbeck noise [33] in the energy levels, leading to dephasing, was evaluated. In [34; 35], the dephasing caused by quantum baths was considered. The effect of broadband colored noise to population transfer in superconducting artificial atoms was studied in [36; 37]. Aside from these works, which concentrated on classical STIRAP, there were also a few studies that investigated the effect of dephasing in transitionless tracking STIRAP [24; 29; 38], where extra counterdiabatic terms were introduced in the Hamiltonian. Additionally, in a recent publication, the efficiency of a Floquet-engineered shortcut, which preserved the STIRAP framework, was studied in the presence of colored noise [39]. In the present article, we evaluate the performance under noise for two shortcuts to adiabaticity, which also preserve the interactions of the original STIRAP Hamiltonian, without making use of additional terms. Both STIRAP shortcuts are obtained following the recipe described in [19; 40]; the first shortcut is such that the mixing angle is a polynomial function of time, while the second one is derived from Gaussian STIRAP pulses.