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arXiv:2607.15915 · Physical Review A

Optimization of multistate STIRAP by pulse shaping

Julian K. Dimitrov, Nikolay V. Vitanov

quant-phSubmitted Jul 17, 2026• Announced Jul 20, 2026• 0 citations
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Abstract

We propose a pulse-shaping method for improving population transfer in multistate stimulated Raman adiabatic passage (STIRAP) with nearest-neighbour couplings only. The method extends the quasiparallel-eigenenergy approach, previously used for two- and three-state systems, to multistate chains without introducing additional shortcut fields. The pump and Stokes fields are shaped so that the eigenenergies closest to the dark state remain nearly parallel to it during the central part of the interaction, where nonadiabatic transitions are most likely to occur. We derive analytic prescriptions for the required pulse shapes and apply them to five-, seven-, and nine-state chains formed by magnetic sublevels of degenerate manifolds with angular momenta $J_g\rightarrow J_e=J_g$ and $J_g\rightarrow J_e=J_g-1$ driven by a pair of right- and left-circularly polarized pulses. Numerical simulations show that the optimized pulses can reduce the population transfer error by several orders of magnitude compared to standard Gaussian pulses. The same shapes also improve robustness against variations of the peak Rabi frequency, the single-photon detuning, and the multiphoton detuning. The comparison between the two angular-momentum families shows that the $J_g\rightarrow J_g$ chains are generally more favourable, because their Clebsch-Gordan coefficients keep the relevant bright-state gap larger in the region where the dark state changes most rapidly. Finally, simulations with spontaneous emission show that the optimized resonant pulses remain advantageous in the lossy regime as well.

Related papers

High-fidelity multistate stimulated Raman adiabatic passage assisted by shortcut fields

Nikolay V. Vitanov

Multistate stimulated Raman adiabatic passage (STIRAP) is a process which allows for adiabatic population transfer between the two ends of a chainwise-connected quantum system. The process requires large temporal areas of the driving pulsed fields (pump and Stokes) in order to suppress the nonadiabatic couplings and thereby to make adiabatic evolution possible. To this end, in the present paper a variation of multistate STIRAP, which accelerates and improves the population transfer, is presented. In addition to the usual pump and Stokes fields it uses shortcut fields applied between the states, which form the dark state of the system. The shortcuts cancel the couplings between the dark state and the other adiabatic states thereby resulting (in the ideal case) in a unit transition probability between the two end states of the chain. Specific examples of five-state systems formed of the magnetic sublevels of the transitions between two degenerate levels with angular momenta ${J}_{g}=2$ (of ground or lower level) and ${J}_{e}=1$ or ${J}_{e}=2$ (of excited or upper level) are considered in detail, for which the shortcut fields are derived analytically. The proposed method is simpler than the usual ``shortcuts to adiabaticity'' recipe, which prescribes shortcut fields between all states of the system, while the present proposal uses shortcut fields between the sublevels forming the dark state only. The results are of potential interest in applications where high-fidelity quantum control is essential, e.g., quantum information, atom optics, formation of ultracold molecules, cavity QED, etc.

arXiv:2004.08341•Physical Review A•Aug 10, 2020•24 citations

Transition time in the stimulated Raman adiabatic passage technique

Iavor I. Boradjiev, Nikolay V. Vitanov

The technique of stimulated Raman adiabatic passage (STIRAP) is an efficient and robust technique for population transfer in three-state chain-wise connected quantum systems, 1-2-3. Here we analyze the transition time in STIRAP, that is the time it takes for the population to be transferred from state 1 to state 3. We derive a very simple formula for this transition time, which shows that it is inversely proportional to the nonadiabatic coupling $\mathrm{\ensuremath{\vartheta}\ifmmode \dot{}\else \.{}\fi{}}({t}_{c})$, estimated at the time ${t}_{c}$ when the pump and Stokes couplings have the same value. Explicit formulas for several pulse shapes of the pump and Stokes fields are derived. Contrary to the naive expectation that the transition time might be proportional to the delay between the pump and Stokes pulses, or to the width of their overlap region, we find that the transition time is inversely proportional to the delay, i.e., larger delays produce faster transitions. We also calculate the transition time in two important variations of the STIRAP technique---bright-STIRAP and STIRAP in multistate systems---where similar features are found.

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Optimal control of population transfer in multi-level systems by dynamical quantum geometric tensor

Guan-Qiang Li, Yu-Qi Zhang, Hao Guo +3 more

The optimal control of population transfer for multi-level systems is investigated from the perspective of quantum geometry. Firstly, the general theoretical framework of optimizing the stimulated Raman adiabatic passage (STIRAP) scheme based on the dynamical quantum geometric tensor is given, and then the dynamical quantum geometric tensor and the nonadiabatic transition rate are calculated by taking the detuned $Λ$-type three-level system and tripod-type four-level system for example. Secondly, the transfer dynamics of the particle population of the system are investigated in detail. For a three-level system, the optimal STIRAP scheme has an efficiency of over 98\% in transferring the population to the final state, while the transfer efficiency of traditional STIRAP is about 72\%. The superposition states with arbitrary proportions can be efficiently prepared for a four-level system due to the decoupling of the degenerate dark states. Finally, the influences of system parameters, such as the operation time of the Rabi pulses, the amplitude fluctuation and the single-photon detuning, on the transfer process are discussed. Especially, the phenomenon of the adiabatic resonance transfer is revealed. Choosing the pulse parameters in the resonance window can reduce the infidelity of the population transfer to below $10^{-3}$. It is found that the optimal STIRAP scheme by the dynamical quantum geometric tensor provides faster and more efficient transfer than the traditional STIRAP scheme.

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Robust multistate quantum control with minimal additional coupling

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Abstract The multistate stimulated Raman adiabatic passage (STIRAP) is an efficient technique to achieve a selective and accurate population transfer in a chainwise-linked system. However, their efficiency is imperfect due to the nonadiabatic losses from the long runtime of the adiabatic evolution. Here, we focus on realizing a perfect and robust coherent control of the quantum states with optimal shortcut to adiabaticity in a realistic five-state hybrid quantum system. In particular, the optimal shortcut field requires minimal additional coupling (only one coupling strength) to accelerate the adiabatic evolution in this five-state system. Compared to the original STIRAP, the optimal shortcut shows the ultra-high fidelity of quantum state manipulations even though the control parameters of the Hamiltonians are changed in different ways. Furthermore, we study the efficiency of the optimal shortcut field technique in the presence of various experimental errors, such as systematic error, Rabi frequency error, and coupling strength error, and it features a broad range of high efficiencies above 99.9%, showing its robustness against the above errors. The results might shed insight on the further applications of shortcuts to adiabaticity on robust quantum information processing in multi-level quantum systems.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 28, 2024•0 citations

Improving the stimulated Raman adiabatic passage via dissipative quantum dynamics

Qi-Cheng Wu, Ye-Hong Chen, Bi-Hua Huang +3 more

We propose a method to improve the stimulated Raman adiabatic passage (STIRAP) via dissipative quantum dynamics, taking into account the dephasing effects. Fast and robust population transfer can be obtained with the scheme by the designed pulses and detuning, even though the initial state of the system is imperfect. With a concrete three-level system as an example, the influences of the imperfect initial state, variations in the control parameters, and various dissipation effects are discussed in detail. The numerical simulation shows that the scheme is insensitive to moderate fluctuations of experimental parameters and the relatively large dissipation effects of the excited state. Furthermore, the dominant dissipative factors, namely, the dephasing effects of the ground states and the imperfect initial state are no longer undesirable, in fact, they are the important resources to the scheme. Therefore, the scheme could provide more choices for the realization of the complete population transfer in the strong dissipative fields where the standard stimulated Raman adiabatic passage or shortcut schemes are invalid.

arXiv:1605.07274•Optics Express•Sep 22, 2016•32 citations

Limitations of STIRAP-like population transfer in extended systems: The three-level system embedded in a web of background states

Werner Jakubetz

This paper presents a systematic numerical investigation of background state participation in STIRAP (stimulated Raman-adiabatic passage) population transfer among vibrational states, focusing on the consequences for the robustness of the method. The simulations, which are performed over extended grids in the parameter space of the Stokes- and pump pulses (frequencies, field strengths, and pulse lengths), involve hierarchies of (3 + N)-level systems of increasing complexity, ranging from the standard three-level STIRAP setup, (N = 0) in Λ-configuration, up to N = 446. A strongly coupled three-level core system is selected from the full Hamiltonian of the double-well HCN∕HNC system, and the couplings connecting this core system to the remaining states are (re-) parameterized in different ways, from very weak to very strong. The systems so obtained represent a three-level system embedded in various ways in webs of cross-linked vibrational background states and incorporate typical molecular properties. We first summarize essential properties of population transfer in the standard three-level system and quantify the robustness of the method and its dependence on the pulse parameters. Against these reference results, we present results obtained for four (3 + 446)-level systems and several subsystems. For pulse lengths of at most few picoseconds the intrinsic robustness of STIRAP with respect to variations in the field strength disappears as soon as the largest core-background couplings exceed about one tenth of the STIRAP couplings. In such cases robustness with respect to variations in the field strength is entirely lost, since at higher field strengths, except for irregularly spaced narrow frequency ranges, transfer probabilities are strongly reduced. STIRAP-like population transfer is maintained, with some restrictions, at low field strengths near the onset of adiabatic transfer. The suppression of STIRAP is traced back to different mechanisms based on a plentitude of single- and multiphoton transitions to background states, which at the high field strengths characteristic for STIRAP proceed readily even along weakly coupled pathways.

The Journal of Chemical Physics•Dec 13, 2012•16 citations
We propose a pulse-shaping method for improving population transfer in multistate stimulated Raman adiabatic passage (STIRAP) with nearest-neighbour couplings only. The method extends the quasiparallel-eigenenergy approach, previously used for two- and three-state systems, to multistate chains without introducing additional shortcut fields. The pump and Stokes fields are shaped so that the eigenenergies closest to the dark state remain nearly parallel to it during the central part of the interaction, where nonadiabatic transitions are most likely to occur. We derive analytic prescriptions for the required pulse shapes and apply them to five-, seven-, and nine-state chains formed by magnetic sublevels of degenerate manifolds with angular momenta Jg→Je=JgJ_g\rightarrow J_e=J_gJg​→Je​=Jg​ and Jg→Je=Jg−1J_g\rightarrow J_e=J_g-1Jg​→Je​=Jg​−1 driven by a pair of right- and left-circularly polarized pulses. Numerical simulations show that the optimized pulses can reduce the population transfer error by several orders of magnitude compared to standard Gaussian pulses. The same shapes also improve robustness against variations of the peak Rabi frequency, the single-photon detuning, and the multiphoton detuning. The comparison between the two angular-momentum families shows that the Jg→JgJ_g\rightarrow J_gJg​→Jg​ chains are generally more favourable, because their Clebsch-Gordan coefficients keep the relevant bright-state gap larger in the region where the dark state changes most rapidly. Finally, simulations with spontaneous emission show that the optimized resonant pulses remain advantageous in the lossy regime as well.
Multistate stimulated Raman adiabatic passage (STIRAP) is a process which allows for adiabatic population transfer between the two ends of a chainwise-connected quantum system. The process requires large temporal areas of the driving pulsed fields (pump and Stokes) in order to suppress the nonadiabatic couplings and thereby to make adiabatic evolution possible. To this end, in the present paper a variation of multistate STIRAP, which accelerates and improves the population transfer, is presented. In addition to the usual pump and Stokes fields it uses shortcut fields applied between the states, which form the dark state of the system. The shortcuts cancel the couplings between the dark state and the other adiabatic states thereby resulting (in the ideal case) in a unit transition probability between the two end states of the chain. Specific examples of five-state systems formed of the magnetic sublevels of the transitions between two degenerate levels with angular momenta Jg=2{J}_{g}=2Jg​=2 (of ground or lower level) and Je=1{J}_{e}=1Je​=1 or Je=2{J}_{e}=2Je​=2 (of excited or upper level) are considered in detail, for which the shortcut fields are derived analytically. The proposed method is simpler than the usual ``shortcuts to adiabaticity'' recipe, which prescribes shortcut fields between all states of the system, while the present proposal uses shortcut fields between the sublevels forming the dark state only. The results are of potential interest in applications where high-fidelity quantum control is essential, e.g., quantum information, atom optics, formation of ultracold molecules, cavity QED, etc.
The technique of stimulated Raman adiabatic passage (STIRAP) is an efficient and robust technique for population transfer in three-state chain-wise connected quantum systems, 1-2-3. Here we analyze the transition time in STIRAP, that is the time it takes for the population to be transferred from state 1 to state 3. We derive a very simple formula for this transition time, which shows that it is inversely proportional to the nonadiabatic coupling $\mathrm{\ensuremath{\vartheta}\ifmmode \dot{}\else \.{}\fi{}}({t}_{c})$, estimated at the time tc{t}_{c}tc​ when the pump and Stokes couplings have the same value. Explicit formulas for several pulse shapes of the pump and Stokes fields are derived. Contrary to the naive expectation that the transition time might be proportional to the delay between the pump and Stokes pulses, or to the width of their overlap region, we find that the transition time is inversely proportional to the delay, i.e., larger delays produce faster transitions. We also calculate the transition time in two important variations of the STIRAP technique---bright-STIRAP and STIRAP in multistate systems---where similar features are found.
The optimal control of population transfer for multi-level systems is investigated from the perspective of quantum geometry. Firstly, the general theoretical framework of optimizing the stimulated Raman adiabatic passage (STIRAP) scheme based on the dynamical quantum geometric tensor is given, and then the dynamical quantum geometric tensor and the nonadiabatic transition rate are calculated by taking the detuned ΛΛΛ-type three-level system and tripod-type four-level system for example. Secondly, the transfer dynamics of the particle population of the system are investigated in detail. For a three-level system, the optimal STIRAP scheme has an efficiency of over 98\% in transferring the population to the final state, while the transfer efficiency of traditional STIRAP is about 72\%. The superposition states with arbitrary proportions can be efficiently prepared for a four-level system due to the decoupling of the degenerate dark states. Finally, the influences of system parameters, such as the operation time of the Rabi pulses, the amplitude fluctuation and the single-photon detuning, on the transfer process are discussed. Especially, the phenomenon of the adiabatic resonance transfer is revealed. Choosing the pulse parameters in the resonance window can reduce the infidelity of the population transfer to below 10−310^{-3}10−3. It is found that the optimal STIRAP scheme by the dynamical quantum geometric tensor provides faster and more efficient transfer than the traditional STIRAP scheme.
Abstract The multistate stimulated Raman adiabatic passage (STIRAP) is an efficient technique to achieve a selective and accurate population transfer in a chainwise-linked system. However, their efficiency is imperfect due to the nonadiabatic losses from the long runtime of the adiabatic evolution. Here, we focus on realizing a perfect and robust coherent control of the quantum states with optimal shortcut to adiabaticity in a realistic five-state hybrid quantum system. In particular, the optimal shortcut field requires minimal additional coupling (only one coupling strength) to accelerate the adiabatic evolution in this five-state system. Compared to the original STIRAP, the optimal shortcut shows the ultra-high fidelity of quantum state manipulations even though the control parameters of the Hamiltonians are changed in different ways. Furthermore, we study the efficiency of the optimal shortcut field technique in the presence of various experimental errors, such as systematic error, Rabi frequency error, and coupling strength error, and it features a broad range of high efficiencies above 99.9%, showing its robustness against the above errors. The results might shed insight on the further applications of shortcuts to adiabaticity on robust quantum information processing in multi-level quantum systems.
We propose a method to improve the stimulated Raman adiabatic passage (STIRAP) via dissipative quantum dynamics, taking into account the dephasing effects. Fast and robust population transfer can be obtained with the scheme by the designed pulses and detuning, even though the initial state of the system is imperfect. With a concrete three-level system as an example, the influences of the imperfect initial state, variations in the control parameters, and various dissipation effects are discussed in detail. The numerical simulation shows that the scheme is insensitive to moderate fluctuations of experimental parameters and the relatively large dissipation effects of the excited state. Furthermore, the dominant dissipative factors, namely, the dephasing effects of the ground states and the imperfect initial state are no longer undesirable, in fact, they are the important resources to the scheme. Therefore, the scheme could provide more choices for the realization of the complete population transfer in the strong dissipative fields where the standard stimulated Raman adiabatic passage or shortcut schemes are invalid.
This paper presents a systematic numerical investigation of background state participation in STIRAP (stimulated Raman-adiabatic passage) population transfer among vibrational states, focusing on the consequences for the robustness of the method. The simulations, which are performed over extended grids in the parameter space of the Stokes- and pump pulses (frequencies, field strengths, and pulse lengths), involve hierarchies of (3 + N)-level systems of increasing complexity, ranging from the standard three-level STIRAP setup, (N = 0) in Λ-configuration, up to N = 446. A strongly coupled three-level core system is selected from the full Hamiltonian of the double-well HCN∕HNC system, and the couplings connecting this core system to the remaining states are (re-) parameterized in different ways, from very weak to very strong. The systems so obtained represent a three-level system embedded in various ways in webs of cross-linked vibrational background states and incorporate typical molecular properties. We first summarize essential properties of population transfer in the standard three-level system and quantify the robustness of the method and its dependence on the pulse parameters. Against these reference results, we present results obtained for four (3 + 446)-level systems and several subsystems. For pulse lengths of at most few picoseconds the intrinsic robustness of STIRAP with respect to variations in the field strength disappears as soon as the largest core-background couplings exceed about one tenth of the STIRAP couplings. In such cases robustness with respect to variations in the field strength is entirely lost, since at higher field strengths, except for irregularly spaced narrow frequency ranges, transfer probabilities are strongly reduced. STIRAP-like population transfer is maintained, with some restrictions, at low field strengths near the onset of adiabatic transfer. The suppression of STIRAP is traced back to different mechanisms based on a plentitude of single- and multiphoton transitions to background states, which at the high field strengths characteristic for STIRAP proceed readily even along weakly coupled pathways.