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Annalen der Physik

Efficient Population Transfer in a Λ‐Type Quantum System Coupled to a Gold Nanoparticle Using STIRAP Shortcuts

Ναταλία Δομένικου, Ioannis Thanopulos, Dionisis Stefanatos, Vassilios Yannopapas, Emmanuel Paspalakis

Published Dec 14, 2022• 0 citations
Publisher

Abstract

Abstract A theoretical investigation on the population transfer in a Λ‐type quantum system near a spherical gold nanoparticle under application of two stimulated Raman adiabatic passage (STIRAP) shortcuts and efficiency comparison with conventional STIRAP. It combines the density matrix approach for system dynamics, with classical electromagnetic calculations used to obtain the modified electric field amplitudes of the applied pulses and the Purcell factor of the quantum system due to the presence of the nanoparticle. The efficiency of population transfer is investigated by varying the distance between the quantum system and the nanoparticle, the free‐space decay rate of quantum states, the mutual polarization, and the Rabi frequencies of each STIRAP shortcut pulses. In all cases, at least one of the applied shortcuts is more efficient than conventional STIRAP, while in most cases both perform better. When the pump and Stokes fields of the shortcuts have radial and tangential polarizations with respect to the nanoparticle surface, respectively, high transfer efficiency is obtained for small distances of the quantum system to the nanoparticle, moderate free space decay rates and large Rabi frequencies of the fields, while when the pulse polarizations are interchanged, the transfer becomes highly efficient only at large distances.

DOI
10.1002/andp.202200478

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Abstract A theoretical investigation on the population transfer in a Λ‐type quantum system near a spherical gold nanoparticle under application of two stimulated Raman adiabatic passage (STIRAP) shortcuts and efficiency comparison with conventional STIRAP. It combines the density matrix approach for system dynamics, with classical electromagnetic calculations used to obtain the modified electric field amplitudes of the applied pulses and the Purcell factor of the quantum system due to the presence of the nanoparticle. The efficiency of population transfer is investigated by varying the distance between the quantum system and the nanoparticle, the free‐space decay rate of quantum states, the mutual polarization, and the Rabi frequencies of each STIRAP shortcut pulses. In all cases, at least one of the applied shortcuts is more efficient than conventional STIRAP, while in most cases both perform better. When the pump and Stokes fields of the shortcuts have radial and tangential polarizations with respect to the nanoparticle surface, respectively, high transfer efficiency is obtained for small distances of the quantum system to the nanoparticle, moderate free space decay rates and large Rabi frequencies of the fields, while when the pulse polarizations are interchanged, the transfer becomes highly efficient only at large distances.
In this work, we present numerical results on the influence of a spherical metallic nanoparticle to the population transfer in a Λ-type quantum system under conditions of Stimulated Raman Adiabatic Passage (STIRAP). For the study of the system’s dynamics, we use the density matrix approach for the quantum system, where the parameters for the electric field amplitudes and the spontaneous decay rates have been calculated using ab initio electromagnetic calculations for the plasmonic nanoparticle. We present results for the evolution of the populations of the different levels of the quantum system as a function of different parameters, in the presence and the absence of the plasmonic nanoparticle. We find that the presence of the plasmonic nanoparticle and the polarization of the pump and Stokes fields with respect to the surface of the nanoparticle, affect the efficiency of the population transfer inside the three-level quantum system. For the right combination of the values of the modified spontaneous decay rates and the fields intensities, high efficiency population transfer is obtained in the quantum system near a plasmonic nanoparticle using STIRAP process.
Abstract We investigate theoretically the population transfer process in a Λ-type three-level quantum system (QS) near a metallic nanosphere using the stimulated Raman adiabatic passage (STIRAP) technique. We combine density matrix quantum dynamical calculations with first-principle electromagnetic calculations, which quantify the influence of the plasmonic nanoparticle on the electric field of the pump and Stokes pulses in STIRAP as well as on the spontaneous emission rates within the Λ-type system. We study the population transfer process by varying the free-space spontaneous emission rate, the distance of the QS from the nanosphere, the polarization direction with respect to the nanoparticle surface and the relative strength of the pump and Stokes pulses used in STIRAP. We find that when the pump and Stokes fields have tangential and radial polarizations with respect to the nanosphere surface, the transfer efficiency is improved due to the increase of the decay rate of the excited state to the target state relatively to the decay to the initial state. The optimal population transfer is achieved for small interparticle distances, moderate free space spontaneous decay rate, large values of the pump Rabi frequency and small values of the Stokes Rabi frequency. When we exchange the polarization directions of the pump and Stokes fields we can still find a range of parameters where the population transfer remains efficient, but larger Stokes Rabi frequencies are necessary to overcome the increased decay rate from the excited state back to the initial state.
Abstract Lewis–Riesenfeld (LR) invariant-based inverse engineering is applied to a Λ -type quantum system coupled to a gold nanoparticle, and three auxiliary-angle paths satisfying the same boundary conditions are constructed. By incorporating the local-field modifications and spontaneous-emission decay rates induced by the metal nanoparticle (MNP), the density-matrix equations are solved to compare the final target-state populations of the three LR paths and conventional stimulated Raman adiabatic passage (STIRAP) under different quantum-system–MNP distances, free-space decay rates, Rabi frequencies, and polarization configurations. The results show that, under the first polarization configuration, the α 2 path maintains a lower intermediate-state population and yields a high and stable final target-state population over most of the parameter range. Under the second polarization configuration, conventional STIRAP yields a higher final target-state population in some parameter regions. These results indicate that the final target-state population is affected by both optical-field-driven coherent transfer and spontaneous emission, and that the choice of LR path should be evaluated by considering the intermediate-state population together with the modifications induced by the plasmonic environment.
Invariant‐based shortcuts to adiabaticity (IB‐STA) approach is demonstrated to speed up the coherent population transfer of a three‐level quantum system on a superconducting circuit. Compared with the conventional stimulated Raman adiabatic passage (STIRAP), the scheme can achieve the same high transfer efficiency with evolution time reduced by 5.96 times. The final transfer efficiency of the scheme is measured to be , which is mainly decoherence limited. Further, the robustness of the scheme is experimentally characterized, which is superior to the time‐optimal resonant Rabi scheme under systematic pulse amplitude error. Therefore, the approach provides an alternative approach to realize high‐fidelity state manipulation and preparation for weakly coupled Λ‐ or Ξ‐type quantum systems.
This work explores the effect of spontaneous emission on the population transfer efficiency in stimulated Raman adiabatic passage (STIRAP). The approach uses adiabatic elimination of weakly coupled density matrix elements in the Liouville equation, from which a very accurate analytic approximation is derived. The loss of population transfer efficiency is found to decrease exponentially with the factor ${\ensuremath{\Omega}}_{0}^{2}∕\ensuremath{\Gamma}$, where $\ensuremath{\Gamma}$ is the spontaneous emission rate and ${\ensuremath{\Omega}}_{0}$ is the peak Rabi frequency. The transfer efficiency increases with the pulse delay and reaches a steady value. For large pulse delay and large spontaneous emission rate STIRAP degenerates into optical pumping.
The stimulated Raman adiabatic passage (STIRAP) allows selective, coherent population transfer in a three-level quantum system by the adiabatic control of two suitably chosen envelopes and delayed laser pulses. However, the long operation time involved with the adiabatic protocols makes them more susceptible to decay and decoherence. A shortcut-to-adiabaticity technique, namely, counterdiabatic driving (CD), suppresses the decoherence-induced loss by speeding up the STIRAP process, thereby enhancing the efficiency and fidelity of population transfer. The superadiabatic STIRAP (saSTIRAP) method requires the application of a shortcut drive or CD pulse, which couples the coherently trapped states in a three-level quantum system. Hence, the closed-loop $\mathrm{\ensuremath{\Lambda}}$ system consisting of all electric dipole-allowed transitions is an essential requirement for saSTIRAP, which is rarely admissible in a natural atom. This paper theoretically investigates an experimentally feasible model for implementing saSTIRAP using a closed-loop $\mathrm{\ensuremath{\Lambda}}$ system with doubly dressed polariton states in a driven circuit QED system. We show a population transfer with efficiencies close to 80.7580.75%80.75 and 98.1098.10%98.10 with fidelities of 89.8689.86%89.86 and 99.0499.04%99.04 for the resonant STIRAP and saSTIRAP protocols, respectively, with experimentally feasible parameters. The efficiency of the population transfer can be further increased by improving the coherence times of the cavity and the transmon qubit. This work may be useful in designing fast, efficient quantum gates for applications in quantum technologies.