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Physica Scripta

Coherent population transfer in the interaction of five-state nuclei with x-ray lasers using chain-STIRAP technique

Mehdi Amiri, M. Saadati-Niari

Published Jun 29, 2023• 2 citations
Publisher

Abstract

Abstract The complete population transfer from the first state to the fifth one in a five-state nuclear system that interacts with four x-ray laser pulses has been theoretically studied using the chain-STIRAP technique. In this scheme, it is assumed that the accelerated nucleus interacts with four x-ray laser pulses, and the relativistic factor is adjusted so that the resonance condition is established between the x-ray laser frequencies and the transition frequency of the nucleus. In this study, by establishing the adiabatic condition, the Hamiltonian of the system remains in the dark state. Therefore, the second and fourth states are not populated during the time evolution. Also, to eliminate the population of the third state during the interaction, the middle pulses are considered more significant compared to the first and last pulses. For the numerical study, 168Er is considered and, it is shown that the population is completely transferred from the first state to the fifth state.

DOI
10.1088/1402-4896/ace2fc

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Abstract The complete population transfer from the first state to the fifth one in a five-state nuclear system that interacts with four x-ray laser pulses has been theoretically studied using the chain-STIRAP technique. In this scheme, it is assumed that the accelerated nucleus interacts with four x-ray laser pulses, and the relativistic factor is adjusted so that the resonance condition is established between the x-ray laser frequencies and the transition frequency of the nucleus. In this study, by establishing the adiabatic condition, the Hamiltonian of the system remains in the dark state. Therefore, the second and fourth states are not populated during the time evolution. Also, to eliminate the population of the third state during the interaction, the middle pulses are considered more significant compared to the first and last pulses. For the numerical study, 168Er is considered and, it is shown that the population is completely transferred from the first state to the fifth state.
Abstract Nuclear-state population transfer in the multi-lambda systems with N = 5 that interact with four x-ray laser pulses are investigated theoretically. By using the coincident pulses and stimulated Raman adiabatic passage (STIRAP) techniques, the population transfer from one initially populated ground state to an arbitrary coherent superposition of other ground states. Since the frequency of currently available x-ray lasers is lower than the gamma rays, in this method, x-ray laser pulses with different frequencies are interacting with the accelerated nuclei. We employ the Morris-Shore transformation to reduce the five-states system to two separate three-state and two-state linkage. The required laser intensities were calculated, which satisfy the conditions of coincident pulses and multi-lambda STIRAP techniques. Considering the spontaneous emission from excited states, the master equation has to be used for numerical study, and it is shown that an arbitrary superposition of final ground states can be obtained. Also, it is observed that by increasing the number of coincident pulses, the population of ground states gets closer to the ideal situation.
The controlled transfer of nuclear state population using two x-ray laser pulses is investigated theoretically. The laser pulses drive two nuclear transitions in a nuclear three-level system facilitating coherent population transfer via the quantum optics technique of stimulated Raman adiabatic passage. To overcome present limitations of the x-ray laser frequency, we envisage accelerated nuclei interacting with two copropagating or crossed x-ray laser pulses in a three-beam setup. We present a systematic study of this setup providing both pulse temporal sequence and laser pulse intensity for optimized control of the nuclear state population. The tolerance for geometrical parameters such as laser beam divergence of the three-beam setup as well as for the velocity spread of the nuclear beam are studied and a two-photon resonance condition to account for experimental uncertainties is deduced. This additional condition gives a less strict requirement for the experimental implementation of the three-beam setup. Present experimental state of the art and future prospects are discussed.
Coherent superposition of nuclear states in tripod systems using three x-ray laser pulses is investigated theoretically. The laser pulses transfer the population from one ground state to an arbitrary superposition of other ground states using coincident pulses and stimulated Raman adiabatic passage techniques. The short wavelengths needed in the frame of the nuclei are achieved by envisaging an accelerated nucleus interacting with three x-ray laser pulses. This study exploits the Morris-shore transformation to reduce the tripod system into a coupled three-state $\mathrm{\ensuremath{\Lambda}}$-like system and a noncoupled state. We calculated the required laser intensities which satisfy the conditions of coincident pulses and adiabatic passage techniques. Considering the spontaneous emission from excited state $|4\ensuremath{\rangle}$ and unstable ground states $(|2\ensuremath{\rangle},|3\ensuremath{\rangle})$ to other states, we have used a master equation for numerical study, and the final fidelity of desired states with respect to the tolerance of laser intensities is studied numerically.
Population transfer of three-level $\mathrm{\ensuremath{\Lambda}}$-like nuclei interacting with x-ray free electron lasers (XFEL) via a train of coincident pulses has been investigated theoretically. This study uses copropagating beams in which the frequency of the pump laser is different from that of the Stokes laser. We calculate the required laser intensities for each step which satisfy the condition of coincident-pulse technique in different nuclei. By employing the master equation and considering the effect of spontaneous emission, we show that complete nuclear population transfer occurs by choosing the appropriate number of pulse pairs. It is shown that the effect of laser intensity fluctuation is suppressed by increasing the number of pulse pairs. In this scheme, after each step, the populations of system are in stable states and the time delays between the neighboring pulses do not affect the transmission efficiency.
The direct interaction between nuclei and strong electromagnetic fields generated by novel coherent x-ray light sources such as the x-ray free electron laser is studied. We investigate the case of various stable or long-lived isotopes with energetically low-lying excited states, where the laser drives the nuclear transition from the ground to the first excited state. We therefore consider the nucleus as a two-level system including the corresponding hyperfine levels in our theoretical description. The performance of present and upcoming x-ray free electron laser facilities in coherently controlling the nuclear excited state population is analyzed for setups involving both solid state as well as accelerated nuclear targets to bridge the gap between photon and transition frequency. Current and predicted laser parameters are applied to calculate excited state populations and signal photon rates of nuclei after a radiation pulse, finding significant improvements compared to former calculations. Furthermore, we determine the parameters necessary to transfer substantial amounts of the nuclear ground state population to the excited state, and therefore to bring nuclear Rabi-oscillation within reach. Additionally, we take into account for the first time collective effects that take place in solid state targets and show that they may provide a significant effect in broadening natural linewidths of nuclear levels depending on the experimental setup. Our findings support the case of nuclear quantum optics for XFEL applications. Therefore, one hopes that eventually coherent control of nuclear transitions can be successfully applied in a number of areas in nuclear physics including preparation, control and detection methods.
Nuclear coherent population transfer to the 229m^{229m}229mTh isomer using x-ray pulses
Population of the 8 eV 229m^{229m}229mTh isomer via the second nuclear excited state at 29.19 keV by means of coherent x-ray pulses is investigated theoretically. We focus on two nuclear coherent population transfer schemes using partially overlapping x-ray pulses known from quantum optics: stimulated Raman adiabatic passage (STIRAP), and successive πππ pulses. Numerical results are presented for three possible experimental setups. Our results identify the Gamma Factory as the most promising scenario, where two ultraviolet pulses combined with relativistically accelerated ions deliver the required intensities for efficient isomer population. Our simulations require knowledge of the in-band and cross-band nuclear transition probabilities. We give theoretically predicted values for the latter and discuss them in the context of recent experiments.