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Physical Review C

Nuclear-state engineering in tripod systems using x-ray laser pulses

Bashir Nedaee-Shakarab, M. Saadati-Niari, Farhad Zolfagharpour

Published Oct 24, 2017• 17 citations
Publisher

Abstract

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.

DOI
10.1103/physrevc.96.044619

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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 \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ-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⟩|4\ensuremath{\rangle}∣4\ensuremath⟩ and unstable ground states (∣2\ensuremath⟩,∣3\ensuremath⟩)(|2\ensuremath{\rangle},|3\ensuremath{\rangle})(∣2\ensuremath⟩,∣3\ensuremath⟩) 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.
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.
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.
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.
We show that the technique of Stark-chirped rapid adiabatic passage (SCRAP), can be implemented in tripod quantum systems. We propose a scheme for coherent superposition among two ground states via Stark-shiftchirped rapid adiabatic passage technique in a tripod system. Tripod-SCRAP uses four laser pulses: an intense far-off-resonance Stark laser pulse modifies the transition frequency between the states by Stark shifting their energies and three nearly resonant pump, Stokes, and control laser pulses that fractionally transfer the population between the ground states via adiabatic passage. In our scheme, the pulse duration of the pump pulse must be larger than the pulse duration of the Stokes and control pulses, although with a smaller amplitude, and the atom encounters with the pump, Stokes, control, and Stark laser pulses with counterintuitive order (Stokes pulse arrives before the rest of the pulses). This technique can be applied to one-photon as well as multiphoton transitions and it is not necessary to vanish the pulses (pump and Stokes) simultaneously and it is a powerful alternative tool for f-STIRAP and tripod-STIRAP techniques at least when inhomogeneous broadenings are included. inhomogeneous broadening. This technique is robust against moderate variations in the intensities of the laser pulses,in detunings, and in delays between the pulses.
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.