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arXiv:2205.02701 · Physical Review A

Robust population transfer of spin states by geometric formalism

K. Z. Li, Guofu Xu

Published May 23, 2022• 7 citations
arXivHTMLPDF

Abstract

Accurate population transfer of uncoupled or weakly coupled spin states is crucial for many quantum-information-processing tasks. In this paper, we propose a fast and robust scheme for population transfer which combines invariant-based inverse engineering and geometric formalism for robust quantum control. Our scheme is not constrained by the adiabatic condition and therefore can be implemented quickly. It can also effectively suppress the dominant noise in spin systems, which together with the fast feature guarantees the accuracy of the population transfer. Moreover, the control parameters of the driving Hamiltonian in our scheme are easy to design because they correspond to the curvature and torsion of a three-dimensional visual space curve derived by using geometric formalism for robust quantum control. We test the efficiency of our scheme by numerically simulating the ground-state population transfer in $^{15}\mathrm{N}$ nitrogen-vacancy centers and comparing our scheme with stimulated Raman transition, stimulated Raman adiabatic passage, and conventional shortcuts to adiabaticity based schemes, three types of schemes popularly used for population transfer. The numerical results clearly show that our scheme is advantageous over these previous ones.

DOI
10.1103/physreva.105.052433

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The stimulated Raman adiabatic passage shows an efficient technique that accurately transfers population between two discrete quantum states with the same parity in three-level quantum systems based on adiabatic evolution. This technique has widely theoretical and experimental applications in many fields of physics, chemistry, and beyond. Here, we present a general approach to robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control. By controlling the dynamical process, we inversely design a family of Hamiltonians with non-divergent Rabi frequencies that can realize fast and accurate population transfer from the first to the third level, while the systematic errors are largely suppressed in general. Furthermore, a detailed trade-off relation between the population of the intermediate state and the amplitudes of Rabi frequencies in the transfer process is illustrated. These results provide an optimal route toward manipulating the evolution of three-level quantum systems in future quantum information processing.
Pure-state inverse engineering among the schemes of shortcuts to adiabaticity is a widespread utility in applications to quantum computation and quantum simulation. While in principle it can realise the fast control of quantum systems with high fidelity, in practice this fast control is severely hindered by infinite energy gaps and impractical control fields. To circumvent this problem, we propose a scheme of shortcuts to adiabaticity of mixed state based on the dynamical invariant of open quantum system. Our scheme can drives a steady state to a target steady state of the open system by a controlled Liouvillian that possesses the same form as the reference (original) one. We apply this scheme to stimulated Raman adiabatic passage (STIRAP) and find that an almost perfect population transfer can be obtained. The experimental observation with currently available parameters for the nitrogen-vacancy (NV) center in diamond is suggested and discussed.
The stimulated Raman adiabatic passage (STIRAP) shows an efficient technique that accurately transfers population between two discrete quantum states with the same parity, in three-level quantum systems based on adiabatic evolution. This technique has widely theoretical and experimental applications in many fields of physics, chemistry, and beyond. Here, we present a generally robust approach to speed up STIRAP with invariant-based shortcut to adiabaticity. By controlling the dynamical process, we inversely design a family of Hamiltonians that can realize fast and accurate population transfer from the first to the third level, while the systematic error is largely suppressed in general. Furthermore, a detailed trade-off relation between the population of the intermediate state and the amplitudes of Rabi frequencies in the transfer process is illustrated. These results provide an optimal route toward manipulating the evolution of three-level quantum systems in future quantum information processing.
Shortcuts to adiabaticity~(STA) enables fast and robust coherent control of quantum system, which has been well placed in quantum technologies. In particular, inverse engineering STA provides much more freedom for the optimization of shortcut, which alleviates the complexity for experimental realization. Here, we implement a STA technique, known as invariant-based inverse engineering, to speed up the adiabatic control of the electron triplet ground state of a single nitrogen-vacancy~(NV) center. The microwave pulses to drive inversely engineered STA are obtained with space curve quantum control, where the evolution of spin transition is mapped to a three-dimensional closed space curve and the design of shortcut is obtained by optimization over the space curve. We demonstrate the fast and high-fidelity drive of dipole-forbidden transition between two spin sublevels of the ground state. Moreover, we demonstrate the robustness of the spin transition by introducing the detuning of driving microwave field. The acceleration and robustness is further confirmed by the comparison with two traditional Raman control schemes. Our results suggest invariant-based inverse engineering is powerful for fast and robust manipulation of NV system, and thus benefits quantum sensing and quantum computation based on the NV platform.
Optimal control of quantum system is significant for information science and technology. Here, an efficient scheme is proposed for implementing fast population transfer in a spin qutrit of nitrogen-vacancy center via shortcuts to adiabaticity (STA) with simplified drivings. At two-photon resonance, a Λ\Lambda Λ -configuration interaction between the spin qutrit and driving fields can be obtained effectively. By the invariant-based STA, the reversible population transfer can be realized using the Rabi pulses with sine and cosine waveforms. Compared with the superadiabatic transitionless driving, the present pulses in our strategy become simplified technically, contributing to reduce the error effect of control parameter deviations. Moreover, the high-fidelity quantum operations can be performed with the accessible decoherence rates. The protocol could offer an optimized avenue towards the STA-based quantum control of spin qutrit experimentally.
Shortcuts to adiabaticity (STA) enables fast and robust coherent control of quantum system, which has been well placed in quantum technologies. In particular, inverse-engineering STA provides much more freedom for the optimization of shortcut, which alleviates the complexity for experimental realization. Here, we implement a STA technique, known as invariant-based inverse engineering, to speed up the adiabatic control of the electron triplet ground state of a single nitrogen-vacancy (N-VVV) center. The microwave pulses to drive inversely engineered STA are obtained with space-curve quantum control, where the evolution of spin transition is mapped to a three-dimensional closed space curve and the design of shortcut is obtained by optimization over the space curve. We demonstrate the fast and high-fidelity drive of dipole-forbidden transition between two spin sublevels of the ground state. Moreover, we demonstrate the robustness of the spin transition by introducing the detuning of driving microwave field. The acceleration and robustness is further confirmed by the comparison with two traditional Raman control schemes. Our results suggest invariant-based inverse engineering is powerful for fast and robust manipulation of N-VVV system, and thus benefits quantum sensing and quantum computation based on the N-VVV platform.