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Physical Review A

Fast conversion of Dicke states |Dn(2)〉 to |Dn+1(2)〉 by transitionless quantum driving

Yan‐Qiang Ji, Y. L. Liu, S. J. Zhou, Xiao‐Ming Xiu, Li Dong, Haikuan Dong, Yajun Gao, X. X. Yi

Published Feb 5, 2019• 16 citations
Publisher

Abstract

A scheme is proposed for fast conversion of two-atom Dicke states to three-atom Dickes state and three-atom Dicke states to four-atom Dicke states based on transitionless quantum driving. This scheme can be achieved within one step through appropriately regulating the Rabi frequencies of classical fields. The effects of decoherence induced by atomic spontaneous emission and leakage of the cavity are also taken into account. The numerical simulation result shows that this scheme is robust against both atomic spontaneous emission and cavity leakage. Furthermore, when multiple atoms are trapped in a cavity, the ($n+1$)-atom Dicke states can be derived directly from the $n$-atom Dicke states with the same principle, which provides a scalable way for the preparation of Dicke states in theory.

DOI
10.1103/physreva.99.023808

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A scheme is proposed for fast conversion of two-atom Dicke states to three-atom Dickes state and three-atom Dicke states to four-atom Dicke states based on transitionless quantum driving. This scheme can be achieved within one step through appropriately regulating the Rabi frequencies of classical fields. The effects of decoherence induced by atomic spontaneous emission and leakage of the cavity are also taken into account. The numerical simulation result shows that this scheme is robust against both atomic spontaneous emission and cavity leakage. Furthermore, when multiple atoms are trapped in a cavity, the (n+1n+1n+1)-atom Dicke states can be derived directly from the nnn-atom Dicke states with the same principle, which provides a scalable way for the preparation of Dicke states in theory.
Abstract Dicke states play an important role in quantum information processing and quantum computing. Here, by virtue of quantum Zeno dynamics and shortcuts to adiabaticity, a scheme for fast conversion of three‐particle symmetric Dicke states to four‐particle symmetric Dicke states () with Rydberg superatoms is proposed. This scheme can be completed within one step through adjusting the Rabi frequencies of classical fields. Moreover, the effect of decoherence induced by atomic spontaneous emission and leakage of the cavity on fidelities are considered. The numerical simulation demonstrates that this scheme has high fidelities and robustness against decoherence.
An approach is presented for converting a two-atom singlet state into a three-atom singlet state based on the quantum Zeno dynamics induced by continuous coupling.The scheme can be achieved within one step through appropriately regulating the Rabi frequencies of the classical fields.The effects of decoherence such as atomic spontaneous emission and the loss of cavity are also considered in virtue of the master equation.The numerical simulation result shows that this proposal is especially robust against the cavity decay, since no cavity-photon population is involved during the whole process because of the quantum Zeno dynamics.Furthermore, if a multilevel atom and a multi-mode cavity are applicable, the N -atom singlet state could be derived directly from the (N -1)-atom singlet state with the same principle, which provides a scalable way for the preparation of |S N in theory.
Motivated by "transitionless quantum driving", we construct shortcuts to adiabatic passage in a three-atom system to create a singlet state with the help of quantum zeno dynamics and non-resonant lasers. The influence of various decoherence processes is discussed by numerical simulation and the results reveal that the scheme is fast and robust against decoherence and operational imperfection. We also investigate how to select the experimental parameters to control the cavity dissipation and atomic spontaneous emission which will have an application value in experiment.
We propose an effective scheme of shortcuts to adiabaticity for generating a three-dimensional entanglement of two atoms trapped in a cavity using the transitionless quantum driving (TQD) approach. The key point of this approach is to construct an effective Hamiltonian that drives the dynamics of a system along instantaneous eigenstates of a reference Hamiltonian to reproduce the same final state as that of an adiabatic process within a much shorter time. In this paper, the shortcuts to adiabatic passage are constructed by introducing two auxiliary excited levels in each atom and applying extra cavity modes and classical fields to drive the relevant transitions. Thereby, the three-dimensional entanglement is obtained with a faster rate than that in the adiabatic passage. Moreover, the influences of atomic spontaneous emission and photon loss on the fidelity are discussed by numerical simulation. The results show that the speed of entanglement implementation is greatly improved by the use of adiabatic shortcuts and that this entanglement implementation is robust against decoherence. This will be beneficial to the preparation of high-dimensional entanglement in experiment and provides the necessary conditions for the application of high-dimensional entangled states in quantum information processing.
A scheme for preparing a three-dimensional entangled state of two atoms is proposed. In the present scheme, two atoms are placed in two cavities that are spatially separated and connected by a fiber. With the help of quantum Zeno dynamics, the shortcuts to adiabaticity can be constructed through transitionless quantum driving to fast achieve the preparation of a three-dimensional entangled state. During this process, we consider the influence of fluctuations about system parameters and various decoherence factors on the fidelity. Numerical simulation results demonstrate that this scheme can not only realize the preparation of a three-dimensional entangled state with a high fidelity, but is also insensitive to parameter fluctuations. Moreover, our scheme can be extended to realize the N-dimensional entanglement of two atoms.
Recently, the technique of counterdiabatic driving, which provides an effective strategy for accelerating adiabatic quantum evolution, has been widely applied in the preparation of many-body quantum states. In this work, we propose a theoretical scheme for the efficient preparation of Dicke states in a system of non-interacting two-level atoms. Our approach leverages the one-axis twisting (OAT) interaction to generate non-classical correlations and combines it with time-dependent external fields to achieve precise control over the dynamics of the system. By employing rapid adiabatic passage (RAP), it demonstrates how the system can be steered from an initial coherent spin state to a target Dicke state with high fidelity [S. C. Carrasco, M. H. Goerz, S. A. Malinovskaya, V. Vuletić, W. P. Schleich, and V. S. Malinovsky, Phys. Rev. Lett. \textbf{132}, 153603 (2024)]. To further optimize the preparation process, we introduce counterdiabatic driving (CD), which suppresses non-adiabatic transitions. Numerical simulations confirm that our scheme can achieve high-fidelity Dicke states for a moderate number of particles. Our results provide a scalable and experimentally feasible approach to prepare Dicke states, with potential applications in quantum metrology, quantum communication, and quantum information processing.