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Chinese Optics Letters

Optimal initial states for quantum parameter estimation based on Jaynes–Cummings model [Invited]

Liwen Qiao, Jia‐Xin Peng, Baiqiang Zhu, Weiping Zhang, Keye Zhang

Published Jan 1, 2023• 5 citations
Publisher

Abstract

Quantum parameter estimation is a crucial tool for inferring unknown parameters in physical models from experimental data.The Jaynes-Cummings model is a widely used model in quantum optics that describes the interaction between an atom and a single-mode quantum optical field.In this Letter, we systematically investigate the problem of estimating the atom-light coupling strength in this model and optimize the initial state in the full Hilbert space.We compare the precision limits achievable for different optical field quantum states, including coherent states, amplitude-and phase-squeezed states, and provide experimental suggestions with an easily prepared substitute for the optimal state.Our results provide valuable insights into optimizing quantum parameter estimation in the Jaynes-Cummings model and can have practical implications for quantum metrology with hybrid quantum systems.

DOI
10.3788/col202321.102701

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Quantum parameter estimation is a crucial tool for inferring unknown parameters in physical models from experimental data.The Jaynes-Cummings model is a widely used model in quantum optics that describes the interaction between an atom and a single-mode quantum optical field.In this Letter, we systematically investigate the problem of estimating the atom-light coupling strength in this model and optimize the initial state in the full Hilbert space.We compare the precision limits achievable for different optical field quantum states, including coherent states, amplitude-and phase-squeezed states, and provide experimental suggestions with an easily prepared substitute for the optimal state.Our results provide valuable insights into optimizing quantum parameter estimation in the Jaynes-Cummings model and can have practical implications for quantum metrology with hybrid quantum systems.
Quantum parameter estimation is one of the most important applications in quantum metrology. The basic theory of quantum parameter estimation-quantum Cramer-Rao bound-shows that the precision limit of quantum parameter estimation is directly related to quantum Fisher information. Therefore quantum Fisher information is extremely important in the quantum parameter estimation. In this paper we use quantum parameter estimation theory to estimate the coupling constant of the Jaynes-Cummings model with large detuning. The initial probing state is the direct product state of qubit and radiation field in which Fock state, thermal state and coherent state are taken into account respectively. We calculate the quantum Fisher information of the hybrid system as well as qubit and radiation field for each probing state after the parameter evolution under the Hamiltonian of the Jaynes-Cummings model with large detuning. The results show that the quantum Fisher information increases monotonically with the average photon number increasing. The optimal detection state is that when the qubit system is in the equal weight superposition of the ground and the excited state, at this time the quantum Fisher information always reaches a maximum value, When the radiation field of probing state is Fock state or the thermal state, the information about the estimated parameter is included only in the qubit. The estimation accuracy of the coupling constant with thermal state or coherent state is higher than that with Fock state.
The properties of the field quantum entropy evolution in a system of a single-mode squeezed coherent state field interacting with a two-level atom is studied by utilizing the complete quantum theory, and we focus our attention on the discussion of the influences of field squeezing parameter γ, atomic distribution angle θ and coupling strength g between the field and the atom on the properties of the evolution of field quantum entropy. The results obtained from numerical calculation indicate that the amplitude of oscillation of field quantum entropy evolution decreases with the increasing of squeezing parameter γ, and that both atomic distribution angle θ and coupling strength g between the field and the atom can influence the periodicity of field quantum entropy evolution.
In this paper, we consider the application of quantum reservoir engineering in quantum metrology. More precisely, we are concerned with a system setup where a sequence of atoms constructing the “time-varying” quantum reservoir interact, in turn, with the trapped field in a cavity through the Jaynes–Cummings Hamiltonian. In particular, we were able to manipulate the initial states of reservoir atoms in order to enhance estimation precision regarding the coupling strength between each atom and the cavity (the coupling strength between each atom and the cavity was assumed to be identical). The novelty of this work lies in alternately preparing the atoms at two different states in a pairwise manner, such that the cavity could converge into a squeezed state with photonic loss to the environment taken into account. The control scheme proposed here thus leads to higher precision compared to the previous work where reservoir atoms were initialized at the same state, which drove the cavity to a coherent state. Detailed theoretical analysis and numerical simulations are also provided. In addition, this system setup and the associated control scheme are easily implemented for quantum metrology, since no entanglement is required for the preparation of atom states, and the final cavity state can stay steady.
Evolution of the squeezed state in a multiphoton Jaynes–Cummings model (JCM) when the field is interacting with an atom prepared initially in a coherent superposition of the ground state and the excited state is studied. Long time and short time evolution of field statistics are discussed and compared with the standard JCM. These properties are found to be sensitive to the initial phase of the atom. For a phased atom, squeezing at later times can be larger than the initial squeezing. It is found that two-photon interaction of a suitably prepared phased atom with the initial vacuum state can yield 45% squeezing below the vacuum noise limit. Multiphoton interaction of a phased atom with the initial vacuum state of the field leads periodically to a pure field state that is a coherent superposition of the vacuum state and the n-photon Fock state.
We considered the anti-Jaynes-Cummings (AJC) interaction of a two-level atom in an initial ground state interacting with a field mode in an initial squeezed coherent state at arbitrary values of squeeze parameter r and provided the Jaynes-Cummings (JC) interaction as a comparison. We analysed the degree of entanglement (DEM) measured by the von Neumann entropy and the nature of the field quantified by the Mandel Q parameter in relation to the atomic population inversion during the AJC interaction and separately the corresponding JC interaction. We noted in our examples that at r>1.4, photon statistics evolved to super-Poissonian from sub-Poissonian during the respective AJC, JC interactions. Further, for high values of r, the form of the time evolution of atomic population inversion depicted enhanced ringing revivals at the collapse region in comparison to the case of an initial coherent state. What is more, at higher values of r the time evolution of DEM showed more rapid oscillations and recorded higher values, concurrently, an increase in the degree of mixedness.