arXiv subjects

Wangjun Lu

Publications and source records attributed to Wangjun Lu.

11 recordsLinked to original sources

arXiv2024

Single-photon triggered quantum entanglement between two qubits or at least 2000 identical qubits

This paper studies the effect of single-photon light fields on quantum entanglement between two qubits and multiple identical qubits initially in a direct state. For two qubits, we first analyze the impact of the excited state's weight on single-photon-triggered entanglement, finding that excessive weight disrupts this process. We then explore how initial coherence affects entanglement, discovering that maximum initial coherence enables the single photon to achieve maximal entanglement. For multiple qubits, we similarly investigate the effects of the excited state's weight and initial coherence on entanglement control. In large qubit systems, we find that single photons cannot trigger entanglement when excited-state weights exceed ground-state weights or when all qubits are initially in the ground state. Interestingly, single photons can still trigger entanglement between any two qubits in systems with at least 2000 qubits, with the entanglement depending on initial state parameters rather than the number of qubits.

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arXiv2024

Information Geometry and Parameter Sensitivity of Non-Hermitian Hamiltonians

Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this paper, we explore the Fisher-Rao metric with the non-Hermitian systems. By approximating the Lindblad master equation in the non-Hermitian Hamiltonian, we calculate the time evolution of the quantum geometric metric. Finally, we give an example of the quantum spin Ising model of the imaginary magnetic field, explore the energy spectrum of $\mathcal{PT}$-symmetric Hamiltonian and the evolution of geometric metric, and discuss that the dissipative effect of the imaginary magnetic field can be eliminated under the condition of adding the control Hamiltonian, so as to improve the accuracy of parameter estimation.

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arXiv2024

Generating Bell states and Werner states of two qubits via optical field

In this paper, we investigate how the evolution of the states of two qubits initially in a direct product state can be controlled by the optical field in a Tavis-Cummings (TC) model. For the two qubits initially in the direct product state, we find that their matrix elements at any moment can be modulated by the coefficients of the optical field initial states in the number state space. We propose a method for preparing an \textit{X}-type state of two qubits. Subsequently, for descriptive convenience, we divide the Bell states of the two qubits into two kinds in the paper. When both qubits are initially in the ground state, we find that the two qubits can be controlled to produce the first type of Bell state by the superposition state optical field that is initially in the next-nearest-neighbor number state and that the production of any of the first type of Bell states can be controlled by controlling the phase between the two next-nearest-neighbor number states. When one of the two qubits is in the ground state, and the other is in the excited state, we can control the two qubits to produce the second type of Bell state by the single-photon number state optical field. Finally, we study the generation of Werner states by controlling two qubits initially, both in the ground state, using an optical field.

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arXiv2023

Tripartite quantum entanglement with squeezed optomechanics

The ability to engineer entangled states that involve macroscopic objects is of particular importance for a wide variety of quantum-enabled technologies, ranging from quantum information processing to quantum sensing. Here we propose how to achieve coherent manipulation and enhancement of quantum entanglement in a hybrid optomechanical system, which consists of a Fabry-P\'{e}rot cavity with two movable mirrors, an optical parametric amplifier (OPA), and an injected squeezed vacuum reservoir. We show that the advantages of this system are twofold: (i) one can effectively regulate the light-mirror interactions by introducing a squeezed intracavity mode via the OPA; (ii) when properly matching the squeezing parameters between the squeezed cavity mode and the injected squeezed vacuum reservoir, the optical input noises can be suppressed completely. These peculiar features of this system allow us to generate and manipulate quantum entanglement in a coherent and controllable way. More importantly, we also find that such controllable entanglement, under some specific squeezing parameters, can be considerably enhanced in comparison with those of the conventional optomechanical system. Our work, providing a promising method to regulate and tailor the light-mirror interaction, are poised to serve as a useful tool for engineering various quantum effects which are based on cavity optomechanics.

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arXiv2023

Quantum metrology enhanced by the $XY$ spin interaction in a generalized Tavis-Cummings model

Quantum metrology is recognized for its capability to offer high-precision estimation by utilizing quantum resources, such as quantum entanglement. Here, we propose a generalized Tavis-Cummings model by introducing the $XY$ spin interaction to explore the impact of the many-body effect on estimation precision, quantified by the quantum Fisher information (QFI). By deriving the effective description of our model, we establish a closed relationship between the QFI and the spin fluctuation induced by the $XY$ spin interaction. Based on this exact relation, we emphasize the indispensable role of the spin anisotropy in achieving the Heisenberg-scaling precision for estimating a weak magnetic field. Furthermore, we observe that the estimation precision can be enhanced by increasing the strength of the spin anisotropy. We also reveal a clear scaling transition of the QFI in the Tavis-Cummings model with the reduced Ising interaction. Our results contribute to the enrichment of metrology theory by considering many-body effects, and they also present an alternative approach to improving the estimation precision by harnessing the power provided by many-body quantum phases.

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arXiv2022

Instantaneous indirect measurement principle in quantum mechanics

In quantum systems, the measurement of operators and the measurement of the quantum states of the system are very challenging tasks. In this Letter, we propose a method to obtain the average value of one operator in a certain state by measuring the instantaneous change of the average value of another operator with the assistance of a known reference state. We refer to this measurement method as the instantaneous indirect measurement method. By studying the application of this method to some typical models, we find that this measurement can be applied to the measurement of an arbitrary state of a quantum system. Furthermore, for the system to be measured, we find that such measurement neither significantly affects the wave function of the system nor causes wave function collapse of the system. Also, our study shows that when two independent systems are coupled, the information mapping between them is done instantaneously. Finally, we discuss applying this measurement method to the measurement of quantum Fisher information, which quantizes the limited accuracy of estimating a parameter from a quantum state.

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arXiv2022

Quantum phase transition in XXZ central spin model

We investigate the quantum phase transition (QPT) in the XXZ central spin model, which can be described as a spin-1/2 particle coupled to N bath spins. In general, the QPT is supposed to occur only in the thermodynamical limit. In contrast, we present that the central spin model exhibits a normal-to-superradiant phase transition in the limit where the ratio of the transition frequency of the central spin to that of the bath spins and the number of the bath spins tend to infinity. We give the low-energy effective Hamiltonian analytically in the normal phase and the superradiant phase, and we find that the longitudinal interaction can significantly influence the excitation number and the coherence of the ground state. These two quantities are remarkably enhanced for the negative longitudinal interaction while suppressed for the positive longitudinal interaction. We also use the quantum Fisher information (QFI) to characterize the QPT and illustrate a measurement scheme that can be applied in practice. This work builds a novel connection between the qubit-spin systems and the qubit-field systems, which provides a possibility for the realization of criticality-enhanced quantum sensing in central spin systems.

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arXiv2022

All-optical generation of deterministic squeezed Schr\"odinger-cat states

Quantum states are important resources and their preparations are essential prerequisites to all quantum technologies. However, they are extremely fragile due to the inevitable dissipations. Here, an all-optical generation of a deterministic squeezed Schr$\ddot{\mathrm{o}}$dinger-cat state based on dissipation is proposed. Our system is based on the Fredkin-type interaction between three optical modes, one of which is subject to coherent two-photon driving and the rest are coherent driving. We show that an effective degenerate three-wave mixing process can be engineered in our system, which can cause the simultaneous loss of two photons, resulting in the generation of a deterministic squeezed Schr$\ddot{\mathrm{o}}$dinger-cat state. More importantly, by controlling the driving fields in our system, the two-photon loss can be adjustable, which can accelerate the generation of squeezed Schr$\ddot{\mathrm{o}}$dinger-cat states. Besides, we exploit the squeezed Schr$\ddot{\mathrm{o}}$dinger-cat states to estimate the phase in the optical interferometer, and show that the quantum Fisher information about the phase can reach the Heisenberg limit in the limit of a large photon number. Meanwhile, it can have an order of magnitude factor improvement over the Heisenberg limit in the low-photon-number regime, which is very valuable for fragile systems that cannot withstand large photon fluxes. This work proposes an all-optical scheme to deterministically prepare the squeezed Schr$\ddot{\mathrm{o}}$dinger-cat state with high speed and can also be generalized to other physical platforms.

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arXiv2021

Extreme expected values and their applications in quantum information processing

We consider the probability distribution when the monotonic function $F(X)$ of the independent variable $X$ takes the maximum or minimum expected value under the two constraints of a certain probability and a certain expected value of the independent variable $X$. We proposed an equal probability and equal expected value splitting method. With this method, we proved four inequalities, and two of them can be reduced to Jensen's inequalities. Subsequently, we find that after dividing the non-monotone function $H(X)$ into multiple monotone intervals, the problem of solving the maximum and minimum expected values of $H(X)$ can be transformed into the problem of solving the extreme value of a multiple-variable function. Finally, we apply the proved theory to solve three problems in quantum information processing. When studying the quantum parameter estimation in Mach-Zehnder interferometer, for an equal total input photon number, we find an optimal path-symmetric input state that makes the quantum Fisher information take the maximum value, and we prove that the NOON state is the path-symmetric state that makes the quantum Fisher information takes the minimum value. When studying the quantum parameter estimation in Landau-Zener-Jaynes-Cummings model, we find the optimal initial state of the cavity field that makes the system obtain the maximum quantum Fisher information. Finally, for an equal initial average photon number, we find the optimal initial state of the cavity field that makes the Tavis-Cummings quantum battery have the maximum stored energy and the maximum average charging power.

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arXiv2021

Single-photon-triggered spin squeezing with decoherence reduction in optomechanics via phase matching

Quantum spin squeezing is an important resource for quantum information processing, but its squeezing degree is not easy to preserve in an open system with decoherence. Here, we propose a scheme to implement single-photon-triggered spin squeezing with decoherence reduction in an open system. In our system, a Dicke model (DM) is introduced into the quadratic optomechanics, which can be equivalent to an effective DM manipulated by the photon number. Besides, the phonon mode of the optomechanical system is coupled to a squeezed vacuum reservoir with a phase matching, resulting in that the thermal noise caused by the environment can be suppressed completely. We show that squeezing of the phonon mode triggered by a single photon can be transferred to the spin ensemble totally, and pairwise entanglement of the spin ensemble can be realized if and only if there is spin squeezing. Importantly, when considering the impact of the environment, our system can obtain a better squeezing degree than the optimal squeezing that can be achieved in the traditional DM. Meanwhile, the spin squeezing generated in our system is immune to the thermal noise. This work offers an effective way to generate spin squeezing with a single photon and to reduce decoherence in an open system, which will have promising applications in quantum information processing.

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arXiv2021

Optimal state for a Tavis-Cummings quantum battery via the Bethe ansatz method

In this paper, we investigate the effect of different optical field initial states on the performance of the Tavis-Cummings (T-C) quantum battery. In solving the dynamical evolution of the system, we found a fast way to solve the Bethe ansatz equation. We find that the stored energy and the average charging power of the T-C quantum battery are closely related to the probability distribution of the optical field initial state in the number states. We define a quantity called the number-state stored energy. With this prescribed quantity, we only need to know the probability distribution of the optical field initial state in the number states to obtain the stored energy and the average charging power of the T-C quantum battery at any time. We propose an equal probability and equal expected value splitting method by which we can obtain two inequalities, and the two inequalities can be reduced to Jensen's inequalities. By this method, we found the optimal initial state of the optical field. We found that the maximum stored energy and the maximum average charging power of the T-C quantum battery are proportional to the initial average photon number, and the quantum battery can be fully charged when the initial average photon number is large enough. We found two phenomena, which can be described by two empirical inequalities. These two phenomena imply the hypersensitivity of the stored energy of the T-C quantum battery to the number-state cavity field. Finally, we discussed the impact of decoherence on battery performance.

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