Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Quadripartite entanglement from a double three-level Λ -type-atom model

Dan Wang, Liyun Hu, Xiu-Mei Pang, Junxiang Zhang, Shi‐Yao Zhu

Published Oct 14, 2013• 8 citations
Publisher

Abstract

We present a theoretical scheme for the generation of four quantized modes in a three-level double-$\ensuremath{\Lambda}$ atomic system driven by two counterpropagating far-detuned pump beams and find the entanglement between the four modes. By using the second-order perturbation method and the phase-matching condition for the four-wave mixing processes, the effective Hamiltonian is derived, which clearly illustrates the generation of four light beams and their entanglement. The dependence of the four-mode entanglement on interaction time, pump detuning, strength of interaction force, and the ratio of Rabi frequency of two pump beams is analyzed with inseparability. The result presented here provides a method for the experimental generation of multipartite entanglement in an atomic system.

DOI
10.1103/physreva.88.042314

Related papers

Double- Λ microscopic model for entangled light generation by four-wave mixing

Quentin C. Glorieux, Romain Dubessy, S. Guibal +4 more

Motivated by recent experiments, we study four-wave-mixing in an atomic double-$\ensuremath{\Lambda}$ system driven by a far-detuned pump. Using the Heisenberg-Langevin formalism, and based on the microscopic properties of the medium, we calculate the classical and quantum properties of seed and conjugate beams beyond the linear amplifier approximation. A continuous-variable approach gives us access to relative-intensity noise spectra that can be directly compared with experiments. Restricting ourselves to the cold-atom regime, we predict the generation of quantum-correlated beams with a relative-intensity noise spectrum well below the standard quantum limit (down to $\ensuremath{-}6$ dB). Moreover, entanglement between seed and conjugate beams measured by an inseparability down to $0.25$ is expected. This work opens the way to the generation of entangled beams by four-wave mixing in a cold-atom sample.

arXiv:1007.1610•Physical Review A•Sep 17, 2010•94 citations

Polychromatic quadripartite entanglement from concurrent four-wave mixing in a three-level atomic system

Huatang Tan, Gao‐xiang Li

In this paper, we investigate the generation of polychromatic quadripartite entanglement of continuous variables from a three-level $\ensuremath{\Lambda}$-type atomic system inside an optical quadruply resonant cavity. The atoms are driven by external lasers and simultaneously coupled to four cavity modes by means of multiply concurrent four-wave mixing interactions. The general master equation of the cavity field is derived explicitly. By solving the Gaussian-type master equation and using the negative-partial-transpose criterion for bipartite entanglement, we show that the genuine quadripartite entanglement of the field can be generated over a wide range of parameters. The entanglement properties of the four-mode field are discussed in detail. We find that the optimal quadripartite entanglement can be obtained when the cavity modes are tuned to be resonant with the Rabi sidebands of the driven atoms.

Physical Review A•Sep 22, 2010•14 citations

Generation of quadripartite entanglement based on four-wave mixing process and linear beam splitter

Shengkai Yu, Huan-Zhang Liu, Shengshuai Liu +1 more

As a crucial quantum resource in quantum information processing, multipartite entanglement plays an important role not only in the field of testing basic quantum effects, but also in the applications of quantum network, quantum communication and quantum computing. The generation of multipartite entanglement usually involves many complex linear processes and nonlinear processes. In this paper, we theoretically propose a scheme for generating genuine quadripartite entanglement by linking two independent four-wave mixing (FWM) processes with one linear beam splitter (BS). Here, we use one linear BS to mix the probe beams amplified by two independent FWM processes. We first set the transmissivity of the linear BS to be 0.5 and study the effect of the intensity gain of the system on quadripartite entanglement by applying the positivity under partial transposition (PPT) criterion. The results show that there exists genuine quadripartite entanglement in all gain regions, and the degree of entanglement increases with intensity gain increasing. And then, the dependence of quadripartite entanglement on the transmissivity of the linear BS is studied when the intensity gains of two independent FWM processes are both set to be 3. We find that the transmissivity of the linear BS can affect the entanglement properties of the system. At the same time, we also find that the system can generate genuine quadripartite entanglement when the transmissivity of the linear BS is not equal to 0 or 1. Finally, in order to reveal the entanglement structure of the system, we further investigate the dependence of the possible tripartite entanglement and bipartite entanglement on the intensity gain of the system by using the PPT criterion. The results show that there exists the genuine tripartite entanglement in this system, and the degree of entanglement increases as the intensity gain increases. However, there exists no genuine bipartite entanglement in this system, some of bipartite states are always separable, and the entanglement of the other bipartite states gradually become weak and eventually disappear with the increase of the intensity gain. Our theoretical result provides a simple and reliable scheme for generating genuine quadripartite entanglement by using FWM process in atomic ensemble and linear BS.

Acta Physica Sinica•Jan 1, 2020•5 citations

Quadripartite entanglement from two-port resonator with second-order harmonic generation

Jing-Chen Hao, Peilin Du, Hengxin Sun +4 more

Quantum entanglement is a crucial resource for performing quantum computing and constructing quantum communication networks. The preparation and manipulation of entangled light field are the basic elements of quantum communication. With the development of science and technology, multicolor multipartite entanglement is becoming a kind of special resource for quantum information, quantum networks, and quantum memory. In this paper, we propose a scheme of generating quadripartite entanglement among four output beams from a two-port frequency doubling resonator, in which a type-II phase matching nonlinear crystal is placed. We make two fundamental-frequency pump beams with the same frequency and vertical polarization pass through the nonlinear crystal to produce two frequency-doubling beams. There is a quadripartite entanglement between the frequency-doubling beams, which are output at two ports of the optical resonator, and the incident fundamental beams. Based on the transmission matrix from the coupled wave equation, the self-consistent equations of the intracavity modes and the corresponding noise properties of the output modes can be obtained. Then, the quadripartite entanglement produced from two second harmonic beams and two reflected fundamental-frequency pump beams, is verified by using the positive partial transposition criterion, in a wide range of pumping power and analysis frequency. The setup proposed in this work is compact and experimentally feasible. It is also convenient to separate the four entangled beams spatially, with different wavelengths and polarizations. When the beam wavelengths are matched with 1560 nm (low loss window of fiber) and 780 nm (atomic absorption line of Rb), this scheme can be more useful in both quantum communication and quantum memory.

Acta Physica Sinica•Jan 1, 2024•1 citation

Generating an entangled coherent state of two cavity modes in a three-level Λ-type atomic system

Qing-Xia Mu, Yonghong Ma, Ling Zhou

In this paper, we present a scheme to generate an entangled coherent state by considering a three-level Λ- type atom interacting with a two-mode cavity driven by classical fields. The two-mode entangled coherent state can be obtained under large detuning conditions. Considering the cavity decay, an analytical solution is deduced.

arXiv:0711.4186•Journal of Physics B Atomic Molecular and Optical Physics•Aug 3, 2007•18 citations

Enhancement of entanglement for two-mode fields generated from four-wave mixing with the help of the auxiliary atomic transition

Gao‐xiang Li, Hua-Tang Tan, Mihai Macovei

The entanglement properties of two mode fields generated from four-wave mixing are discussed in the system of an ensemble of $V$-type three-level atoms embedded in a two-mode cavity, in which the atomic transitions from the two excited states to the ground state are driven by one strong and one relative weak laser field, respectively. The nondegenerate four-wave mixing process occurs in the strong laser-driven transition, which is also coupled by the two cavity modes. With the help of the auxiliary atomic transition driven by the weak laser field and adjusting the frequency difference of the two modes, highly squeezed and entangled light with high intensity can be generated.

Physical Review A•Nov 20, 2007•87 citations
We present a theoretical scheme for the generation of four quantized modes in a three-level double-\ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ atomic system driven by two counterpropagating far-detuned pump beams and find the entanglement between the four modes. By using the second-order perturbation method and the phase-matching condition for the four-wave mixing processes, the effective Hamiltonian is derived, which clearly illustrates the generation of four light beams and their entanglement. The dependence of the four-mode entanglement on interaction time, pump detuning, strength of interaction force, and the ratio of Rabi frequency of two pump beams is analyzed with inseparability. The result presented here provides a method for the experimental generation of multipartite entanglement in an atomic system.
Motivated by recent experiments, we study four-wave-mixing in an atomic double-$\ensuremath{\Lambda}$ system driven by a far-detuned pump. Using the Heisenberg-Langevin formalism, and based on the microscopic properties of the medium, we calculate the classical and quantum properties of seed and conjugate beams beyond the linear amplifier approximation. A continuous-variable approach gives us access to relative-intensity noise spectra that can be directly compared with experiments. Restricting ourselves to the cold-atom regime, we predict the generation of quantum-correlated beams with a relative-intensity noise spectrum well below the standard quantum limit (down to $\ensuremath{-}6$ dB). Moreover, entanglement between seed and conjugate beams measured by an inseparability down to 0.250.250.25 is expected. This work opens the way to the generation of entangled beams by four-wave mixing in a cold-atom sample.
In this paper, we investigate the generation of polychromatic quadripartite entanglement of continuous variables from a three-level $\ensuremath{\Lambda}$-type atomic system inside an optical quadruply resonant cavity. The atoms are driven by external lasers and simultaneously coupled to four cavity modes by means of multiply concurrent four-wave mixing interactions. The general master equation of the cavity field is derived explicitly. By solving the Gaussian-type master equation and using the negative-partial-transpose criterion for bipartite entanglement, we show that the genuine quadripartite entanglement of the field can be generated over a wide range of parameters. The entanglement properties of the four-mode field are discussed in detail. We find that the optimal quadripartite entanglement can be obtained when the cavity modes are tuned to be resonant with the Rabi sidebands of the driven atoms.
As a crucial quantum resource in quantum information processing, multipartite entanglement plays an important role not only in the field of testing basic quantum effects, but also in the applications of quantum network, quantum communication and quantum computing. The generation of multipartite entanglement usually involves many complex linear processes and nonlinear processes. In this paper, we theoretically propose a scheme for generating genuine quadripartite entanglement by linking two independent four-wave mixing (FWM) processes with one linear beam splitter (BS). Here, we use one linear BS to mix the probe beams amplified by two independent FWM processes. We first set the transmissivity of the linear BS to be 0.5 and study the effect of the intensity gain of the system on quadripartite entanglement by applying the positivity under partial transposition (PPT) criterion. The results show that there exists genuine quadripartite entanglement in all gain regions, and the degree of entanglement increases with intensity gain increasing. And then, the dependence of quadripartite entanglement on the transmissivity of the linear BS is studied when the intensity gains of two independent FWM processes are both set to be 3. We find that the transmissivity of the linear BS can affect the entanglement properties of the system. At the same time, we also find that the system can generate genuine quadripartite entanglement when the transmissivity of the linear BS is not equal to 0 or 1. Finally, in order to reveal the entanglement structure of the system, we further investigate the dependence of the possible tripartite entanglement and bipartite entanglement on the intensity gain of the system by using the PPT criterion. The results show that there exists the genuine tripartite entanglement in this system, and the degree of entanglement increases as the intensity gain increases. However, there exists no genuine bipartite entanglement in this system, some of bipartite states are always separable, and the entanglement of the other bipartite states gradually become weak and eventually disappear with the increase of the intensity gain. Our theoretical result provides a simple and reliable scheme for generating genuine quadripartite entanglement by using FWM process in atomic ensemble and linear BS.
Quantum entanglement is a crucial resource for performing quantum computing and constructing quantum communication networks. The preparation and manipulation of entangled light field are the basic elements of quantum communication. With the development of science and technology, multicolor multipartite entanglement is becoming a kind of special resource for quantum information, quantum networks, and quantum memory. In this paper, we propose a scheme of generating quadripartite entanglement among four output beams from a two-port frequency doubling resonator, in which a type-II phase matching nonlinear crystal is placed. We make two fundamental-frequency pump beams with the same frequency and vertical polarization pass through the nonlinear crystal to produce two frequency-doubling beams. There is a quadripartite entanglement between the frequency-doubling beams, which are output at two ports of the optical resonator, and the incident fundamental beams. Based on the transmission matrix from the coupled wave equation, the self-consistent equations of the intracavity modes and the corresponding noise properties of the output modes can be obtained. Then, the quadripartite entanglement produced from two second harmonic beams and two reflected fundamental-frequency pump beams, is verified by using the positive partial transposition criterion, in a wide range of pumping power and analysis frequency. The setup proposed in this work is compact and experimentally feasible. It is also convenient to separate the four entangled beams spatially, with different wavelengths and polarizations. When the beam wavelengths are matched with 1560 nm (low loss window of fiber) and 780 nm (atomic absorption line of Rb), this scheme can be more useful in both quantum communication and quantum memory.
The entanglement properties of two mode fields generated from four-wave mixing are discussed in the system of an ensemble of VVV-type three-level atoms embedded in a two-mode cavity, in which the atomic transitions from the two excited states to the ground state are driven by one strong and one relative weak laser field, respectively. The nondegenerate four-wave mixing process occurs in the strong laser-driven transition, which is also coupled by the two cavity modes. With the help of the auxiliary atomic transition driven by the weak laser field and adjusting the frequency difference of the two modes, highly squeezed and entangled light with high intensity can be generated.