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

arXiv:0804.1600 · Journal of Physics B Atomic Molecular and Optical Physics

Multipartite entanglement of three trapped ions in a cavity and W-state generation

S Shelly Sharma, Eduardo de Almeida, Naresh K Sharma

Published Aug 8, 2008• 13 citations
arXivHTMLPDF

Abstract

A scheme to generate three qubit maximally entangled W-states, using three trapped ions interacting with the red sideband tuned single-mode field of a high finesse cavity, is proposed. For the cavity field initially prepared in a number state, the probability of generating the three-ion W-state is calculated. By using the ion-cavity coupling strengths achieved in experimental realizations, the interaction time needed for W-state generation is found to be of the order of 10 µs. It is found that for a fixed number of photons in the cavity the nature of entanglement of ionic internal states can be manipulated by an appropriate choice of the initial-state phonon number. The ionic qubits in the W-like state are found to be entangled to cavity photons. Analytical expressions for global negativity and partial K -way negativities ( K = 2 to 4) are obtained to study the evolution of entanglement distribution as a function of the interaction parameter. Reversible entanglement exchange between different entanglement modes is observed. For specific values of the interaction parameter, the three ions and photon–phonon system are found to have 4-partite entanglement, generated by 2-way and 3-way correlations.

DOI
10.1088/0953-4075/41/16/165503

Related papers

Multipartite entanglement of three trapped ions and the cavity field

S. Shelly Sharma, Eduardo de Almeida, Naresh Kumar Sharma

The entanglement dynamics of three trapped ion interacting with red sideband tuned single mode of a cavity field is examined. Analytical expressions for the state of three ions and the cavity field are used to obtain the global, four-way, three-way and two-way negativities. For the cavity field initially prepared in a number state, the probability of generating three ion W-state is calculated. Analytical expressions for K-way entanglement measures (K=2 to 4) are obtained and plotted as a function of time.

Quantum-Atom Optics Downunder (QAO)•Jan 1, 2007•0 citations

Dynamics of Tripartite Entanglement

S. Shelly Sharma, Naresh Kumar Sharma

Maximally entangled states are of utmost importance to quantum communication, dense coding, and quantum teleportation. With a trapped ion placed inside a high finesse optical cavity, interacting with field of an external laser and quantized cavity field, a scheme to generate a maximally entangled three qubit GHZ state, is proposed. The dynamics of tripartite entanglement is investigated, using negativity as an entanglement measure and linear entropy as a measure of mixedness of a state. It is found that (a) the number of modes available to the subsystem determines the maximum entanglement of a subsystem, (b) at entanglement maxima and minima, linear entropy and negativity uniquely determine the nature of state, but the two measures do not induce the same ordering of states, and (c) for a special choice of system parameters maximally entangled tripartite two mode GHZ state is generated. The scheme presented for GHZ state generation is a single step process and is reduction-free.

arXiv:quant-ph/0502008•Physica Scripta•Jan 1, 2005•2 citations

Preparation of hybrid entangled states and entangled coherent states for a single trapped ion in a cavity

Jie‐Qiao Liao, Yu Guo, Hao‐Sheng Zeng +1 more

In this paper, we study generation of entangled states in a system which consists of a single trapped ion in a cavity. We obtain a cross-Kerr-like interaction between the cavity field (photons) and the centre-of-mass motion (phonons) of the trapped ion in the Lamb–Dicke and large detuning regime. Based on this cross-Kerr-like interaction, we create hybrid entangled states between the phonon mode and the ionic internal states, and between the cavity field and ionic internal states, respectively. We also show that it is possible to prepare entangled coherent states between the cavity field and the phonon mode. We explicitly obtain an entangled state between two pairs of Schrödinger-cat states.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 7, 2006•14 citations

Two Schemes for Generation of Entanglement for Vibronic Collective States of Multiple Trapped Ions

Wen‐Xing Yang, Jiahua Li, Anshou Zheng

We propose two schemes to prepare entanglement for the vibronic collective states of multiple trapped ions. The first scheme aims to generating multipartite entanglement for vibrational modes of trapped ions, which only requires a single laser beam tuned to the ionic carrier frequency. Our scheme works in the mediated excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Beyond their fundamental importance, these states may be of interest for experimental studies on decoherence since the present scheme operates in a fast way. The second scheme aims to preparing the continuous variable multimode maximally Greenberger–Horne–Zeilinger state. The distinct advantage is that the operation time is only limited by the available laser intensity, not by the inherent mechanisms such as off-resonant excitations. This makes it promising to obtain entanglement of multiple coherent and squeezing states with desired amplitudes in a reasonable time.

Communications in Theoretical Physics•Mar 1, 2007•3 citations

Toward coherent ion-cavity coupling

Markus O. Vogt

Entanglement is an established resource in quantum information processing, and there is a clear imperative to study many-body systems both in quantum technology applications and for probing fundamental physical laws. Ion trap cavity quantum electrodynamics is a highly promising platform for research. Prerequisites are the controlled coupling of many ions to the cavity field along with the ability to initialize the quantum states and drive coherent transitions between them. A coaxial ion trap and high finesse cavity system has been shown to couple strings of up to five ions to the cavity mode with nearly optimal coupling strength thanks to precise control over their positions in the standing wave and their mutual Coulomb interaction. The predictive power of the theoretical model demonstrates that the scheme can be extended to more ions or to higher coupling regimes. In a separate experiment it has been demonstrated that a quantum state can be initialized, before coherently transferring the population to a qubit state through the cavity interaction. The emission of polarized photons in the cavity mode has been measured, taking the system closer to the generation of cluster states for quantum information research and fundamental studies in many-body entanglement. Building on the aforementioned work, an infrastructure has been put in place for the direct observation of vacuum Rabi oscillations between a single ion and the cavity. In this scheme, the contribution to the dynamics from the dominant incoherent channel is minimized through post-selection of the data. As a quantum system coupled to a reservoir with memory, it will provide experimental constraints on theoretical work in the field of non-Markovian dynamics.

•May 22, 2017•0 citations

A simple Scheme for Generating an n -Qubit W State in a Trapped-Ion System without a Lamb–Dicke Limit

Zheng Xiao-Juan, Xue-mei Xu, Fangping Ouyang +1 more

A simple and scalable scheme is proposed to generate a n-qubit W state in a trapped-ion system without the Lamb–Dicke limit. The n-qubit W state can be generated by the interaction between the ions and the laser field if the collective mode is initially prepared in the single-phonon state and each ion is in the ground state. The scheme only requires a single laser and avoids laser manipulation of the individual ion. The time required to complete the process decreases with the number of ions. The present scheme is not limited to small values of the LD parameter, which greatly enhances operation speeds.

Chinese Physics Letters•Mar 31, 2009•1 citation
A scheme to generate three qubit maximally entangled W-states, using three trapped ions interacting with the red sideband tuned single-mode field of a high finesse cavity, is proposed. For the cavity field initially prepared in a number state, the probability of generating the three-ion W-state is calculated. By using the ion-cavity coupling strengths achieved in experimental realizations, the interaction time needed for W-state generation is found to be of the order of 10 µs. It is found that for a fixed number of photons in the cavity the nature of entanglement of ionic internal states can be manipulated by an appropriate choice of the initial-state phonon number. The ionic qubits in the W-like state are found to be entangled to cavity photons. Analytical expressions for global negativity and partial K -way negativities ( K = 2 to 4) are obtained to study the evolution of entanglement distribution as a function of the interaction parameter. Reversible entanglement exchange between different entanglement modes is observed. For specific values of the interaction parameter, the three ions and photon–phonon system are found to have 4-partite entanglement, generated by 2-way and 3-way correlations.
The entanglement dynamics of three trapped ion interacting with red sideband tuned single mode of a cavity field is examined. Analytical expressions for the state of three ions and the cavity field are used to obtain the global, four-way, three-way and two-way negativities. For the cavity field initially prepared in a number state, the probability of generating three ion W-state is calculated. Analytical expressions for K-way entanglement measures (K=2 to 4) are obtained and plotted as a function of time.
Maximally entangled states are of utmost importance to quantum communication, dense coding, and quantum teleportation. With a trapped ion placed inside a high finesse optical cavity, interacting with field of an external laser and quantized cavity field, a scheme to generate a maximally entangled three qubit GHZ state, is proposed. The dynamics of tripartite entanglement is investigated, using negativity as an entanglement measure and linear entropy as a measure of mixedness of a state. It is found that (a) the number of modes available to the subsystem determines the maximum entanglement of a subsystem, (b) at entanglement maxima and minima, linear entropy and negativity uniquely determine the nature of state, but the two measures do not induce the same ordering of states, and (c) for a special choice of system parameters maximally entangled tripartite two mode GHZ state is generated. The scheme presented for GHZ state generation is a single step process and is reduction-free.
In this paper, we study generation of entangled states in a system which consists of a single trapped ion in a cavity. We obtain a cross-Kerr-like interaction between the cavity field (photons) and the centre-of-mass motion (phonons) of the trapped ion in the Lamb–Dicke and large detuning regime. Based on this cross-Kerr-like interaction, we create hybrid entangled states between the phonon mode and the ionic internal states, and between the cavity field and ionic internal states, respectively. We also show that it is possible to prepare entangled coherent states between the cavity field and the phonon mode. We explicitly obtain an entangled state between two pairs of Schrödinger-cat states.
We propose two schemes to prepare entanglement for the vibronic collective states of multiple trapped ions. The first scheme aims to generating multipartite entanglement for vibrational modes of trapped ions, which only requires a single laser beam tuned to the ionic carrier frequency. Our scheme works in the mediated excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Beyond their fundamental importance, these states may be of interest for experimental studies on decoherence since the present scheme operates in a fast way. The second scheme aims to preparing the continuous variable multimode maximally Greenberger–Horne–Zeilinger state. The distinct advantage is that the operation time is only limited by the available laser intensity, not by the inherent mechanisms such as off-resonant excitations. This makes it promising to obtain entanglement of multiple coherent and squeezing states with desired amplitudes in a reasonable time.
Entanglement is an established resource in quantum information processing, and there is a clear imperative to study many-body systems both in quantum technology applications and for probing fundamental physical laws. Ion trap cavity quantum electrodynamics is a highly promising platform for research. Prerequisites are the controlled coupling of many ions to the cavity field along with the ability to initialize the quantum states and drive coherent transitions between them. A coaxial ion trap and high finesse cavity system has been shown to couple strings of up to five ions to the cavity mode with nearly optimal coupling strength thanks to precise control over their positions in the standing wave and their mutual Coulomb interaction. The predictive power of the theoretical model demonstrates that the scheme can be extended to more ions or to higher coupling regimes. In a separate experiment it has been demonstrated that a quantum state can be initialized, before coherently transferring the population to a qubit state through the cavity interaction. The emission of polarized photons in the cavity mode has been measured, taking the system closer to the generation of cluster states for quantum information research and fundamental studies in many-body entanglement. Building on the aforementioned work, an infrastructure has been put in place for the direct observation of vacuum Rabi oscillations between a single ion and the cavity. In this scheme, the contribution to the dynamics from the dominant incoherent channel is minimized through post-selection of the data. As a quantum system coupled to a reservoir with memory, it will provide experimental constraints on theoretical work in the field of non-Markovian dynamics.
A simple and scalable scheme is proposed to generate a n-qubit W state in a trapped-ion system without the Lamb–Dicke limit. The n-qubit W state can be generated by the interaction between the ions and the laser field if the collective mode is initially prepared in the single-phonon state and each ion is in the ground state. The scheme only requires a single laser and avoids laser manipulation of the individual ion. The time required to complete the process decreases with the number of ions. The present scheme is not limited to small values of the LD parameter, which greatly enhances operation speeds.