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arXiv:1811.06176 · Physical Review A

Atomic Bell measurement via two-photon interactions

Carlos A. González-Gutiérrez, Juan Mauricio Torres

Published Feb 26, 2019• 28 citations
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Abstract

We introduce a complete Bell measurement on atomic qubits based on two-photon interactions with optical cavities and discrimination of coherent states of light. The dynamical system is described by the Dicke model for two three-level atoms interacting in two-photon resonance with a single mode of the radiation field, which is known to effectively generate a nonlinear two-photon interaction between the field and two states of each atom. For initial coherent states with a large mean photon number, the field state is well represented by two coherent states at half-revival time. For certain product states of the atoms, we prove the coherent generation of Greenberger-Horne-Zeilinger states with two atomic qubits and two orthogonal Schr\"odinger cat states as a third qubit. For arbitrary atomic states, we show that discriminating the two states of the field corresponds to different operations in the Bell basis of the atoms. By repeating this process with a second cavity prepared in a phase-shifted coherent state, we demonstrate the implementation of a complete Bell measurement. The experimental feasibility of our protocols is discussed for cavity-QED, circuit-QED, and trapped-ion setups.

DOI
10.1103/physreva.99.023854

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We introduce a complete Bell measurement on atomic qubits based on two-photon interactions with optical cavities and discrimination of coherent states of light. The dynamical system is described by the Dicke model for two three-level atoms interacting in two-photon resonance with a single mode of the radiation field, which is known to effectively generate a nonlinear two-photon interaction between the field and two states of each atom. For initial coherent states with a large mean photon number, the field state is well represented by two coherent states at half-revival time. For certain product states of the atoms, we prove the coherent generation of Greenberger-Horne-Zeilinger states with two atomic qubits and two orthogonal Schr"odinger cat states as a third qubit. For arbitrary atomic states, we show that discriminating the two states of the field corresponds to different operations in the Bell basis of the atoms. By repeating this process with a second cavity prepared in a phase-shifted coherent state, we demonstrate the implementation of a complete Bell measurement. The experimental feasibility of our protocols is discussed for cavity-QED, circuit-QED, and trapped-ion setups.
We derive an analytical approximate solution of the time-dependent state vector in terms of material Bell states and coherent states of the field for a generalized two-atom Tavis-Cummings model with nonlinear intensity-dependent matter-field interaction. Using this solution, we obtain simple expressions for the atomic concurrence and purity in order to study the entanglement in the system at specific interaction times. We show how to implement entangling atomic operations through measurement of the field. We illustrate how these operations can lead to a complete Bell measurement. Furthermore, when considering two orthogonal states of the field as levels of a third qubit, it is possible to implement a unitary three-qubit gate capable of generating authentic tripartite entangled states such as the Greenberger-Horne-Zeilinger state and the WWW state. As an example of the generic model, we present an ion-trap setting employing the quantized mode of the center-of-mass motion instead of the photonic field, showing that the implementation of realistic entangling operations from intrinsic nonlinear matter-field interactions is indeed possible.
Schrödinger cat states, representing coherent superpositions of macroscopically distinguishable states, are indispensable nonclassical resources for continuous-variable quantum information processing. Existing generation protocols typically rely on strong nonlinear interactions, complicated control techniques, or engineered dissipation, posing challenges for experimental implementation. Here, we propose a simple measurement-based protocol for generating Schrödinger cat states in a cavity-QED system by combining coherent driving, dispersive atom--cavity interactions, and atomic postselection. The atom--cavity interaction establishes coherent correlations between the atomic and photonic degrees of freedom, while the subsequent atomic postselection projects the cavity field onto a non-Gaussian superposition state with pronounced Wigner negativity. Numerical simulations based on the Lindblad master equation show that the generated Schrödinger cat states remain robust against moderate cavity dissipation. Our results demonstrate that conditional atomic measurements provide an effective and experimentally accessible approach for preparing nonclassical cavity states without relying on strong optical nonlinearities or engineered dissipation.
We derive an analytical approximate solution of the time-dependent state vector in terms of material Bell states and coherent states of the field for a generalized two-atom Tavis-Cummings model with nonlinear intensity dependent matter-field interaction. Using this solution, we obtain simple expressions for the atomic concurrence and purity in order to study the entanglement in the system at specific interaction times. We show how to implement entangling atomic operations through measurement of the field. We illustrate how these operations can lead to a complete Bell measurement. Furthermore, when considering two orthogonal states of the field as levels of a third qubit, it is possible to implement a unitary three-qubit gate capable of generating authentic tripartite entangled states such as the Greenberger-Horne-Zeilinger (GHZ) state and the W-state. As an example of the generic model, we present an ion-trap setting employing the quantized mode of the center of mass motion instead the photonic field, showing that the implementation of realistic entangling operations from intrinsic nonlinear matter-field interactions is indeed possible.
We propose a scheme to prepare the Bell states for atomic qubits trapped in separate optical cavities via atom-cavity-laser interaction.The quantum information of each qubit is encoded on the degenerate ground states of the atom, so the entanglement between them is relatively stable against spontaneous emission.The proposed scheme consists of a Mach-Zehnder interferometer (MZI) with two arms, and each arm contains a cavity with an N-type atom in it.It requires two classical fields and a single-photon source.By controlling the sequence and time of atom-cavity-laser interaction, the deterministic production of the atomic Bell states is shown.We also introduce the generalization of the present scheme to generate the 2N -atom Greenberger-Horne-Zeilinger state.
In the context of cavity quantum electrodynamics (QED),a potential scheme is proposed to generate entangled coherent states. The scheme includes twice interactions of two-level atoms with cavities. In the first interaction,two atoms are sent into a microwave cavity with the large detuning respectively. And then the second interaction is that the two atoms enter another microwave cavity and are driven by a resonant classical field meantime. When we choose the proper interaction time and make measurement on the two atoms,the two microwave cavity mode fields are determinatively entangled. In addition,it is easy to generalize the scheme to multi-cavity and multi-atom.
We propose an approach for achieving a two-photon process in which a single two-level atom can simultaneously absorb or emit two photons separately distributed in two cavities. This two-photon process is realized by a two-level atom dispersively coupled to a classical pulse and two cavities. The main advantage of this proposal lies in the fact that because only two levels of the atom are used, i.e., no auxiliary atomic levels are utilized, decoherence from the higher energy levels of the atom is avoided. In addition, we find that the two-photon process can enable the synthesis of a hybrid atom-cavity-cavity Greenberger-Horne-Zeilinger (GHZ) entangled state. As an example, we further discuss the experimental feasibility of creating the proposed hybrid GHZ state in a circuit QED system. This proposal is quite general and can be implemented in a wide range of physical systems, such as a natural or artificial atom coupled to two optical or microwave cavities.