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The observation of hyperradiance accompanied by enhanced entanglement in a hybrid optomechanical system

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Abstract

We have theoretically investigated an optomechanical system and presented the scenario of significantly enhanced bipartite photon–phonon entanglement for two qubits coupled to the single mode of the cavity. The results are compared with the one qubit case for reference. The tripartite atom–photon–phonon interaction is considered as only three-body resonant interaction, while the two-body actions are ignored under some potential approximations. Furthermore, we have studied the phenomenon of hyperradiance in which the well-known Dicke superradiant (\(N^2\) scaling law) can be surpassed due to the inter-atomic correlations. Jointly, a parameter regime is explored to observe the entanglement of photon–phonon pairs and their hyperradiance simultaneously. As it is important to show that the generation of photons and phonons is antibunched, the equal time second-order correlation function \(g^{(2)}(0)\) is characterized as witness. This system can be realized in Circuit Cavity Quantum Electrodynamics (CCQED) in which the direct coupling of the atom and mechanical resonator is possible.

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Data availability statement

As all data have been presented in the main text graphically, therefore this manuscript has no associated data information.

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Author information

Authors and Affiliations

  1. National Institute of Lasers and Optronics College, Pakistan Institute of Engineering and Applied Science, Nilore, Islamabad, 45650, Pakistan

    Zeshan Haider, Tahira Nasreen, Muhammad Imran, Rameez Ul Islam & Manzoor Ikram

  2. Pakistan Institute of Nuclear Science and Technology, Nilore, Islamabad, 45650, Pakistan

    Muhammad Altaf

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  1. Zeshan Haider
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  2. Muhammad Altaf
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  3. Tahira Nasreen
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Correspondence to Zeshan Haider.

Appendices

Appendix 1: Definition of basis states for one-atom and two-atoms system

The collective basis states in 1-photon manifold for one-atom system are \(| g00 \rangle \), \(| g10 \rangle \), \(| g01 \rangle \), and \(| 00 \rangle _{\pm }\). However, for the two-atoms system, these basis states are defined as \(| gg00 \rangle \), \(| gg10 \rangle \), \(| gg01 \rangle \), \(| gg11 \rangle \), and \(| \pm 00 \rangle \) The entangled states are defined as:

$$\begin{aligned} | 00 \rangle _{\pm }=\frac{| g11 \rangle \pm | e00 \rangle }{\sqrt{2}}, \end{aligned}$$
(11)

and

$$\begin{aligned} | \pm 00 \rangle =\frac{| ge00 \rangle \pm | eg00 \rangle }{\sqrt{2}} \end{aligned}$$
(12)

Appendix 2: Eigenvalues and Eigenstates of one-atom and two-atom systems

On diagonalizing the Hamiltonian presented in the main text for both the case of one-atom and two-atom system, the eigenvalues and their corresponding eigenfunction are presented in Tables 1 and 2, respectively. The dressed state diagram in Fig. 2a is constructed based on these eigenstates.

Table 1 One-atom system
Full size table
Table 2 Two-atom system
Full size table

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Haider, Z., Altaf, M., Nasreen, T. et al. The observation of hyperradiance accompanied by enhanced entanglement in a hybrid optomechanical system. Eur. Phys. J. Plus 139, 303 (2024). https://doi.org/10.1140/epjp/s13360-024-05073-7

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