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Physica Scripta

Pairwise dressed states and twin photon-phonon generation in a tripartite quantum system

Jadelson Ribeiro dos Santos Júnior, J P D A Ribeiro, O. P. de Sá Neto, Amjad Sohail

Published Sep 26, 2025• 0 citations
Publisher

Abstract

Abstract We present a theoretical formulation of a tripartite hybrid quantum circuit composed of a resonator, a transmon qubit, and a nanoelectromechanical oscillator coupled via effective nonlinear interactions. Starting from the full Hamiltonian, we derive an effective model that captures the essential features of the tripartite coupling, including coherent driving and dissipative mechanisms. By solving the steady-state regime of the system’s quantum dynamics, we compute the reflection and transmission spectra using input-output theory. Our results reveal clear signatures of energy-level quantization in the single-excitation limit, demonstrating the formation of pairwise-dressed states emerging from the tripartite interaction. This work provides a theoretical framework for probing hybrid quantum systems in the few-quanta regime and highlights their potential for quantum information and sensing applications.

DOI
10.1088/1402-4896/ae0c72

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Abstract We present a theoretical formulation of a tripartite hybrid quantum circuit composed of a resonator, a transmon qubit, and a nanoelectromechanical oscillator coupled via effective nonlinear interactions. Starting from the full Hamiltonian, we derive an effective model that captures the essential features of the tripartite coupling, including coherent driving and dissipative mechanisms. By solving the steady-state regime of the system’s quantum dynamics, we compute the reflection and transmission spectra using input-output theory. Our results reveal clear signatures of energy-level quantization in the single-excitation limit, demonstrating the formation of pairwise-dressed states emerging from the tripartite interaction. This work provides a theoretical framework for probing hybrid quantum systems in the few-quanta regime and highlights their potential for quantum information and sensing applications.
We propose a hybrid system with quantum mechanical three-body interactions between photons, phonons, and qubit excitations. These interactions take place in a circuit quantum electrodynamical architecture with a superconducting microwave resonator coupled to a transmon qubit whose shunt capacitance is free to mechanically oscillate. We show that this system design features a three-mode polariton-mechanical mode and a nonlinear transmon-mechanical mode interaction in the strong coupling regime. Together with the strong resonator-transmon interaction, these properties provide intriguing opportunities for manipulations of this hybrid quantum system. We show, in particular, the feasibility of cooling the mechanical motion down to its ground state and preparing various nonclassical states including mechanical Fock and cat states and hybrid tripartite entangled states.
In this thesis, we study two different physical systems, namely superconducting circuits and optomechanical cavities. \nIn the first part of the thesis, we study superconducting qubits and resonators and their potential to implement quantum information processing tasks. We propose a circuit quantum electrodynamics realization of a protocol to generate a Greenberger-Horne-Zeilinger (GHZ) state for transmon qubits homogeneously coupled to a microwave cavity in the dispersive limit. We derive an effective Hamiltonian with pairwise qubit exchange interactions of the XY type that can be globally controlled. Starting from a separable initial state, these interactions allow to generate a multi-qubit GHZ state within a time that does not depend on the number of qubits. We discuss how to probe the non-local nature and the genuine multipartite entanglement of the generated state. Finally, we investigate the stability of the proposed scheme to inhomogeneities in the physical parameters and the weak anharmonicity of transmon qubits. \nIn the second part of the thesis, we study optomechanical systems in which the position of a mechanical resonator modulates the resonance frequency of an optical cavity. The resulting radiation-pressure interaction is intrinsically nonlinear and can be used to implement strong Kerr nonlinearities and an effective interaction between photons. We investigate the optical bistability of such a system. The steady-state mean-field equation of the optical mode is identical to the one for a Kerr medium, and thus we expect it to have the same characteristic behavior with a lower, a middle, and an upper branch. However, the presence of position fluctuations of the mechanical resonator leads to a new feature: the upper branch will become unstable at sufficiently strong driving in certain parameter regimes. We identify the appropriate parameter regime for the upper branch to be stable, and we confirm, by numerical investigation of the quantum steady state, that the mechanical mode indeed acts as a Kerr nonlinearity for the optical mode in the low-temperature limit. This equivalence of the optomechanical system and the Kerr medium will be important for future applications of cavity optomechanics in quantum nonlinear optics and quantum information science. \n
We demonstrate genuine tripartite strong coupling in a solid-state hybrid quantum system comprising a superconducting transmon qubit, a fixed-frequency coplanar-waveguide resonator, and an ensemble of NV−^-− centers in diamond. Frequency-domain spectroscopy reveals a characteristic three-mode avoided crossing, indicating that single excitations are coherently shared across all three subsystems. At higher probe powers, we observe nonlinear features including multiphoton transitions and signatures of transmon-14N{}^{14}\mathrm{N}14N nuclear-spin interactions, highlighting the accessibility of higher-excitation manifolds in this architecture. These results establish a new regime of hybrid cavity QED that integrates superconducting and spin degrees of freedom, providing a platform for exploring complex multicomponent dynamics and developing hybrid quantum interfaces.
Efficient generation of multiquanta emission is crucial for quantum information processing but remains challenging due to its typical reliance on higher-order quantum processes. Here, we theoretically demonstrate strongly correlated photon-phonon emission enabled by direct tripartite interaction. This interaction facilitates the formation of high-order multiquanta states without more intermediate state transitions, thereby avoiding the suppressed transition rates associated with multiple sequential processes and substantially improving resonant transitions. As a result, high-efficiency strongly correlated even-quanta emission (e.g., two photons and two phonons) can be achieved in the presences of dissipation. Beyond that, we show that introducing two-photon dissipation enables strongly correlated odd-quanta emission (e.g., two photons and one phonon) in the tripartite interaction system by parity-protected suppression of single-photon loss and reconstruction of higher-order multiquanta processes. Our work extends multiquanta emission into the tripartite coupling regime and holds promising potential for applications in hybrid quantum networks.
Phonon nonlinearities play an important role in hybrid quantum networks and on-chip quantum devices. We investigate the phonon statistics of a mechanical oscillator in hybrid systems composed of an atom and one or two standard optomechanical cavities. An efficiently enhanced atom-phonon interaction can be derived via a tripartite atom-photon-phonon interaction, where the atom-photon coupling depends on the mechanical displacement without practically changing a cavity frequency. This novel mechanism of optomechanical interactions, as predicted recently by Cotrufo et al. [Phys. Rev. Lett. 118, 133603 (2017)], is fundamentally different from standard ones. In the enhanced atom-phonon coupling, the strong phonon nonlinearity at a single-excitation level is obtained in the originally weak-coupling regime, which leads to the appearance of phonon blockade. Moreover, the optimal parameter regimes are presented both for the cases of one- and two- cavities. We compared phonon-number correlation functions of different orders for mechanical steady states generated in the one-cavity hybrid system, revealing the occurrence of phonon-induced tunneling and different types of phonon blockade. Our approach offers an alternative method to generate and control a single phonon in the quantum regime, and has potential applications in single-phonon quantum technologies.
In this work, we investigate the emergence and control of genuine tripartite entanglement in a hybrid cavity quantum electrodynamics architecture consisting of two linearly coupled single mode resonators, one of which interacts coherently with a two level atom. An analytical framework is developed in a weak driving regime, where the system dynamically supports a delocalized hybrid excitation shared by the two photonic modes and the atomic degree of freedom. Tripartite concurrence fill has been used to characterize and identify parameter regimes of maximal multipartite quantum correlation that can be generated in this model. Additionally, we demonstrate how dissipative rates and detuning asymmetries govern the conversion of bipartite entanglement into a genuinely tripartite state, establishing a controllable transition from localized Jaynes Cummings correlations to delocalized photonic atomic entanglement networks. These findings outline a clear route to engineering steady state multipartite quantum resources in coupled cavity QED platforms, with direct relevance to quantum networking, distributed quantum information processing, and photonic state routing in scalable quantum architectures.