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arXiv:2207.00775

Ultrafast adiabatic passages in ultrastrongly coupled light-matter systems

Xun Gao, Liwei Duan, Tang, Pinghua, Tian, Junlong, Zhongzhou Ren, Solano, Enrique, Peng, Jie

Published Jul 2, 2022• 0 citations
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Abstract

We have obtained the solutions of the multimode quantum Rabi model when all modes have identical frequencies $ω$, including dark states $|ϕ_K\rangle$ with at least $K$ $(K=1,2,3,\ldots)$ photons. Extended to the multiqubit case, they lie close to another dark state $\vert ψ\rangle$ with at most one photon in the spectrum. Taking advantages of such solutions, we find a linear and symmetry-protected adiabatic passage through $\vert ψ\rangle$ to fast generate arbitrary single-photon $M$-mode $W$ states $\vert W_M\rangle$ with exactly the same speed. The effective minimum energy gap during the adiabatic evolution is further enlarged to $0.63ω$ when Stark shifts are included, such that arbitrary $\vert W_M\rangle$ can be ultrafast generated in $1.55\times 2πω^{-1}$ with fidelity $99\%$, indepedent of $M$. This work reveals the existence of linear ultrafast adiabatic passages in light-matter systems.

DOI
10.48550/arxiv.2207.00775

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General solutions to the quantum Rabi model involve subspaces with an unbounded number of photons. However, for the multiqubit multimode case, we find special solutions with at most one photon for an arbitrary number of qubits and photon modes. Such solutions exist for arbitrary single qubit-photon coupling strength with constant eigenenergy, while still being qubit-photon entangled states. Taking advantage of their peculiarities and the reach of the ultrastrong coupling regime, we propose an adiabatic scheme for the fast and deterministic generation of a two-qubit Bell state and arbitrary single-photon multimode W states with nonadiabatic error less than 1%. Finally, we propose a superconducting circuit design to catch and release the W states, and shows the experimental feasibility of the multimode multiqubit quantum Rabi model.
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Abstract We study the two-qubit asymmetric quantum Rabi model (AQRM) and find its dark-state solution. Such solutions have at most one photon and constant eigenenergy in the whole coupling regime, causing level crossings in the spectrum, although there is no explicit conserved quantity except for energy. We find an operator in the eigenenergy basis to label all the degeneracies with its eigenvalues, and compare it with the well-known hidden symmetry which exists when bias parameter ϵ is a multiple of half of the resonator frequency ω . Extended to the multimode case, we find symmetries related with conserved bosonic number operators, which also cause level crossings. This paves the way for further symmetry studies on generalized Rabi models.
We studied the two-qubit quantum Rabi model and found its dark state solutions with at most N photons. One peculiar case presents when N=3N=3N=3, which has constant eigenenergy in the whole coupling regime and leads to level crossings within the same parity subspace. We also discovered asymptotic solutions with at most N=2i+3N=2i+3N=2i+3 (i=1,2,3,… )(i=1,2,3,\dots)(i=1,2,3,…) photons, and constant eigenenergy NℏωN\hbar ωNℏω when coupling ggg becomes much larger than photon frequency ωωω. Although generally all photon number states are involved in the two-qubit quantum Rabi model, such NNN-photon solutions exist and may have applications in quantum information processing with ultrastrong couplings.
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