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arXiv:2008.04078 · Physical Review Letters

Shortcuts to Adiabaticity for the Quantum Rabi Model: Efficient Generation of Giant Entangled Cat States via Parametric Amplification

Ye‐Hong Chen, Wei Qin, Xin Wang, Adam Miranowicz, Franco Nori

Published Jan 13, 2021• 192 citations
arXivHTMLPDF

Abstract

We propose a method for the fast generation of nonclassical ground states of the Rabi model in the ultrastrong and deep-strong coupling regimes via the shortcuts-to-adiabatic (STA) dynamics. The time-dependent quantum Rabi model is simulated by applying parametric amplification to the Jaynes-Cummings model. Using experimentally feasible parametric drive, this STA protocol can generate large-size Schrödinger cat states, through a process that is ∼10 times faster compared to adiabatic protocols. Such fast evolution increases the robustness of our protocol against dissipation. Our method enables one to freely design the parametric drive, so that the target state can be generated in the lab frame. A largely detuned light-matter coupling makes the protocol robust against imperfections of the operation times in experiments.

DOI
10.1103/physrevlett.126.023602

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We propose a method for the fast generation of nonclassical ground states of the Rabi model in the ultrastrong and deep-strong coupling regimes via the shortcuts-to-adiabatic (STA) dynamics. The time-dependent quantum Rabi model is simulated by applying parametric amplification to the Jaynes-Cummings model. Using experimentally feasible parametric drive, this STA protocol can generate large-size Schrödinger cat states, through a process that is ∼10 times faster compared to adiabatic protocols. Such fast evolution increases the robustness of our protocol against dissipation. Our method enables one to freely design the parametric drive, so that the target state can be generated in the lab frame. A largely detuned light-matter coupling makes the protocol robust against imperfections of the operation times in experiments.
In this paper, we generalize the shortcuts to adiabacity for the quantum Rabi model by simultaneously modulating its two components, namely, the two-level system and the cavity mode. This will eliminate the counterrotating terms which in turn helps to simulate the Rabi model by the Jaynes-Cummings model without requiring a largely detuned light-matter coupling. We focus on the low-frequency modulations since it is easy to realize them experimentally. The results show that these modulations can significantly shorten the evaluation time, generate much larger entanglement cat states, and robust against imperfection of time evaluation and dissipation.
The efficient generation of highly nonclassical quantum states is essential for emerging quantum technologies, yet it remains challenging due to decoherence and the long preparation times associated with conventional adiabatic protocols. Here, we employ time-optimal control methods based on the quantum brachistochrone formalism to engineer nonclassical states in light--matter systems described by the time-dependent Jaynes--Cummings and quantum Rabi models. We demonstrate the deterministic generation of Fock states and highly entangled Schrödinger cat states at unit fidelity, and characterize their nonclassical properties through joint Wigner phase-space distributions. We further show that the wind control generates these non-classical states at speed limit which leads to a reduced energetic cost and robustness against dissipation, relaxation, and dephasing across a broad range of environmental conditions. Our results establish time-optimal control as an efficient and experimentally feasible approach for fast and nonclassical state engineering in hybrid quantum platforms.
Shortcuts to adiabaticity (STA) are fast methods to realize the same final state evolution of quantum adiabatic process. We develop a general theory to construct a new kind of STA by solely sampling the points of the adiabatic path of the original adiabatic Hamiltonian. In contrast to previous methods, our approach does not require any additional control resources, has inherent robustness, and does not use any complicated unitary transformation. Based on path sampling, the resulting STA protocols are simple and can avoid points of adiabatic path that are challenging to implement. As applications of our theory, we demonstrate reduction of the effects of both dissipation and dephasing noise by a novel robust three-level control, as well as reliable and fast ground state evolution in an adiabatic quantum computing model. Our theory offers a new route to design robust and fast control methods for general quantum systems.
We propose an efficient and robust protocol for the generation of entanglement between a superconducting qubit and a squeezed cavity. By applying a parametric drive to the cavity coupled to the qubit, the dynamical evolution of the system is precisely described by an anisotropic Rabi model within a squeezed reference frame. Utilizing high-order time-averaging methods, we analytically derive the resonance conditions and the effective Rabi frequency for the high-order three-photon process. By implementing an adiabatic passage, slowly tuning the cavity frequency across the resonance, the system is steered into a maximally entangled state, e.g., between the three-photon state ∣g,3⟩\ket{g,3}∣g,3⟩ and the qubit excited state ∣e,0⟩\ket{e,0}∣e,0⟩ in the squeezed picture. Numerical simulation results confirm the high fidelity and robustness of the proposed protocol. Our method provides a practical pathway for generating complex non-Gaussian entangled states, which are of significant value for fault-tolerant quantum computation and quantum metrology beyond the standard quantum limit.
The implementation of shortcuts to adiabaticity (STA) enables a substantial reduction in the evolution time relative to traditional adiabatic methods, concurrently mitigating detrimental environmental interference. In this manuscript, we present a protocol using STA for the one-step generation of squeezed-light states of arbitrary photons. By starting from different initial Fock states, high-fidelity (>0.99) squeezed-light states can be generated with the same control Hamiltonian. We investigate the protocol's robustness under conditions of systematic errors and environmental noises through numerical simulations, which confirm the feasibility of the proposed scheme. The protocol may facilitate the investigation of quantum state control process, with the potential for significant impact in the near future.
ABSTRACT We propose an efficient and robust protocol for the generation of entanglement between a superconducting qubit and a squeezed cavity. By applying a parametric drive to the cavity coupled to the qubit, the dynamical evolution of the system is precisely described by an anisotropic Rabi model within a squeezed reference frame. Utilizing time‐averaging methods, we analytically derive the resonance conditions and the effective Rabi frequency for the high‐order three‐photon process. By implementing an adiabatic passage, slowly tuning the cavity frequency across the resonance, the system is steered into a maximally entangled state, e.g., between the three‐photon state and the qubit excited state in the squeezed picture. Numerical simulations confirm that the target state can be prepared with a population close to 1 under ideal conditions, and even in the presence of realistic environmental noise, an appreciable state fidelity of 0.77 and an entanglement concurrence of 0.71 can still be preserved, demonstrating the high robustness of our protocol. Our method provides a practical pathway for generating complex non‐Gaussian entangled states, which are of significant value for fault‐tolerant quantum computation and quantum metrology beyond the standard quantum limit.