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arXiv:1111.6424 · Physical Review Letters

Photonic Realization of the Quantum Rabi Model

Andrea Crespi, Stefano Longhi, Roberto Osellame

Published Apr 19, 2012• 155 citations
arXivHTMLPDF

Abstract

We realize a photonic analog simulator of the quantum Rabi model, based on light transport in femtosecond-laser-written waveguide superlattices, which provides an experimentally accessible test bed to explore the physics of light-matter interaction in the deep strong coupling regime. Our optical setting enables us to visualize dynamical regimes not yet accessible in cavity or circuit quantum electrodynamics, such as the bouncing of photon number wave packets in parity chains of Hilbert space.

DOI
10.1103/physrevlett.108.163601

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We realize a photonic analog simulator of the quantum Rabi model, based on light transport in femtosecond-laser-written waveguide superlattices, which provides an experimentally accessible test bed to explore the physics of light-matter interaction in the deep strong coupling regime. Our optical setting enables us to visualize dynamical regimes not yet accessible in cavity or circuit quantum electrodynamics, such as the bouncing of photon number wave packets in parity chains of Hilbert space.
The quantum Rabi model describing the fundamental interaction between light and matter is a cornerstone of quantum physics. It predicts exotic phenomena like quantum phase transitions and ground-state entanglement in ultrastrong and deep-strong coupling regimes, where coupling strengths are comparable to or larger than subsystem energies. Demonstrating dynamics remains an outstanding challenge, the few experiments reaching these regimes being limited to spectroscopy. Here, we employ a circuit quantum electrodynamics chip with moderate coupling between a resonator and transmon qubit to realise accurate digital quantum simulation of deep-strong coupling dynamics. We advance the state of the art in solid-state digital quantum simulation by using up to 90 second-order Trotter steps and probing both subsystems in a combined Hilbert space dimension of ∼80, demonstrating characteristic Schrödinger-cat-like entanglement and large photon build-up. Our approach will enable exploration of extreme coupling regimes and quantum phase transitions, and demonstrates a clear first step towards larger complexities such as in the Dicke model.
A classical realization of the Jaynes-Cummings (JC) model, describing the interaction of a two-level atom with a quantized cavity mode, is proposed based on light transport in engineered waveguide superlattices. The optical setting enables us to visualize in Fock space dynamical regimes not yet accessible in quantum systems, providing new physical insights into the deep strong coupling regime of the JC model. In particular, bouncing of photon number wave packets in Hilbert space and revivals of populations are explained as generalized Bloch oscillations in an inhomogeneous tight-binding lattice.
The Quantum Rabi model serves as a pivotal theoretical framework for elucidating the nuanced interplay between light and matter. Utilizing circuit quantum electrodynamics on a chip, we address the challenge of achieving deep strong coupling in Quantum Cavity Electrodynamics (cQED). Despite progress in superconducting circuits and trapped ions, experimental realization has been limited to spectroscopy. Our focus is on a transformative digital quantum simulation, employing Trotterization with an augmented number of steps to deconstruct a complex unitary Hamiltonian. This approach showcases the benefits of digital techniques within superconducting circuits, offering universality, flexibility, scalability, and high fidelity. Our goal is to demonstrate deep strong coupling in cQED and understand the advantages of digital methods, particularly in coherent measurement during time evolution with varying photon counts in resonators. This opens avenues to leverage quantum mechanics for overcoming hardware limitations.
The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.An analog quantum simulation scheme has been explored with a quantum hardware based on a superconducting circuit. Here the authors investigate the time evolution of the quantum Rabi model at ultra-strong coupling conditions, which is synthesized by slowing down the system dynamics in an effective frame.
Realizing optical analogues of quantum phenomena in atomic, molecular, or condensed matter physics has underpinned a range of photonic technologies. Rabi splitting is a quantum phenomenon induced by a strong interaction between two quantum states, and its optical analogues are of fundamental importance for the manipulation of light-matter interactions with wide applications in optoelectronics and nonlinear optics. Here, we propose and theoretically investigate purely optical analogues of Rabi splitting in integrated waveguide-coupled resonators formed by two Sagnac interferometers. By tailoring the coherent mode interference, the spectral response of the devices is engineered to achieve optical analogues of Rabi splitting with anti-crossing behavior in the resonances. Transitions between the Lorentzian, Fano, and Rabi splitting spectral lineshapes are achieved by simply changing the phase shift along the waveguide connecting the two Sagnac interferometers, revealing interesting physical insights about the evolution of different optical analogues of quantum phenomena. The impact of the device structural parameters is also analyzed to facilitate device design and optimization. These results suggest a new way for realizing optical analogues of Rabi splitting based on integrated waveguide-coupled resonators, paving the way for many potential applications that manipulate light-matter interactions in the strong coupling regime.
Realizing optical analogues of quantum phenomena in atomic, molecular, or condensed matter physics has underpinned a range of photonic technologies. Rabi splitting is a quantum phenomenon induced by a strong interaction between two quantum states, and its optical analogues are of fundamental importance for the manipulation of light-matter interactions with wide applications in optoelectronics and nonlinear optics. Here, we propose and theoretically investigate purely optical analogues of Rabi splitting in integrated waveguide-coupled resonators formed by two Sagnac interferometers. By tailoring the coherent mode interference, the spectral response of the devices is engineered to achieve optical analogues of Rabi splitting with anti-crossing behavior in the resonances. Transitions between the Lorentzian, Fano, and Rabi splitting spectral lineshapes are achieved by simply changing the phase shift along the waveguide connecting the two Sagnac interferometers, revealing interesting physical insights about the evolution of different optical analogues of quantum phenomena. The impact of the device structural parameters is also analyzed to facilitate device design and optimization. These results suggest a new way for realizing optical analogues of Rabi splitting based on integrated waveguide-coupled resonators, paving the way for many potential applications that manipulate light-matter interactions in the strong coupling regime.