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arXiv:1709.10201 · Applied Physics Letters

Quantum simulation of the general semi-classical Rabi model in regimes of arbitrarily strong driving

Kunzhe Dai, Haiteng Wu, Peng Zhao, Mengmeng Li, Qiang Liu, Guangming Xue, Xinsheng Tan, Haifeng Yu, Yang Yu

Published Dec 11, 2017• 18 citations
arXivHTMLPDF

Abstract

We propose and experimentally demonstrate a scheme to simulate the interaction between a two-level system and a classical light field. Under the transversal driving of two microwave tones, the effective Hamiltonian in an appropriate rotating frame is identical to that of the general semi-classical Rabi model. We experimentally realize this Hamiltonian with a superconducting transmon qubit. By tuning the strength, phase, and frequency of the two microwave driving fields, we simulate the quantum dynamics from the weak to extremely strong driving regime. Under these conditions, we observe that, as a function of increased Rabi drive strength, the qubit evolution gradually deviates from the normal sinusoidal Rabi oscillation, in accordance with the predictions of the general semi-classical Rabi model far beyond the weak driving limit. Our scheme provides an effective approach to investigate the extremely strong interaction between a two-level system and a classical light field. Such strong interactions are usually inaccessible in experiments.

DOI
10.1063/1.5006745

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We propose and experimentally demonstrate a scheme to simulate the interaction between a two-level system and a classical light field. Under the transversal driving of two microwave tones, the effective Hamiltonian in an appropriate rotating frame is identical to that of the general semi-classical Rabi model. We experimentally realize this Hamiltonian with a superconducting transmon qubit. By tuning the strength, phase, and frequency of the two microwave driving fields, we simulate the quantum dynamics from the weak to extremely strong driving regime. Under these conditions, we observe that, as a function of increased Rabi drive strength, the qubit evolution gradually deviates from the normal sinusoidal Rabi oscillation, in accordance with the predictions of the general semi-classical Rabi model far beyond the weak driving limit. Our scheme provides an effective approach to investigate the extremely strong interaction between a two-level system and a classical light field. Such strong interactions are usually inaccessible in experiments.
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.
Abstract We analyze the dynamics of a two-level quantum system (TLS) under the influence of a strong sinusoidal driving signal whose origin is the interaction of the two-level system with a quantum field. In this approach the driving field is replaced by a harmonic oscillator that is either strongly coupled to the TLS or populated with a large number of photons. Starting from the Rabi model, we derive expressions for the TLS’s oscillation frequencies and compare the results with those obtained from the model where the driving signal is treated classically. We show that in the limits of weak coupling and large photon number, the well-known expression for the Rabi frequency in the strong driving regime is recovered. In the opposite limit of strong coupling and small photon number, we find differences between the predictions of the semiclassical and quantum models. The results of the quantum picture can therefore be understood as Landau–Zener–Stueckelberg interferometry in the fully quantum regime.
Anisotropic quantum Rabi model is a generalization of quantum Rabi model, which allows its rotating and counter-rotating terms to have two different coupling constants. It provides us with a fundamental model to understand various physical features concerning quantum optics, solid-state physics, and mesoscopic physics. In this paper, we propose an experimental feasible scheme to implement anisotropic quantum Rabi model in a circuit quantum electrodynamics system via periodic frequency modulation. An effective Hamiltonian describing the tunable anisotropic quantum Rabi model can be derived from a qubit-resonator coupling system modulated by two periodic driving fields. All effective parameters of the simulated system can be adjusted by tuning the initial phases, the frequencies and the amplitudes of the driving fields. We show that the periodic driving is able to drive a coupled system in dispersive regime to ultrastrong coupling regime, and even deep-strong coupling regime. The derived effective Hamiltonian allows us to obtain pure rotating term and counter-rotating term. Numerical simulation shows that such effective Hamiltonian is valid in ultrastrong coupling regime, and stronger coupling regime. Moreover, our scheme can be generalized to the multi-qubit case. We also give some applications of the simulated system to the Schrödinger cat states and quantum gate generalization. The presented proposal will pave a way to further study the stronger anisotropic Rabi model whose coupling strength is far away from ultrastrong coupling and deep-strong coupling regimes in quantum optics.
We show that the counter-rotating terms of the dispersive qubit-cavity Rabi model can produce relatively large and nonmonotonic Bloch-Siegert shifts in the cavity frequency as the system is driven through a quantum-to-classical transition. Using a weak microwave probe tone, we demonstrate experimentally this effect by monitoring the resonance frequency of a microwave cavity coupled to a transmon and driven by a microwave field with varying power. In the weakly driven regime (quantum phase), the Bloch-Siegert shift appears as a small constant frequency shift, while for a strong drive (classical phase) it presents an oscillatory behavior as a function of the number of photons in the cavity. The experimental results are in agreement with numerical simulations based on the quasienergy spectrum.
In this work, I investigate how to implement and quantify \\emph{in-situ} tunable quantum interface between superconducting qubits and resonators using external transverse driving fields beyond the rotating wave approximation (RWA). When studying the system under the time-periodic driving field, we typically rely on RWA, a useful technique that significantly reduces the analytical difficulties in solving the dynamics with time-dependent Hamiltonian. Nonetheless, it does not correctly describe the systems' dynamics when the drive fields are excessively strong and far off-resonant. Especially in circuit QED platform, the RWA often breakdowns. Many studies before, however, mainly focus on the transition frequency shifts. How the RWA distorts the interaction rates between two systems has been rarely explored. I have performed quantitative studies over two different systems. One is the quantum Rabi model (QRM) where a two-level atom is dispersively coupled to a resonator mode. The other is dispersively coupled a transmon and resonator system, which is the same as the QRM except that the transmon replaces the two-level atom in QRM. In both cases, I have revealed that the RWA significantly mislead the sideband transition rates between two elements. In the latter case, I have performed the experiments, and the results nicely agree with the analytical and numerical calculations. In addition to these, I also have introduced a study where the tunable coupling between a transmon and resonator is used for non-invasive resonator probing.
Multi-qubit quantum Rabi model, which is a fundamental model describing light-matter interaction, plays an important role in various physical systems. In this paper, we propose a theoretical method to simulate multi-qubit quantum Rabi model in a circuit quantum electrodynamics system. By means of external transversal and longitudinal driving fields, an effective Hamiltonian describing the multi-qubit quantum Rabi model is derived. The effective frequency of the resonator and the effective splitting of the qubits depend on the external driving fields. By adjusting the frequencies and the amplitudes of the driving fields, the stronger coupling regimes could be reached. The numerical simulation shows that our proposal works well in a wide range of parameter space. Moreover, our scheme can be utilized to generate two-qubit gate, Schrödinger states, and multi-qubit GHZ states. The maximum displacement of the Schrödinger cat states can be enhanced by increasing the number of the qubits and the relative coupling strength. It should be mention that we can obtain high fidelity Schrödinger cat states and multi-qubit GHZ states even the system suffering dissipation. The presented proposal may open a way to study the stronger coupling regimes whose coupling strength is far away from ultrastrong coupling regimes.