Non-perturbative interpretation of the Bloch vector's path beyond rotating wave approximation

Abstract

The Bloch vector's path of a two-level system exposed to a monochromatic field exhibits, in the regime of strong coupling, complex corkscrew trajectories. By considering the infinitesimal evolution of the two-level system when the field is treated as a classical object, we show that the Bloch vector's rotation speed oscillates between zero and twice the rotation speed predicted by the rotating wave approximation. Cusps appear when the rotation speed vanishes. We prove analytically that in correspondence to cusps the curvature of the Bloch vector's path diverges. On the other hand, numerical data show that the curvature is very large even for a quantum field in the deep quantum regime with mean number of photons $\bar{n}\lesssim 1$. We finally compute numerically the typical error size in a quantum gate when the terms beyond rotating wave approximation are neglected.

9 pages, 8 figures

References in corpus (11)

• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Deep Strong Coupling Regime of the Jaynes-Cummings model
• Ultrastrong coupling regime of cavity QED with phase-biased flux qubits
• Quantum Zeno and Anti-Zeno Effect without Rotating Wave Approximation
• Quantum anti-Zeno effect without rotating wave approximation
• Qubit-oscillator system: An analytical treatment of the ultra-strong coupling regime
• Dissipative dynamics of a biased qubit coupled to a harmonic oscillator: Analytical results beyond the rotating wave approximation
• Qubit-oscillator system under ultrastrong coupling and extreme driving
• Determination of the phase of an electromagnetic field via incoherent detection of fluorescence
• Non-Markovian dynamics for an open two-level system without rotating wave approximation: Indivisibility versus backflow of information

Cited by in corpus (5)

• Dynamical Casimir Effect in Quantum Information Processing
• Exotic States in the Dynamical Casimir Effect
• Can the dynamical Lamb effect be observed in a superconducting circuit?
• Dynamical Casimir effect and state transfer in the ultrastrong coupling regime
• Visualization of Rabi oscillations in a magnetic resonance