Optimized t-expansion method for the Rabi Hamiltonian

Jay D. Mancini, Vassilios Fessatidis, Samuel P. Bowen +1 more

Vassilios Fessatidis, Jay D. Mancini, Samuel P. Bowen

Anirban Dey, Davide Lonigro, Kazuya Yuasa +1 more

We present a general, nonperturbative method for deriving effective Hamiltonians of arbitrary order for periodically driven systems based on an iterated integration-by-parts technique. The resulting family of effective Hamiltonians reproduces the well-known Floquet-Magnus expansion, now enhanced with explicit error bounds that quantify the distance between the exact and approximate dynamics at each order, even in cases where the Floquet-Magnus series fails to converge. We apply the method to the semiclassical Rabi model and provide explicit error bounds for both the Bloch-Siegert Hamiltonian and its third-order refinement. Our analysis shows that, while the rotating-wave approximation more accurately captures the true dynamics than the Bloch-Siegert Hamiltonian in most regimes, the third-order approximation ultimately outperforms both.

Paolo Amore, Francisco Marcelo Fernández, Martin Rodriguez-Vega

Abstract We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large-order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.

Ki-min Park B, Petr Marek, Radim Filip

Simulating unitary dynamics unavailable in nature by finite perturbative expansion of its Hamiltonian is a straightforward and intuitive approach which often fails when continuous-variable systems are considered. We propose a solution to this problem, which lies in constructing these expansions from suitably bounded operators. We demonstrate this by suggesting an elementary bounded gate based on Rabi coupling and showing its optimality and suitability for approximations of unitary operators.

R. F. Bishop, NEIL J. DAVIDSON, R. M. Quick +1 more