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arXiv:0905.0426 · Europhysics Letters (EPL)

The generalized analytical approximation to the solution of the single-mode spin-boson model without rotating-wave approximation

T. Liu, K. L. Wang, Mang Feng

Published Jun 1, 2009• 44 citations
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Abstract

The single-mode spin-boson model (SMSBM) has extensive application in different subfields of physics. In the absence of rotating-wave approximation (RWA), we try to solve the SMSBM analytically. We argue that the analytical expression obtained might be the most exact approximation to the solution of the system in our case under the assumption of the Abel-Ruffini theorem, which works for a wide range of the parameters such as coupling strength and detuning and would be practical for currently available experiments.

DOI
10.1209/0295-5075/86/54003

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The single-mode spin-boson model (SMSBM) has extensive application in different subfields of physics. In the absence of rotating-wave approximation (RWA), we try to solve the SMSBM analytically. We argue that the analytical expression obtained might be the most exact approximation to the solution of the system in our case under the assumption of the Abel-Ruffini theorem, which works for a wide range of the parameters such as coupling strength and detuning and would be practical for currently available experiments.
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The Jaynes-Cummings model without the rotating-wave approximation can be solved exactly by an extended Swain ansatz with conserved parity. Analytical approximations are then performed at different levels. The well-known rotating-wave approximation (RWA) is naturally covered in the present zeroth- and first-order approximations. A first-order correction to the RWA can be obtained in a second-order approximation, by which the effect of the counter-rotating-wave term emerges clearly. Concise analytical expressions are given explicitly and can be applicable up to the ultrastrong-coupling regime. A preliminary application to vacuum Rabi splitting is shown to be very successful.
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Generalized spin-boson (GSB) models describe the interaction between a quantum mechanical system and a structured boson environment, mediated by a family of coupling functions known as form factors. We propose an extension of the class of GSB models, which can accommodate non-normalizable form factors provided that they satisfy a weaker growth constraint, thus accounting for a rigorous description of a wider range of physical scenarios; we also show that such “singular” GSB models can be rigorously approximated by GSB models with normalizable form factors. Furthermore, we discuss in greater detail the structure of the spin-boson model with a rotating wave approximation: for this model, the result is improved via a nonperturbative approach that enables us to further extend the class of admissible form factors as well as to compute its resolvent and characterize its self-adjointness domain.