Adiabatic Elimination in Quantum Stochastic Models

Abstract

We consider a physical system with a coupling to bosonic reservoirs via a quantum stochastic differential equation. We study the limit of this model as the coupling strength tends to infinity. We show that in this limit the solution to the quantum stochastic differential equation converges strongly to the solution of a limit quantum stochastic differential equation. In the limiting dynamics the excited states are removed and the ground states couple directly to the reservoirs.

Approximation and limit theorems for quantum stochastic models with unbounded coefficients

“…In order for the above expression to define the generator of T (αβ) t , at the very least the last two terms must vanish-after all, they are quadratic in β i and α * i , respectively, which is inconsistent with (3). However, this is immediate from Assumption 2(d), as it implies that F † j P 0 = P 0 F i = 0.…”

“…The singular perturbation results in this paper extend and bridge the gap between the results of [3,16]. We consider a family of quantum stochastic differential equations whose coefficients are not necessarily bounded but possess a common invariant domain.…”

Zeno dynamics for open quantum systems

“…At this stage, the Zeno limit can be reformulated explicitly as an adiabatic elimination problem with the Zeno subspace h Zeno being the slow space. At this stage we can invoke the results of Bouten, van Handel and Silberfarb [23], [9], [10] on adiabatic elimination for quantum stochastic systems.…”

“…We shall equate the limit procedure leading to a Zeno dynamics as adiabatic elimination. This choice is a matter of convenience as we at once have access to powerful results due to Luc Bouten and Andrew Silberfarb [9], and later with Ramon van Handel [10], on the adiabatic elimination procedure in the framework of quantum stochastic models. This is a significantly richer theory than for closed systems.…”

Fighting decoherence in a continuous two-qubit odd- or even-parity measurement with a closed-loop setup

“…Following the procedure outlined in [18,19], we formally assume gâ ∝ k, ∝ k 2 , and ∝ k 2 and take the limit k → ∞, which transforms (1) into…”