Model discrimination for dephasing two-level systems

Abstract

The problem of model discriminability and parameter identifiability for dephasing two-level systems subject to Hamiltonian control is studied. Analytic solutions of the Bloch equations are used to derive explicit expressions for observables as functions of time for different models. This information is used to give criteria for model discrimination and parameter estimation based on simple experimental paradigms.

Controlling non-Markovian dynamics using a light-based structured environment

“…However, N D = 0 is obtained for a Gaussian environment coupled to the system by means of a coupling that can be seen as a dephasing channel [20]. For such channels, it has been demonstrated [21] that the evolution of the system satisfies a Lindbladian master equation with all the characteristics that correspond to a Markovian dynamics guaranteeing that, in our case, N D = 0 is a sufficient condition to claim Markovianity. Since mathematically, the fact that N D reaches values equal to zero reflects that the first derivative of |κ(d c )| with respect to d c is not positive for some values of d v , in our case we can use the monotonic behavior of the trace distance to recognize a Markovian dynamics.…”

Ubiquitous problem of learning system parameters for dissipative two-level quantum systems: Fourier analysis versus Bayesian estimation

“…Then we find the range of 8co for which the actual likelihood exp(L(&> + <5o>,y|d) ^ j exp(Lmax) (21) to determine the full width at half maximum (FWHM) 5&>FWHM…”

“…For example, for two-level atoms in a cavity driven resonantly by a laser, the effective Hamiltonian with regard to a suitable rotating frame is H = Qax, where Q is the Rabi frequency of the driving field. Assuming the driving field does not alter the dephasing processes, so that we still have v the resulting measurement trace is given by [21]: If £22 < y 2/ 4 then co is purely imaginary and the sine and cosine terms above turn into their respective hyperbolic sine and cosine equivalents. If Q2 = y 2/ 4, the expression to-1 sin(mf) must be analytically continued.…”

“…To estimate the uncertainty in ω we compute the log-likelihood L(ω +δω, γ|d) for values δω where L is significantly larger than 0 (implemented by sampling under the assumption that L is not too far off a peaked distribution). Then we find the range of δω for which the actual likelihood exp(L(ω + δω, γ|d) ≥ 1 2 exp(L max ) (21) to determine the full width at half maximum (FWHM)…”

“…For example, for two-level atoms in a cavity driven resonantly by a laser, the effective Hamiltonian with regard to a suitable rotating frame is H = Ωσ x , where Ω is the Rabi frequency of the driving field. Assuming the driving field does not alter the dephasing processes, so that we still have V = γ 2 σ z , the resulting measurement trace is given by [21]:…”