Exceptional points for parameter estimation in open quantum systems: analysis of the Bloch equations

Abstract

We suggest to employ the dissipative nature of open quantum systems for the purpose of parameter estimation: the dynamics of open quantum systems is typically described by a quantum dynamical semigroup generator . The eigenvalues of  are complex, reflecting unitary as well as dissipative dynamics. For certain values of parameters defining , non-Hermitian degeneracies emerge, i.e. exceptional points (EP). The dynamical signature of these EPs corresponds to a unique time evolution. This unique feature can be employed experimentally to locate the EPs and thereby to determine the intrinsic system parameters with a high accuracy. This way we turn the disadvantage of the dissipation into an advantage. We demonstrate this method in the open system dynamics of a two-level system described by the Bloch equation, which has become the paradigm of diverse fields in physics, from NMR to quantum information and elementary particles.

Parameter estimation in atomic spectroscopy using exceptional points

“…Close to each of the resonances between the upper and lower levels, there is an EPcurve which is similar to the deltoid EP -curve we got for the Bloch system [25]. The exact frequency of the resonances can be found by locating pairs of EP s with detunings above and below the resonance, while maintaining a fixed amplitude.…”

“…[20,24]. The divergence of the amplitudes d k in the vicinity of exceptional points is employed to accurately locate them in the parameter space [24,25].…”

“…This procedure was used to estimate the parameters of the Bloch system from iterations of time series [25]. This parameter estimation is robust to uncertainties in the location of the EP s. The noise sensitivity is affected by the harmonic inversion.…”

Chiral behaviour of the wave functions for three wave guides in the vicinity of an exceptional point of third order

“…Exceptional points of higher order have also been studied in the literature, even though mostly theoretically [6][7][8][9][10][11][12][13][14][15][16]. In [8] the suggestion was made that exceptional points of third order (EP3) could be realized experimentally in a PT -symmetric arrangement of three coupled optical wave guides with balanced gain and loss in the outer wells.…”

A model of three coupled wave guides and third order exceptional points

“…Specifically, as a natural next step we consider a PT triple wave guide system and search for the physical conditions under which an exceptional point of third order (EP3) could be observed. The effects of exceptional points of higher order in particular of third order (EP3s), have received increasing attention in recent years [7][8][9][10][11][12][13][14][15]. Extending the model by Klaiman et al [5] we place a third wave guide between the guides with gain and loss, but with only a real part of the refractive index that may be different from that of the outer wave guides.…”