Experimental Investigation of Spectra of Dynamical Maps and their Relation to non-Markovianity

Abstract

The spectral theorem of von Neumann has been widely applied in various areas, such as the characteristic spectral lines of atoms. It has been recently proposed that dynamical evolution also possesses spectral lines. As the most intrinsic property of evolution, the behavior of these spectra can, in principle, exhibit almost every feature of this evolution, among which the most attractive topic is non-Markovianity, i.e., the memory effects during evolution. Here, we develop a method to detect these spectra, and moreover, we experimentally examine the relation between the spectral behavior and non-Markovianity by engineering the environment to prepare dynamical maps with different non-Markovian properties and then detecting the dynamical behavior of the spectral values. These spectra will lead to a witness for essential non-Markovianity. We also experimentally verify another simplified witness method for essential non-Markovianity. Interestingly, in both cases, we observe the sudden transition from essential non-Markovianity to something else. Our work shows the role of the spectra of evolution in the studies of non-Makovianity and provides the alternative methods to characterize non-Markovian behavior.

Microscopically Reversible Pathways with Memory

“…. This expression appears by taking sums over subscript t on Equation (35) and using Equations ( 17), (22), and (27). This result was demonstrated in a previous work through a different strategy [24].…”

“…The proof to Equation ( 22) is similar to this for Equation (17) and can be found in Reference [27] in the context of Information Theory for the therein called conditional entropy. The proofs to Equation (27) and to Equation (32) for a general thermodynamic potential "A" (following Equations ( 28) and ( 29)) parallel those for Equations ( 17) and (22).…”

“…Tsallis entropy generalization enabled non-extensive analyses of physical systems that keep memory on previous events, that is, of systems that recall not only the present but also the past events (non-Markovian evolutions) [17]; this generalization in turn compacts non-equilibrium dynamics elegantly. Open system formalisms, including spectral analysis, introduce memory effects through non-Markovian approaches to address the environment surrounding the system under study [18][19][20][21][22]. Complete memory effects have been considered in the study of spatial chains made up of physical subunits, including those with symbolic meaning, to access non-equilibrium dynamics [23] and information management in nanoscale systems [24].…”

Revealing memory effects in phase-covariant quantum master equations

“…Despite its clear mathematical formulation, in general, detecting the violation of the CP-divisibility condition is not experimentally straightforward. A hierarchy of non-Markovianity indicators, based on the violation of k-divisibility, have been introduced and the extreme case of essentially non-Markovian maps have been experimentally studied [30].…”

Experimental realization of high-fidelity teleportation via a non-Markovian open quantum system

“…These developments have influenced, and have been influenced by, the increasing ability to realize experimentally reservoir engineering [10], various fundamental open system models in non-Markovian regimes [11], and the control of open system dynamics [12]. Indeed, a number of various physical platforms have been used for this purpose including, e.g., optical systems [11][12][13][14][15][16][17][18][19][20][21], NV centers [22,23], trapped ions [24], and NMR systems [25,26]. In addition to fundamental studies and tests, recent experimental work also includes some of the first exploitations of non-Markovian memory effects in basic quantum information protocols including, e.g., single-qubit Deutsch-Josza algorithm [27].…”