Non-Markovianity and system-environment correlations in a microscopic collision model

Abstract

We show that the use of a recently proposed iterative collision model with inter-environment swaps displays a signature of strongly non-Markovian dynamics that is highly dependent on the establishment of system-environment correlations. Two models are investigated; one in which such correlations are cancelled iteratively and one in which they are kept all across the dynamics. The degree of non-Markovianity, quantified using a measure based on the trace distance, is found to be much greater for all coupling strengths, when system-environment correlations are maintained.

Collision models in quantum optics

“…Eq. (6) shows that the open dynamics of S is manifestly Markovian (according to any non-Markovianity measure [2]) since the evolution of S at all steps n ≥ n depends only on the state of S at step n: the system keeps no memory of its past history. In more rigorous terms, Eq.…”

“…The last property alongside their simple and intrinsically discrete nature make CMs advantageous case studies to investigate major open problems in quantum non-Markovianity once the basic model outlined above is modi ed so as to introduce a memory mechanism. Among the ways to endow a CM with memory are: adding ancillaancilla collisions [4][5][6][7][8][9][10], embedding S into a larger system [11][12][13][14][15], allowing S to collide with each ancilla more than once [16,17], assuming a correlated initial bath state instead of a product one [18][19][20][21][22][23][24][25] or initial system-bath correlations [26][27][28]. Typical tasks that can be accomplished through NM CMs constructed in one of these ways are: deriving well-de ned (i.e., unconditionally completely positive) NM MEs [4,5,[37][38][39], gaining quantitative information about the role of system-bath and/or intra-bath correlations in making a dynamics NM [6,10,[19][20][21][22], simulating highly NM dynamics or indivisible channels [7,18,24].…”

Precursors of non-Markovianity

“…Let us begin by outlining the basic collision model framework [30,33,34,[47][48][49][50][51][52] which provides a versatile tool for exploring the emergence of non-Markovianity and, due to their construction, serves as the ideal testbed for studying the precursors of non-Markovianity captured in equation (2) by exploiting equations (3) and (4). Following [30,47], the environment is composed of an array of individual ancillae, E i , initially factorized and all with the same initial state. The time evolution is discretized such that at 'time-step' n the system, S, collides with ancilla, E n , after which we retain all correlations established by this system-ancilla (SA) interaction while E n subsequently collides with E n+1 .…”

Composite quantum collision models

“…[5] and more recently studied in Refs. [6,7] have proved to be a promising tool to analyze quantum non-Markovian dynamics [8][9][10][11][12][13] as well as of quantum thermodynamical systems (see, e.g., Refs. [14][15][16]).…”

“…A memoryless collision model thus entails a fully Markovian evolution for the open system as long as the ancillas are initially in a product state, they do not mutually interact and the system collides only once with each of the ancillas. To account for non-Markovian processes in collision models, one has to somehow relax such assumptions, e.g., by allowing the initial reservoir state to be correlated [8,11] or enabling interancillary interactions between next system-ancilla interactions [9,12].…”