Structural features of non-Markovian open quantum systems using quantum chains

Abstract

We propose a simple structure for stationary non-Markovian quantum chains in the framework of collisional dynamics of open quantum systems. To this end, we modify the microscopic Markovian system-reservoir model, consider multiple collisions with each of the molecules with an overlap between the collisional time intervals. We show how the equivalent Markovian quantum chain can be constructed with the addition of satellite quantum memory to the system. We distinguish quantum from classical non-Markovianity. Moreover, we define the counts of non-Markovianity by the required number of satellite qubits and bits, respectively. As the particular measure of quantum non-Markovianity the discord of the satellite w.r.t. the system is suggested. Simplest qubit realizations are discussed, and the significance for real system-environment dynamics is also pointed out.

Divisibility of quantum dynamical maps and collision models

“…Moreover, environment particles may be initially correlated (quantumly or classically) due to interactions between each other as it takes place in solids and quantum gases, and such correlations may result in non-Markovian dynamics [12,[41][42][43][44]. Non-Markovian effects also appear in collision models, where the system can interact with the same environment particle several times [45,46], or an environment particle impacted by a system collides with another environment particle, which later collides with the system [47][48][49][50]. The latter scheme is equivalent to a scenario, when the quantum system in question is coherently coupled to an auxiliary system interacting with Markovian bath via collisions [51,52].…”

Thermalization of Finite Many-Body Systems by a Collision Model

“…For the evaluation of bath correlation spectra, we must specify our open system setup which consists of the same basic ingredients as [ 6 , 19 , 20 , 25 ]. We first consider a two-level system with time-independent Hamiltonian The reservoir consists of, an in principle infinite number of, two-level systems prepared at an inverse temperature for a bath Hamiltonian where the index n indicates that the operator acts on the n -th spin of the reservoir.…”

“…The controllable degree of non-Markovianity and its effect on the dynamics of quantum coherence has been examined [ 17 ]. Further attempts to study non-Markovian dynamics are made by using initially entangled ancillae [ 18 ], introducing time overlap of two consecutive collisions [ 6 , 19 , 20 ] and using a two-spin system in which only one of the pair interacts with the environment resulting in a Markovian dynamics for the composite system, while tracing out the spin interacting with the bath gives a non-Markovian dynamics for the remaining spin [ 21 ]. The versatility of collision models has resulted in other interesting research directions, such as the introduction of collisions with non-thermalized ancillae to study non-equilibrium effects in quantum thermodynamics [ 8 , 11 , 22 , 23 , 24 , 25 ] and the generation of multi-qubit entanglement via a shuttle qubit colliding with disjoint qubit registers [ 26 ].…”

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]).…”