Non-Markovianity in the collision model with environmental block

Abstract

We present an extended collision model to simulate the dynamics of an open quantum system. In our model, the unit to represent the environment is, instead of a single particle, a block which consists of a number of environment particles. The introduced blocks enable us to study the effects of different strategies of system-environment interactions and states of the blocks on the non-Markovianities. We demonstrate our idea in the Gaussian channels of an all-optical system and derive a necessary and sufficient condition of non-Markovianity for such channels. Moreover, we show the equivalence of our criterion to the non-Markovian quantum jump in the simulation of the pure damping process of a single-mode field. We also show that the non-Markovianity of the channel working in the strategy that the system collides with environmental particles in each block in a certain order will be affected by the size of the block and the embedded entanglement and the effects of heating and squeezing the vacuum environmental state will quantitatively enhance the non-Markovianity.

Quantum synchronization in a collision model

“…Among numerous ways to simulate open quantum systems, collision models have recently attracted considerable attention due to their versatility in modeling different regimes of the dynamics, such as with or without memory [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], which is much harder to implement with other approaches. In a collision model framework, the environment is constituted by a number of particles, which can be both finite dimensional and continuous variable, and the dynamics of the system is determined by its sequential interaction with these environmental units.…”

Information scrambling in a collision model

“…jâ j is the displacement operator for the j-th mode. The interferometric network characterized by the scattering matrix S maps the χ in J (µ) to the output characteristic function via the following formula [25]…”

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.…”

“…We exactly recover the standard evolution according to the Markovian master equation when there are no AA collisions, under the condition that the unitary  is an energy preserving exchange interaction and all constituents have the same free Hamiltonian terms [47,53]. Despite the framework is independent of the dimensionality of system and ancilla, most studies restrict to the discrete variable (DV) qubit states [30,[47][48][49], with only a few exceptions [50]. Therefore in this work, we are interested in examining any effect that dimensionality may have on the properties of the non-Markovian dynamics, and on the precursors of non-Markovianity, by comparing and contrasting when system and ancilla are DV qubits with when they are CV Gaussian states.…”

“…the beam splitter realizing the SA interaction. This corresponds to the shift of a phase factor from the second environmental mode to the first one and allows to avoid a 'jagged' behavior of the covariance matrix phases (see [50]). We will consider thermal squeezed initial states for the system with covariance matrices given by In what follows we will initialize all environmental ancillae in their ground, respectively vacuum, state for both the DV and CV settings and we will fix the SA (AA) interaction strengths, equations (6) and (9), for both the DV and CV cases to be q = p 0.05 2 (q = p 0.9 2 ).…”