Effects of Non-Markovian Squeezed Bath on the Dynamics of Open Systems

Control of the dynamics of an open quantum system is crucial in quantum information processing. Basically there are two ways: one is the control on the system and the other is tuning the bath parameters. In this paper, we use the latter to analyze the non-Markovian dynamics of the open system. The model is that the system is immersed in non-Markovian squeezed baths. For the dynamics, a non-Markovian master eqation is obtained using the quantum state diffusion (QSD) equation technique for the weak system-bath couplings. We use the adiabatic evolution or quantum state transmission as examples to analyze the effects of the bath parameters: non-Markovianity $γ$ , the squeezed direction $θ$ and squeezed strength $r$ . For the adiabatic or state transmission fidelity, the calculation results show that they both can be enhanced by a smaller $γ$ or bigger $p$ -quadrature. Interestingly, when $0<θ<π/2$ , the squeezed quadrature is determined by the combination of $r$ and $θ$ , and by numerical simulation we find that the fidelity peak occurs at $r=1-2θ/π$ . The fidelities increase with increasing $r$ when $r\in (0,1-2θ/π]$ . When $θ\geπ/2$ , lower fidelities are obtained due to the squeezed bath. Our results show that the dynamics of the open systems can be effectively controlled by reservoir enginerring.Control of the dynamics of an open quantum system is crucial in quantum information processing. Basically there are two ways: one is the control on the system and the other is tuning the bath parameters. In this paper, we use the latter to analyze the non-Markovian dynamics of the open system. The model is that the system is immersed in non-Markovian squeezed baths. For the dynamics, a non-Markovian master eqation is obtained using the quantum state diffusion (QSD) equation technique for the weak system-bath couplings. We use the adiabatic evolution or quantum state transmission as examples to analyze the effects of the bath parameters: non-Markovianity $γ$, the squeezed direction $θ$ and squeezed strength $r$. For the adiabatic or state transmission fidelity, the calculation results show that they both can be enhanced by a smaller $γ$ or bigger $p$-quadrature. Interestingly, when $0<θ<π/2$, the squeezed quadrature is determined by the combination of $r$ and $θ$, and by numerical simulation we find that the fidelity peak occurs at $r=1-2θ/π$. The fidelities increase with increasing $r$ when $r\in (0,1-2θ/π]$. When $θ\geπ/2$, lower fidelities are obtained due to the squeezed bath. Our results show that the dynamics of the open systems can be effectively controlled by reservoir enginerring.

arXiv:2304.04223Apr 9, 20231 citation

Non-Markovian Quantum Dynamics in a Squeezed Reservoir

Valentin Link, Walter T. Strunz, Kimmo Luoma

We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system-environment coupling strength and, thus, the strength of the dissipation.We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system-environment coupling strength and, thus, the strength of the dissipation.

EntropyFeb 28, 202216 citations

Quantum limit for driven linear non-Markovian open-quantum-systems

Andres Estrada, Leonardo A. Pachón

The interplay between non-Markovian dynamics and driving fields in the survival of entanglement between two non-degenerate oscillators is considered here. Based on exact analytical results for the non-Markovian dynamics of two parametrically coupled non-degenerate oscillators in contact with non-identical independent thermal baths, the out-of-equilibrium quantum limit derived in [ Phys. Rev. Lett. 105 180501 (2010)] is generalised to the non-Markovian regime. Specifically, it is shown that non-Markovian dynamics, when compared to the Markovian case, allow for the survival of stationary entanglement at higher temperatures, with larger coupling strength to the baths and at smaller driving rates. The effect of the asymmetry of the (i) coupled oscillators, (ii) coupling strength to the baths at equal temperature, and (iii) temperature at equal coupling strength is discussed. In particular, it is shown that the non-Markovian character of the dynamics is capable of beating the resonant condition that states that the driving frequency equals the sum of the natural frequencies for the maximum rate of squeezing generation; hence, squeezing generation is more robust under non-Markovian dynamics.The interplay between non-Markovian dynamics and driving fields in the survival of entanglement between two non-degenerate oscillators is considered here. Based on exact analytical results for the non-Markovian dynamics of two parametrically coupled non-degenerate oscillators in contact with non-identical independent thermal baths, the out-of-equilibrium quantum limit derived in [ Phys. Rev. Lett. 105 180501 (2010)] is generalised to the non-Markovian regime. Specifically, it is shown that non-Markovian dynamics, when compared to the Markovian case, allow for the survival of stationary entanglement at higher temperatures, with larger coupling strength to the baths and at smaller driving rates. The effect of the asymmetry of the (i) coupled oscillators, (ii) coupling strength to the baths at equal temperature, and (iii) temperature at equal coupling strength is discussed. In particular, it is shown that the non-Markovian character of the dynamics is capable of beating the resonant condition that states that the driving frequency equals the sum of the natural frequencies for the maximum rate of squeezing generation; hence, squeezing generation is more robust under non-Markovian dynamics.

arXiv:1411.3382New Journal of PhysicsMar 27, 201531 citations

γ

, the squeezed direction

θ

and squeezed strength

r

. For the adiabatic or state transmission fidelity, the calculation results show that they both can be enhanced by a smaller

γ

or bigger

p

-quadrature. Interestingly, when

0<θ<π/2

, the squeezed quadrature is determined by the combination of

r

and

θ

, and by numerical simulation we find that the fidelity peak occurs at

r=1-2θ/π

. The fidelities increase with increasing

r

when

r\in (0,1-2θ/π]

. When

θ\geπ/2

, lower fidelities are obtained due to the squeezed bath. Our results show that the dynamics of the open systems can be effectively controlled by reservoir enginerring.