Decoherence speed limit in the spin-deformed boson model

In this paper, we study the role of the nonlinear environment on the bound passage time of dynamical quantum spin systems, which is of great interest in quantum control and has been applied to quantum metrology, quantum computation, and quantum chemical dynamics. We consider the decoherence speed limit for the spin-deformed bosonic model and the impacts of the nonlinear environment and its temperature on the decoherence speed limit. Moreover, we show that, at an early enough time, the parameters associated with the nonlinear environment exhibit important roles in controlling the decoherence process. In addition our results reveal that, in long times, these parameters do not affect the decoherence process.

Figure 1

Variations of the relative purity of a spin system as a function of $t$ and the dimensionless parameter $a$, which describes the deformed harmonic oscillator in the infinite well as a nonlinear environment, are shown in panel (a) and those for the dimensionless parameter of a well with a finite depth $D$ are shown in panel (c). The figures show the evolution of an environment consisting of $N=20$ harmonic oscillators. Also, the coupling $g_i$ and frequencies ${\omega }_i$ were chosen randomly from the interval $[0,1]$. In addition, variations of relative purity as a function of $t$ are plotted in panels (b) and (d), respectively, for different values of $a$ and $D$.

Figure 2

(a) The variation of the relative purity of a spin system as a function of $t$, for definite values of $a$ and a constant temperature. (b) Variation of the relative purity of a spin system as a function of $T$, with a constant value of $a$. Panels (c) and (d) indicate the variation of relative purity as function of $D$ with a constant temperature and as a function of $T$ with a constant $D$, respectively.

Figure 3

Variation of the minimum bound passage ${\left({\tau }_{\zeta }\right)}_{\min }$ as a function of well depth $D$ in panel (a) and as a function of well width $a$ in panel (b).

Figure 4

Counter plot of variation of the minimum bound passage ${\left({\tau }_{\zeta }\right)}_{\min }$ as a function of temperature and well depth $D$ in panels (a)–(c) and as functions of temperature and well width $a$ in panels (d)–(f).