We consider the quantum Rabi model as an open system that is subject to dissipation, dephasing, and sinusoidal qubit driving. One can change to an interaction picture where the qubit-driving term disappears at the expense of changing the free energy of the qubit which becomes time dependent. If the driving frequency is large with respect to the rest of the parameters with the exception of the driving strength, then one can obtain an effective Hamiltonian that accurately describes the dynamics of the system. The driving has two effects: the qubit-transition frequency is changed and the qubit has reduced dephasing. The driving strength can be chosen so that the qubit-transition frequency is reduced, made equal to zero, or even made negative so that the excited and ground states of the qubit are interchanged. Therefore, sinusoidal qubit driving offers another method to control the qubit-transition frequency and to reduce qubit dephasing. Adjusting the driving strength allows one to consider a qubit with degenerate energy levels. Not taking dissipation into account, the evolution operator of the qubit-harmonic oscillator system is given by a linear combination of the orthogonal projectors onto the eigenstates of ${\widehat{\sigma }}_x$ followed by the evolution operator of a forced harmonic oscillator, the harmonic oscillator can be prepared in such a way that it is always found in a Schrödinger cat state, and the transition probability of the qubit can exhibit a collapse-revival behavior. In addition, the Born-Markov-secular master equation is deduced and the effects of dissipation are presented. In particular, smaller ultrastrong-coupling values are preferable over larger ultrastrong-coupling values and deep strong-coupling values in order to have long-lived, easily distinguishable Schrödinger cat states because the decoherence rate is inversely proportional to the square of the coupling. Finally, the qubit-harmonic oscillator system can be prepared in highly entangled states that are stable under dissipation.

中文翻译：

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具有耗散和量子位驱动的量子 Rabi 模型

我们将量子 Rabi 模型视为一个开放系统，它会受到耗散、移相和正弦量子位驱动。人们可以改变为一个交互图，其中量子位驱动项消失，代价是改变变得依赖于时间的量子位的自由能。如果驱动频率相对于除驱动强度之外的其他参数较大，则可以获得准确描述系统动力学的有效哈密顿量。驱动有两个作用：改变量子位跃迁频率和量子位减少移相。可以选择驱动强度，从​​而降低量子位跃迁频率，使其等于 0，甚至设为负值，从而使量子位的激发态和基态互换。所以，正弦量子位驱动提供了另一种控制量子位跃迁频率和减少量子位相移的方法。调整驱动强度允许人们考虑具有简并能级的量子位。不考虑耗散，量子位谐波振荡器系统的演化算子由正交投影到本征态的线性组合给出${\widehat{\sigma }}_X$其次是强迫谐振子的演化算子，谐振子可以以这样的方式准备，即它总是处于薛定谔猫状态，并且量子比特的转移概率可以表现出崩溃 - 复兴行为。此外，推导了Born-Markov-secular主方程，并给出了耗散的影响。特别是，较小的超强耦合值比较大的超强耦合值和深强耦合值更可取，以便获得长寿命、易于区分的薛定谔猫状态，因为退相干率与耦合的平方成反比。最后，可以在耗散下稳定的高度纠缠态中制备量子位谐波振荡器系统。