doubly-driven TLS oscillates forever?

[ltmsyvag]

Describe the Issue!

Not sure if it's a bug, but my qutip result seems unphysical to me: it appears that I got some perpetual oscillation in a dissipative system.

What I modeled is a TLS driven by two tones, i.e.:

$$H = \frac{\omega_0}{2} \begin{pmatrix} -1 & 0 \\ 0&1 \end{pmatrix} + \begin{pmatrix} 0 & 1 \\ 1&0 \end{pmatrix} (\Omega_1\cos\omega_1 t + \Omega_2\cos\omega_2 t)$$

In addition, the TLS has a spontaneous emission rate $\Gamma_{21}$.

To implement the above system, I used the following code (fully time-dependent, no rotating-wave approximation):

from numpy import pi, cos, sqrt, linspace
import matplotlib.pyplot as plt
from qutip import (
    sigmax, sigmaz, fock_dm, mesolve, 
    basis, Qobj)

omega0 = 100*2*pi # TLS atom level spacing
omega1 = omega0 # 1st tone, resonant with the TLS
omega2 = omega0 -1*2*pi # 2nd tone, detuned from TLS
omegaR1 = 1*2*pi # Rabi freq of 1st tone
omegaR2 = 1*2*pi # Rabi freq of 2nd tone
gamma21 = 1 # spontaneous emission rate

H0 = -sigmaz()/2*omega0
H1, H2 = sigmax()*omegaR1, sigmax()*omegaR2
t = linspace(0,10,501)
def H1_coeff(t, args):
    return cos(omega1*t)
def H2_coeff(t, args):
    return cos(omega2*t)

H = [H0, [H1, H1_coeff], [H2, H2_coeff]]
c_ops = [Qobj([[0,1],[0,0]])*sqrt(gamma21)]
e_ops = [fock_dm(2,0), fock_dm(2,1)]
psi0 = basis(2,0)
result = mesolve(H, psi0, t, c_ops, e_ops)

plt.plot(t, result.expect[1])
plt.ylim(0,1)

One can directly run the above code to produce a perpetual oscillation, which seems unphysical to me. If one suppresses either tone (e.g. by setting omegaR1 or omegaR2 to zero), or set the 2nd tone's detuning to zero (i.e. omega2 = omega0), one gets the expected damping behavior at large times.

Did I implement this physics correctly? Or is qutip being weird?

Finally, my system info:

QuTiP Version:      4.7.5
Numpy Version:      1.24.3
Scipy Version:      1.10.1
Cython Version:     0.29.36
Matplotlib Version: 3.7.1
Python Version:     3.11.0
Number of CPUs:     10
BLAS Info:          OPENBLAS
OPENMP Installed:   False
INTEL MKL Ext:      False
Platform Info:      Darwin (arm64)