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correlation_2op_1t() and spectrum() giving the physically incorrect result unless solver='es'

See original GitHub issue

Describe the bug See discussion here:

https://groups.google.com/g/qutip/c/2lod1DuFZiE/m/y8Bj6dKHDAAJ?pli=1

To my surprise, my PhD student had this problem again today, I am a bit surprised nothing has been done about this.

At least making es the default solver for correlation and spectrum, updating the docs to give a warning to only use the es solver (for now?), and maybe longer term figuring out why the other solvers are not handling it properly

To Reproduce

https://github.com/gsteele13/gary-exploring-qutip/blob/master/Correlations.ipynb

import numpy as np
import pylab as plt
from qutip import *

N = 5
w = 1 * 2 * np.pi              # 1 Hz oscillator frequency
Q = 40
kappa = w / Q

# Set up some operators
a = destroy(N)
n = num(N)
x = (a + a.dag())/np.sqrt(2)
p = -1j * (a - a.dag())/np.sqrt(2)
H = w * a.dag() * a

c_ops = []

psi0 = fock(N,0)
tlist = np.linspace(0, 10, 500)

corr = correlation_2op_1t(H, psi0, tlist, c_ops, x, x, solver='me')

wlist1, spec1 = spectrum_correlation_fft(tlist, corr)

plt.figure(figsize=(14,8))
plt.plot(tlist, np.real(corr))
plt.plot(tlist, np.imag(corr))
plt.show()

plt.figure(figsize=(14,8))
plt.plot(wlist1, np.abs(spec1))
plt.show()

Expected behavior Correlation should have an imaginary component and quantum PSD should not be symmetric about f = 0

Your Environment Software Version QuTiP 4.4.1 Numpy 1.17.4 SciPy 1.4.1 matplotlib 3.3.4 Cython 0.29.14 Number of CPUs 4 BLAS Info INTEL MKL IPython 7.9.0 Python 3.7.5 (default, Oct 25 2019, 10:52:18) [Clang 4.0.1 (tags/RELEASE_401/final)] OS posix [darwin] Wed Mar 10 08:51:15 2021 CET

Additional context Add any other context about the problem here.