Continuous-time quantum walks + classical random telegraphic noise

 

The classical random telegraphic (RT) noise can be used to study lattice defects or the relaxation processes of quantum systems under thermal fluctuations, leading to Markovian or Non-Markovian dynamics. The RT noise is a non-Gaussian process  described by the noise amplitude “a” which can switch between two values (+a,-a) with switching rate gamma. The probability for the fluctuator to switch n times after time t follows a Poisson distribution

 

such that the autocorrelation function follows a Lorentzian spectrum

 

The dynamics of particle moving on an optical lattice under time-dependent fluctuations of the tunneling amplitudes between nearest neighbors is modelled by 

where epsilon is the on-site energy and gj(t) is the stochastic fluctuator given by the RT noise, such that the evolved density matrix is averaged over hundreds of noise realizations

Results from ref.[1] shows that the strong coupling with the environment (slow RT Noise i.e. small gamma) restrict the walker into few lattice points, whereas  the weak coupling ( fast RT Noise i.e. big gamma +high noise amplitude) induces a quantum-classical transition where the end state resembles a binomial distribution typical of the classical random walk.

The below movie shows continuous-time quantum walks + fast RT noise + high noise amplitude, where in all cases initially the particle is located at the center of the lattice.

 

Next movie shows continuous-time quantum walks + fast RT noise + small noise amplitude 

 

Next movie shows continuous-time quantum walks + slow RT noise + high noise amplitude

 

 

The below movie shows continuous-time quantum walks + slow RT noise + small noise amplitude

 

 

Finally, let’s introduce the RT noise in a quantum ratchet [2], consisting of 3 sites and 5 particles,  with the aim to model random impurities

 

 with driven field

 

The below picture shows noiseless simulations of the system and plots the average particle current and quantum measures such as coherences, inverse participation ratio and depletion

 

Next picture, shows the quantum ratchet with the fast RT noise placed on the hopping term. We can observe a nice damping on the particle current similar to the effect of a thermal bath.

 

 

Finally, the below picture shows the quantum ratchet with the slow RT noise placed on the potential term. We can see that the RT noise induces current reversals a typycal phenomena of chaos

 

References

[1] Benedetti, Claudia, et al. "Non-markovian continuous-time quantum walks on lattices with dynamical noise." Physical Review A 93.4 (2016): 042313.

[2] Valdez, Marc Andrew, et al. "Many-body quantum chaos and entanglement in a quantum ratchet." Physical review letters 120.23 (2018): 234101.