One-component dynamical equation and noise-induced adiabaticity

Abstract

The adiabatic theorem addresses the dynamics of a target instantaneous eigenstate of a time-dependent Hamiltonian. We use a Feshbach P-Q partitioning technique to derive a closed one-component integro-differential equation. The resultant equation properly traces the footprint of the target eigenstate. The physical significance of the derived dynamical equation is illustrated by both general analysis and concrete examples. We find an interesting phenomenon showing that a dephasing white noise can enhance and even induce adiabaticity. This phenomenon, distinguishing itself from any artificial control process, may occur in natural physical processes. We also show that particular white noises can shorten the total duration of dynamic processing, such as in adiabatic quantum computing.

Effect of Poisson noise on adiabatic quantum control

“…The strength of the strikes ξ i is statistically independent of the times and is distributed according to a probability density P (ξ ). The quantity ν (which corresponds to the quantity W in [38]) can be thought of as the average frequency of the noise shots. Note that z(t) is dimensionless and the strength of a strike ξ i has dimensions of time.…”

“…While the Poisson noise used in [38] is always Gaussian, we will continue to use the notation for Poisson white noise since obtaining the results for Gaussian white noise requires only a relabeling, J → J and D → D. The noise Hamiltonian is H 1 = H 0 such that the master equation iṡ…”

“…In a recent paper by Jing et al [38] it is claimed that Poisson noise can counterintuitively help improve adiabaticity for increasing noise strength. We will show that what is referred to as strong noise is actually a large noise bias which implies a stronger Hamiltonian.…”

“…In Sec. IV, we solve the master equation numerically for several cases, including the setting described in [38] and stimulated Raman adiabatic passage (STIRAP) [44] type schemes in three-level systems. The examples we present will illustrate the different effects of Poisson noise.…”

Overview of quantum memory protection and adiabaticity induction by fast signal control

“…Recently, we proposed a nonperturbative dynamical decoupling [16,29,30,31] protocol by employing the quantum-state-diffusion (QSD) equation [32,33,34,35,36], where we can treat the free evolution and control of the system in a united way. Combined with the Feshbach PQ-partitioning technique [5], a one-component differential equation [37] has been derived to address the dynamics of one target instantaneous eigenstate of the system, by which the fast signals control on leakage of quantum memory can be used in manipulating adiabatic condition. Under fast signals control, adiabaticity can be established even when the original Hamiltonian lives in a nonadiabatic regime.…”