TY - JOUR

T1 - Effect of noise on Bloch oscillations and Wannier-Stark localization

AU - Bhakuni, Devendra Singh

AU - Dattagupta, Sushanta

AU - Sharma, Auditya

N1 - Funding Information:
A.S. is grateful to Arul Lakshminarayan for lively discussions of the topic of this paper, and acknowledges financial support from Science and Engineering Research Board (SERB) via the startup grant (File No. YSS/2015/001696). D.S.B. acknowledges Ph.D. fellowship support from University Grants Commission (UGC), India. S.D. is grateful to the Indian National Science Academy and its Senior Scientist scheme for support and to IISER, Bhopal for its kind hospitality.
Publisher Copyright:
© 2019 American Physical Society.

PY - 2019/4/24

Y1 - 2019/4/24

N2 - We calculate an exact expression for the probability propagator for a noisy electric field driven tight-binding lattice. The noise considered is a two level jump process or a telegraph process (TP) which jumps randomly between two values ±μ. In the absence of a static field, and in the limit of zero jump rate of the noisy field, we find that the dynamics yields Bloch oscillations with frequency μ, while with an additional static field ϵ we find oscillatory motion with a superposition of frequencies (ϵ±μ). On the other hand, when the jump rate is rapid, and in the absence of a static field, the stochastic field averages to zero if the two states of the TP are equally probable a priori. In that case we see a delocalization effect. The intimate relationship between the rapid relaxation case and the zero field case seems to be a generic effect found in a wide variety of systems. It is interesting to note that even for zero static field and rapid relaxation, Bloch oscillations ensue if there is a bias δp in the probabilities of the two levels. Remarkably, the Wannier-Stark localization caused by an additional static field is destroyed if the latter is tuned to be exactly equal and opposite to the average stochastic field μδp. This is an example of incoherent destruction of Wannier-Stark localization.

AB - We calculate an exact expression for the probability propagator for a noisy electric field driven tight-binding lattice. The noise considered is a two level jump process or a telegraph process (TP) which jumps randomly between two values ±μ. In the absence of a static field, and in the limit of zero jump rate of the noisy field, we find that the dynamics yields Bloch oscillations with frequency μ, while with an additional static field ϵ we find oscillatory motion with a superposition of frequencies (ϵ±μ). On the other hand, when the jump rate is rapid, and in the absence of a static field, the stochastic field averages to zero if the two states of the TP are equally probable a priori. In that case we see a delocalization effect. The intimate relationship between the rapid relaxation case and the zero field case seems to be a generic effect found in a wide variety of systems. It is interesting to note that even for zero static field and rapid relaxation, Bloch oscillations ensue if there is a bias δp in the probabilities of the two levels. Remarkably, the Wannier-Stark localization caused by an additional static field is destroyed if the latter is tuned to be exactly equal and opposite to the average stochastic field μδp. This is an example of incoherent destruction of Wannier-Stark localization.

UR - http://www.scopus.com/inward/record.url?scp=85065244190&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.99.155149

DO - 10.1103/PhysRevB.99.155149

M3 - Article

AN - SCOPUS:85065244190

VL - 99

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 15

M1 - 155149

ER -