Slow oscillating dynamics of a two-level system subject to a fast telegraph noise: beyond the NIBA approximation

We study the dynamics of a two-site model in which the tunneling amplitude between the sites is not constant, but rather a high-frequency noise. Obviously, the population imbalance in this model decays exponentially with time. Remarkably, the decay is modified dramatically when the level asymmetry fluctuates in-phase with fluctuations of the tunneling amplitude. For a particular type of these in-phase fluctuations, namely, the telegraph noise, we find the exact solution for the average population dynamics. It appears that the population imbalance between the sites starting from 1 at time t = 0 approaches a constant value in the limit t→∞. At finite bias, the imbalance goes to zero at t→∞, while the dynamics of the decay governed by noise acquires an oscillatory character.

References

1. A. O. Caldeira, and A. J. Leggett, “Influence of dissipation on quantum tunneling in macroscopic systems,” Phys. Rev. Lett. 46, 211 (1981). CrossRef Google Scholar

2. A. J. Bray, and M. A. Moore, “Influence of dissipation on quantum coherence,” Phys. Rev. Lett. 49, 1545 (1982). CrossRef Google Scholar

3. H. Grabert, and U. Weiss, “Quantum tunneling rates for asymmetric double-well systems with ohmic dissipation,” Phys. Rev. Lett. 54, 1605 (1985). CrossRef Google Scholar

4. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1 (1987). CrossRef Google Scholar

5. M. Grifoni and P. Hänngi, “Driven quantum tunneling,” Phys. Rep. 304, 229 (1998). CrossRef Google Scholar

6. K. Le Hur, “Quantum phase transitions in spin-boson systems dissipation and light phenomena,” in Understanding Quantum Phase Transitions, edited by L. D. Carr (Taylor and Francis, Boca Raton, 2010). Google Scholar

7. U. Weiss, Quantum Dissipative Systems, 4th ed. (World Scientific, Singapore, 2012). Google Scholar

8. I. de Vega, and D. Alonso, “Dynamics of non-Markovian open quantum systems,” Rev. Mod. Phys. 89, 015001 (2017). CrossRef Google Scholar

9. L. M. Cangemi, V. Cataudella, M. Sassetti, and G. De Filippis, “Dissipative dynamics of a driven qubit: Interplay between non-adiabatic dynamics and noise effects from weak to strong coupling regime,” Phys. Rev. B 100, 014301 (2019). CrossRef Google Scholar

10. L. M. Cangemi, G. Passarelli, V. Cataudella, P. Lucignano, and G. De Filippis, “Beyond the Born-Markov approximation: Dissipative dynamics of a single qubit,” Phys. Rev. B 98, 184306 (2018). CrossRef Google Scholar

11. M. Wiedmann, J. T. Stockburger, and J. Ankerhold, “Time-correlated blip dynamics of open quantum systems,” Phys. Rev. A 94, 052137 (2016). CrossRef Google Scholar

12. S. Bera, H. U. Baranger, and S. Florens, “Dynamics of a qubit in a high-impedance transmission line from a bath perspective,” Phys. Rev. A 93, 033847 (2016). CrossRef Google Scholar

13. H. Shapourian, “Dynamical renormalization-group approach to the spin-boson model,” Phys. Rev. A 93, 032119 (2016). CrossRef Google Scholar

14. P. P. Orth, A. Imambekov, and K. Le Hur, “Nonperturbative stochastic method for driven spin-boson model,” Phys. Rev. B 87, 014305 (2013). CrossRef Google Scholar

15. F. Nesi, E. Paladino, M. Thorwart, and M. Grifoni, “Spin-boson dynamics beyond conventional perturbation theories,” Phys. Rev. B 76, 155323 (2007). CrossRef Google Scholar

16. M. Thoss, H. Wang, and W. H. Miller, “Self-consistent hybrid approach for complex systems: Application to the spin-boson model with Debye spectral density,” J. Chem. Phys. 115, 2991 (2001). CrossRef Google Scholar

17. C. H. Mak, and R. Egger, “Quantum Monte Carlo study of tunneling diffusion in a dissipative multistate system,” Phys, Rev. E 49, 1997 (1994). CrossRef Google Scholar

18. G. B. Lesovik, A. V. Lebedev, and A. O. Imambekov, “Dynamics of two-level system interacting with random classical field,” JETP Lett. 75, 474 (2002). CrossRef Google Scholar

19. This reformulation of the problem was first proposed by H. Dekker, Noninteracting-blip approximation for a two-level system coupled to a heat bath, Phys. Rev. A 35, 1436 (1987). CrossRef Google Scholar

20. V. V. Mkhitaryan, C. Boehme, J. M. Lupton, and M. E. Raikh, “Two-photon absorption in a two-level system enabled by noise,” Phys. Rev. B 100, 214205 (2019). CrossRef Google Scholar

21. P. W. Anderson, and P. R. Weiss, “Exchange narrowing in paramagnetic resonance,” Rev. Mod. Phys. 25, 269 (1953). CrossRef Google Scholar

22. R. Kubo, “Note on the stochastic theory of resonance absorption,” J. Phys. Soc. Jpn. 9, 935 (1954). CrossRef Google Scholar

23. J. R. Klauder, and P. W. Anderson, “Spectral diffusion decay in spin resonance experiments,” Phys. Rev. 125, 912 (1962). CrossRef Google Scholar

24. N. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, 1981). Google Scholar

25. E. Paladino, Y. M. Galperin, G. Falci, and B. L. Altshuler, “1/f noise: Implications for solid-state quantum information,” Rev. Mod. Phys. 86, 361 (2014). CrossRef Google Scholar