This paper investigates the dynamics of a two-level system coupled to a super-Ohmic boson bath, which is the so-called driven spin-boson model. Using the polaron transformation we derive the Bloch vector of a master equation where the bar tunneling parameter is used as the basis for a perturbation expansion. Our method is based on the canonical quantization provided by the Bloch-Redfield formalism. We apply quantum optimal control theory to the realization of a quantum $Z$ gate and also the coherent destruction of tunneling. To solve our optimal control problem, we use the techniques of automatic differentiation as an alternative to Pontryagin's minimum principle. The latter is less straightforward since the master equation is complex.This paper investigates the dynamics of a two-level system coupled to a super-Ohmic boson bath, which is the so-called driven spin-boson model. Using the polaron transformation we derive the Bloch vector of a master equation where the bar tunneling parameter is used as the basis for a perturbation expansion. Our method is based on the canonical quantization provided by the Bloch-Redfield formalism. We apply quantum optimal control theory to the realization of a quantum $Z$ gate and also the coherent destruction of tunneling. To solve our optimal control problem, we use the techniques of automatic differentiation as an alternative to Pontryagin's minimum principle. The latter is less straightforward since the master equation is complex.

Physical Review AOct 16, 20244 citations

Advances in Quantum Control Theory

Jeffrey L. Krause

APSMar 1, 20010 citations

Understanding mechanism in quantum optimal control

Abhra Mitra

Jan 1, 20080 citations

Broadened coherent destruction of tunneling

Liping Li, Quanwei Zhao, Qing He +2 more

This paper investigates the manipulation of coherent quantum tunneling by controlling second-order coupling in zigzag-shaped lattice arrays with only one site periodically driven against the others. Different from normal coherent destruction of tunneling (CDT), we propose a surprisingly large and nontrivial effect of second-order coupling on broadened CDT essentially attributed to avoided level crossings and localized Floquet states. Moreover, our results at high-frequency approximation supported by exact numerical ones demonstrate that the extent to which the normal CDT is broadened depends on the separation of quasienergy levels in the vicinity of zeros of ${J}_{0}(A/\ensuremath{\omega})$. Remarkably, beyond the intensity of second-order coupling, the lattice size and its parity also significantly influence Floquet dynamics by either facilitating or suppressing tunneling probabilities, which in essence are also determined by noncrossing quasienergies and localized Floquet states. These findings substantially extend the theory of normal CDT, unveil the intrinsic physics behind broadened CDT, and open up an exciting possibility for quantum state control.This paper investigates the manipulation of coherent quantum tunneling by controlling second-order coupling in zigzag-shaped lattice arrays with only one site periodically driven against the others. Different from normal coherent destruction of tunneling (CDT), we propose a surprisingly large and nontrivial effect of second-order coupling on broadened CDT essentially attributed to avoided level crossings and localized Floquet states. Moreover, our results at high-frequency approximation supported by exact numerical ones demonstrate that the extent to which the normal CDT is broadened depends on the separation of quasienergy levels in the vicinity of zeros of ${J}_{0}(A/\ensuremath{\omega})$. Remarkably, beyond the intensity of second-order coupling, the lattice size and its parity also significantly influence Floquet dynamics by either facilitating or suppressing tunneling probabilities, which in essence are also determined by noncrossing quasienergies and localized Floquet states. These findings substantially extend the theory of normal CDT, unveil the intrinsic physics behind broadened CDT, and open up an exciting possibility for quantum state control.

Physical Review AFeb 10, 20252 citations

Coherent destruction of tunnelling in a symmetrical double well driven by a series of time dependent δ functions

Dipayan Seal, Pinaki Chaudhury, Subhasree Ghosh

Abstract It is analytically and numerically shown that the coherent tunnelling between the individual wells of a symmetrical double well potential can be totally suppressed when it is driven by a periodic series of δ function in time, depending on the time period and strength of the δ function. We have applied time dependent perturbation theory to have an understanding over the process. In absence of any kind of perturbation, the average position of the particle makes a sinusoidal oscillation between two wells. With the application of a periodic δ function, the amplitude and the frequency of the oscillation both get modified. In this article we have explored how the frequency and strength of the applied perturbation controls the quantum dynamics of tunnelling and finally, how these parameters drive the system towards a complete stand still situation, which is described as coherent destruction of tunnelling.Abstract It is analytically and numerically shown that the coherent tunnelling between the individual wells of a symmetrical double well potential can be totally suppressed when it is driven by a periodic series of δ function in time, depending on the time period and strength of the δ function. We have applied time dependent perturbation theory to have an understanding over the process. In absence of any kind of perturbation, the average position of the particle makes a sinusoidal oscillation between two wells. With the application of a periodic δ function, the amplitude and the frequency of the oscillation both get modified. In this article we have explored how the frequency and strength of the applied perturbation controls the quantum dynamics of tunnelling and finally, how these parameters drive the system towards a complete stand still situation, which is described as coherent destruction of tunnelling.

Journal of Physics A Mathematical and TheoreticalOct 21, 20220 citations

Z

gate and also the coherent destruction of tunneling. To solve our optimal control problem, we use the techniques of automatic differentiation as an alternative to Pontryagin's minimum principle. The latter is less straightforward since the master equation is complex.