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Physics of Atomic Nuclei

Particle localization in a double-well potential by pseudo-supersymmetric fields

Vladislav G. Bagrov, B. F. Samsonov, V. V. Shamshutdinova

Published Jun 1, 2011• 2 citations
Publisher

Abstract

We study properties of a particle moving in a double-well potential in the two-level approximation placed in an additional external time-dependent field. Using previously established property (J. Phys. A 41 , 244023 (2008)) that any two-level system possesses a pseudo-supersymmetry we introduce the notion of pseudo-supersymmetric field. It is shown that these fields, even if their time dependence is not periodical, may produce the effect of localization of the particle in one of the wells of the double-well potential.

DOI
10.1134/s1063778811060056

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•Jul 1, 2015•0 citations
We study properties of a particle moving in a double-well potential in the two-level approximation placed in an additional external time-dependent field. Using previously established property (J. Phys. A 41 , 244023 (2008)) that any two-level system possesses a pseudo-supersymmetry we introduce the notion of pseudo-supersymmetric field. It is shown that these fields, even if their time dependence is not periodical, may produce the effect of localization of the particle in one of the wells of the double-well potential.
The roles of spatial symmetry and strength of external time-dependent perturbation on the dynamics of a quantum particle, initially localized in one of the wells of an asymmetric double-well potential are studied using the recently developed techniques incorporating quantum theory of motion and time-dependent Fourier grid Hamiltonian methods. The model used here includes a mimic of the related experimental situations which is considered as a perturbation to the static double-well potential. Analysis of localized and delocalized phase space structures and corresponding time-profile of tunneling probability reveal the recipe toward controlling the tunneling oscillations by modulating the parameters of applied perturbation. A study on a stochastic pulsating potential also reveals the root to the quantum localization, even in moderate field strength.
For a flux qubit considered as a two-level system, for which a hidden polynomial pseudo-supersymmetry was previously discovered, we propose a special time-dependent external control field. We show that for a qubit placed in this field there exists a critical value of tunnel frequency. When the tunnel frequency is close enough to its critical value, the external field frequency may be tuned in a way to keep the probability to detect a definite direction of the current circulating in a Josephson-junction circuit above 1/2 during a desirable time interval. We also show that such a behavior is not much affected by a sufficiently small dissipation.
Potential wells are widely studied entities nowadays, because of their wide range of applications in many fields of science. Experimental and technological improvements make it possible to design and control the potential shape. For instance, one can modify a single-well potential into a double well and backwards. To investigate this kind of problems, one needs to properly take into account the time-dependency of the system Hamiltonian. We used split operator method to study the dynamics of wavepacket in general, and in time-dependent potential wells in particular. While considering time-dependent potential wells, we concentrated on the case when a single-well is transformed into a double-well. Our goal was to explore the range of validity of the adiabatic theorem. We have made observations on the dynamics of the wavepacket for different barrier heights and widths. For each case, we estimated how long the switching time should be in order to leave the system in the ground state. In doing this, we established a link between the eigenvalues of potential well and the time taken by the wavepacket to be in the ground state of potential well. The greater the difference between the first two eigenvalues of the double well, the lesser the switching time requested to go from single- to double well. Moreover, we simulated the system dynamics while going from single- to asymmetric doublewell. We noticed that the superposition of left and right states is very fragile with respect to asymmetry. By introducing any asymmetry in the double-well, the wavepacket tends to be trapped in the deeper side of the potential well. While talking in terms of eigenvalues of asymmetric double-well, we again observed that the greater the difference between eigenvalues, the lesser the time needed by the wavepacket to be in ground state of double-well. Finally, we applied the theoretically discussed approach to estimate the switching time needed by a trapped ion to be in the ground state of a double-well potential, for realistic experimental parameters.