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Single-point position and transition defects in continuous time quantum walks.

Li ZJ, Wang JB - Sci Rep (2015)

Bottom Line: The number of bound states is found to be critically dependent on the defect parameters, and the localized probability peaks can be readily obtained by projecting the state vector of CTQW on to these bound states.The interference between two bound states are also observed in the case of a transition defect.The spreading of CTQW probability over the line can be finely tuned by varying the position and transition defect parameters, offering the possibility of precision quantum control of the system.

View Article: PubMed Central - PubMed

Affiliation: Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, China.

ABSTRACT
We present a detailed analysis of continuous time quantum walks (CTQW) with both position and transition defects defined at a single point in the line. Analytical solutions of both traveling waves and bound states are obtained, which provide valuable insight into the dynamics of CTQW. The number of bound states is found to be critically dependent on the defect parameters, and the localized probability peaks can be readily obtained by projecting the state vector of CTQW on to these bound states. The interference between two bound states are also observed in the case of a transition defect. The spreading of CTQW probability over the line can be finely tuned by varying the position and transition defect parameters, offering the possibility of precision quantum control of the system.

No MeSH data available.


The probability at defect position as a function of the transition defect strength when t = 30 and jd = j0.
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f6: The probability at defect position as a function of the transition defect strength when t = 30 and jd = j0.

Mentions: The last terms in the square brackets of the above equations represent the interference between the two bound states. The values of Eqs. (27) and (28) are approximately equal to the peak values in Fig. 5(c,d), fully indicating that these peaks are the eigen localization. In Fig. 6, we plot the localized probability at defect position as a function of the transition defect strength β when jd = j0. The oscillatory behavior in the range of /γ + β/ > 1 displays clearly the coherent effect between the two bound states. Similar oscillation also occurs for the probabilities at the neighbors of the defect position. When β = −γ = −1, complete disconnection between the initial position and its neighbors, we have . Smooth variation of with the small deviation from β = −1 indicates the disconnection effect remains.


Single-point position and transition defects in continuous time quantum walks.

Li ZJ, Wang JB - Sci Rep (2015)

The probability at defect position as a function of the transition defect strength when t = 30 and jd = j0.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4555049&req=5

f6: The probability at defect position as a function of the transition defect strength when t = 30 and jd = j0.
Mentions: The last terms in the square brackets of the above equations represent the interference between the two bound states. The values of Eqs. (27) and (28) are approximately equal to the peak values in Fig. 5(c,d), fully indicating that these peaks are the eigen localization. In Fig. 6, we plot the localized probability at defect position as a function of the transition defect strength β when jd = j0. The oscillatory behavior in the range of /γ + β/ > 1 displays clearly the coherent effect between the two bound states. Similar oscillation also occurs for the probabilities at the neighbors of the defect position. When β = −γ = −1, complete disconnection between the initial position and its neighbors, we have . Smooth variation of with the small deviation from β = −1 indicates the disconnection effect remains.

Bottom Line: The number of bound states is found to be critically dependent on the defect parameters, and the localized probability peaks can be readily obtained by projecting the state vector of CTQW on to these bound states.The interference between two bound states are also observed in the case of a transition defect.The spreading of CTQW probability over the line can be finely tuned by varying the position and transition defect parameters, offering the possibility of precision quantum control of the system.

View Article: PubMed Central - PubMed

Affiliation: Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, China.

ABSTRACT
We present a detailed analysis of continuous time quantum walks (CTQW) with both position and transition defects defined at a single point in the line. Analytical solutions of both traveling waves and bound states are obtained, which provide valuable insight into the dynamics of CTQW. The number of bound states is found to be critically dependent on the defect parameters, and the localized probability peaks can be readily obtained by projecting the state vector of CTQW on to these bound states. The interference between two bound states are also observed in the case of a transition defect. The spreading of CTQW probability over the line can be finely tuned by varying the position and transition defect parameters, offering the possibility of precision quantum control of the system.

No MeSH data available.