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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 distribution of CTQW with a single-point transition defect when t = 30, jd = j0 = 0, and β = −0.9, −0.5, 0.5, 2.
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f5: The probability distribution of CTQW with a single-point transition defect when t = 30, jd = j0 = 0, and β = −0.9, −0.5, 0.5, 2.

Mentions: When the defect is located at the initial position (jd = j0 = 0), the resulting probability distribution over the discrete position space at time t = 30 is shown in Fig. 5. Some important features to note: (1) if (γ + β) = 0, the initial position is disconnected from its neighbors and consequently the CTQW stays at the initial position; (2) as /γ + β/ deviates slightly from zero, the residual effect of the disconnection still shows and the probability distribution has a peak at the initial position (see Fig. 5(a)); this peak decreases with time, which distinguishes it from the localized peak induced by eigen bound state; (3) as /γ + β/ increases until it approaches 1, the CTQW spreads in a similar way as a free QW since there is no bound state yet (see Fig. 5(b)); and (4) when /γ + β/ > 1 (e.g. β = 0.5 and 2, as shown in Fig. 5(c,d) respectively), the transition defect induces two bound states surrounding the defect, resulting in a large probability in the vicinity of the defect position due to eigen-localization.


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

Li ZJ, Wang JB - Sci Rep (2015)

The probability distribution of CTQW with a single-point transition defect when t = 30, jd = j0 = 0, and β = −0.9, −0.5, 0.5, 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: The probability distribution of CTQW with a single-point transition defect when t = 30, jd = j0 = 0, and β = −0.9, −0.5, 0.5, 2.
Mentions: When the defect is located at the initial position (jd = j0 = 0), the resulting probability distribution over the discrete position space at time t = 30 is shown in Fig. 5. Some important features to note: (1) if (γ + β) = 0, the initial position is disconnected from its neighbors and consequently the CTQW stays at the initial position; (2) as /γ + β/ deviates slightly from zero, the residual effect of the disconnection still shows and the probability distribution has a peak at the initial position (see Fig. 5(a)); this peak decreases with time, which distinguishes it from the localized peak induced by eigen bound state; (3) as /γ + β/ increases until it approaches 1, the CTQW spreads in a similar way as a free QW since there is no bound state yet (see Fig. 5(b)); and (4) when /γ + β/ > 1 (e.g. β = 0.5 and 2, as shown in Fig. 5(c,d) respectively), the transition defect induces two bound states surrounding the defect, resulting in a large probability in the vicinity of the defect position due to eigen-localization.

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.