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Viewing Majorana Bound States by Rabi Oscillations.

Wang Z, Liang QF, Yao DX, Hu X - Sci Rep (2015)

Bottom Line: The system consists of a quantum dot (QD) and an rf-SQUID with MBSs at the Josephson junction.Rabi oscillations between energy levels formed by MBSs are induced by ac gate voltage controlling the coupling between QD and MBS when the photon energy proportional to the ac frequency matches gap between quantum levels formed by MBSs and QD.The present scheme is expected to provide a clear evidence for MBSs under intensive searching.

View Article: PubMed Central - PubMed

Affiliation: 1] School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, China [2] International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science, Tsukuba 305-0044, Japan.

ABSTRACT
We propose to use Rabi oscillation as a probe to view the fractional Josepshon relation (FJR) associated with Majorana bound states (MBSs) expected in one-dimensional topological superconductors. The system consists of a quantum dot (QD) and an rf-SQUID with MBSs at the Josephson junction. Rabi oscillations between energy levels formed by MBSs are induced by ac gate voltage controlling the coupling between QD and MBS when the photon energy proportional to the ac frequency matches gap between quantum levels formed by MBSs and QD. As a manifestation of the Rabi oscillation in the whole system involving MBSs, the electron occupation on QD oscillates with time, which can be measured by charge sensing techniques. With Floquet theorem and numerical analysis we reveal that from the resonant driving frequency for coherent Rabi oscillation one can directly map out the FJR cos(ฯ€ฮฆ/ฮฆ0) as a signature of MBSs, with ฮฆ the magnetic flux through SQUID and ฮฆ0โ€‰= hc/2e the flux quantum. The present scheme is expected to provide a clear evidence for MBSs under intensive searching.

No MeSH data available.


Related in: MedlinePlus

Time evolution of the weights for the quantum states and the QD occupation probability, with the initial condition, (a) for ฮฆโ€‰=โ€‰0 and driving frequency ฮฉโ€‰=โ€‰2.402 J and T1โ€‰=โ€‰0.015 J, (b) for ฮฆโ€‰=โ€‰0 and ฮฉโ€‰=โ€‰1.602 J and T1โ€‰=โ€‰0.015 J, (c) for ฮฆโ€‰=โ€‰0 and ฮฉโ€‰=โ€‰2.402 J and T1โ€‰=โ€‰0.03 J, and (d) for ฮฆโ€‰=โ€‰0.436 ฮฆ0 and ฮฉโ€‰=โ€‰0.8 J and T1โ€‰=โ€‰0.015 J, respectively. Other parameters are T0โ€‰=โ€‰0.05 J, ฮดLโ€‰=โ€‰0.02 J, ฮดRโ€‰=โ€‰0.005 J, and โ€‰=โ€‰0.4 J. ฤงโ€‰=โ€‰1 is taken through the paper.
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f2: Time evolution of the weights for the quantum states and the QD occupation probability, with the initial condition, (a) for ฮฆโ€‰=โ€‰0 and driving frequency ฮฉโ€‰=โ€‰2.402 J and T1โ€‰=โ€‰0.015 J, (b) for ฮฆโ€‰=โ€‰0 and ฮฉโ€‰=โ€‰1.602 J and T1โ€‰=โ€‰0.015 J, (c) for ฮฆโ€‰=โ€‰0 and ฮฉโ€‰=โ€‰2.402 J and T1โ€‰=โ€‰0.03 J, and (d) for ฮฆโ€‰=โ€‰0.436 ฮฆ0 and ฮฉโ€‰=โ€‰0.8 J and T1โ€‰=โ€‰0.015 J, respectively. Other parameters are T0โ€‰=โ€‰0.05 J, ฮดLโ€‰=โ€‰0.02 J, ฮดRโ€‰=โ€‰0.005 J, and โ€‰=โ€‰0.4 J. ฤงโ€‰=โ€‰1 is taken through the paper.

Mentions: The time evolution of the system can be obtained in terms of the weights Pi(t) with by integrating Eq. (3). Typical time evolutions of the quantum state are given in Fig. 2. It is clear that the tunneling interaction T stimulates resonant and oscillations and associated oscillations in the occupation probability on QD at two different frequencies ฮฉ for a given magnetic flux ฮฆ, as shown in Fig. 2(a,b). When the amplitude of ac component T1 in T is doubled, the frequency of oscillation is doubled as shown explicitly in Fig. 2(c), which evidences Rabi oscillations in the system.


Viewing Majorana Bound States by Rabi Oscillations.

Wang Z, Liang QF, Yao DX, Hu X - Sci Rep (2015)

Time evolution of the weights for the quantum states and the QD occupation probability, with the initial condition, (a) for ฮฆโ€‰=โ€‰0 and driving frequency ฮฉโ€‰=โ€‰2.402 J and T1โ€‰=โ€‰0.015 J, (b) for ฮฆโ€‰=โ€‰0 and ฮฉโ€‰=โ€‰1.602 J and T1โ€‰=โ€‰0.015 J, (c) for ฮฆโ€‰=โ€‰0 and ฮฉโ€‰=โ€‰2.402 J and T1โ€‰=โ€‰0.03 J, and (d) for ฮฆโ€‰=โ€‰0.436 ฮฆ0 and ฮฉโ€‰=โ€‰0.8 J and T1โ€‰=โ€‰0.015 J, respectively. Other parameters are T0โ€‰=โ€‰0.05 J, ฮดLโ€‰=โ€‰0.02 J, ฮดRโ€‰=โ€‰0.005 J, and โ€‰=โ€‰0.4 J. ฤงโ€‰=โ€‰1 is taken through the paper.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4495447&req=5

f2: Time evolution of the weights for the quantum states and the QD occupation probability, with the initial condition, (a) for ฮฆโ€‰=โ€‰0 and driving frequency ฮฉโ€‰=โ€‰2.402 J and T1โ€‰=โ€‰0.015 J, (b) for ฮฆโ€‰=โ€‰0 and ฮฉโ€‰=โ€‰1.602 J and T1โ€‰=โ€‰0.015 J, (c) for ฮฆโ€‰=โ€‰0 and ฮฉโ€‰=โ€‰2.402 J and T1โ€‰=โ€‰0.03 J, and (d) for ฮฆโ€‰=โ€‰0.436 ฮฆ0 and ฮฉโ€‰=โ€‰0.8 J and T1โ€‰=โ€‰0.015 J, respectively. Other parameters are T0โ€‰=โ€‰0.05 J, ฮดLโ€‰=โ€‰0.02 J, ฮดRโ€‰=โ€‰0.005 J, and โ€‰=โ€‰0.4 J. ฤงโ€‰=โ€‰1 is taken through the paper.
Mentions: The time evolution of the system can be obtained in terms of the weights Pi(t) with by integrating Eq. (3). Typical time evolutions of the quantum state are given in Fig. 2. It is clear that the tunneling interaction T stimulates resonant and oscillations and associated oscillations in the occupation probability on QD at two different frequencies ฮฉ for a given magnetic flux ฮฆ, as shown in Fig. 2(a,b). When the amplitude of ac component T1 in T is doubled, the frequency of oscillation is doubled as shown explicitly in Fig. 2(c), which evidences Rabi oscillations in the system.

Bottom Line: The system consists of a quantum dot (QD) and an rf-SQUID with MBSs at the Josephson junction.Rabi oscillations between energy levels formed by MBSs are induced by ac gate voltage controlling the coupling between QD and MBS when the photon energy proportional to the ac frequency matches gap between quantum levels formed by MBSs and QD.The present scheme is expected to provide a clear evidence for MBSs under intensive searching.

View Article: PubMed Central - PubMed

Affiliation: 1] School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, China [2] International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science, Tsukuba 305-0044, Japan.

ABSTRACT
We propose to use Rabi oscillation as a probe to view the fractional Josepshon relation (FJR) associated with Majorana bound states (MBSs) expected in one-dimensional topological superconductors. The system consists of a quantum dot (QD) and an rf-SQUID with MBSs at the Josephson junction. Rabi oscillations between energy levels formed by MBSs are induced by ac gate voltage controlling the coupling between QD and MBS when the photon energy proportional to the ac frequency matches gap between quantum levels formed by MBSs and QD. As a manifestation of the Rabi oscillation in the whole system involving MBSs, the electron occupation on QD oscillates with time, which can be measured by charge sensing techniques. With Floquet theorem and numerical analysis we reveal that from the resonant driving frequency for coherent Rabi oscillation one can directly map out the FJR cos(ฯ€ฮฆ/ฮฆ0) as a signature of MBSs, with ฮฆ the magnetic flux through SQUID and ฮฆ0โ€‰= hc/2e the flux quantum. The present scheme is expected to provide a clear evidence for MBSs under intensive searching.

No MeSH data available.


Related in: MedlinePlus