Interferometry using spatial adiabatic passage in quantum dot networks

Lenneke M. Jong and Andrew D. Greentree

Phys. Rev. B 81, 035311 – Published 8 January 2010

Abstract

We show that techniques of spatial adiabatic passage can be used to realize an electron interferometer in a geometry analogous to a conventional Aharonov-Bohm ring, with transport of the particle through the device modulated using coherent transport adiabatic passage. This device shows an interesting interplay between the adiabatic and nonadiabatic behavior of the system. The transition between nonadiabatic and adiabatic behavior may be tuned via system parameters and the total time over which the protocol is enacted. Interference effects in the final state populations analogous to the electrostatic Aharonov-Bohm effect are observed.

Received 25 September 2009

DOI:https://doi.org/10.1103/PhysRevB.81.035311

Authors & Affiliations

Lenneke M. Jong^*

Centre for Quantum Computer Technology, School of Physics, University of Melbourne, Victoria 3010, Australia

Andrew D. Greentree

School of Physics, University of Melbourne, Victoria 3010, Australia

^*lmjong@unimelb.edu.au

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Vol. 81, Iss. 3 — 15 January 2010

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Images

Figure 1
The interferometer structure consisting of six coupled sites with gate-controlled TMEs $Ω_{1} (t)$ and $Ω_{2} (t)$ . The particle is moved from $| 1 ⟩$ to $| 5 ⟩$ using the alternating CTAP protocol via the two intermediate states $| 3_{u} ⟩$ and $| 3_{d} ⟩$ . The control gates, labeled $Δ_{u}$ and $Δ_{d}$ , break the symmetry of the paths, leading to interference effects seen in the final state population as a function of the magnitude of the energy shifts and the total time of the transport. Note that we assume that the energy that the electron has at each site has been set equal.Reuse & Permissions
Figure 2
(a) Tunneling matrix elements $Ω_{1} (t)$ and $Ω_{2} (t)$ , effecting the counterintuitive pulse sequence. (b) Eigenspectra with varying detuning, $Δ_{u} = Δ_{d} = 0$ (solid lines), $Δ_{u} = - Δ_{d} = 0.25 Ω_{max}$ (dashed), and $Δ_{u} = - Δ_{d} = Ω_{max}$ (dotted). The eigenstates can be ordered as indicated. The double degeneracy of the null space is lifted with nonzero detunings of the central sites, we arbitrarily label the more energetic eigenstate of the pair $| D_{0}^{(+)} ⟩$ , and the less energetic $| D_{0}^{(-)} ⟩$ .Reuse & Permissions
Figure 3
(Color online) Map of the final state population $(ρ_{55})$ for finite time showing the regions of adiabatic and nonadiabatic evolution. Dark regions indicate high-fidelity transfer, the result of adiabatic evolution. Light regions indicate where the transport is low-fidelity transfer. Note the overall “cross” of high-fidelity adiabatic transfer, with the EAB like oscillations along the line $Δ_{u} = - Δ_{d}$ .Reuse & Permissions
Figure 4
Maximum adiabaticity through the protocol as a function of middle site detuning for ACTAP in a five-site system, corresponding to the case in the interferometer where one detuning has been taken to $\infty$ . The solid line is the numerical determination, Eq. (16) and the dashed is the analytical result to second order in $Δ$ , Eq. (19). The smooth increase in adiabaticity correlates to the smooth reduction in fidelity seen in Fig. 3 in the zones where $Δ_{u}$ and $Δ_{d}$ have the same sign.Reuse & Permissions
Figure 5
(Color online) (a) Final state population as a function of total time for antisymmetric detunings $(Δ_{u} = - Δ_{d})$ . As the total time increases we may resolve more instances of interference when the accumulated phase difference between the two paths is $π / 2$ . (b) Trace of the final state population as a function of $Δ_{u}$ for the maximum time shown in (a).Reuse & Permissions
Figure 6
(Color online) (a) Derivative of the final state population with respect to $Δ_{u}$ . Regions with a large rate of change may be considered useful for charge sensing applications. The very light regions are of high negative derivative and dark regions high positive derivative. The presence of a charge will alter the final state population due to its effect on the energy of the detuned site $| 3_{u} ⟩$ or $| 3_{d} ⟩$ in the arm being used as the sensor. (b) Dependence of the sensitivity (derivative of the final state population) on $t_{max}$ .Reuse & Permissions

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