Dark-state adiabatic passage with spin-one particles

Andrew D. Greentree and Belita Koiller

Phys. Rev. A 90, 012319 – Published 14 July 2014

Abstract

Adiabatic transport of information is a widely invoked resource in connection with quantum information processing and distribution. The study of adiabatic transport via spin-half chains or clusters is standard in the literature, while in practice the true realization of a completely isolated two-level quantum system is not achievable. We explore here, theoretically, the extension of spin-half chain models to higher spins. Considering arrangements of three spin-one particles, we show that adiabatic transport, specifically a generalization of the dark-state adiabatic passage procedure, is applicable to spin-one systems. We thus demonstrate a qutrit state transfer protocol. We discuss possible ways to physically implement this protocol, considering quantum dot and nitrogen-vacancy implementations.

Received 12 March 2014

DOI:https://doi.org/10.1103/PhysRevA.90.012319

Authors & Affiliations

Andrew D. Greentree^*

Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne 3001, Australia

Belita Koiller^†

Instituto de Física, Universidade Federal do Rio de Janeiro, Cx. Postal 68528, Rio de Janeiro 21941-972, Brazil

^*andrew.greentree@rmit.edu.au
^†bk@if.ufrj.br

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Issue

Vol. 90, Iss. 1 — July 2014

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Images

Figure 1
(a) Schematic representation of the three-spin system. Individual spin states are labeled according to their $z$ projection and spin-spin coupling is nearest neighbor only. (b) Dark-state adiabatic passage is effected by varying the couplings according to the counterintuitive pulse sequence, in this case illustrated using sinusoidal modulation of $d_{12}$ and $d_{23}$ .
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Figure 2
Eigenspectra over the counterintuitive pulse sequence with $B = 1$ , $d = 0.2$ . The states separate into various manifolds, which are discussed in the text. Highlighted are some of the kets with constant energy throughout the DSAP protocol.
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Figure 3
Populations in the $E = 2 B$ manifold throughout the protocol determined using density matrix analysis as a function of time, confirming the DSAP evolution. The red line is $P_{011}$ and the green line is $P_{110}$ . Note that the system is initialized in the state $| 011 〉$ $(P_{011} = 1)$ and evolves to the state $| 110 〉$ , staying in the state $| D_{0}^{2} 〉$ as expected, with $P_{101} = 0$ throughout the protocol. Population in the $E = - 2 B$ manifold follows similarly. For this simulation, $t_{max} = 100 B^{- 1}$ . The path of the adiabatic passage is schematically shown at the top, where only the lower states are populated. This representation also makes clear the connection between the DSAP pathway under consideration and STIRAP in the $Λ$ configuration.
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Figure 4
Time evolution of the populations in the $E = B$ manifold when the starting state is $| \bar{1} 11 〉$ , corresponding to evolution in the state $| D^{1} 〉$ . The purple line shows $P_{\bar{1} 11}$ , the cyan line shows $P_{010}$ , and the orange line shows $P_{11 \bar{1}}$ . This evolution is completely analogous to the evolution observed in alternating adiabatic passage protocols with five states. The system is initially in the state $| \bar{1} 11 〉$ and evolves to the state $| 11 \bar{1} 〉$ , with transient population in the state $| 010 〉$ .
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Figure 5
(a) Arrangement of three spins in the $x$ - $y$ plane. (b) Interspin separations with magic angles for each pair of spins marked. Because there are points of intersection of the magic angles, it is possible to define a magnetic field trajectory that effects the counterintuitive pulse sequence, and one such trajectory is shown here in yellow with the start and stop points marked with yellow dots.
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Figure 6
Eigenspectrum for the magic-angle control protocol, where the angle of the applied field is according to the trajectory outlined in Eq. (15) for the case that the three spins are located at the vertices of an equilateral triangle.
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