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arXiv:cond-mat/0303458 · Physical Review Letters

Quantum Toys for Quantum Computing: Persistent Currents Controlled by the Spin Josephson Effect

Gen Tatara, N. Garcı́a

Published Aug 15, 2003• 21 citations
arXivHTMLPDF

Abstract

Quantum devices and computers will need operational units in different architectural configurations for their functioning. The unit should be a simple "quantum toy," an easy to handle superposition state. Here such a novel unit of quantum mechanical flux state (or persistent current) in a conducting ring with three ferromagnetic quantum dots is presented. The state is labeled by the two directions of the persistent current, which is driven by the spin chirality of the dots, and is controlled by the spin (the spin Josephson effect). It is demonstrated that by the use of two connected rings, one can carry out unitary transformations on the input flux state by controlling one spin in one of the rings, enabling us to prepare superposition states. The flux is shown to be a quantum operation gate, and may be useful in quantum computing.

DOI
10.1103/physrevlett.91.076806

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Quantum devices and computers will need operational units in different architectural configurations for their functioning. The unit should be a simple "quantum toy," an easy to handle superposition state. Here such a novel unit of quantum mechanical flux state (or persistent current) in a conducting ring with three ferromagnetic quantum dots is presented. The state is labeled by the two directions of the persistent current, which is driven by the spin chirality of the dots, and is controlled by the spin (the spin Josephson effect). It is demonstrated that by the use of two connected rings, one can carry out unitary transformations on the input flux state by controlling one spin in one of the rings, enabling us to prepare superposition states. The flux is shown to be a quantum operation gate, and may be useful in quantum computing.
A formal definition of a computer would be that it is a system whose mechanical time evolution is used to do computation. A computer just like an dassical computer has the bit as unit of information, in the context of computation called a qubit. Because a computer operates in the mechanical domain, a collection of qubits can hold not one value but a superposition of many values. This quantum parallelism is a fundamental advantage that a computer has over a classical computer and algorithms that exploit this feature can be significantly faster than any classical algorithm. That said, the number of algorithm available today is small and their usefulness is limited. Several hardware implementations of computers have been made. Unfortunately existing hardware technology limits the size of these experimental computers to just a few qubits. In chapter 1 we review the field of computation and introduce an interesting new hardware candidate, dubbed the quantum by its creators. This toy is a metallic ring with three embedded ferromagnets. In certain configurations these ferromagnets can induce a current in the ring. In fact the configurations that will or will not induce a current can be identified with an CNOT(XOR) gate. This motivates us to explore the viability of this system using computer simulations. The toy system is related to a long standing problem in condensed matter physics, that of the persistent currents. When a small metal ring is placed in a static magnetic field, the magnetic field will induce a current in the ring. Persistent currents have been observed experimentally and a great discrepancy between theory and experiment was found. The qualitative features of the phenomenon are explained well by theory, but the size of the current measured was one to two orders of magnitude larger then that predicted by experiment. As a second object of this master thesis we will study persistent current numerically using a simple fight-binding model and compare this to existing theory and experiment. In chapter two we review the field of persistent currents and we give an overview of existing theory. To make a simulation tool of a mechanical system basically means that we have to solve the Schrodinger equation numerically. In chapter 3 we briefly discuss two such method, namely the Cranck- Nicholson method and the Suzuki-Trotter method. We will use the latter in our simulation tool. The actual simulation is described in chapter 4. In this chapter we detail the development of the numerical tool and show its correctness at each step. We find that the simulations qualitatively show the same features as we would expect theoretically and experimentally. The size of current is a different matter. When compared to experiment we find that although our results are of the same order of magnitude we cannot make an accurate fit to the experimental data using our simple model. In the last chapter we investigate the properties of the toy system by computer simulations. We will explore its application for computation and its use as a measurement device. Upon investigating how a toy system can be used in a circuit, we find that the toy is not useful for computation. We then focus on the second application1 that of a measurement device. The idea being that we can exploit the dependence of the induced current to the direction of the embedded ferromagnets. To verify if such a scheme will work, we need to investigate if we can reproduce the theoretical values of the induced current. We found major discrepancies between theory and our simulations. We found for instance that the induced current has an erratic dependence on the electron density. We then split our investigation between the single electron case and the half-filled case found in most metals. The single electron case only matches the theory qualitatively. We find that indeed such a single electron system can be build and be used as a measurement device. In the half-filled case we find that the dependence of the current on the various parameters is so erratic that we condude that according to our simulations, a metallic toy could not be used as a measurement device. An explanation for the difference between theory and our simulations could unfortunately not be found. To investigate this we would have to repeat the original calculations, which is outside the scope of this master thesis
The Josephson effect in a superconductor/triple-quantum-dot ring/superconductor structure is theoretically investigated. We find that in this structure, interdot spin correlation can be driven, which contributes to the occurrence of new 0 and $\ensuremath{\pi}$ phases of the Josephson current. Moreover, in the 0-$\ensuremath{\pi}$ phase-transition process, an intermediate bistable phase appears in which the Josephson current is completely suppressed. By analyzing the interdot spin correlation, the electron motion mechanism is clarified. We then attribute the disappearance of the Josephson current to the occurrence of the Josephson-Fano effect. What is interesting is that the disappearing Josephson current is accompanied by the apparent persistent current in the ring whose direction is determined by the superconducting phase difference. With the calculated results, we consider such a structure to be a candidate for the realization of the persistent current bit.
A qubit was designed that can be fabricated with conventional electron beam lithography and is suited for integration into a large quantum computer. The qubit consists of a micrometer-sized loop with three or four Josephson junctions; the two qubit states have persistent currents of opposite direction. Quantum superpositions of these states are obtained by pulsed microwave modulation of the enclosed magnetic flux by currents in control lines. A superconducting flux transporter allows for controlled transfer between qubits of the flux that is generated by the persistent currents, leading to entanglement of qubit information.
We analyze the posibility of employing the mesoscopic-nanoscopic ring of a normal metal in a doubly degenerate persistent current state with a third auxihilary level and in the presence of the Aharonov-Bohm flux equal to the half of the normal flux quantum ℏc/e\hbar c/eℏc/e as a qubit. The auxiliary level can be effectively used for all fundamental quantum logic gate (qu-gate) operations which includes the initialization, phase rotation, bit flip and the Hadamard transformation as well as the double-qubit controlled operations (conditional bit flip). We suggest a tentative realization of the mechanism as either the mesoscopic structure of three quantum dots coherently coupled by mesoscopic tunnelling in crossed magnetic and electric fields, or as a nanoscopic structure of triple anionic vacancy (similar to F3F_3F3​ centers in alkali halides) with one trapped electron in one spin projection state.
A qubit was designed that can be fabricated with conventional electron beam lithography and is suited for integration into a large quantum computer. The qubit consists of a micrometer-sized loop with three or four Josephson junctions; the two qubit states have persistent currents of opposite direction. Quantum superpositions of these states are obtained by pulsed microwave modulation of the enclosed magnetic flux by currents in control lines. A superconducting flux transporter allows for controlled transfer between qubits of the flux that is generated by the persistent currents, leading to entanglement of qubit information.
Ground-state properties of one-dimensional quantum rings with a few electrons, which interact with each other in the form of 1∕r1∕r1∕r Coulomb repulsion, are studied by exact diagonalization. For three electrons, the fully spin-polarized ground state is uniquely realized when the diameter of the ring is sufficiently large. In contrast, for four and five electrons, the fully polarized state never becomes the unique ground state, however large the diameter is. These results can be understood in terms of the multiple-spin exchange. When a perpendicular magnetic field is applied to the ring (i.e., the Aharonov-Bohm flux is introduced), the persistent current occurs, and the spin chirality is finite for a certain value of the flux. The difference between the quantum ring and the circularly arranged quantum dots is also discussed.