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Modern Physics Letters B

GEOMETRIC PHASE OF DICKE STATE OF EXCITONS IN N COUPLED QUANTUM DOTS

D. M. Tong, L. C. Kwek, Christophe Couteau, C. H. Oh

Published Dec 20, 2004• 2 citations
Publisher

Abstract

We investigate the nature of geometric phases generated by the evolution of the superposition of Dicke states of excitons in N coupled quantum dots. Based on a sequence of laser pulses, arbitrary superposition of the Dicke states of excitons can be generated. By properly choosing the superposition and using the controllable laser pulses, geometric phase with any expected value can be realized. The main advantage of using coupled quantum dots is that one uses a collective behavior, rather than addressing individually qubits, for instance, like with trapped ions configuration, which require a heavy setup in order to perform a gate.

DOI
10.1142/s0217984904008018

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We investigate the nature of geometric phases generated by the evolution of the superposition of Dicke states of excitons in N coupled quantum dots. Based on a sequence of laser pulses, arbitrary superposition of the Dicke states of excitons can be generated. By properly choosing the superposition and using the controllable laser pulses, geometric phase with any expected value can be realized. The main advantage of using coupled quantum dots is that one uses a collective behavior, rather than addressing individually qubits, for instance, like with trapped ions configuration, which require a heavy setup in order to perform a gate.
Optically controlled exciton dynamics in coupled quantum dots is studied. We show that the maximally entangled Bell states and Greenberger-Horne-Zeilinger (GHZ) states can be robustly generated by manipulating the system parameters to be at the avoided crossings in the eigenenergy spectrum. The analysis of population transfer is systematically carried out by using a dressed-state picture. In addition to the quantum dot configuration that has been discussed by Quiroga and Johnson [Phys. Rev. Lett. 83, 2270 (1999)], we show that the GHZ states also may be produced in a ray of three quantum dots with a shorter generation time.
We propose a fast and efficient technique to create classes of highly entangled states of trapped ions, such as arbitrary Dicke states and superpositions of them, e.g. NOON states. The ions are initialized in the phonon ground state and are addressed globally with a composite pulse that is resonant with the first motional sideband. The technique is fairly robust to parameter fluctuations and operates on comparatively short time scales, as resonant interactions allow one to use the minimum laser pulse area. The number of single pulses from the composite sequence is equal to the number of ions; thus the implementation complexity grows only linearly with the size of the system. The approach does not require individual addressing of the ions in the trap and can be applied both inside and outside the Lamb–Dicke regime.
We propose an implementation scheme for holonomic, i.e., geometrical, quantum information processing based on semiconductor nanostructures. Our quantum hardware consists of coupled semiconductor macroatoms addressed/controlled by ultrafast multicolor laser-pulse sequences. More specifically, logical qubits are encoded in excitonic states with different spin polarizations and manipulated by adiabatic time control of the laser amplitudes. The two-qubit gate is realized in a geometric fashion by exploiting dipole-dipole coupling between excitons in neighboring quantum dots.
We study a 2-qubit spin model for the possibility of realizing an arbitrary geometric quantum phase gate in terms of a single coherent magnetic pulse with multi-harmonic frequency. Using resonant transition approximation, the time-dependent Hamiltonian of two coupled spins can be solved analytically. The time evolution of the wave function is obtained without adiabatic approximation. The parameters of magnetic pulse, such as the frequency, amplitude, phase of each harmonic part as well as the time duration of the pulse are determined for achieving an arbitrary non-adiabatic geometric phase gate. The requirement of materials for realizing such a gate is analyzed. As a result, the non-adiabatic geometric controlled phase gates and A–A phase are also addressed.