Resonant transfer of excitons and quantum computation

Abstract

Resonant energy transfer mechanisms have been observed in the sensitized luminescence of solids, in quantum dots and in molecular nanostructures, and they also play a central role in light harvesting processes in photosynthetic organisms. We demonstrate that such mechanisms, together with the exciton-exciton binding energy shift typical of these nanostructures, can be used to perform universal quantum logic. In particular, we show how to generate controlled exciton entanglement and identify two different regimes of quantum behaviour.PACS numbers: 03.67. Lx, 78.67.Hc, 73.20.Mf The Förster energy transfer was first studied in the context of the sensitized luminescence of solids [1,2], in which an excited sensitizer atom can transfer its excitation to a neighbouring acceptor atom, via an intermediate virtual photon. This mechanism is also responsible for photosynthetic energy processes in antenna complexes, biosystems (BSs) that harvest sunlight [3]. More recently, interest has focussed on such a transfer in quantum dot (QD) nanostructures [4] and within molecular systems (MSs) [5]. In this Letter we give a general scheme for quantum computation that can be implemented in different nanostructures (NSs) by exploiting the Förster and exciton-exciton interactions. Thus, methods for controlled generation of exciton entanglement that use both diagonal and off-diagonal interactions are given.Consider two coupled generic NSs (scalability will be addressed later). We assume that the excitations of each NS are charge neutral (i.e., of an excitonic nature) and that they can be produced by optical means [6]. We also assume that tunnelling processes between them may be neglected, but that there is a strong exciton-exciton electromagnetic coupling. Our two-level-qubit system is represented in each NS by a single low-lying exciton (qubit state |1 ) and the ground state (qubit state |0 ). Then the interaction Hamiltonian can be written in the computational basis ({|00 , |01 , |10 , |11 }, with the first digit referring to NS I and the second to NS II) as follows:where the diagonal interaction V XX is the direct Coulomb binding energy between the two excitons, one located on each NS, and the off-diagonal V F denotes the Coulomb exchange (Förster) interaction which induces the transfer of an exciton from one NS to the other. These are the only Coulomb interaction terms which act between the qubits. ω 0 denotes the ground state energy and we define ∆ 0 ≡ ω 1 − ω 2 as the difference between the exciton creation energy for NS I (ω 1 ) and that for NS II (ω 2 ).Energy contributions due to spin singlet-triplet splittings do not significantly affect the present gating scheme and such effects are dealt with elsewhere [7]. The eigenenergies and eigenstates of the interacting qubit system are E 00 = ω 0 , Single qubit operations can be achieved by inducing Rabi oscillations in the excitonic system (e.g., see Ref.[8]). The V XX and V F interactions lead to two regimes for achieving quantum entanglement. First, if the ratio V F /∆ 0 ≫ 1, t...

Temporal resources for global quantum computing architectures

“…The first column of Table III shows the general result associated to an arbitrary coupling intensity J F . The last column shows the result for J F = 1.5 THz ≈ 1 meV, which is a representative estimate for exchange interactions between quantum dots [23][24][25][26]. In this case, the parameters of "transport" g 1 and g 2 decrease by a factor of one half, expressing the fact that the Förster interaction is a more efficient interaction for energy transfer.…”

“…The latter equation is directly deduced from Table IV. Next, we compute the optimal additional time for general computational two-qubit gates for the case of a generic physical system where the qubits interact via the Förster coupling: J XY ≡ J F , J = 0 in Eq. (6) [23][24][25][26]. We do so for the model BM1.…”

“…The calculation for the models LM3 and BM2 remains an open question due to the fact that optimal simulation for three qubit quantum gates under Förster interaction is still, hitherto, an unsolved problem. The J F coupling appears in many different physical systems, ranging from nanostructures such as quantum dots and wells [23][24][25][26] through to biomolecular systems [27][28][29]. The first column of Table III shows the general result associated to an arbitrary coupling intensity J F .…”

Resonance Energy Transfer: Theoretical Foundations and Developing Applications

“…There is growing interest in a variety of schemes that are based on the transfer of excitation between adjacent quantum dots, [55][56][57][58][59][60][61][62][63][64] and are now being envisaged for performing quantum computation. Such proposals generally aim to exploit the discrete, size-tunable, and intense character of quantum dot exciton transitions, as well as the fact that these processes can be switched very rapidly using optical excitation.…”

Mechanistic principles and applications of resonance energy transfer

“…The phenomenon has an important function in the operation of organic light-emitting diodes (OLEDs) and luminescence detectors (10)(11)(12)(13)(14): in crystalline solids and glasses doped with transition metal ions, mechanisms based on RET are also engaged for laser frequency conversion (15)(16)(17)(18)(19). In the fields of optical communications and computation, a number of optical-switching and logicgate devices are founded on the same principle (20)(21)(22). In the realm of molecular biology, the determination of protein structures and the characterization of dynamical processes is furthered by studies of the transfer of energy between intrinsic or "tag" chromophores (23)(24)(25)(26)(27)(28); other ultra-sensitive molecular-imaging applications are again based on the same underlying principle (29)(30)(31).…”