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Journal of Communications Technology and Electronics

A photon echo in a system of ensemble qubits that are selectively radiated by short laser pulses

O. N. Gadomskiĭ, Yu. Ya. Kharitonov

Published Jun 1, 2007• 0 citations
Publisher

Abstract

Equations of quantum computing in a system of two ensemble qubits are solved. The qubits are spherical nanoparticles activated by two-level atoms. It is proved that a photon echo may occur during quantum computations in an optical quantum computer when the ensemble qubits are selectively excited by short optical pulses. The photon echo phenomenon is caused by time reversal of oscillations of induced dipole moments of the qubits. It is shown that this effect can be observed in the case of interference of oscillating dipoles in the wave zone.

DOI
10.1134/s1064226907060101

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Equations of quantum computing in a system of two ensemble qubits are solved. The qubits are spherical nanoparticles activated by two-level atoms. It is proved that a photon echo may occur during quantum computations in an optical quantum computer when the ensemble qubits are selectively excited by short optical pulses. The photon echo phenomenon is caused by time reversal of oscillations of induced dipole moments of the qubits. It is shown that this effect can be observed in the case of interference of oscillating dipoles in the wave zone.
The operation principle of a quantum computer is proposed based on a system of dielectric nanoparticles activated with two-level atoms — cubits, in which electric dipole transitions are excited by short intense optical pulses. It is proved that the logical operation (logical operator) CNOT (controlled NOT) is performed by means of time-dependent transfer of quantum information over `long' (of the order of 10 4 nm) distances between spherical nanoparticles owing to the delayed interaction between them in the optical radiation field. It is shown that one-cubit and two-cubit logical operators required for quantum calculations can be realised by selectively exciting dielectric particles with short optical pulses.
The possibility of a class of optical echo-producing mechanisms is suggested that does not invoke the phase-reversal action of the second pulse. The mechanisms act selectively on the radiating atomic dipole moments, or on their radiation fields, with a periodic dependence on Δτ, where Δ is the angular frequency of the radiator relative to the central angular frequency of the distribution and τ the interpulse time. In the new formulation, the customary expression for the field radiated by an atomic dipole following a two-pulse excitation sequence is multiplied by a factor periodic in Δτ. It is shown that a sequence of echo pulses is predicted when the average over the radiators is calculated. One such mechanism is proposed: the selective absorption or amplification of the dephased free-induction decay field as they propagate through the sample.
The photon echo application for optical digital processing of discrete images by the method of managing operators was examined. Photon echo is the pulse of light which is emitted spontaneously from a system of atoms previously irradiated by two or more coherent light pulses with length and power of 102divided by10-1 ps and 104divided by105 kW, respectively. These systems of resonant atoms are crystals with various paramagnetic activators. By using photon echo, the resonant systems are able to store and retrieve wave-front and temporal form of one of the excitation pulses. The photon echo application for information processing allows one to solve a number of problems with high efficiency. Different photon echo generating conditions can be utilized practically in all processor components, which creates certain prospects for using this effect in optical computing purposes.
Photon echoes, observed recently in ruby and in NH2{\mathrm{NH}}_{2}NH2​D gas by two-pulse laser excitation, exhibit a modulation behavior as the pulse delay time is varied. The effect, which arises in a three-level quantum system, is due to the interference of two optically coupled transitions that share a common level. In this article, the three-level echo problem is treated exactly. Wave-function solutions are incorporated that are handled conveniently by a Laplace-transform technique. We, therefore, extend the earlier theory of echo modulation by Lambert et al., by removing their restriction of on-resonance pulse excitation. This procedure allows us to examine the effect of inhomogeneous broadening on echo amplitude explicitly, and we treat the problem by numerical and also by analytical means for the case of a Doppler-broadened gas. Analytic expressions are derived either for a high or a low laser power regime corresponding to excitation of either a large or a small fraction of the Doppler linewidth. The former case is analogous to pulsed nuclear magnetic resonance and is well known, whereas the latter result is new and applies to current photon echo measurements.