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arXiv:quant-ph/0108061 · Physical Review Letters

Laser Phase Modulation Approaches towards Ensemble Quantum Computing

Debabrata Goswami

Published Apr 15, 2002• 25 citations
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Abstract

Selective control of decoherence is demonstrated for a multilevel system by generalizing the instantaneous phase of any chirped pulse as individual terms of a Taylor series expansion. In the case of a simple two-level system, all odd terms in the series lead to population inversion, while the even terms lead to self-induced transparency. These results also hold for multiphoton transitions that do not have any lower-order photon resonance or any intermediate virtual state dynamics within the laser pulse width. Such results form the basis of a robustly implementable CNOT gate.

DOI
10.1103/physrevlett.88.177901

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Selective control of decoherence is demonstrated for a multilevel system by generalizing the instantaneous phase of any chirped pulse as individual terms of a Taylor series expansion. In the case of a simple two-level system, all odd terms in the series lead to population inversion, while the even terms lead to self-induced transparency. These results also hold for multiphoton transitions that do not have any lower-order photon resonance or any intermediate virtual state dynamics within the laser pulse width. Such results form the basis of a robustly implementable CNOT gate.
Control of multiphoton transitions is demonstrated for a multilevel system by generalizing the instantaneous phase of any chirped pulse as individual terms of a Taylor series expansion. In the case of a simple two-level system, all odd terms in the series lead to population inversion while the even terms lead to self-induced transparency. The results hold for multiphoton transitions that do not have any lower-order photon resonance or any intermediate virtual state dynamics within the laser pulse width.
Selective control of decoherence is demonstrated for a multilevel system by generalizing the instantaneous phase of any chirped pulse as individual terms of a Taylor series expansion. In the case of a simple two-level system, all odd terms in the series lead to population inversion while the even terms lead to self-induced transparency. These results also hold for multiphoton transitions that do not have any lower-order photon resonance or any intermediate virtual state dynamics within the laser pulse-width. Typeset using REVTEX 1 Minimizing decoherence is an important challenge towards the realization of quantum computing. Nuclear Magnetic Resonance (NMR) spectroscopy of molecules in liquid phase has become an important approach to quantum computing due to their long decoherence times [1]. But it suffers in terms of scalability to larger number of qubits [2], therefore, alternative approaches are being sought [3]. Optical spectroscopy of molecules and nanoparticles could potentially become a highly scalable approach, but for the intramolecular relaxation
A robust implementation of quantum logical gates for a multilevel system is possible through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. Selective population inversion and Hamiltonian evolution with time through ultrafast pulse shaping techniques essentially amount to adiabatic quantum computing (AQC) instead of the standard unitary transformation. An important aspect of the AQC model is in addressing the atomic or molecular ensemble and hence in robust implementation. We argue that experimental demonstrations of selective population transfer through adiabatic rapid passage form useful adiabatic quantum computing logic. Similarly, a simple Hadamard operation can be demonstrated with phase-modulated laser pulses. Finally, we present a framework to efficiently solve approximate Euclidean Traveling Salesman Problem (Approx-TSP) with bounded error in the AQC model. We present an efficient and intuitive encoding for Approx-TSP in a quantum computing paradigm. Optical approaches to quantum computing have the potential to be used in a distributive sense to defray the present caveat of limited resources and scalability. We present how we make use of such schemes towards practicality issues in AQC. As far as we know, our results are the first realistic demonstration of the possibility of using ensemble states for AQC in multilevel systems.
A selective excitation technique based on light interference is proposed to control quantum systems by frequency-chirped laser fields. Interference of two identical, delayed and phase-shifted pulses is used to modulate the laser spectrum and project it onto the time domain. By adjusting the delay and phase shift, selected transitions can be brought into the ``holes'' of the spectrum and thus remain nonexcited. The possibility to selectively manipulate or even ``shut down'' resonant transitions, making the medium transparent to the field, is shown for the Rb atom.
A chirped laser pulse transfers population from one level to another level accessible by one photon dipole transition. We have used a pair of phase-locked chirped pulses of same frequency instead of a single chirped pulse to achieve phase control over the population transfer and thus creating coherent population distribution in hydrogen molecule. Simultaneous actions of the phase controlled interference and rapid adiabatic passages due to chirped pulses lead to the control in population transfer from the ground X(v = 0, j = 0) level to the C(v = 2, j = 1) level. We have extended this two-level system to a three-level 1 + 1 ladder system for population transfer from the X level to the J(v = 2, j = 2) level via the C intermediate level using two pairs of phase-locked laser chirped pulses and have achieved laudable control over the coherent population distribution.