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Control of Decoherence with Simple Chirped Pulses

Debabrata Goswami

Published Aug 13, 2001• 0 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. 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

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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. 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
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.
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.
Recently, the advances in generation and characterization techniques of ultrashort laser pulses made it practical to prepare precisely defined laser pulses, these open up new possibilities for studying and controlling dynamical processes in femtosecond time scale. Hitherto, frequency-synthesized or chirped laser pulses have been widely applied to high-order harmonic generation (HHG) [3], population transfer [4], multiphoton transitions between Rydberg states [5], ect. Both the interference of two-color pulses and the nontrivial time dependence of chirped pulse laser field may lead to very interesting results. Moreover, recent studies have manifested that chirping can also have much impacts on the laser pulses as it propagates through different medium. For example, the propagation properties of chirped soliton pulses in optical nonlinear Kenmedia were investigated by Desaix et al. [6]. The result indicates that the properties of asymptotically emerging solitons depend not only on the magnitude, but also on the form of the initial chirp. In particular, the splitting of an initial pulse into separating soliton pulse pairs only occurs for certain classes of initial chirp functions. The influence of pulse shape and frequency chirp on stability of optical solitons was studied by Klaus and Shaw [7]. They found that destabilization occurs when eigenvalues of an associated Zakharov-Shabat system, which move along the positive imaginary axis with increasing chirp parameter, either are absorbed into the lower half plane or collide with a nother eigenvalue. Furthermore, the signal and group velocities for chirped pulses propagating through a GaAs cavity were measured by Centini et al. [8]. They showed that the chirp substantially modifies the group velocity of the pulse, but leaves the signal velocity unaltered.
We discuss a novel method to create maximum coherence in a two-level system that is selectively excited among many having similar frequencies by making use of two specifically chirped pulses in the Raman configuration. The feasibility of the method is analyzed in the presence of decoherence caused by vibrational energy relaxation and collisional dephasing. It has been demonstrated that a high value of coherence may be sustained by the implementation of two chirped pulse trains prepared in accordance with the proposed method and having the same period as the vibrational energy relaxation time. Maximum coherence between predetermined states in atoms and molecules is an important aspect of many problems in quantum optics. One possible example is the generation of optimal CARS signal in the CARS microscopy aiming to reveal structures constituted of particular molecular groups. Presently, in experiments on biological imaging, the CARS signal is generated with implementation of picosecond laser pulses (1), a narrow spectral bandwidth of which allows one to address a particular molecular group with a good accuracy. Aiming to improve chemical sensitivity and to get optimal CARS signal for given pulse intensity we propose to use the quantum control methods for selective excitation of required vibrations in complex molecular systems. We developed a novel method that allows one to achieve maximum coherence in a predetermined vibrational mode in a multimode mole- cular system via the Raman transitions induced by the pump and Stokes chirped pulses. According to the Maxwell-Bloch equations, maximum coherence is the condition for the CARS signal to acquire the highest intensity upon propagation through a molecular medium (2). The mechanism of creation of maximum coherence underlying the proposed method is based on the adiabatic passage. An important aspect in the investigations asso- ciated with a condense phase is decoherence. Two main sources of decoherence, the vibrational energy relaxa- tion and collisional dephasing, may significantly affect the CARS signal intensity. The phase control of molecular processes in the presence of collisions was