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The Journal of Chemical Physics

Coherent control of molecular alignment of homonuclear diatomic molecules by analytically designed laser pulses

Shiyang Zou, Cristina Sanz‐Sanz, Gabriel G. Balint‐Kurti

Published Sep 24, 2008• 10 citations

Abstract

We present an analytic scheme for designing laser pulses to manipulate the field-free molecular alignment of a homonuclear diatomic molecule. The scheme is based on the use of a generalized pulse-area theorem and makes use of pulses constructed around two-photon resonant frequencies. In the proposed scheme, the populations and relative phases of the rovibrational states of the molecule are independently controlled utilizing changes in the laser intensity and in the carrier-envelope phase difference, respectively. This allows us to create the correct coherent superposition of rovibrational states needed to achieve optimal molecular alignment. The validity and efficiency of the scheme are demonstrated by explicit application to the H(2) molecule. The analytically designed laser pulses are tested by exact numerical solutions of the time-dependent Schrodinger equation including laser-molecule interactions to all orders of the field strength. The design of a sequence of pulses to further enhance molecular alignment is also discussed and tested. It is found that the rotating wave approximation used in the analytic design of the laser pulses leads to small errors in the prediction of the relative phase of the rotational states. It is further shown how these errors may be easily corrected.

DOI: 10.1063/1.2976154

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We present an analytic scheme for designing laser pulses to manipulate the field-free molecular alignment of a homonuclear diatomic molecule. The scheme is based on the use of a generalized pulse-area theorem and makes use of pulses constructed around two-photon resonant frequencies. In the proposed scheme, the populations and relative phases of the rovibrational states of the molecule are independently controlled utilizing changes in the laser intensity and in the carrier-envelope phase difference, respectively. This allows us to create the correct coherent superposition of rovibrational states needed to achieve optimal molecular alignment. The validity and efficiency of the scheme are demonstrated by explicit application to the H(2) molecule. The analytically designed laser pulses are tested by exact numerical solutions of the time-dependent Schrodinger equation including laser-molecule interactions to all orders of the field strength. The design of a sequence of pulses to further enhance molecular alignment is also discussed and tested. It is found that the rotating wave approximation used in the analytic design of the laser pulses leads to small errors in the prediction of the relative phase of the rotational states. It is further shown how these errors may be easily corrected.

The lack of a direct map between control fields and desired control objectives poses a significant challenge in applying quantum control theory to quantum technologies. Here, we propose an analytical framework to precisely control a limited set of quantum states and construct desired coherent superpositions using a well-designed laser pulse sequence with optimal amplitudes, phases, and delays. This theoretical framework that corresponds to a multilevel pulse-area theorem establishes a straightforward mapping between the control parameters of the pulse sequence and the amplitudes and phases of rotational states within a specific subspace. As an example, we utilize this approach to generate 15 distinct and desired rotational superpositions of ultracold polar molecules, leading to 15 desired field-free molecular orientations. By optimizing the superposition of the lowest 16 rotational states, we demonstrate that this approach can achieve a maximum orientation value of | 〈 cos θ 〉 | max above 0.99, which is very close to the global optimal value of 1 that could be achieved in an infinite-dimensional state space. This work marks a significant advancement in achieving precise control over multilevel subsystems within molecules. It holds potential applications in molecular alignment and orientation, as well as in various interdisciplinary fields related to the precise quantum control of ultracold polar molecules, opening up considerable opportunities in molecular-based quantum techniques.

Optimal field-free molecular orientation for a given number of populated states, achieved by using resonant laser pulses, is theoretically investigated for linear molecules. An optimal phase difference between the rotational states can be obtained, at full revival times, after the laser pulses have decayed and these phase conditions are analytically derived for multilevel systems (

J>2

). The dependence of the phase difference on the duration and absolute area of the laser pulses is analyzed. Finally, the optimal degree of molecular orientation can be obtained by adjusting the ratios of the peak amplitudes of the laser pulses, with the carrier-envelope phases or the delay time between the pulses fulfilling the phase conditions.

We explore the possibility of using shaped infrared laser pulses to deexcite a homonuclear diatomic molecule from its highest vibrational state down to its ground vibrational state. The motivation for this study arises from the need to deexcite alkali metal dimers in a similar way so as to stabilize molecular Bose-Einstein condensates. We demonstrate that for the case of the H(2) molecule, where it is possible to evaluate all the necessary high accuracy ab initio data on the interaction of the molecule with an electric field, we are able to successfully design a sequence of infrared laser pulses to accomplish the desired deexcitation process in a highly efficient manner.

We theoretically study the control of two-photon excitation to bound and dissociative states in a molecule induced by trains of laser pulses, which are equivalent to certain sets of spectral phase modulated pulses. To this end, we solve the time-dependent Schr\"odinger equation for the interaction of molecular model systems with an external intense laser field. Our numerical results for the temporal evolution of the population in the excited states show that, in the case of an excited dissociative state, control schemes, previously validated for the atomic case, fail due to the coupling of electronic and nuclear motion. In contrast, for excitation to bound states the two-photon excitation probability is controlled via the time delay and the carrier-envelope phase difference between two consecutive pulses in the train.

We propose a scheme to coherently control the field-free orientation of NO molecule whose rotational temperature is above 0 K. It is found that the maximum molecular orientation is affected by two factors: one is the sum of the population of M = 0 rotational states and the other is their distribution, however, their distribution plays a much more significant role in molecular orientation than the sum of their population. By adopting a series of linearly polarized pulses resonant with the rotational states, the distribution of M = 0 rotational states is well rearranged. Though the number of pulses used is small, a relatively high orientation degree can be obtained. This scheme provides a promising approach to the achievement of a good orientation effect.

We have numerically examined optimization of the experimentally achievable shapes of mid-infrared femtosecond laser pulses to construct elementary quantum gates using molecular rovibrational states of a single molecule. Instead of optimizing the electric field by optimal control theory, the method generally used in theoretical studies of coherent control, the transmittance and the phase shift of conventional pulse shapers were optimized in the frequency domain by a genetic algorithm. The target molecular system we examined was the rotation-vibration states of CO in the $X({^{1}\ensuremath{\Sigma}}^{+})$ ground electronic state. Although the existence of the rotational degrees of freedom makes the quantum gate operation complicated, high fidelity of over 0.95 was achieved for one-rovibrational-qubit systems, which indicates that a molecular quantum computer may be feasible for at least one-qubit calculations on a diatomic molecule. On the other hand, two-qubit calculations are more difficult to achieve in a single CO molecule using rotational and vibrational degrees of freedom as different qubits. The importance of the control of the rotational in addition to the vibrational wave packet in order to realize a molecular quantum computer is discussed.