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Physical Review A

Quantum control of ground-state rotational coherence in a linear molecule

E. Hertz, O. Faucher, B. Lavorel, F. Dalla Via, R. Chaux

Published Feb 17, 2000• 26 citations
Publisher

Abstract

We present an experimental and theoretical investigation of the quantum control of ground-state rotational coherence in a linear molecule. A sequence of two temporally separated laser pulses creates a rotational superposition state in ${\mathrm{CO}}_{2}$ whose evolution is monitored through a polarization technique. We study the influence of the phase difference between the two pulses. We show that the overlapping of the two wave packets, produced by each pulse, gives rise to quantum interference that affects the orientational anisotropy of the sample. Because of the large number of coherently excited levels, the interference produces well-separated temporal structures, whose magnitude can be controlled through the relative delay of the two pulses.

DOI
10.1103/physreva.61.033816

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We present an experimental and theoretical investigation of the quantum control of ground-state rotational coherence in a linear molecule. A sequence of two temporally separated laser pulses creates a rotational superposition state in CO2{\mathrm{CO}}_{2}CO2​ whose evolution is monitored through a polarization technique. We study the influence of the phase difference between the two pulses. We show that the overlapping of the two wave packets, produced by each pulse, gives rise to quantum interference that affects the orientational anisotropy of the sample. Because of the large number of coherently excited levels, the interference produces well-separated temporal structures, whose magnitude can be controlled through the relative delay of the two pulses.
Quantum control over molecular alignment rephasing is experimentally investigated in gaseous CO2. The control process is achieved by illuminating the medium with a pair of pump-pulses separated in time by approximately an integer value of T0=1/8B0, where B0 is the rotational constant. Through a Raman-type process, each pulse alone produces rotational coherence leading to a periodic orientational anisotropy. It is the combination of the two pulses that yields to quantum interference, resulting in a modification of this anisotropy probed by a third delayed pulse. The effect is accurately analyzed for different time delays between the two pulses. A theoretical analysis supplies a clear understanding of the role played by the different rotational motions involved in the overall process. The relative orientation of the electric field vector for the two pulses is discussed in terms of an additional control parameter.
We present an analysis of two experimental approaches to controlling the directionality of molecular rotation with ultrashort laser pulses. The two methods are based on the molecular interaction with either a pair of pulses (a ``double-kick'' scheme) or a longer pulse sequence (a ``chiral-pulse-train'' scheme). In both cases, rotational control is achieved by varying the polarization of and the time delay between the consecutive laser pulses. Using the technique of polarization-sensitive resonance-enhanced multiphoton ionization, we show that both methods produce significant rotational directionality. We demonstrate that increasing the number of excitation pulses supplements the ability to control the sense of molecular rotation with quantum-state selectivity, i.e., predominant excitation of a single rotational state. We also demonstrate the ability of both techniques to generate counterrotation of molecular nuclear-spin isomers (here, ortho- and para-nitrogen) and molecular isotopologs (here, 14{}^{14}14N2{}_{2}2​ and 15{}^{15}15N2{}_{2}2​).
Multiphoton orientational wave packets induced by short resonant polarized laser pulses in a rotationally-frozen interacting molecule contain relevant information. The entanglement of the orbital, rotational and orientational degrees of freedom shows a strong dependence on the polarization state of the absorbed photons and the space orientation of the interacting molecule and enables one to assign the orbital state of the excited molecular electron, to measure the space orientation of the interacting molecule from the orientational recurrences, to relate the measured temporal widths to the angular momentum photon state and the coherence of the laser pulse, to obtain information on the ground rotational state, or to measure the effective temperature of an isotropic molecular assembly. The space orientation of a small number of independent molecules can be distinguished from their distinct orientational dependence in the formation of the individual orientational wave packets.
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.
The transfer of the intrinsic coherence of short pulses to molecular systems is investigated and an explicit derivation of the excitation probability of the ultrafast multiphoton process is presented. We show that for ultrafast excitation the angular cross section splits into two distinct factors: the ``frozen orientation weight,'' which involves the space configuration and nonlinear dependence, and the ``laser-induced coherence,'' which reflects the coherent superposition of the ground- and excited-state orientations. Quantum interferences give rise to a ``coherent polarizability'' and provide evidence for a sharp confinement of the excited electron motion. The confinement is inversely proportional to the number of coherently excited rotational states.