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Physical Review Letters

Real-Time Observation of Phase-Controlled Molecular Wave-Packet Interference

Kenji Ohmori, Hiroyuki Katsuki, H. Chiba, Masahiro Honda, Yusuke Hagihara, Katsutoshi Fujiwara, Yukinori Sato, Kiyoshi Ueda

Published Mar 6, 2006• 98 citations
Publisher

Abstract

The quantum interference of two molecular wave packets has been precisely controlled in the B electronic state of the I2 molecule by using a pair of fs laser pulses whose relative phase is locked within the attosecond time scale and its real-time evolution has been observed by another fs laser pulse. It is clearly observed that the temporal evolution changes drastically as a function of the relative phase between the locked pulses, allowing us to read both amplitude and phase information stored in the wave functions of the molecular ensemble.

DOI
10.1103/physrevlett.96.093002

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The quantum interference of two molecular wave packets has been precisely controlled in the B electronic state of the I2 molecule by using a pair of fs laser pulses whose relative phase is locked within the attosecond time scale and its real-time evolution has been observed by another fs laser pulse. It is clearly observed that the temporal evolution changes drastically as a function of the relative phase between the locked pulses, allowing us to read both amplitude and phase information stored in the wave functions of the molecular ensemble.
The interference is an intrinsic feature of waves. In the quantum world, a variety of interferometric measurements of matter waves have so far been performed to demonstrate the wave-particle duality. In this short note, we review such quantum interferometric measurements of wave packets (WP's) in atoms and molecules such as Rydberg WP's in atoms and vibrational WP's in molecules. We also show the results of our recent WP interferometry with the iodine molecules, which have been performed by phase-locking a pair of femtosecond laser pulses on the attosecond time scale.
We demonstrate an experimental approach to read and write populations and relative phases of vibrational eigenstates within a wave packet created in the BBB state of the iodine molecule by using a pair of phase-locked femtosecond laser pulses. Our highly stabilized optical interferometer provides attosecond stability and resolution in the interpulse delay. The stability and resolution have realized an exquisite tuning of the interference of two vibrational wave packets to manipulate the relative populations and the relative quantum phases among the vibrational eigenstates within the wave packets. These populations and phases have been retrieved by measuring fluorescence from the upper EEE state induced by another nanosecond (ns) or femtosecond (fs) probe laser pulse. The bandwidth of the ns probe pulse is narrow enough to select only a small portion of the rotational progression of a particular vibrational band of the $E\ensuremath{-}B$ transition. By scanning the probe wavelength, we measure the population distribution of the vibrational eigenstates within the wave packet. The fs probe pulse is used to measure quantum beats arising from the temporal evolution of the wave packet. Combining these two complementary measurements, we can read both population and phase information written and stored in the wave packet.
Experimental and theoretical work is presented on the control of wave packet dynamics in atomic and molecular systems. Using sequences of phase-locked optical pulses, the link between optical phase and quantum mechanical phase is explored in the Na atom and Naj dimer, representing a step towards the logical engineering of quantum states in more complicated systems. A novel apparatus, constructed to study and control the vibrational dynamics of vibrational wave packets on the Na ionic potential surface, is described in chapter 3. Theoretical simulations for proposed experiment are presented in chapter 4. Control is achieved by exploiting the phase-evolution of the constituent vibrational quantum states within the wave packet superposition. The phase relationship and the accumulated phase difference between the various components of the wave packet is determined, and a sequence of phase-locked optical pulses is employed to selectively enhance or depopulate specific vibrational states, or sets of vibrational states. The quantum state composition of the resulting wave packet, and the efficiency of the control scheme, is determined by calculating the multi-pulse response of the time-dependent vibrational state populations. In chapter 5, the quantum interference between Rydberg electron wave packets in the Na atom is investigated using pairs of phase-locked wave packets, allowing manipulation of the total orbital angular momentum of Na Rydberg atoms. Initially the wave packet is composed of a superposition of s and d Rydberg series. Exploitation of the difference between the quantum defects of the two series allows specific angular momentum compositions within the resultant wave packet to be engineered. Experimentally, this final quantum state distribution is analysed in the frequency domain using state selective field ionisation, and in the time domain using the optical Ramsey method. The theoretical calculations show how the phase difference between pairs of optical pulses is linked to the corresponding Rydberg frequency spectrum, therefore enabling the control of the quantum state composition of the wave packets.
Coherent control is a technique to manipulate the amplitudes and phases of wave functions by exploiting the coherent property of light. It is of great importance for the development of quantum technologies including quantum information processing and chemical reaction control as well as for addressing fundamental problems in quantum mechanics such as the quantum–classical boundary. In this chapter, we describe the development and applications of coherent control based on wave-packet interferometry with attosecond precision, which has been made possible by tuning the delay between two laser pulses on the attosecond time scale. This technique has been applied to several different hierarchies from simple to complex quantum systems: (i) isolated iodine molecules in the gas phase, (ii) molecular crystals of para-hydrogen, and (iii) single crystals of bismuth. In system (i), we have controlled and visualized the interference of vibrational wave packets in the isolated iodine molecules, and that wave-packet interference has been utilized to develop a molecular computer, which executes ultrafast Fourier transform. In system (ii), we have manipulated vibrational wave-functions delocalized in a para-hydrogen crystal. The long coherence lifetime of para-hydrogen crystals is a promising resource to preserve quantum information in bulk solids. In system (iii), we have controlled the excitation ratio of two orthogonal coherent phonon modes, whose coherent superposition has allowed for active control of ultrafast two-dimensional atomic motions in a single crystal of bismuth. Those atomic motions have been visualized by density functional theory calculations. Finally, the coherent control of an ensemble of ultracold Rydberg atoms is briefly discussed as future perspectives for exploring the quantum–classical boundary.
The predissociation of a diatomic molecule after excitation by an ultrashort laser pulse leads to a succession of partial nuclear wave packets on the dissociative potential curve. Matter wave interferences result from their evolution. We show here theoretically how control pulses inducing Rabi oscillations on the electronic atomic part of the wave function can change totally the shape of the nuclear interference pattern. This is a consequence of the entanglement between the electronic and nuclear parts of the wave function. Application to information storage is finally discussed.
It is observed in a double-slit experiment by Tonomura and coworkers that single electrons recorded as dots on a detector screen build up to show an interference pattern, which is delocalized over the screen [1]. This observation indicates that a delocalized wave function of an isolated electron interacts with the screen, which is a bulk solid composed of many nuclei and electrons interacting with each other, and becomes localized in space. This change, referred to as “collapse” in quantum mechanics, is often accepted as a discontinuous event, but a basic question arises: when and how the delocalized wave function becomes localized? It could be hypothesized that the wave function is delocalized over many particles in the screen just after the arrival of an electron, and the interaction among those many particles promotes localization of this delocalized wave function continuously, but very fast as if it changed discontinuously. My dream is testing this hypothesis by observing the spatiotemporal evolution of a wave function delocalized over many particles interacting with each other. Having this dream in mind, we have developed an experimental toolbox in which ultrafast wave-packet interference in a molecule is visualized and controlled by tailored laser fields with precisions on the picometer spatial and attosecond temporal scales [2-5].