# Optically Engineered Quantum States in Ultrafast and Ultracold Systems

## Abstract

This short account summarizes our recent achievements in ultrafast coherent control of isolated molecules in the gas phase, and its ongoing applications to an ensemble of ultracold Rydberg atoms to explore quantum many-body dynamics.

### Keywords

Quantum-classical boundary Wavefunction Laser Wave packet Interferometry Coherent control Femtosecond Attosecond Ultrafast Quantum simulator Molecular computer Fourier transform## 1 Introduction

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, 2]. 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. A basic question arises, however, when and how the delocalized wave becomes localized. It could be hypothesized that a wavefunction 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. We wish to test this hypothesis by observing the spatiotemporal evolution of a wave function delocalized over many particles interacting with each other, envisaging the quantum-classical boundary connected smoothly.

We employ two different systems as these many-particle systems: one is a bulk solid, and the other is an ensemble of ultracold Rydberg atoms. The ensemble of Rydberg atoms serves as a model system of a bulk solid to offer longer coherence lifetime and a higher controllability than a bulk solid. The long-range dipole interactions among many Rydberg atoms are expected to produce a band structure whose electronic wave functions are delocalized over the ensemble [3, 4]. We anticipate that the spatiotemporal evolution of those delocalized electronic wave functions could simulate the collapse of the electronic wave function in a bulk solid.

## 2 Ultrahigh-Precision Wave-Packet Interferometry

Coherent control is a technique that uses coherent light to manipulate matter-wave interference [5, 6, 7, 8]. We have developed coherent control of gas-phase molecules with attosecond precision [8], which could also be useful for the observation of ultrafast evolution of many-body wave functions in condensed phases.

^{1}Schematic of this ultrafast Fourier transform is shown in Fig. 3, in which a molecular input is encoded into complex coefficients of four vibrational eigenstates of an isolated iodine molecule with a shaped femtosecond laser pulse. This molecular input evolves temporally for 145 fs to give a molecular output retrieved by our high-precision wave-packet interferometry.

This ultra-precise coherent control we have thus developed with gas-phase molecules is now being applied to many-body systems to explore the quantum-classical boundary.

## 3 Exploring Quantum Many-Body Dynamics

Two phase-locked laser pulses in such wave-packet interferometry of an ultra-cold Rydberg gas could be spatially displaced to observe spatiotemporal evolutions of the electronic wave functions delocalized over many Rb atoms; the visibility of the interferogram is expected to develop as the wave function produced by the first excitation becomes delocalized to be spatially overlapped with the second excitation. The coherence of this delocalized wave function could be actively disturbed by an external field. We have established a method to disturb vibrational coherence in an isolated molecule with a strong non-resonant femtosecond laser pulse [17]. A similar method could be combined with our ultrahigh-precision interferometry applied to an ultracold Rydberg gas to mimic the localization of a delocalized wave function in a detector screen in the double-slit experiment [1, 2].

## Footnotes

- 1.
The maximum clock rate of IBM Power 6 is 5.0 GHz, giving its clock period to be 200 ps.

## Notes

### Acknowledgments

The author acknowledges Professor Nobuyuki Takei (IMS) and Professor Christian Sommer (IMS) for the measurements with ultracold Rb atoms. These works have been supported by Grant-in-Aid for Scientific Research by JSPS, CREST by JST, and Photon-Frontier-Consortium Project by MEXT of Japan.

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