Foundations of Physics

, Volume 44, Issue 8, pp 813–818 | Cite as

Optically Engineered Quantum States in Ultrafast and Ultracold Systems

Article

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.

Figure 1 shows the spatiotemporal image of the interference of two vibrational wave-packets in the gas-phase iodine molecule that we have visualized [9]. The image has picometer and femtosecond spatiotemporal resolution. It is predicted theoretically that such an interferometric image could be actively designed by tuning the relative phase of two wave packets generated by a pair of phase-locked laser pulses [10]. We have developed an optical interferometer, referred to as an “attosecond phase modulator (APM)”, that produces a pair of two femtosecond laser pulses whose interpulse delay is tuned and stabilized on the attosecond timescale [10, 11, 12]. This APM has allowed us to actively design the spatiotemporal image of the wave-packet interference in the iodine molecule by tuning the relative phase of the two laser pulses at \({\sim }594\,\mathrm{nm}\) in steps of 90\(^{\circ }\) [10]. Those actively tailored spatiotemporal images are shown in Fig. 2.
Fig. 1

Spatiotemporal images of the interference of vibrational wave-packets in the iodine molecule visualized experimentally (left column) and the theoretical simulations of the experimental signal (middle column) and the wave packets (right column). \(\lambda _\mathrm{{pr}}\) and \({r}\) denote the wavelength of the probe pulse and the internuclear distance, respectively. From Ref [9]. Reprinted with permission from AAAS

Fig. 2

Spatiotemporal images of the wave-packet interference measured (left) and simulated (right) with the relative phases of the two laser pulses to be a 0\(^{\circ }\), b 90\(^{\circ }\), c 180\(^{\circ }\), and d 270\(^{\circ }\). The color scaling is common within each set of measured or simulated images; the maxima of those two sets have the same color. From Ref [10]. Reprinted with permission from APS (Color figure online)

This high-precision wave-packet interferometry has been utilized to implement ultrafast computing with a molecular wave-packet that executes discrete Fourier transform in 145 fs, which is shorter than the typical clock period of the current fastest Si-based computers by three orders of magnitude [13].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.
Fig. 3

Schematic of the ultrafast Fourier transform. The common transform matrices could be operated for any arbitrary inputs and outputs, respectively, by the indicated hardware. From Ref [13]. Reprinted with permission from APS

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

We have so far applied our coherent control to bulk solids such as \(\mathrm{YBa_{2}Cu_{3}O_{7-\delta }}\), solid para-hydrogen, and bismuth to investigate nuclear coherence delocalized in those crystals [14, 15, 16]. We also employ an ensemble of ultracold Rb atoms as a model system to mimic a bulk solid. The model system offers longer coherence lifetime and more tunable parameters such as interatomic distance and interactions than a bulk solid. Since the interatomic distance is not shorter than submicrometers in this model system, longer than that of a bulk solid by more than three orders of magnitude, we generate Rydberg electronic wave-packets in those Rb atoms to induce interatomic interactions. Moreover these interactions can be actively tuned by changing the principal quantum numbers of Rydberg levels to be excited; the higher quantum numbers give larger diameters of Rydberg orbitals and hence stronger interactions. Briefly, a picosecond laser pulse produces Rydberg electronic wave-packets in laser-cooled Rb atoms in an optical dipole trap. We measure the temporal evolution of those Rydberg wave-packets. We also measure the interferogram of two Rydberg wave-packets generated in each atom with a phased pair of picosecond laser pulses, whose delay is scanned in steps of attoseconds by APM. Those temporal evolutions and interferograms of Rydberg wave-packets are measured as a function of the atom density, which can be converted to an atom-atom distance. We have observed that the interferogram is phase-shifted when we change the atom density. This observation suggests that the interatomic interactions have been induced by Rydberg wave-packets in Rb atoms. We plan to load these ultracold Rydberg atoms into an optical lattice to have better-defined interatomic configurations, as shown in Fig. 4. Our ultrafast coherent control of an ultracold Rydberg gas could lead to the development of a novel simulator of quantum many-body dynamics.
Fig. 4

Schematic of the Rydberg induced many-body interaction among ultracold Rb atoms in an optical lattice

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. 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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute for Molecular ScienceNational Institutes of Natural SciencesOkazakiJapan

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