## RESEARCH

### Coherent Control, Information Processing, and Quantum/Classical Boundary

Coherent control is based on manipulation of quantum phases of wave functions. It is a basic scheme of controlling a variety of quantum systems from simple atoms to nanostructures with possible applications to novel quantum technologies such as bond-selective chemistry and quantum computation. Coherent control is thus currently one of the principal subjects of various fields of science and technology such as atomic and molecular physics, solid-state physics, quantum electronics, and information science and technology. We have developed high-precision wave-packet interferometry by stabilizing the relative quantum phase of two molecular wave packets on the attosecond time scale [1-5]. We have also succeeded in tailoring and visualizing spatiotemporal images of such wave-packet interference on the picometer and femtosecond scales as shown in Fig. 1 [1,6].

We are now tackling the following three projects by making use of these techniques.

- Ultrafast quantum simulator with an ultracold Rydberg gas
- Coherent control of bulk solids
- Information processing with molecular wave functions

Fig. 1. Actively tailored spatiotemporal images of quantum interference on the picometer and femtosecond scales. The relative phase of two vibrational wave-packets counterpropagating in the iodine molecule has been tuned to (a) 0, (b) 90, (c) 180, and (d) 270 degrees, respectively. Adopted from Ref. 1. |

### Ultrafast quantum simulator with an ultracold Rydberg gas

We are developing a new quantum simulator by applying our ultrafast coherent control technique to ultracold atoms trapped in an optical lattice. Our strategy is as follows: A short laser pulse excites Rb atoms in an optical lattice to Rydberg states. The spectrum of the pulsed laser is wide enough to cover several Rydberg states, so that a superposition state of them , i.e. a wave-packet (WP) is created. The spread and shape of WPs can be tuned by adjusting laser parameters such as wavelength and shape. Accordingly the interaction among neighboring sites can be controlled. This many-body interaction would manifest itself in the temporal evolution of those WPs.

We are now working on quantum interference of Rydberg WPs created in a magnet-optical trap and an optical dipole trap, and studying density dependence of many-body interaction arising from van der Waals interaction among WPs. In parallel with this, we have prepared an all-optically produced Bose-Einstein condensate (our first observation in 2015), observed a superfluid-Mott insulator transition in an optical lattice (our first observation in 2016), and generated a unit-filling Mott insulator (our first observation in 2016).

We have recently developed the prototype of the ultrafast quantum simulator, in which ultrafast many-body electron dynamics in a strongly correlated ultracold Rydberg gas, which is generated with an optical dipole trap, has been observed and controlled on the attosecond timescale by ultra-precise coherent control [7]. We have also developed a theoretical model which describes the many-body dynamics of the strongly correlated Rydberg gas in a dipole trap as well as in an optical lattice [8].

Fig. 2. Rydberg WPs spread over an optical lattice. Many-body interaction can be controlled by shaping WPs and adjusting the overlap among neighboring WPs. |

### Coherent control of bulk solids

For practical realization of a molecular computer and also exploring a mystery of quantum/classical boundary, we pursue the realization of coherent control of condensed matter systems. As long as coherent control is based on wave nature of matter, the quest to coherently control macroscopic objects would lead to verification of a mystery of wave/particle duality in the quantum world. By applying control schemes of quantum coherence, which could be obtained from our new quantum simulator, to real bulk solids, we are trying to realize coherent control of condensed matter systems. We already suceeded in optical manipulation of coherent phonons in superconducting YBa2Cu3O7-d thin films [9], and in optical engineering of quantum interference of delocalized wavefunctions in solid para-hydrogen as shown in Fig. 3 [10]. We have also succeeded in all optical control and visualization of ultrafast two-dimensional atomic motions in a single crystal of bismuth [11].

Fig. 3. Real-time observation of the actively controlled quantum interference of the vibron state delocalized in solid p-H_{2}. The delay t_{IRE} between the first and second laser pulse pairs is different by 4 fs between the red and blue traces [10]. |

### Information processing with molecular wave functions

Our high-precision spatiotemporal coherent-control is applied to information processing with molecular wave functions [12,13]. We succeeded in discrete Fourier transfomation with a single 0.3-nanometer-size molecule, and the execution time was about 150fs, which is 1000 times faster than the current fastest supercomputer [12]. To implement universal logic gates, we also demonstrated that a strong non-resonant fs laser pulse in the near-infrared region can modulate the population of each eigenstate within a molecular wave-packet (WP) [13]. This result has another interesting aspect. In quantum mechanics different eigenstates are orthogonal and do not interfere with each other, but we demonstrated that unusual interference among multiple quantum waves in different eigenstates is induced actively and controlled with a strong fs laser pulse. This new concept, which we refer to as "strong-laser-induced interference" is not specific to the molecular eigenstates, but universal to any type of eigenstates of a variety of quantum systems, being a new tool for quantum logic gates, and providing a new option to manipulate WPs with fs laser pulses in general applications of coherent control.

Fig. 4. Schematic of the strong-laser-induced interference. Starting from a common initial state, there are multiple quantum-mechanical pathways indicated by red, black, and blue lines, respectively, to the common final state. Those multiple pathways interfere quantum-mechanically with each other [13]. |

**References**

[1] H. Katsuki *et al.*, Phys. Rev. Lett., **102**, 103602 (2009).

[2] K. Ohmori, Annu. Rev. Phys. Chem. **60**, 487-511 (2009).

[3] H. Katsuki *et al.*, Phys. Rev. A **76**,013403 (2007).

[4] K. Ohmori *et al.*, Phys. Rev. Lett., **96**, 093002 (2006).

[5] K. Ohmori *et al.*, Phys. Rev. Lett., **91**, 243003 (2003).

[6] H. Katsuki *et al.*, Science **311**, 1589-1592 (2006).

[7] N. Takei, C. Sommer *et al.*, Nature Communications **7**, 13449 (2016).

[8] C. Sommer *et al.*, Phys. Rev. A **94**,053607 (2016).

[9] Y. Okano *et al.*, Faraday Discuss., **153**, 375-382 (2011).

[10] H. Katsuki *et al.*, Phys. Rev. B **88**,014507 (2013).

[11] H. Katsuki *et al*., Nature Communications **4**, 2801 (2013).

[12] K. Hosaka *et al.*, Phys. Rev. Lett., **104**, 180501 (2010).

[13] H. Goto * et al.*, Nature Physics **7**, 383-385 (2011).