Observation of Bloch Oscillations in Molecular Rotation

Topological Charges of Periodically Kicked Molecules

We show that the simplest of existing molecules-closed-shell diatomics not interacting with one another-host topological charges when driven by periodic far-off-resonant laser pulses. A periodically kicked molecular rotor can be mapped onto a "crystalline" lattice in angular momentum space. This allows us to define quasimomenta and the band structure in the Floquet representation, by analogy with the Bloch waves of solid-state physics. Applying laser pulses spaced by 1/3 of the molecular rotational period creates a lattice with three atoms per unit cell with staggered hopping. Within the synthetic dimension of the laser strength, we discover Dirac cones with topological charges. These Dirac cones, topologically protected by reflection and time-reversal symmetry, are reminiscent of (although not equivalent to) that seen in graphene. They-and the corresponding edge states-are broadly tunable by adjusting the laser strength and can be observed in present-day experiments by measuring molecular alignment and populations of rotational levels. This paves the way to study controllable topological physics in gas-phase experiments with small molecules as well as to classify dynamical molecular states by their topological invariants.

Realizing topological edge states with Rydberg-atom synthetic dimensions

A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold ⁸⁴Sr atom, we demonstrate a synthetic-dimension based on Rydberg levels coupled with millimeter waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian, a paradigmatic model of topological matter. Band structure is probed through optical excitation from the ground state to Rydberg levels, revealing symmetry-protected topological edge states at zero energy. Edge-state energies are robust to perturbations of tunneling-rates that preserve chiral symmetry, but can be shifted by the introduction of on-site potentials.

Synthetic dimensions, states of a system engineered to act as if they were a reconfigurable extra spatial dimension, have been demonstrated with different systems previously. Here the authors create a synthetic dimension using Rydberg atoms and configure it to support topological edge states.

Real-time observation of frequency Bloch oscillations with fibre loop modulation

Bloch oscillations (BOs) were initially predicted for electrons in a solid lattice to which a static electric field is applied. The observation of BOs in solids remains challenging due to the collision scattering and barrier tunnelling of electrons. Nevertheless, analogies of electron BOs for photons, acoustic phonons and cold atoms have been experimentally demonstrated in various lattice systems. Recently, BOs in the frequency dimension have been proposed and studied by using an optical micro-resonator, which provides a unique approach to controlling the light frequency. However, the finite resonator lifetime and intrinsic loss hinder the effect from being observed practically. Here, we experimentally demonstrate BOs in a synthetic frequency lattice by employing a fibre-loop circuit with detuned phase modulation. We show that a detuning between the modulation period and the fibre-loop roundtrip time acts as an effective vector potential and hence a constant effective force that can yield BOs in the modulation-induced frequency lattices. With a dispersive Fourier transformation, the pulse spectrum can be mapped into the time dimension, and its transient evolution can be precisely measured. This study offers a promising approach to realising BOs in synthetic dimensions and may find applications in frequency manipulations in optical fibre communication systems.

Topological Swing of Bloch Oscillations in Quantum Walks

We report new oscillations of wave packets in quantum walks subjected to electric fields, that decorate the usual Bloch-Zener oscillations of insulators. The number of turning points (or suboscillations) within one Bloch period of these oscillations is found to be governed by the winding of the quasienergy spectrum. Thus, this provides a new physical manifestation of a topological property of periodically driven systems that can be probed experimentally. Our model, based on an oriented scattering network, is readily implementable in photonic and cold atomic setups.

Direct imaging of direction-controlled molecular rotational wave packets created by a polarization-skewed double-pulse

High-precision, time-resolved Coulomb explosion imaging of rotational wave packets in nitrogen molecules created with a pair of time-delayed, polarization-skewed femtosecond laser pulses is presented, providing insight into the creation process and dynamics of direction-controlled wave packets. To initiate unidirectional rotation, the interval of the double-pulse was set so that the second, polarization-tilted pulse hit the molecules at the time when molecules were aligned or antialigned along the polarization vector of the first pulse. During the revival period of the rotational wave packet, pulse intervals around both the full and half revival times were used. The observed molecular wave packet movies clearly show the signatures of quantum rotation, such as angular localization (alignment), dispersion, and revival phenomena, during the unidirectional motion. The patterns are quite different depending on the pulse interval even when the angular distribution at the second pulse irradiation is similar. The observed interval-dependence of the dynamics was analyzed on the basis of the real-time images, with the aid of numerical simulations, and the creation process of the packets was discussed. We show that the observed image patterns can be essentially rationalized in terms of rotational period and alignment parameter. Because the double-pulse scheme is the most fundamental in the creation of direction-controlled rotational wave packets, this study will lead to more sophisticated control and characterization of directional molecular motions.

Probing Quantum Criticality and Symmetry Breaking at the Microscopic Level

We report on an experimental study of the Lipkin-Meshkov-Glick model of quantum spins interacting at infinite range in a transverse magnetic field, which exhibits a ferromagnetic phase transition in the thermodynamic limit. We use dysprosium atoms of electronic spin J=8, subjected to a quadratic Zeeman light shift, to simulate 2J=16 interacting spins 1/2. We probe the system microscopically using single magnetic sublevel resolution, giving access to the spin projection parity, which is the collective observable characterizing the underlying Z_{2} symmetry. We measure the thermodynamic properties and dynamical response of the system, and we study the quantum critical behavior around the transition point. In the ferromagnetic phase, we achieve coherent tunneling between symmetry-broken states, and we test the link between symmetry breaking and the appearance of a finite order parameter.

Experimental Evidence of Rainbow Trapping and Bloch Oscillations of Torsional Waves in Chirped Metallic Beams

The Bloch oscillations (BO) and the rainbow trapping (RT) are two apparently unrelated phenomena, the former arising in solid state physics and the latter in metamaterials. A Bloch oscillation, on the one hand, is a counter-intuitive effect in which electrons start to oscillate in a crystalline structure when a static electric field is applied. This effect has been observed not only in solid state physics but also in optical and acoustical structured systems since a static electric field can be mimicked by a chirped structure. The RT, on the other hand, is a phenomenon in which the speed of a wave packet is slowed down in a dielectric structure; different colors then arrive to different depths within the structure thus separating the colors also in time. Here we show experimentally the emergence of both phenomena studying the propagation of torsional waves in chirped metallic beams. Experiments are performed in three aluminum beams in which different structures were machined: one periodic and two chirped. For the smaller value of the chirping parameter the wave packets, with different central frequencies, are back-scattered at different positions inside the corrugated beam; the packets with higher central frequencies being the ones with larger penetration depths. This behavior represents the mechanical analogue of the rainbow trapping effect. This phenomenon is the precursor of the mechanical Bloch oscillations, which are here demonstrated for a larger value of the chirping parameter. It is observed that the oscillatory behavior observed at small values of the chirp parameter is rectified according to the penetration length of the wave packet.

Frequency diffraction management through arbitrary engineering of photonic band structures

It is of fundamental interest to control light diffraction in discrete optical systems. However, photon hopping in discrete systems is dominated by the nearest-neighbor coupling, limiting the realization of nonlocal diffraction phenomena. Here, we generalize the discrete diffraction from spatial to the frequency domain using optical phase modulators. By inducing long-rang couplings in the frequency lattice through periodic modulation signals, we find the lattice band structure can be artificially engineered, giving rise to the realization of arbitrary frequency diffraction. Particularly, we create linear, bilinear and semicircular band structures using sawtooth, triangular and semicircular modulation waveforms and realize the directional, bidirectional, omnidirectional frequency diffraction as well as the spectral "superlens". We also revisit frequency discrete Talbot effect and generalize the allowed incident period to arbitrary integers through band structure engineering. Moreover, as the frequency transition also carries a wave vector mismatch, an effective electric field will emerge, through which we can realize frequency Bloch oscillations that manifest the effects of arbitrary spectral routing and self-imaging. The study paves a promising way towards versatile spectrum management for both optical communications and signal processing.

Synthetic dimensions in ultracold polar molecules

Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic dimensions have been engineered in ongoing experiments with ultracold matter. We show that rotational states of ultracold molecules can be used as synthetic dimensions extending to many - potentially hundreds of - synthetic lattice sites. Microwaves coupling rotational states drive fully controllable synthetic inter-site tunnelings, enabling, for example, topological band structures. Interactions leads to even richer behavior: when molecules are frozen in a real space lattice with uniform synthetic tunnelings, dipole interactions cause the molecules to aggregate to a narrow strip in the synthetic direction beyond a critical interaction strength, resulting in a quantum string or a membrane, with an emergent condensate that lives on this string or membrane. All these phases can be detected using local measurements of rotational state populations.

Experimental Demonstration of Coherent Control in Quantum Chaotic Systems

We experimentally demonstrate coherent control of a quantum system, whose dynamics is chaotic in the classical limit. Interaction of diatomic molecules with a periodic sequence of ultrashort laser pulses leads to the dynamical localization of the molecular angular momentum, a characteristic feature of the chaotic quantum kicked rotor. By changing the phases of the rotational states in the initially prepared coherent wave packet, we control the rotational distribution of the final localized state and its total energy. We demonstrate the anticipated sensitivity of control to the exact parameters of the kicking field, as well as its disappearance in the classical regime of excitation.

Experimental Observation of Dynamical Localization in Laser-Kicked Molecular Rotors

The periodically kicked rotor is a paradigm system for studying quantum effects on classically chaotic dynamics. The wave function of the quantum rotor localizes in angular momentum space, similarly to Anderson localization of the electronic wave function in disordered solids. Here, we observe dynamical localization in a system of true quantum rotors by subjecting nitrogen molecules to periodic sequences of femtosecond pulses. Exponential distribution of the molecular angular momentum-the hallmark of dynamical localization-is measured directly by means of coherent Raman scattering. We demonstrate the suppressed rotational energy growth with the number of laser kicks and study the dependence of the localization length on the kick strength. Because of its quantum coherent nature, both timing and amplitude noise are shown to destroy the localization and revive the diffusive growth of energy.

Exciting Molecules Close to the Rotational Quantum Resonance: Anderson Wall and Rotational Bloch Oscillations

We describe a universal behavior of linear molecules excited by a periodic train of short laser pulses under conditions close to the quantum resonance. The quantum resonance effect causes an unlimited ballistic growth of the angular momentum. We show that a disturbance of the quantum resonance, either by the centrifugal distortion of the rotating molecules or a controlled detuning of the pulse train period from the so-called rotational revival time, eventually halts the growth by causing Anderson localization beyond a critical value of the angular momentum, the Anderson wall. Below the wall, the rotational excitation oscillates with the number of pulses due to a mechanism similar to Bloch oscillations in crystalline solids. We suggest optical experiments capable of observing the rotational Anderson wall and Bloch oscillations at near-ambient conditions with the help of existing laser technology.

Generating long sequences of high-intensity femtosecond pulses

We present an approach to creating pulse sequences extending beyond 150 ps in duration, comprised of 100 μJ femtosecond pulses. A quarter of the pulse train is produced by a high-resolution pulse shaper, which allows full controllability over the timing of each pulse. Two nested Michelson interferometers follow to quadruple the pulse number and the sequence duration. To boost the pulse energy, the long train is sent through a multipass Ti:sapphire amplifier, followed by an external compressor. A periodic sequence of 84 pulses of 120 fs width and an average pulse energy of 107 μJ, separated by 2 ps, is demonstrated as a proof of principle.