Engineering Arbitrary Hamiltonians in Phase Space.

We introduce a general method to engineer arbitrary Hamiltonians in the Floquet phase space of a periodically driven oscillator, based on the noncommutative Fourier transformation technique. We establish the relationship between an arbitrary target Floquet Hamiltonian in phase space and the periodic driving potential in real space. We obtain analytical expressions for the driving potentials in real space that can generate novel Hamiltonians in phase space, e.

Topological phonon transport in an optomechanical system.

Light is a powerful tool for controlling mechanical motion, as shown by numerous applications in the field of cavity optomechanics. Recently, small scale optomechanical circuits, connecting a few optical and mechanical modes, have been demonstrated in an ongoing push towards multi-mode on-chip optomechanical systems. An ambitious goal driving this trend is to produce topologically protected phonon transport.

Pseudomagnetic fields for sound at the nanoscale.

There is a growing effort in creating chiral transport of sound waves. However, most approaches so far have been confined to the macroscopic scale. Here, we propose an approach suitable to the nanoscale that is based on pseudomagnetic fields.

Topological phase transitions and chiral inelastic transport induced by the squeezing of light.

There is enormous interest in engineering topological photonic systems. Despite intense activity, most works on topological photonic states (and more generally bosonic states) amount in the end to replicating a well-known fermionic single-particle Hamiltonian. Here we show how the squeezing of light can lead to the formation of qualitatively new kinds of topological states.

Photon-assisted confinement-induced resonances for ultracold atoms.

We solve the two-particle s-wave scattering for an ultracold-atom gas confined in a quasi-one-dimensional trapping potential which is periodically modulated. The interaction between the atoms is included via Fermi's pseudopotential. For a modulated isotropic transverse harmonic confinement, the atomic center of mass and relative degrees of freedom decouple and an exact solution is possible.