It is demonstrated that the effective scattering length can be highly manipulated via time-periodic driving of a short-range interparticle potential. By developing a Floquet-scattering theory we show that sharp Floquet resonances occur at which the effective interaction can be tuned to very large attractive or repulsive values. The resulting s-wave scattering length can be obtained in analytic form and the shape of these resonances is given by a simple formula describing how resonance position and width can be altered by the driving strength. Our approach allows the identification of the underlying physical mechanism of the scattering resonances as Floquet bound states with positive energies, which are dynamically created by the drive. This insight is valuable for a detailed analysis and uncovers a general resource for enhanced or reduced scattering in Floquet systems, as was recently confirmed experimentally.
It is demonstrated that the effective scattering length can be highly manipulated via time-periodic driving of a short-range interparticle potential. By developing a Floquet-scattering theory we show that sharp Floquet resonances occur at which the effective interaction can be tuned to very large attractive or repulsive values. The resulting s-wave scattering length can be obtained in analytic form and the shape of these resonances is given by a simple formula describing how resonance position and width can be altered by the driving strength. Our approach allows the identification of the underlying physical mechanism of the scattering resonances as Floquet bound states with positive energies, which are dynamically created by the drive. This insight is valuable for a detailed analysis and uncovers a general resource for enhanced or reduced scattering in Floquet systems, as was recently confirmed experimentally.
In this work we establish a general scattering theory for two-dimensional quantum systems with periodically modulated interactions. We show that scattering quantities, such as the scattering cross section, effective scattering length, and effective-range parameter, can be defined in a manner analogous to conventional scattering theory, even in the presence of modulation. Unlike systems with static interactions, the incident wave in our setup can be scattered inelastically into different Floquet channels, absorbing or emitting quanta from the modulation field. A family of Floquet resonances is identified, at which universal recurrence relations are derived for the Floquet scattering amplitudes. These relations are equivalent to a discrete Schr\"odinger equation describing a pointlike source trapped by an effective potential. The resonance mechanism is explained as the coincidence of the point source's energy with the bound states of the effective potential. We discuss the scattering properties both at and near the resonances, finding that the resonance width and the ratio of the inelastic to elastic cross sections can be effectively controlled through the modulation of the interaction. Our results provide a pathway to precisely manipulate many-body interactions in periodically driven quantum systems.
In systems of ultracold atoms, pairwise interactions are resonantly enhanced by the application of an oscillating magnetic field that is parallel to the spin-quantization axis of the atoms. The resonance occurs when the frequency of the applied field is precisely tuned near the transition frequency between the scattering atoms and a diatomic molecule. The resulting cross section can be made more than two orders of magnitude larger than the cross section in the absence of the oscillating field. The low momentum resonance properties have a universal description that is independent of the atomic species. To arrive at these conclusions, we first develop a formal extension of Floquet theory to describe scattering of atoms with time-periodic, short-range interaction potentials. We then calculate the atomic scattering properties by modeling the atomic interactions with a square well potential with oscillating depth and then explicitly solving the time-dependent Schrodinger equation. We then apply the Floquet formalism to the case of atoms scattering with a contact interaction described by a time-periodic scattering length, obtaining analytic results that agree with those obtained by solving the time-dependent Schrodinger equation.
Scattering resonances are fundamental to many areas of physics, occurring across a wide range of energy scales. In ultracold quantum gases, magnetic Feshbach resonances have transformed quantum many-body research by enabling precise interaction control between atoms. Here, we demonstrate unprecedented control to engineer Feshbach resonances at tunable positions via Floquet driving in a lithium-6 (^{6}Li) atom gas, achieved through strong magnetic field modulation at megacycles per second frequencies. This periodic modulation creates scattering resonances whenever dressed molecular levels cross the atomic threshold. By adding a second modulation at twice the base frequency, we tune the asymmetry of resonance loss profiles and suppress two-body losses from Floquet heating. This technique enhances control over atomic interactions, expanding possibilities for quantum simulations of complex systems and studies of exotic quantum phases.
We investigate the impurity problem of a highly polarized Fermi gas with periodically modulated atom-atom interactions. We find that generalized time-periodic Floquet polaron and molecule emerge as quasistationary quasiparticle states of the system, which exhibit peculiar features distinct from those in a static system. Even in the high-frequency limit, the periodic driving can renormalize the scattering length of the static (effective) Hamiltonian and thus modify the polaron-to-molecule transition. Remarkably, due to the folding of the quasienergy of the Floquet states in the Floquet Brillouin zone, unusual energy-level crossings beyond the conventional polaron-to-molecule transition occur. In particular, when the driving frequency is in resonance with the quasienergy difference, both branches of the Floquet polaron can intersect with the molecular state or even themselves under weak driving. The unique physics of these Floquet impurity states is further characterized and elucidated by the experimentally measurable spectral functions and the radio-frequency spectra. Our results pave a way to explore the intriguing nonequililbrium impurity physics beyond a static system via “Floquet engineering.”
Motivated by recent experimental implementations of artificial gauge fields for gases of cold atoms, we study the scattering properties of particles that are subjected to time-periodic Hamiltonians. Making use of Floquet theory, we focus on translationally invariant situations in which the single-particle dynamics can be described in terms of spatially extended Floquet-Bloch waves. We develop a general formalism for the scattering of these Floquet-Bloch waves. An important role is played by the conservation of Floquet quasienergy, which is defined only up to the addition of integer multiples of $\ensuremath{\hbar}\ensuremath{\omega}$ for a Hamiltonian with period $T=2\ensuremath{\pi}/\ensuremath{\omega}$. We discuss the consequences of this for the interpretation of ``elastic'' and ``inelastic'' scattering in cases of physical interest. We illustrate our general results with applications to the scattering of a single particle in a Floquet-Bloch state from a static potential and the scattering of two bosonic particles in Floquet-Bloch states through their interparticle interaction. We analyze examples of these scattering processes that are closely related to the schemes used to generate artificial gauge fields in cold-atom experiments, through optical dressing of internal states, or through time-periodic modulations of tight-binding lattices. We show that the effects of scattering cannot, in general, be understood by an effective time-independent Hamiltonian, even in the limit $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty}$ of rapid modulation. We discuss the relative sizes of the elastic scattering (required to stabilize many-body phases) and of the inelastic scattering (leading to deleterious heating effects). In particular, we describe how inelastic processes that can cause significant heating in the current experimental setup can be switched off by additional confinement of transverse motion.
We investigate the Floquet spectrum and excitation properties of a two-ultracold-atom system with periodically driven interaction in a three-dimensional harmonic trap. The interaction between the atoms is changed by varying the s-wave scattering length in two ways, the cosine and the square-wave modulations. It is found that as the driving frequency increases, the Floquet spectrum exhibits two main features for both modulations, the accumulating and the spreading of the quasienergy levels, which further lead to different dynamical behaviors. The accumulation is associated with collective excitations and the persistent growth of the energy, while the spread indicates that the energy is bounded at all times. The initial scattering length, the driving frequency and amplitude can all significantly change the Floquet spectrum as well as the dynamics. However, the corresponding relation between them is valid universally. Finally, we propose a mechanism for selectively exciting the system to one specific state by using the avoided crossing of two quasienergy levels, which could guide preparation of a desired state in experiments.