We report on the experimental realization of a Kapitza trap for ultracold atoms. Using time-periodic attractive and repulsive Gaussian potentials, we create an effective trap for ultracold neutral atoms in a regime where the time average of the potential is equal to zero. We analyze the role of experimental imperfections, the stability of the trapped atomic cloud, and the magnitude of the effective potential. We find good agreement with the high-frequency expansion of the underlying system dynamics. Our experimental approach opens up new possibilities to study Floquet systems of neutral atoms.
We report on the experimental realization of a Kapitza trap for ultracold atoms. Using time-periodic attractive and repulsive Gaussian potentials, we create an effective trap for ultracold neutral atoms in a regime where the time average of the potential is equal to zero. We analyze the role of experimental imperfections, the stability of the trapped atomic cloud, and the magnitude of the effective potential. We find good agreement with the high-frequency expansion of the underlying system dynamics. Our experimental approach opens up new possibilities to study Floquet systems of neutral atoms.
Kapitza’s pendulum is an inverted pendulum that is dynamically stabilized by rapidly driving its pivot point. Many applications of Kapitza stabilization in quantum systems have been proposed, such as optical molasses, the stability of optical resonators, preparation of molecular ions, the breaking of translation symmetry, the periodically driven sine-Gordon model, polariton Rabi oscillation, and the stabilization of bright solitons in a Bose-Einstein condensate. In particular, Kapitza stabilization can be used to trap particles. The most notable example of such an application is the Paul trap. Recently, the Kapitza trap was created by superimposing time-tuned focused laser beams to produce a periodically driven harmonic potential for ultracold atomic gases. This work opens up new possibilities to study Floquet systems of ultracold atomic gases. So we consider the periodically driven harmonic potential, and investigate the properties of soliton in ultracold atomic gases by numerical simulations. It is found interestingly that when a soliton is located at the center of the harmonic potential, a resonance phenomenon of soliton amplitude oscillation occurs at a specific driven frequency. In addition, the oscillation amplitude increases with the increase of the trapping frequency of the harmonic potential, and the resonance frequency increases with theaugment of soliton initial amplitude. The change of driven frequency and initial phase has a significant effect on soliton motion when the soliton is located at the edge of the harmonic potential. When the initial phase is zero, there is a characteristic driven frequency. For the case where the driven frequency is equal to the characteristic frequency, soliton motion exhibits periodic oscillations. For the case where the driven frequency is slightly lower than the characteristic frequency, the resonance of soliton oscillation can be found. When the driven frequency is slightly higher than the characteristic frequency, the anti-resonance of soliton oscillation can be found. In addition, it is found that the characteristic driven frequency increases linearly with the increase of the trapping frequency of the harmonic potential. When the initial phase is not equal to zero, the irregular oscillation, quasi-periodic oscillation, and periodic oscillation can be observed with the increase of driven frequency. When the driven frequency is equal to a specific value, the resonance of soliton oscillation can also obtained. Furthermore, the fast driving has no effect on the motion trajectory of solitons. These results can help to precisely control ultracold atomic gases.
Bose-Einstein condensation (BEC) and superfluidity are both remarkable manifestations of quantum mechanics on a macroscopic scale and have opened up the exploration of quantum phenomena in a qualitatively novel regime. The effort to realise BEC in dilute atomic gases, culminating in 1995, brought with it a powerful new set of ways to control and manipulate atoms and opened up a host of new scientific goals including quantum control, precision measurement, the study of phase transitions and the study of superfluidity – a peculiar phase of matter which is characterised by the absence of dissipation. In the 1940s, the Soviet physicist Lev Landau provided a qualitative theory for these dissipationless “super”fluids by providing an explanation of the critical velocity, below which the formation of fluid excitations is forbidden by the conservation of energy and momentum. This theory has stood the test of time and still forms the basis of our understanding today. Building on the work of Landau, we investigate the interplay between BEC and superfluidity using a novel Floquet analysis, which forms a natural way to characterise time-periodic systems. As a starting point to achieve this goal, we apply our Floquet analysis to another area of interest – the engineering of trapping potentials via the technique of time-averaging. We use Floquet theory to analyse the lowest energy state of time-periodic trapping potentials and characterise the transition from a localised state in a slowly moving trap to a delocalised trap in a rapidly oscillating time-averaged potential. We investigate how the driving parameters affect the density and phase of the Floquet ground state, and provide a quantitative measure of the degree to which they can be considered time-averaged. We investigate the conditions under which resonances occur in Floquet systems which can inform the implementation of experimental time-averaged traps since such resonances can lead to experiment-destroying, uncontrollable heating. We then investigate the breakdown of superfluidity in systems with moving obstacles using nonlinear conjugate gradient optimisation. We first perform a stability analysis, finding that superfluid Floquet states likely become unstable at the critical velocity and thus will not converge with optimisation techniques. We are unable to obtain convergence in a large region of parameter space and find that our optimisers converge best when the driving frequency is a multiple of the Bogoliubov frequency. We find that we are able to characterise the breakdown of superfluidity with two complementary measures of optimality, providing an operational definition of the critical velocity and transcritical regime which can replace the drag force in situations when it cannot be calculated.
Time-averaged trapping potentials have played an important role in the development of the field of ultracold atoms. Despite their widespread application, there is not yet a complete understanding of when a system can be considered time-averaged. Here we use Floquet theory to analyze the lowest energy state of time-periodic trapping potentials, and characterize the transition from a localized state in a slowly moving trap to a delocalized state in a rapidly oscillating time-averaged potential. We investigate how the driving parameters affect the density and phase of the Floquet ground state, and provide a quantitative measure of the degree to which they can be considered time-averaged. We study a number of simple representative systems, and comment on the features affecting the experimental realization of time-averaged trapping potentials.
Experiments with ultracold atoms in optical lattices usually involve a weak parabolic trapping potential which merely serves to confine the atoms, but otherwise remains negligible. In contrast, we suggest a different class of experiments in which the presence of a stronger trap is an essential part of the set-up. Because the trap-modified on-site energies exhibit a slowly varying level spacing, similar to that of an anharmonic oscillator, an additional time-periodic trap modulation with judiciously chosen parameters creates nonlinear resonances which enable efficient Floquet engineering. We employ a Mathieu approximation for constructing the near-resonant Floquet states in an accurate manner and demonstrate the emergence of effective ground states from the resonant trap eigenstates. Moreover, we show that the population of the Floquet states is strongly affected by the phase of a sudden turn-on of the trap modulation, which leads to significantly modified and rich dynamics. As a guideline for further studies, we argue that the deliberate population of only the resonance-induced effective ground states will allow one to realize Floquet condensates which follow classical periodic orbits, thus providing challenging future perspectives for the investigation of the quantum-classical correspondence.
Abstract Experiments with ultracold atoms in optical lattices usually involve a weak parabolic trapping potential which merely serves to confine the atoms, but otherwise remains negligible. In contrast, we suggest a different class of experiments in which the presence of a stronger trap is an essential part of the set-up. Because the trap-modified on-site energies exhibit a slowly varying level spacing, similar to that of an anharmonic oscillator, an additional time-periodic trap modulation with judiciously chosen parameters creates nonlinear resonances which enable efficient Floquet engineering. We employ a Mathieu approximation for constructing the near-resonant Floquet states in an accurate manner and demonstrate the emergence of effective ground states from the resonant trap eigenstates. Moreover, we show that the population of the Floquet states is strongly affected by the phase of a sudden turn-on of the trap modulation, which leads to significantly modified and rich dynamics. As a guideline for further studies, we argue that the deliberate population of only the resonance-induced effective ground states will allow one to realize Floquet condensates which follow classical periodic orbits, thus providing challenging future perspectives for the investigation of the quantum–classical correspondence.
Ultracold atoms and trapped ions are among the most formidable sources of coherent matter available in a laboratory. In a hybrid quantum system of atoms and ions, ultracold atoms and trapped ions are combined in a single experimental apparatus, thus realizing an innovative platform to experimentally investigate open problems of quantum physics from a new standpoint. An atom-ion hybrid system not only brings together the advantages of each single physical system, but moreover gives rise to atom-ion interactions, which are two orders of magnitude longer-ranged than atom-atom interactions. Despite a strong interest in atom-ion experiments in recent years, atom-ion systems have not yet been brought to an s-wave scattering regime in which atoms and ions experience a long-living coherent evolution. I will report on the advancements in the realization of an experimental apparatus in which a single trapped Barium ion will be immersed into an ultracold gas of fermionic Lithium. In particular, I will report on the a number of technical advancements that we have realized in order to achieve the highest possible level of control over the atom-ion quantum mixture. These include a new ion trap for creating confining potentials for the ions with a combination of optical and electric fields [1], and a high-finesse optical cavity for confining and rapidly cool neutral atoms via unconventional sideband cooling [2]. Notably, this apparatus was recently used to successfully trap Ba+ ions, thus realizing the first ion trapping experiment in Italy. [1] E. Perego, L. Duca, C. Sias Appl. Sci. 10, 2222 (2020) [2] F. Berto, E. Perego, L. Duca, C. Sias arXiv:2107.04110 Phys. Rev. Research (in press)