No Arabic abstract
We explore, both experimentally and theoretically, the response of an elongated Bose-Einstein condensate to modulated interactions. We identify two distinct regimes differing in modulation frequency and modulation strength. Longitudinal surface waves are generated either resonantly or parametrically for modulation frequencies near the radial trap frequency or twice the trap frequency, respectively. The dispersion of these waves, the latter being a Faraday wave, is well-reproduced by a mean-field theory that accounts for the 3D nature of the elongated condensate. In contrast, in the regime of lower modulation frequencies we find that no clear resonances occur, but with increased modulation strength, the condensate forms an irregular granulated distribution that is outside the scope of a mean-field approach. We find that the granulated condensate is characterized by large quantum fluctuations and correlations, which are well-described with single-shot simulations obtained from wavefunctions computed by a beyond mean-field theory at zero temperature, the multiconfigurational time-dependent Hartree for bosons method.
We study the formation of Faraday waves in an elongated Bose-Einstein condensate in presence of a one-dimensional optical lattice, where phonons are parametrically excited by modulating the radial confinement of the condensate. For very shallow optical lattices, phonons with a well-defined wave vector propagate along the condensate, as in the absence of the lattice, and we observe the formation of a Faraday pattern. By increasing the potential depth, the local sound velocity decreases and when it equals the condensate local phase velocity, the condensate becomes dynamically unstable and the parametric excitation of Faraday waves is suppressed.
We propose a generalized Mathieu equation (GME) which describes well the dynamics for two different models in spin-1 Bose-Einstein condensates. The stability chart of this GME differs significantly from that of Mathieus equation and the unstable dynamics under this GME is called generalized parametric resonance. A typical region of $epsilon gtrsim 1$ and $delta approx 0.25$ can be used to distinguish these two equations. The GME we propose not only explains the experimental results of Hoang et al. [Nat. Commun. 7, 11233 (2016)] in nematic space with a small driving strength, but predicts the behavior in the regime of large driving strength. In addition, the model in spin space we propose, whose dynamics also obeys this GME, can be well-tuned such that it is easily implemented in experiments.
The interaction between atoms in a two-component Bose-Einstein condensate (BEC) is effectively modulated by the Rabi oscillation. This periodic modulation of the effective interaction is shown to generate Faraday patterns through parametric resonance. We show that there are multiple resonances arising from the density and spin waves in a two-component BEC, and investigate the interplay between the Faraday-pattern formation and the phase separation.
We experimentally and theoretically investigate the lowest-lying axial excitation of an atomic Bose-Einstein condensate in a cylindrical box trap. By tuning the atomic density, we observe how the nature of the mode changes from a single-particle excitation (in the low-density limit) to a sound wave (in the high-density limit). Throughout this crossover the measured mode frequency agrees with Bogoliubov theory. Using approximate low-energy models we show that the evolution of the mode frequency is directly related to the interaction-induced shape changes of the condensate and the excitation. Finally, if we create a large-amplitude excitation, and then let the system evolve freely, we observe that the mode amplitude decays non-exponentially in time; this nonlinear behaviour is indicative of interactions between the elementary excitations, but remains to be quantitatively understood.
We investigate the collective excitations of a Raman-induced spin-orbit coupled Bose-Einstein condensate confined in a quasi one-dimension harmonic trap using the Bogoliubov method. By tuning the Raman coupling strength, three phases of the system can be identified. By calculating the transition strength, we are able to classify various excitation modes that are experimentally relevant. We show that the three quantum phases possess distinct features in their collective excitation properties. In particular, the spin dipole and the spin breathing modes can be used to clearly map out the phase boundaries. We confirm these predictions by direct numerical simulations of the quench dynamics that excites the relevant collective modes.