Density Waves and Jet Emission Asymmetry in Bose Fireworks

Abstract

A Bose condensate subject to a periodic modulation of the two-body interactions was recently observed to emit matter-wave jets resembling "fireworks" [Nature 551, 356(2017)]. In this paper, combining experiment with numerical simulation, we demonstrate that these "Bose fireworks" represent a late stage in a complex time evolution of the driven condensate. We identify a "density wave" stage which precedes jet emission and results from interference of matterwaves. The density waves self-organize and self-amplify without the breaking of long range translational symmetry. Importantly, this density wave structure deterministically establishes the template for the subsequent patterns of the emitted jets. Our simulations, in good agreement with experiment, also address the apparent asymmetry in the jet pattern and show it is fully consistent with momentum conservation.Time-periodic driving, which allows coherent manipulation of many-body systems, is becoming an exciting tool in the ultracold atomic gases. This provides access to new quantum physics, for example, topological states, synthetic gauge fields and Mott transitions [1][2][3][4][5]. Of particular interest is the rather unique capability these atomic systems afford into understanding non-equilibrium many-body dynamics [6]. Also unique to the ultracold gases is the ability, through the Feshbach resonance, to periodically modulate atomic interactions [7]. Recently, this was implemented by the Chicago group [8,9] and the Rice group [10-12] on Bose-Einstein condensates. In the Chicago experiment, a collective emission of matter-wave jets resembling fireworks occurs above a threshold modulation amplitude.The jets were associated with a form of runaway stimulated inelastic scattering occurring in the driven condensate [8].In this paper we use the time-dependent Gross-Pitaevskii (GP) equation to study the evolution of the modulated BEC and the emission of these jets [8]. An unbiased or random noise term is introduced initially to model the fluctuations that seed the jet emission. We show that the simulations capture well the "fireworks" dynamics seen in experiments. Moreover, in combination with a new set of experiments, we identify a previously unobserved stage of the evolution that precedes and underlies the jet-emission. Immediately after modulation, we observe that density waves emerge and grow rapidly in the condensate with quantized wavenumbers determined by the modulation frequency [13]. The density waves arise from the interference between excited matterwaves and the condensate. The pattern is reminiscent of Faraday waves in nonlinear fluids [14,15] and related to that predicted for driven atomic gases [16][17][18][19] as well as observed in the one-dimensional condensate [20].The amplification of these density waves can be considered the matterwave analog of superradiant 30 µm 0 5 9 14 18 t = 28 ms Time t Experiment Simulation Density n (µm -2 ) 0 30 15 Density n/ n 0 0 0.6 0.3FIG. 1. The real space density distribution n(r) (denoted as n) as a comparison betw...

Pattern formation in a driven Bose–Einstein condensate

“…1A). The interaction modulation is realized by applying an oscillating magnetic field to the sample [28,29]. The magnetic field is in the z−direction, perpendicular to the sample while the pattern forms in the horizontal x−y plane ( Fig.…”

Driving quantum correlated atom-pairs from a Bose–Einstein condensate

“…Note that the anomalous density diverges in general as the Hankel function of the first kind as a function of the relative distance | | r r 1 2 close to the origin. This is an analytic result that can be derived by solving the scattering equation, equation (9), in 2D [33]. This emphasizes an important point; the anomalous density cannot be accessed directly in experiment and does not form an observable.…”

“…The Dirac delta function in equation (9) implies that we are implicitly building a scattering model from a contact interaction. This is convenient as it simplifies the resulting field theory, but care must be taken to account for divergences that can arise at small and large scales.…”

“…On the other hand, a given experiment is fundamentally different in that it represents a single trial that exhibits shot-to-shot noise associated with the projection that occurs in a single quantum measurement. In order to model this projection noise it would be necessary to simulate quantum trajectories [34], rather than solving for the density matrix evolution, and this may be done by adding white noise to the initial condensate wavefunction(see for example [9]).…”

“…When the excitations are not weak, and the non-condensate fraction can be significant, a more complete approach must be used such as the timedependent self-consistent HFB equations [8], and that is the method we will focus on in this paper. Note that one alternative approach that can incorporate the excitations is through the addition of a noise source to introduce fluctuations directly into the GPE [9]. However, this assumes by construction that the many-body state can be accurately described by a unique macroscopic wavefunction, and therefore a more complete theory is needed to describe two-body correlations.…”