We investigate the atom-optical analog of degenerate four-wave mixing by colliding two Bose-Einstein condensates of metastable helium. The momentum distribution of the scattered atoms is measured in three dimensions. A simple analogy with photon phase matching conditions suggests a spherical final distribution. We find, however, that it is an ellipsoid with radii smaller than the initial collision momenta. Numerical and analytical calculations agree with this and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate. The field of atom optics has developed to the point that one can now speak of the beginning of ''quantum-atom optics'' [1] in which atoms are manipulated in ways similar to photons and in which quantum fluctuations and entanglement play an important role. The demonstration of atom pair production [2,3], either from the dissociation of ultracold molecules, a process analogous to parametric downconversion [4-6], or from collisions of Bose-Einstein condensates (BECs) [7][8][9][10], analogous to four-wave mixing (FWM) [11][12][13][14][15][16][17][18][19][20][21], holds considerable promise for generating atomic squeezed states and demonstrating nonlocal Einstein-Podolsky-Rosen (EPR) correlations [4,5,22,23]. In both these systems, atom-atom interactions play the role of the nonlinear medium that allows conversion processes. Atoms are not, however, exactly like photons, and in spite of their formal similarity, the processes of pair production of photons and of atoms exhibit some interesting and even surprising differences that must be understood in order for the quantum-atom optics field to advance. In this work, we discuss one such effect.In optical FWM or parametric down-conversion [24], energy conservation requires that the sum of the energies of the outgoing photons be fixed by the energy of the input photon(s). Phase matching requirements impose constraints on the directions and values of the individual photon momenta. A simple case is degenerate, spontaneous FWM (i.e., two input photons of equal energy) in an isotropic medium, for which energy conservation and phase matching require that the momenta of the output photons lie on a spherical shell whose radius is that of the momenta of the input photons.We have performed the atom-optical analog of degenerate FWM in colliding BECs while paying careful attention to the momenta of the outgoing atoms. We find that unlike the optical case, the output momenta do not lie on a sphere, but rather on an ellipsoid with short radius smaller than the input momentum. This behavior is due to a subtle combination of atom-atom interactions, which impose an energy cost for pair production, and the anisotropy of the condensates, which affects the scattered atoms as they leave the interaction region.Although an analogous effect could exist in optics, optical nonlinearities are typically so small that the effect is negligible. However, in the process of high-harmonic generation in intense laser fields, a simil...

We study the beyond-mean-field corrections to the energy of a dipolar Bose gas confined to two dimensions by a box potential with dipoles oriented in plane. At a critical strength of the dipolar interaction the system becomes unstable on the mean field level. We find that the ground state of the gas is strongly influenced by the corrections, leading to formation of a self-bound droplet, in analogy to the free space case. Properties of the droplet state can be found by minimizing the extended Gross-Pitaevskii energy functional. In the limit of strong confinement we show analytically that the correction can be interpreted as an effective three-body repulsion which stabilizes the gas at finite density. arXiv:1911.02384v1 [cond-mat.quant-gas]

We formulate the time-dependent Bogoliubov dynamics of colliding Bose-Einstein condensates in terms of a positive-P representation of the Bogoliubov field. We obtain stochastic evolution equations for the field which converge to the full Bogoliubov description as the number of realisations grows. The numerical effort grows linearly with the size of the computational lattice. We benchmark the efficiency and accuracy of our description against Wigner distribution and exact positive-P methods. We consider its regime of applicability, and show that it is the most efficient method in the common situation -when the total particle number in the system is insufficient for a truncated Wigner treatment.

We consider a sonic analog of a black hole realized in the one-dimensional flow of a Bose-Einstein condensate. Our theoretical analysis demonstrates that one- and two-body momentum distributions accessible by present-day experimental techniques provide clear direct evidence (i) of the occurrence of a sonic horizon, (ii) of the associated acoustic Hawking radiation, and (iii) of the quantum nature of the Hawking process. The signature of the quantum behavior persists even at temperatures larger than the chemical potential.