Space-time crystals in Bose-Einstein condensates

Discrete time crystals are a phase of matter, for which the discrete time symmetry of the driving Hamiltonian is spontaneously broken. A superfluid cloud of sodium atoms is trapped in a cigar-shaped harmonic magnetic trap. The width of the cloud is briefly modulated at t=0 and left to oscillate for the entire experiment. Due to non-linear (density-density) interaction in the cloud, the longitudinal modes experience a parametric driving as a result of this oscillation. A spatial pattern appears which oscillates at twice the driving period. The sub-harmonic response, combined with the fact that no dissipation of either the longitudinal mode or driving mode is observed, leads us to classify the longitudinal mode as a discrete time crystal. Combined with the observed spatial period in the longitudinal direction, the term space-time crystal is warranted. The work is structured as follows. First, the setup to make Bose-Einstein condensates, the superfluid used in the time crystal experiments, is described. Special emphasis is put on the non-destructive holographic imaging method, implementation of which reduced the particle loss per image by a factor of 50-100 compared to the previously employed non-destructing imaging method. Subsequently, the first observation of the space-time crystal is discussed. In the following part, details of the space-time crystal such as its long term stability and formation are discussed. It is found that length oscillations of the condensate have to be suppressed in order to realize a stable space-time crystal in our system. In the final part of this thesis, the details of the symmetry breaking are discussed. As the period of the crystal is double that of the drive, it is expected that two states of the crystal exist in time, which are π out of phase and energetically identical. Experimental results are combined with simulations to show that the split between these states is indeed 50/50. From this, it is argued that the observed symmetry breaking is spontaneous in the quantummechanical sense: that the system exists in a superposition up to the first observation, and is only in one state or the other after observation.