Quantum simulation of (quasi-)particles creation from vacuum
Studying entanglement of collective excitations in a parametrically excited Bose-Einstein condensate
Related publication: Gondret V, Lamirault C, Dias R et al., Observation of entanglement in a cold atom analog of cosmological preheating, arXiv:2506.22024 (2025), PDF or HTML. See also this talk, this poster or the Chapter 6 of my thesis.
Inflation and particle creation in the Early Universe
According to the standard model of cosmology, the Universe underwent a rapid expansion known as inflation. This expansion was driven by a field called the inflaton, which was initially in a false vacuum state and then transitioned to its true vacuum, where it began to oscillate. These oscillations, coupled to matter fields, created particles through a broad parametric resonance, a stage often referred to as preheating.
As inflation ended, the Universe was initially empty, and particles were produced from the vacuum. They were created in pairs with opposite momenta, and it was vacuum fluctuations that triggered the growth of the matter field. As a result, the created particles are expected to form a two-mode squeezed vacuum state, exhibiting momentum entanglement. When the number of particles becomes large, interactions between them lead to decoherence and eventual thermalization.
Quasi-particle creation in a Bose gas
The direct observation of particle creation in the early Universe is impossible, as any remnants of entanglement have been erased by particle interactions. However, this parametric amplification mechanism is universal and can be observed in other systems. In our work, we investigate the evolution of entanglement between quasi-particles generated by parametric excitation in an elongated Bose gas.
To achieve this, we modulate the transverse frequency of the dipole trap confining a Bose-Einstein condensate. This modulation induces a radial collective oscillation at twice the transverse frequency, known as the breathing mode. This excitation is particularly noteworthy due to its weak coupling to thermal excitations via Landau damping. Notably, the breathing mode couples to two longitudinal modes with opposite momenta, whose frequency is half that of the breathing mode. Upon releasing the cloud, the collective excitations are transferred to individual atoms, which then move away from the central condensate. We detect these atoms using a micro-channel plate positioned 46 cm below the trap, allowing for the electronic detection of the position and impact time of individual particles: we measure the gas 3D momentum distribution at the single particle level.
Studying entanglement
If the initial population is zero, the state evolves into a product of two-mode squeezed vacuum states, with vacuum fluctuations driving the growth. However, in a BEC, the temperature never reaches 0 K, meaning there is always a small thermal population: the associated thermal fluctuations also contribute to triggering the parametric growth. The distinction between the roles of vacuum fluctuations and thermal fluctuations becomes ambiguous when considering particle growth alone. However, the contribution of vacuum fluctuations can be identified by examining the entanglement of the two-mode state, as only the vacuum component generates entanglement. Thus, detecting entanglement directly reveals the role of particle production from the vacuum.
To detect entanglement we compute number correlations between opposite momentum modes. On the image shown here, we compute the correlation between the blue and orange 3D voxels in momentum space. Using our theoretical work linking the measurement of correlation functions with mode entanglement of bosonic Gaussian states, we observe that the two-mode state is indeed entangled.