Entanglement in an analog cosmological preheating
Probing 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.
Analog gravity
It was first noted in 1981 that the equations governing the dynamics of collective excitations—quasiparticles—in a fluid are mathematically equivalent to those describing the dynamics of particles in curved spacetime. This insight opened the door to analog quantum field theory, where specific spacetime scenarios can be simulated by carefully engineering the properties of the fluid in which the quasiparticles propagate.
The most famous example is the analog of Hawking radiation from black holes. In this setup, a fluid is shaped to have both subsonic and supersonic regions. The transition between these regions acts as an analog event horizon. Near this horizon, quantum fluctuations are amplified, leading to the creation of quasiparticle pairs—one on each side of the horizon. In real black holes, only the particle outside the horizon can escape and be detected. However, in analog gravity systems, both quasiparticles can be observed, offering a unique opportunity to study such phenomena in the laboratory.
Comological preheating
In our work, we realize an analog of cosmological preheating, a stage expected to occur just after the inflationary period of the early universe. During inflation, the universe undergoes rapid exponential expansion, driven by a hypothetical scalar field known as the inflaton which goes from a false vacuum state towards its true vacuum. After inflation ends, the universe is nearly empty, and the inflaton field begins to oscillate and couple to other (initially empty) matter fields. This interaction leads to parametric opposite momentum pairwise particle creation from the vacuum, producing highly two-mode squeezed states. However, in cosmology, decoherence and thermalization make it nearly impossible to directly observe the quantum entanglement generated during preheating. Instead, we use a condensed matter system to realize analog of this phenomenon.
We use an elongated Bose–Einstein condensate as our analog fluid, in which the transverse degrees of freedom play the role of the inflaton. By coherently driving oscillations of these transverse modes, we induce parametric coupling to longitudinal quasiparticles. The low thermal occupation of these modes ensures that their growth is predominantly seeded by vacuum fluctuations, leading to the emergence of an entangled two-mode squeezed state. We observe this entanglement by measuring two-particle correlations, building upon our recent theoretical work.
Spicy details
Our setup allows for the detection of individual atoms after a long time-of-flight, which we relate to the in-trap velocity distribution. This enables us to directly measure the number of particles in momentum modes with opposite directions. In the image, each dot represents a single atom, with its velocity indicated along the (x, y, z) axes, and each frame corresponds to a single experimental realization. The orange and blue boxes highlight two longitudinally excited modes with opposite momenta. While the number of particles in each mode fluctuates significantly from shot to shot, the difference between the two is strongly suppressed. This behavior is a hallmark of two-mode squeezed states and provides direct evidence of quantum entanglement between the modes.
As the system continues to evolve, the number of created quasiparticles increases exponentially, and interactions between them become significant. These interactions eventually lead to thermalization of the system. At this stage, the Bogoliubov approximation is no longer valid, and entanglement can no longer be probed via simple particle number correlation functions. Indeed, we observe a clear reduction in two-body correlations between opposite-momentum modes, marking a deviation from Bogoliubov predictions. Future work will explore this long-term, interacting regime in greater detail.