Ground State of a Quantum Particle Coupled to a Scalar Bose Field

Masao Hirokawa

Volker Betz, Fumio Hiroshima, József Lőrinczi +2 more

The Nelson model describes a quantum particle coupled to a scalar Bose field. We study properties of its ground state through functional integration techniques in case the particle is confined by an external potential. We obtain bounds on the average and the variance of the Bose field both in position and momentum space, on the distribution of the number of bosons, and on the position space distribution of the particle.

龍蔵 阿部

Christian F. Schmidt, S. Brunner, Stefan Floerchinger

We consider excitations of a spin-1 Bose-Einstein-condensate in the vicinity of different mean-field configurations and derive mappings to emergent relativistic quantum field theories minimally coupled to curved acoustic spacetimes. The quantum fields are typically identified with Nambu-Goldstone bosons, such that the structure of the analog quantum field theories on curved spacetimes depends on the (spontaneous) symmetry breaking pattern of the respective ground state. The emergent spacetime geometries are independent of each other and exhibit bimetricity in the polar and antiferromagnetic phase, whereas one has trimetricity in the ferromagnetic phase. Compared to scalar BECs, the spinor degrees of freedom allow us to investigate massive vector and scalar fields where the former is a spin-nematic rotation mode in the polar phase, which can be cast into a Proca field that is minimally coupled to a curved spacetime that emerges on length scales larger than the spin-healing length. Finally, we specify the Zeeman couplings and the condensate trap to be spacetime-dependent such that a cosmological Friedmann-Lemaître-Robertson-Walker metric can be achieved. This work enables a pathway towards quantum-simulating cosmological particle production of Proca quanta via quenching the quadratic Zeeman coefficient or via magnetic field ramps, which both result in the creation of spin-nematic squeezed states.

Asao Arai, Hiroyuki Kawano

We consider, in an abstract form, a system of "quantum particles" coupled to a Bose field. It is shown that, under suitable hypotheses, the composed system can have a ground state even if the uncoupled particle system has no ground state.

Lea Boßmann, Nikolai Leopold, Sören Petrat +1 more