Controllable interatomic interaction mediated by diffractive coupling in a cavity

• Main Author: Krešić, Ivor
• Format: Journal Article
• Language: English
• Published: 15-07-2024
• Subjects: Physics - Atomic Physics; Physics - Quantum Gases
• DOI: 10.48550/arxiv.2407.10690

Photon-mediated interaction can be used for simulating complex many-body
phenomena with ultracold atoms coupled to electromagnetic modes of an optical
resonator. We theoretically study a method of producing controllable
interatomic interaction mediated by forward-diffracted photons circulating
inside a ring cavity. One example of such a system is the three-mode cavity,
where an on-axis mode can coexist with two diffracted sidebands. We demonstrate
how the self-organized stripe states of a Bose-Einstein condensate (BEC)
occurring in this cavity geometry can exhibit supersolid properties, due to
spontaneous breaking of the Hamiltonian's continuous translational symmetry. A
numerical study of the collective excitation spectrum of these states
demonstrates the existence of massles and finite-gap excitations, which are
identified as phase (Goldstone) and amplitude (Higgs) atomic density modes. We
further demonstrate how judicious Fourier filtering of intracavity light can be
used to engineer the effective atom-atom interaction profile for many cavity
modes. The numerical results in this configuration show the existence of
droplet array and single droplet BEC states for commensurate and incommensurate
cavity modes, respectively. Diffractive coupling in a cavity is thereby
introduced as a novel route towards tailoring the photon-mediated interaction
of ultracold atoms. Spatial features of the self-organized optical potentials
can here be tuned to scales several times larger than the pump laser
wavelength, such that the corresponding atomic density distributions could be
imaged and manipulated using low numerical aperture optics. These calculations
and insights pave the way towards quantum simulation of exotic nonequilibrium
many-body physics with condensates in a cavity.