This paper proposes a way to make a uniform imaginary magnetic field for ultracold atoms. Instead of a real magnetic field that deflects charged particles, an imaginary magnetic field appears in systems with controlled loss and gain. The authors show how laser coupling and state-dependent particle loss can produce an imaginary vector potential whose curl is constant across space — in other words, a spatially uniform imaginary synthetic magnetic field.

The authors start from four internal atomic levels. Two of those are the main Raman-coupled states that will carry the atomic motion. The other two are auxiliary levels that are coupled to the main levels and then strongly and irreversibly emptied (lost). By eliminating those lossy auxiliary states under the assumption that their decay is much faster than the other dynamics, the authors obtain an effective two-level, non‑Hermitian Hamiltonian for the Raman pair. Projecting further onto a single dressed state of the light–atom coupling gives a one-component wave equation in which the atom’s motion sees a complex (imaginary) vector potential with a constant curl. A suitable choice of Raman amplitude and controlled, state-by-state losses is used to keep the dressed-state energy gap fixed while producing a spatially uniform imaginary magnetic field.

The paper works out how atomic wavepackets move in this imaginary magnetic field. The authors derive analytic formulas for Gaussian wavepackets, including the center-of-mass motion and how the packet width changes (covariance and squeezing). They identify a transverse drift that depends on differential attenuation (a loss difference between the two Raman states) and a form of transport that depends on the packet width — a behavior that does not appear in ordinary, lossless (Hermitian) magnetic systems. They also compare the adiabatic projection description to direct numerical evolution of the two-level non‑Hermitian Hamiltonian and report agreement, which supports the validity of their adiabatic approach.