Pseudo-APT symmetry with Four-Wave Mixing in hot Rubidium atoms

In the last decades physicists are increasingly interested in properties of systems with non-Hermitian Hamiltonian H symmetric under Parity-Time(PT) transformation (such that [H,PT]=0). Such systems can undergo a transition from having real to imaginary eigenvalues at a singular point of the parameter space, referred to as an Exceptional Point (EP). Since minimal changes in the system near EP yield dramatic alterations in the output, such behavior enables, in principle, extremely sensitive sensors. Later it was shown that analogous behavior is expected for an anti-Parity-Time (APT) symmetric system, for which {H,PT}=0, but without intrinsic losses, making it attractive for quantum sensing. Here we investigate the prospective of implementing an APT symmetric system via nonlinear four-wave mixing interaction in a thermal Rb vapor, widely used for two-mode squeezing and entanglement generation. We theoretically demonstrate that the propagation of two conjugate optical fields in a double-Λ scheme under realistic experimental conditions can be equivalent to the anti-PT Hamiltonian. We also experimentally characterize classical and quantum properties of the two twin outputs around EP. Our experimental observations show good agreement with the numerical simulations.