Leggett-Garg tests of macrorealism for dynamical cat states evolving in a nonlinear medium

We show violations of Leggett-Garg inequalities to be possible for single-mode cat states evolving dynamically in the presence of a nonlinear quantum interaction arising from, for instance, a Kerr medium. In order to prove the results, we derive a generalized version of the Leggett-Garg inequality involving different cat states at different times. The violations demonstrate failure of the premise of macrorealism as defined by Leggett and Garg, provided extra assumptions associated with experimental tests are valid. With the additional assumption of stationarity, violations of the Leggett-Garg inequality are predicted for the multicomponent cat states observed in the Bose-Einstein condensate and superconducting circuit experiments of Greiner et al. [Nature (London) 419, 51 (2002)NATUAS0028-083610.1038/nature00968] and Kirchmair et al. [Nature (London) 495, 205 (2013)NATUAS0028-083610.1038/nature11902]. The violations demonstrate a mesoscopic quantum coherence, by negating that the system can be in a classical mixture of mesoscopically distinct coherent states. Higher orders of nonlinearity are also studied and shown to give strong violation of Leggett-Garg inequalities. Loopholes for testing macrorealism are discussed.