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We investigate the properties of the condensates of cold atoms at zerotemperature in the tunable binary Bose-Einstein condensate system with a Rabitransition between atomic hyperfine states. We use this system to examine theeffect of quantum fluctuations in a tunable quantum gas on phonon propagation.We show that the system can be represented by a coupled two-field model of agapless phonon and a gapped mode, which are analogous to the Goldstone andHiggs particles in particle physics. We then further trace out the gapped modesto give an effective purely phononic theory using closed-time-path formalism.In particular, we are interested in the sound cone fluctuations due to thevariation of the speed-of-sound acoustic metric, induced by quantumfluctuations of the gapped modes. These fluctuations can be interpreted asinducing a stochastic space-time, and thus are regarded as analogue phenomenaof light cone fluctuations presumably arising from quantum gravity effects. Theeffects of fluctuations can be displayed in the variation in the travel time ofsound waves. We suggest the relevant experiments to discuss the possibility ofexperimental observations.

Analogue stochastic gravity phenomena in two-component Bose-Einstein condensates: Sound cone fluctuations