Continuous quantum systems in a fluctuating environment

Abstract

We explore the effect of temperature fluctuations on continuous-variable quantum systems, with particular interest in wave packet dynamics, entanglement properties, and the standard quantum limit. Our method relies on the formalism of superstatistics and consists in the superposition of a distribution $$f(\beta )$$, characterizing fluctuations, over thermal wave packets. Fluctuations appear to increase the uncertainty of the wave packets, which tend to develop heavy tails. As a direct consequence, entanglement vanishes at a lower temperature in comparison with their counterpart in the absence of fluctuations. On that basis, a classification of the three universality classes of fluctuations ($$\chi ^2$$, inverse $$\chi ^2$$, and lognormal) is established, depending on their impact on quantum effects. Interestingly enough, the separability criterion holds even when thermal wave packets are not accessible in closed form as long as the moments of $$f(\beta )$$ are known. As the finite size of the bath is accounted for, this may counterbalance the effect of fluctuations, allowing to maintain entanglement at higher temperature.