Sonic Superradiance in Bose Einstein Condensates

Abstract

There are a number of interesting phenomena that are predicted to be a result of the behaviour of general relativity close to a black hole. The most well known of these is Hawking radiation. Although well established, the theory of Hawking radiation is unsupported by experiment, since black holes cannot be investigated in the lab. However, there is a strong similarity between the equations governing the behaviour of a sound wave in inviscid irrotational fluid systems and a massless scalar field in a gravitational system. This similarity provides hope that effects like Hawking radiation can be investigated in analogous fluid systems. The requirement that potential fluid analogues be barotropic, inviscid and irrotational indicates that superfluids would be the logical object of experiments designed to analyse such systems. The most easily controlled superfluid to which experimentalists have access is a Bose Einstein Condensate in an appropriately designed trap, and there is interest in designing an experiment to look for Hawking radiation in a BEC. A BEC is also ideal for that purpose because of the extremely low temperatures at which the condensation occurs, given the very low temperature of Hawking radiation. However, Hawking radiation itself is a very subtle effect, and it would be very hard to detect. This means that a related but more conspicuous effect is interesting as a stepping stone to a test for the more well known Hawking radiation. This related effect is Superradiance, a result of the reflection of an incoming scalar field with appropriate angular characteristics from the ergoregion of a massive rotating body such as a black hole. An ergoregion is a region around a rotating black hole or supermassive rotating star within which it is impossible to remain stationary with respect to an observer at infinity without exceeding the speed of light. Before an experiment can be designed to test for superradiance in a BEC it is necessary to establish whether the theory describing Bose-Einstein Condensates predicts that it will actually occur. Work on this problem thus far has either failed to consider whether the effect occurs, and instead focused on the consequences it would have, or has involved approximations that are not strictly valid. Here therefore, after an overview of both the analogy between fluid and gravitational systems and the specific theory related to Bose Einstein Condensates is an analysis using the full quantum theory of BECs. The initial consideration is analytic in character, but the equations do not allow for an exact solution within the approximations attempted that predict superradiance, so a change is made to a numerical simulation using the XMDS numerical simulation package. Unfortunately, this attempt also fails, since ongoing problems encountered in running the simulation consumed all the time available. A discussion of these problems is included. Show more