The continuous spontaneous localization (CSL) theory alters the Schr\"odinger equation. It describes wave-function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter $\ensuremath{\lambda}$ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultracold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a Bose-Einstein condensate (BEC) in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BECs, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter $\ensuremath{\lambda}$. We obtain $\ensuremath{\lambda}\ensuremath{\lesssim}1(\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ ${\mathrm{s}}^{\ensuremath{-}1}$.The continuous spontaneous localization (CSL) theory alters the Schr\"odinger equation. It describes wave-function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter $\ensuremath{\lambda}$ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultracold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a Bose-Einstein condensate (BEC) in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BECs, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter $\ensuremath{\lambda}$. We obtain $\ensuremath{\lambda}\ensuremath{\lesssim}1(\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ ${\mathrm{s}}^{\ensuremath{-}1}$.

arXiv:1409.5388Physical Review ANov 24, 201495 citations

Transport Phenomena in a Bose-Einstein Gas

William Band

This paper develops the formal first order perturbation theory of transport phenomena in an ideal Bose-Einstein gas.The perturbation relaxation time is an unknown parameter in the theory. The ratio of thermal conductivity to viscosity is independent of this relaxation time; it increases discontinuously by a factor almost 2 at the Bose-Einstein condensation temperature ${T}_{\ensuremath{\lambda}}$. The isothermal Knudsen heat of transport through a small hole, classically equal to $2kT$ , drops rapidly to zero as $T$ falls to ${T}_{\ensuremath{\lambda}}$: the Bose-Einstein gas flowing isothermally through a small hole carries no heat when its temperature is below ${T}_{\ensuremath{\lambda}}$ and it exhibits corresponding thermo-mechanical effects.The mathematical analysis is carried out in terms of an approximation in which the lowest energy states of the gas are treated discretely while above an arbitrary level they are treated by an integration approximation. The treatment is capable of generalization to models in which there are anomalies in the lowest level spacings.This paper develops the formal first order perturbation theory of transport phenomena in an ideal Bose-Einstein gas.The perturbation relaxation time is an unknown parameter in the theory. The ratio of thermal conductivity to viscosity is independent of this relaxation time; it increases discontinuously by a factor almost 2 at the Bose-Einstein condensation temperature ${T}_{\ensuremath{\lambda}}$. The isothermal Knudsen heat of transport through a small hole, classically equal to $2kT$, drops rapidly to zero as $T$ falls to ${T}_{\ensuremath{\lambda}}$: the Bose-Einstein gas flowing isothermally through a small hole carries no heat when its temperature is below ${T}_{\ensuremath{\lambda}}$ and it exhibits corresponding thermo-mechanical effects.The mathematical analysis is carried out in terms of an approximation in which the lowest energy states of the gas are treated discretely while above an arbitrary level they are treated by an integration approximation. The treatment is capable of generalization to models in which there are anomalies in the lowest level spacings.

Physical ReviewJun 15, 19494 citations

Nonlinear real-time response of a BEC to perturbation

Rodger M. Walser, Jonathan Cooper, Mark Holland

APSMay 1, 20010 citations

BEC manipulation with fictitious magnetic fields

Jeffrey Heward, Mark Edwards, Charles W. Clark

Bulletin of the American Physical SocietyMay 27, 20100 citations

2kT

, drops rapidly to zero as

T

falls to ${T}_{\ensuremath{\lambda}}$: the Bose-Einstein gas flowing isothermally through a small hole carries no heat when its temperature is below ${T}_{\ensuremath{\lambda}}$ and it exhibits corresponding thermo-mechanical effects.The mathematical analysis is carried out in terms of an approximation in which the lowest energy states of the gas are treated discretely while above an arbitrary level they are treated by an integration approximation. The treatment is capable of generalization to models in which there are anomalies in the lowest level spacings.