The app called mySleepButton works by preventing sleep-interfering thoughts and activating a mechanism that could help trigger sleep.
It incorporates concepts from cognitive science, a multidisciplinary study of the mind and its processes.
Based on the "cognitive shuffle" technique developed by Simon Fraser University, Canada, researcher Luc Beaudoin, the app works by prompting users to imagine various objects or scenes in rapid succession.
"For example, one moment, users may be directed to think of a baby, then next a football game, then beans, a ball, London and so on," he said.
The method is based on the uniquely incoherent nature of sleep onset "mentation" a term used by Beaudoin that refers to all kinds of mental activity.
"As you fall asleep, you tend to entertain various detached thoughts and images. The app gets users to think in a manner that, like sleep onset, is both visual and random," said Beaudoin.
"In a nutshell, it's a case of fake it until you make it," said Beaudoin.
"Brain areas involved in controlling sleep detect that sense-making has been suspended. This basically gives them an implicit license to continue the transition to sleep," he said.
Executive functions - brain functions like planning, worrying and problem solving that are vital for helping us make sense of the world during waking hours - can delay sleep when they don't switch off at bed time.
By prompting users to interpret and visualise words, mySleepButton can help deactivate these executive functions.
"While you're thinking about random objects or scenes, you can't think about your mortgage, an important meeting or an impending divorce," said Beaudoin.
"That's because, to a certain extent, we all have one track minds. It's very hard to think about multiple distinct things at the same time," Beaudoin said.
The app could also help increase cognitive productivity as well.
"Quality of work decreases when people are sleep-deprived and getting adequate sleep is very important for cognitive performance," he said.