“We wanted to accommodate all the exhausted New Yorkers,” explains Stacy Veloric, the company’s marketing director. “It’s really hard to find peace and quiet within New York City.”

The business opened with seven cabins, but demand quickly exceeded supply and they added 22 more. Soon there will also be hammocks on the roof, where half an hour’s kickback will cost US$15.

The US sleep deficit is real. According to the US Centres for Disease Control and Prevention, a third of Americans sleep less than they should.

Only 24 per cent of New Yorkers get eight or more hours of sleep, and nearly half get six or less, according to a statewide survey for Siena College.

Lack of sleep causes moodiness, low productivity and poor concentration. It also costs the US economy up to US$411 billion and the equivalent of 1.23 million working days a year, according to a Rand Corporation study in 2016.

How much sleep do you really need? Read our chart to find out

Laura Li, a 28-year-old copy editor for a travel company, is someone who prefers a 35-minute kip to a coffee. Each week she pops along to YeloSpa, a luxurious, spa-style Fifth Avenue fixture opposite Trump Tower.

Li steps into a hexagonal cockpit that looks straight out of a science fiction film and lies on a bed suspended in a position of zero gravity, knees bent and feet elevated to lower the heart rate and induce sleep.

Thirty-five minutes later, she will be woken by “a simulated sunrise”, says Maya Daskalova, YeloSpa manager.

The price? A dollar a minute, with a minimum of 20 and a maximum of 40.

I come here specially on days where I have a lot of work – just to get more energy for the rest of the afternoon,” says Li. “I don’t drink coffee so if I feel tired there’s nothing I can really do, other than sleeping.”

She may not have told colleagues that she naps during lunch, but has confessed to friends, who are baffled by the concept of paying to sleep.

“They might think this is a waste of time or a waste of money,” she says. “As long as I can afford it, then it’s worth it. I just feel better afterward, that’s enough.”

Daskalova has seen her clientele grow gradually and believes that cultural attitudes in America are changing. “Resetting you for the rest of the day is much better than crashing in your desk in the middle of work,” she says.

Hong Kong’s sleep-deprived workers resort to desperate measures as they bed down at city’s nap lounges

Who escapes to take a nap? Those who work long hours or live miles away and want time out before a night out. Pregnant women who are exhausted. Parents of babies suffering sleepless nights and party-goers who need a breather.

In 2004, Christopher Lindholst created MetroNaps, a company that designs super-modern “energy pods” for quick naps.

He installed several in the Empire State Building until security requirements forced them out, then focused sales on companies, universities, hospitals and airports. Google and Nasa are among those who have bought his pods.

People’s attitudes changed dramatically in the last 15 years, there’s much more awareness of the importance of sleep and the benefit,” Lindholst says.

But in a city with the longest working day in the States, travel time included, he thinks it will take a full generation to erase old stigmas about laziness.

“We use the argument all the time that we are talking about a very short period of time, 10 to 20 minutes, essentially the same [as] a coffee break or in New York a smoke break,” he says.

One MetroNaps capsule lives in the SoHo offices of Thrive Global, a wellness start-up founded by Arianna Huffington, author of bestselling 2016 tome T he Sleep Revolution and a founder of The Huffington Post.

Her book calls for an end to “the delusion that we need to burn out to succeed”.

“We’re in the middle of a cultural shift, one in which more of us are taking steps to reclaim sleep,” she writes.