Ash Barty ruthlessly dispatched British wildcard Harriet Dart 6-1 6-1 in her centre court debut as the World No.1, saying she is now in “new territory” at Wimbledon.

Having not dropped a set since the French Open semi-finals, Barty made short work of Dart, hitting 11 aces, and will next meet American Alison Riske in the Round of 16.

World No.55 Riske set up the showdown with the Australian by beating Swiss player Belinda Bencic 4-6 6-4 6-4.

Ash Barty reaches for a ball during her match against Harriet Dart.

Barty is now on track for a quarter final showdown with Serena Williams, who won her third round match 6-3 6-4 against German Julia Georges.

Barty was pleased with her form, having never been this far at Wimbledon as a singles player.

“New territory,” she told Channel Seven. “Have had a taste in doubles before. Excited to be here in singles for the first time.

“I served well when I needed to. I think the game I got out from love- 40 was massive. I tried to do as best I can to get a quick start and continue the ball rolling from there.

“Today I was able to overpower her [Dart] a touch. It wasn’t a one on one score line by any means. There were a lot of games it could have gone either way. Particularly early. If she was able to get a couple more games in and settle quickly.

“She’s going to have a fantastic career and will turn-out to be her favourite court in the world. It’s mine and I know she will make it through.

Barty knocked off Dart in 53 minutes with countryman Rod Laver in the stands after being presented with a replica trophy before the match to recognise the 50th anniversary of his 1969 Wimbledon triumph.

Barty broke Dart on her first two service games to race to a 5-0 lead before pocketing the opening set with three booming aces.

There was no let-up for the French Open champion in the second set as Barty dropped just one more game in securing a commanding victory.

The 23-year-old received a standing ovation from Laver and the rest of the crowd after sealing her place in the fourth round for the first time in four visits to the All England Club.

“It’s incredible to be here. It’s a first for me. I’ve had a taste of it in doubles, but really excited to be here in singles for the first time,” said the 2013 doubles runner-up and 2011 junior champion.

Barty had appeared on Centre Court for the first time since she was 17 and partnering fellow Australian Casey Dellacqua in the 2014 women’s doubles final.

For her part Serena Williams was just pleased to still be in the tournament, saying post-match that her mixed doubles pairing with Andy Murray was designed to help her fine-tune.

“Every time I go out there I try. You know I’m getting a really late start. All that matters is I’m still here,” she said on Channel Seven.

“I wanted to play mixed because I haven’t played not even 15 matches or just about 15 matches this year. So I thought it could help me. It’s such a buzz going around about me and Andy that I have got nervous now.

“I feel like I have got nervous now. I feel like I have a little bit of performance anxiety. I hope I can live up to the hype. You know. I’m ready and I’m excited but I’m definitely nervous.”

Earlier in the night, Australia’s only other remaining entry John Millman was edged out 7-6 (7-3) 7-6 (10-8) 6-3 to huge-serving American Sam Querrey.

Querrey hurled down 27 aces against the battling Millman, who was backed by a noisy and partisan Australian following who managed to enrage the former world No.11 during a tense second-set tiebreak.

“You can cheer but don’t be a jerk,” Querrey told a fan sitting on the sidelines of the intimate Court 17 who questioned the American’s conditioning.

“Come on, Sam. You’ve got no cardio,” the heckler said.

Millman made a great start to the match when he broke Querrey to take a 3-1 lead but immediately surrendered that initiative in the next game where he was broken to love.

He then doubled-faulted in the tiebreak to hand Querrey the decisive mini-break and the Californian closed out the set.

John Millman battled hard, but was eventually bundled out of the tournament. Photo: Getty

The second set was another close affair and Millman had two set points only for Querrey to find a big serve just when he needed to and to take a two-set lead.

Querrey then grabbed the early break in the third set and closed out the win on his second match point in just under two hours to reach the round of 16 at Wimbledon for the fourth time.

The defeat means Millman has not passed the third round in five visits to the All England Club.

-with AAP