At the age of 10 Elizabeth Olsen put her acting career on hold. Yes, she wanted to be an actor, but no, she didn't want to be a child actor. What kind of 10-year-old makes a sensible decision like that? "Right!" Olsen exclaims, waggling a heavily ringed hand and explaining how her ballet teacher had just banned her from the Christmas show for missing rehearsals to audition for the flicks. "When I think about it, it's ridiculous. I was a little kid. But my dad said: 'All right, Lizzie, write down the pros and cons and make your decision.'" Mr Olsen was big on work ethic – giving his girls the tools to be independent women.

To see how that panned out, consider Olsen's big sisters, twins Mary Kate and Ashley. For non-subscribers of glossies, the Olsens are kid TV stars turned fashion uber-moguls marshalling a $100m empire. Before Sundance last year no one had heard of little sister Elizabeth (Lizzie to her friends), an acting student at New York University. That all changed when her two low budget films – Silent House and Martha Marcy May Marlene – screened back-to-back on day three of the film festival. Afterwards they talked of little else: a-star-is-born, festival It-girl chatter and breathless predictions of awards glory for Martha Marcy.

Should we smell a rat? Or at least the faint whiff of manufactured hype at this rolling out of the other sister? (Or should that be "alt sister"?) No, apparently not. By the time Martha Marcy, an icily clever arthouse thriller, premieres in London, the dust has settled. General consensus: Elizabeth Olsen is the real deal (even if that Oscar nomination proved elusive).

We meet in London the day after Martha Marcy opens to a chorus of praise in America. "A genuine discovery," writes Roger Ebert. And it's true. She's a revelation as Martha, who we meet running away from a hippy-ish grow-your-own commune in rural upstate New York. At first glance the set-up looks harmless if half-arsed – a retreat for guitar-playing waifs in worn Levi's and plaid shirts. But something doesn't add up. Why do the men eat dinner before the women? Why is Martha scrambling terrified through the woods to escape? Isn't that guy in charge just too charismatic for his own good? With nowhere else to go, Martha calls her sister (Sarah Paulson) and moves into her snazzy lakeside home. Flashbacks to life on the farm ratchet up the suspense. We start clocking: this is less Waltons, more Mansons.

In person Olsen is barely recognisable. In the film her face is scrubbed of expression, frighteningly blank. ("I think my face was partially swollen everyday because I had to cry so much.") She's exceedingly pretty, with siren Michelle Pfeiffer blue eyes and luminous skin. Dressed in a slouchy sequinned silver top, skinny black trousers and vertigo-heeled ankle boots, she's a walking advert for the no-fuss glam that's made her sisters their millions.

She finds Martha's life "terrifying". "It's really strange, because when we were filming I felt so close to her, like we were one and the same: that she was so much of me, my thoughts and secrets. And then I saw the movie …" She shakes her head laughing. "I'm such a light person. That is so far away from who I am."

And it's true. Olsen is breezy, articulate and seemingly baggage-free. It's tempting to poke about for a glint of deadly ambition or a poor-me-forgotten-sister-complex. At the very least I expected her to be prickly talking about her family. But no … or at least not any more. What's obvious, though, is that she has taken the most unglamorous route into acting wherever possible. As if to say: OK, so I'll be the serious sister.

Growing up in LA, she saw acting as an unremarkable career option, and after school she moved to New York to study drama. Did she feel the need to distance herself from her sisters? "I felt it significantly when I was starting college. I really wanted to prove all these things, so I overcompensated." In her second year she juggled being a full-time student with working as understudy (not a diva-ish gig). "Basically I had no social life." What was she trying to prove? "That I'm here because I worked to be here. All those complexes." She giggles.

Spending a term studying in Moscow helped: "When I came back I just felt more relaxed and in my skin and OK about it all. I think it comes as you get a bit older – you're okay with who you are and where you come from. And I'm so close to my family so why would I have a complex about them? When they're great people and good to me."

She'd been auditioning for six months when she met writer/director Sean Durkin, who was looking for an unknown actor to star in his film debut. "I had never seen a young female character this interesting in a film," says Olsen. They started shooting three weeks later. Durkin is part of the three-man (all under 30) Brooklyn collective Borderline Films (sensibility: Altman meets Haneke).

Some critics are calling it this year's Winter's Bone: it's got a similar Hicksville-rural setting and co-stars John Hawkes (scary Uncle Teardrop in Winter's Bone). He is dynamite here as cult leader Patrick, playing this sinewy psychopath like a gentle-souled poet; the temperature changes every time he walks in the room. He manipulates Martha with terrifying, insidious care. Like all the women on the commune she goes through an initiation "cleansing" – rape dressed up as a holistic remedy (she's drugged with sedatives crushed into a herbal drink).

It's striking how often Olsen appears naked in front of the camera (and not in that strategically positioned silk sheets way: this is fully exposing – and not remotely erotic). She had some qualms before accepting the role. "This is only my second film. I thought that if other films required nudity that I didn't agree with, they could say: 'Well you did it in that movie.'" Her agent told her she was crazy. Then someone told her to watch Kate Winslet in Jane Campion's Holy Smoke, which swung it: "I started thinking: a lot of actresses have done nudity in films – some of my favourite actresses. And I never think of them as actresses who do nudity.

"And here it felt important and honest to the story. One the biggest ways that someone can brainwash you – and it happened in the Manson family – is by taking your sexuality and your body, and letting it be everyone's to share. If you give that away to someone then you've lost total awareness of your body and your mind."

I ask if her character is based on a real-life cult victim. "Nooo …" she answers tentatively. No one in particular. Although Durkin did a lot of research and spoke to a friend who had run away from a cult. Did she meet her? "No. I never wanted to. I didn't want to feel like I had to make this film in reverence of her, or owing her."

Privacy is a big deal for Olsen. Her sisters are paparazzi-magnets and seeing the intrusion into their lives almost put her off acting altogether. Just recently she was door-stopped by a photographer, leaving her flat in New York to go to the airport. "I was so confused: how does he know I live here? And he's talking to me: 'Have a good flight Lizzie!'" She pulls a sarcastic face: "Thanks, stranger with a camera that looks like a weapon."

You have to wonder whether another actor would be getting the door-to-door paparazzi service this early in their career. Her pap-factor must have something to do with the family likeness. The Olsen gene is one heck of a fighter. This has her in giggles: "We used to take family photos for Christmas cards and every year it just got weirder and weirder." In high school, with longer blonder hair she'd be mistaken for Mary Kate. She adds that's she's certain the attention will die off: "It's harder for young women, but also I think some bring it on themselves. And I'm not going to do anything to to make people interested in my private life."

I don't have the heart to mention the straggle of photographers loitering shiftily outside.

• Martha Marcy May Marlene is released on 3 February