In 1962, Arthur Miller and his third wife, the Austrian photographer Inge Morath, travelled to her native land and visited Mauthausen concentration camp. For many at the time, the Holocaust was both an inconvenient truth and a repressed memory. As Miller later remarked, ‘the whole Nazi thing was slipping into history’. The camp, not yet a place of pilgrimage, was practically deserted. Miller wandered around, taking stock of its high walls, iron gates, ‘monstrous’ buildings and torture rooms with drains in each of them.

For Morath, the visit was an opportunity to reckon with past pain. As she put it: ‘If the past wants you, you have to face it.’ For Miller, the visit was a catalyst that influenced future work. ‘It made me certain that I had to write about this,’ he said. ‘What was interesting to me was that… the whole thing described the death of love, people incapable any more of the human connection.’ He went on to finish his play After the Fall, which now featured a hulking, looming colourless stone tower, a symbol of the Nazi camps. He also took the themes of prejudice and persecution – which he previously explored to supreme effect in his great allegory for McCarthyism, The Crucible – and re-examined them in a series of dramas that dealt with the plight of Jews during the Third Reich. ‘I have never analysed a gentile who did not have, somewhere hidden in his mind, a dislike if not a hatred for the Jews,’ says the psychiatrist Leduc in Incident at Vichy (1964).

Another of those plays was Broken Glass, set during the aftermath of Kristallnacht, the Nazi-organised pogrom of November 1938 that resulted in the destruction of thousands of Jewish buildings. This work from 1994 is easily the finest play from Miller’s late period. It requires, however, a good creative team to make credible its somewhat outlandish premise – a woman reads about the barbarity of the night of broken glass and loses her ability to walk.

The cast and crew of a new production of the play at London’s Young Vic work wonders at synthesising those separate traumas – what Miller called ‘a public concern and a private neurosis’ – into a singular story. That story takes place in Brooklyn and revolves around the Jewish American couple Phillip and Sylvia Gellburg and their rocky marriage. In Jordan Fein’s revival, Eli Gelb and Pearl Chanda expertly embody a husband and wife driven further apart by threats an ocean away and problems closer to home.

When the play opens, marital cracks are deepening. Sylvia despairs as she loses herself in newspaper reports about the brutal attacks being carried out in Nazi Germany. Phillip looks on, increasingly baffled and disturbed. Dr Harry Hyman believes her condition is psychosomatic and labels it ‘hysterical paralysis’. His wife, Margaret, wonders if Sylvia is mad: ‘Getting this hysterical about something on the other side of the world is sane?’ But antisemitism is on the rise in 1930s New York. Anti-Jewish sentiment also festers in Phillip, who is at odds with his identity and at pains to impress on people he is ‘Gellburg, not Goldberg’. As the play unfolds, it becomes clear that Sylvia’s illness is less a consequence of Jewish persecution and more a result of her husband’s lack of physical affection. Can Phillip heal his marital rifts and cure his wife by following the good doctor’s orders and giving Sylvia ‘a lot of loving’? And can this self-hating Jew start appreciating himself into the bargain?

Gelb and Chanda bring equal amounts of rage and desperation to their roles. Gelb makes his first entrance as a stiff businessman in a black three-piece suit; by the time we reach the play’s closing scene he is unbuttoned and undone and howling about the emotional cost of marriage and the ordeal of being ‘a full-time Jew’. Chanda wails at a newspaper photograph of two old Jewish men made to clean a dirty street with toothbrushes while a mob stands around them jeering. Her anguish is palpable as she rails against global indifference to the worsening political crisis: ‘Where’s Roosevelt?’ she cries. ‘Where’s England?’ Chanda sounds grief-stricken when uttering one of the play’s best lines about her squandered life: ‘Gave it away like a couple of pennies – I took better care of my shoes.’

Alex Waldmann plays Hyman with panache. The charismatic doctor, ‘a real hotshot’ in his heyday, has an unorthodox bedside manner and he soon emerges as the third point of a spiky love triangle. Waldmann affects an air of breeziness when declaring that the current strife in Germany will pass. ‘German music and literature is some of the greatest in the world; it’s impossible for those people to suddenly change into thugs like this.’ He assumes a more earnest tone to impart worldly wisdom regarding persecution.

I’ll tell you a secret – I have all kinds coming into my office, and there’s not one of them who one way or another is not persecuted. Yes. Everybody’s persecuted. The poor by the rich, the rich by the poor, the black by the white, the white by the black, the men by the women, the women by the men, the Catholics by the Protestants, the Protestants by the Catholics – and of course all of them by the Jews. Everybody’s persecuted – sometimes I wonder, maybe that’s what holds this country together!

At key junctures, Juliet Cowan injects the play with light doses of humour as Sylvia’s sister Harriet. Nancy Carroll’s Margaret is equally comic as she interferes and rubs Phillip up the wrong way, but she deftly slides into seriousness when sharing with Sylvia her simple advice about how to live life based on her experience of hard knocks: ‘You draw your cards face down; you turn them over and do your best with the hand you got. What else is there, my dear? What else can there be?’

Rosanna Vize’s effective set consists of puce-carpeted floors and walls, stacks of newspapers with headlines from both 1938 and the present, and rows of clocks showing different times in different cities. There is a bed on which an immobile Chanda reclines and a defeated Gelb collapses. None of it changes, so the whole arrangement doubles as the Gellburgs’ Brooklyn interior and the doctor’s office and waiting room.

Tim Gibbons conjures up a beguiling sound design. The cellist that introduces each of Miller’s acts is replaced by background strains of jazz. Loud discordant bursts of noise jolt the audience at dramatic moments – including one, added by Fein, in which Gelb scrubs the floor with an imaginary toothbrush while the other cast members mock him.

Some elements don’t work. Miller’s subplot about a real-estate deal feels tacked on. Fein’s decision to leave the house lights largely undimmed comes across as a clumsy attempt to ratchet up the intensity and facilitate close scrutiny. Cast members who remain onstage after their scenes have concluded prove distracting.

These are minor gripes, for this is a superb production of a morally complex play. Miller’s biographer Christopher Bigsby argued that Broken Glass was one of several works that saw the dramatist changing tack, making an effort to ‘press beyond the social and psychological to the metaphysical’. Miller himself admitted it was ‘full of ambiguities’. The actors bring those ambiguities to the surface as they invite us to draw parallels between atrocities committed in the past and horrors perpetrated today, and a woman’s paralysis and international complacency and complicity. More than 30 years on, the brute force of Miller’s late-career triumph continues to reverberate.

Broken Glass will be performed at the Young Vic, London until 18 April.