Inside a radio-frequency trap at Oxford’s Clarendon Laboratory, a single strontium ion hangs in a vacuum, cooled to near stillness, vibrating with an energy so close to nothing that quantum mechanics itself sets the floor. The ion is about ten nanometres across. Its motion is the harmonic oscillator, the same mathematical beast that describes a child’s swing, a plucked guitar string, the electromagnetic shiver of light itself. For decades, physicists have been squeezing that motion, redistributing its quantum uncertainty to sharpen one property at the cost of another. What Oana Băzăvan and her colleagues at Oxford have now done is push the squeezing to a place no one has gone before.
The result, published in Nature Physics, is something called quadsqueezing: a fourth-order quantum interaction that, until now, existed mostly as a theoretical curiosity. Getting there required a trick that was, in a way, hiding in plain sight.
The Quantum Noise Problem
Squeezing is already a workhorse of precision physics. It works because quantum mechanics does not let you know everything about a system at once. Position and momentum, for instance, cannot both be pinned down simultaneously; this is Heisenberg’s uncertainty principle, not as a failure of measurement but as a hard feature of reality. Squeezing reshapes that uncertainty: make position sharper and momentum gets blurrier, or vice versa. Squeezed light is already used in gravitational-wave detectors like LIGO, where the sensitivity needed to catch the faint ripple of two colliding black holes requires beating quantum noise itself. Ordinary, second-order squeezing does that job. But physicists have long suspected that going further, to third-order (trisqueezing) and fourth-order (quadsqueezing) interactions, would unlock genuinely different quantum territory. Non-Gaussian states, they are called, and they matter because the classical computers that can efficiently simulate ordinary Gaussian quantum systems hit a wall when the Gaussianity breaks. Higher-order squeezing, if it could be achieved, would be a resource for a new generation of quantum computing and simulation.
The obstacle, bluntly, is that higher-order interactions are weak. Very weak. In a trapped-ion system, every step up in interaction order means the coupling shrinks by roughly an order of magnitude, because the driving field’s spatial derivatives fall off quickly. Getting to the fourth order using conventional techniques would require interaction strengths so small they drown in decoherence before anything useful happens.
The Oxford team found their way around this by combining two forces rather than searching for one strong enough. Each force, on its own, is a straightforward linear interaction: it displaces the ion’s quantum state in phase space, conditioned on the ion’s internal spin. Individually, they are unremarkable. But apply both at once, with their spin components chosen so they do not commute with each other, and something nontrivial emerges. The two forces interfere, in a quantum mechanical sense, and that interference generates effective nonlinear interactions with a resonance condition that the experimenters can tune by adjusting the frequency difference between the two drives. Shift that frequency ratio and you move through squeezing, trisqueezing, quadsqueezing, without changing anything else about the apparatus.
“In the lab, non-commuting interactions are often seen as a nuisance because they introduce unwanted dynamics,” said Băzăvan. “Here, we took the opposite approach and used that feature to generate stronger quantum interactions.”
A Hundred Times Faster
The practical payoff is striking. The quadsqueezing interaction they generated was more than a hundred times stronger than what would be expected using conventional techniques with the same laser power. That is not a marginal improvement; it is the difference between an effect that exists in principle and one that can actually be observed and characterised before the quantum coherence falls apart. The team confirmed each interaction by reconstructing its Wigner function, a kind of quantum phase-space portrait that reveals whether a state is Gaussian or something stranger. The squeezed state came out as the familiar stretched ellipse. The trisqueezed state showed a clear departure from any Gaussian shape. The quadsqueezed state, the one no experiment had ever touched before, showed a Wigner function with four-fold geometry, the signature of the interaction order stamped directly into the fabric of the quantum state.
“The result is more than the creation of a new quantum state,” Băzăvan said. “It is a demonstration of a new method for engineering interactions that were previously out of reach. The fourth-order quadsqueezing interaction was generated more than 100 times faster than expected using conventional approaches. This makes effects that were previously out of reach accessible in practice.”
There are caveats worth noting. The trisqueezed and quadsqueezed states achieved here are relatively weakly squeezed compared with what would eventually be needed for, say, fault-tolerant quantum computing. The initial thermal motion of the ion is also not quite zero, which muddies the Wigner functions a little and makes the expected negativity harder to observe cleanly. These are engineering challenges rather than fundamental limits, and the paper includes a supplementary demonstration of Wigner negativity in the quadsqueezed state when the laser power is increased and the pulse shortened.
What makes the approach genuinely interesting beyond this particular experiment is its generality. The spin-mediated trick works on any platform that supports spin-dependent linear interactions, which is rather a lot of them: trapped ions, superconducting circuits, atoms in cavities, nitrogen-vacancy centres in diamond. And there is, in principle, no fundamental ceiling on the interaction order. Want fifth-order? Sixth? The theory, originally proposed in 2021 by Raghavendra Srinivas and Robert Sutherland, says you can get there by extending the same idea. Srinivas, who supervised the experimental work and is a co-author on the paper, is already thinking about multimode extensions, where similar mediated interactions could generate entanglement between different vibrational modes of a single ion or an entire crystal. That points toward universal continuous-variable quantum computing, where the ability to generate arbitrary non-Gaussian operations is the missing ingredient. Beyond computing, the technique could also feed into quantum simulation of interacting boson models, which show up in condensed matter physics and even in the quantum field theories that particle physicists use to describe fundamental forces.
“Fundamentally, we have demonstrated a new type of interaction that lets us explore quantum physics in uncharted territory,” said Srinivas, “and we are genuinely excited for the discoveries to come.” Uncharted is perhaps not hyperbole: a family of quantum states that have never been made before is now accessible, and the machinery to make them is, it turns out, already sitting in labs around the world.
Frequently Asked Questions
Why does squeezing matter if quantum computers already use qubits?
Qubits store information in two discrete states, but quantum harmonic oscillators encode information continuously, in the amplitude and phase of oscillation. This continuous-variable approach can represent quantum states more compactly in some cases, and higher-order squeezing operations like trisqueezing and quadsqueezing are precisely the non-Gaussian resources needed to make continuous-variable quantum computation universal. Without them, you can do a lot of quantum maths efficiently, but certain computations and error-correction schemes remain out of reach.
How is this different from the squeezing already used in LIGO?
LIGO uses ordinary second-order squeezing, which redistributes quantum noise between the phase and amplitude of light to make gravitational-wave detection more sensitive. That is a Gaussian operation, meaning it can in principle be simulated efficiently by a classical computer. Trisqueezing and quadsqueezing are non-Gaussian operations, which generate fundamentally different kinds of quantum states, ones that classical simulation struggles to handle. The Oxford experiment is exploring the rungs above the one LIGO sits on.
Could this technique work in quantum platforms other than trapped ions?
That is one of the more practically significant aspects of the result. The approach relies on spin-dependent linear interactions, which are available in superconducting microwave circuits, atoms in optical cavities, nitrogen-vacancy centres in diamond, and other platforms. The Oxford team worked with a trapped strontium ion, but the underlying method is not specific to that system, which suggests the technique could spread relatively quickly across the field.
What is a Wigner function, and why does its shape matter here?
A Wigner function is a way of representing a quantum state as a kind of probability distribution spread over phase space, plotting the joint quasi-probability of position and momentum values. Gaussian states produce smooth, blob-like Wigner functions; non-Gaussian states produce distorted, multi-lobed, or even negative-valued distributions. The four-fold geometry seen in the Oxford team’s quadsqueezed Wigner function is a direct fingerprint of the fourth-order interaction, confirmation that they reached the quantum state they were aiming for.
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