Quantum Interference Reveals How Particles Defy Uncertainty

Yuki Senoo at Hiroshima University and colleagues have conducted a thorough experimental study of photons, using a Sagnac interferometer to generate superpositions of position and momentum. The experiment reveals an interference effect that localises photons within narrow ranges of both position and momentum, resulting in a measurable deviation from classical Newtonian physics. The resulting data provides evidence for the negativity of the Wigner function, furthering understanding of non-classical particle behaviour and the fundamental limits imposed by the uncertainty principle.

Demonstrating non-classical behaviour through Wigner function negativity and momentum localisation

Initial position and momentum uncertainties are approximately equal to each other. The interference effect localizes the photons in narrow intervals of position and momentum, resulting in a quantitative violation of Newton’s first law as the interference pattern spreads out at the intermediate position. The obtained data can demonstrate the negativity of the Wigner function in regions outside the position and momentum intervals where position and momentum contributions are confined.

The relation between wave propagation and the detection of individual particles represents one of the most fundamental problems of quantum mechanics. Moyal pointed out that the Wigner function is the only quasi-probability of position and momentum consistent with straight-line motion in free space. Therefore, negative Wigner functions represent violations of Newton’s first law, indicating that classical concepts of motion are not valid in quantum mechanics. Rather than introducing modified laws of motion, it may be better to investigate the specific violations of classical expectations associated with negative Wigner function values.

Quantum backflow demonstrates such a violation, where a probability current flows opposite to the available values of momentum. A superposition of momentum eigenstates with p > 0 can describe a probability current from x > 0 to x, clearly demonstrating that the classical constraints a momentum distribution would impose on the spatial distribution’s time evolution are not valid. A closely related quantum phenomenon is the violation of an inequality by a superposition of position and momentum.

This inequality relates the probability of finding a particle in the position interval L and the probability of finding it in the momentum interval B to the probability of finding it in a position interval M at a later time. Classical laws of motion would require all particles in both L and B to arrive at M. The predicted violation has been confirmed experimentally in a setup generating an equal superposition of position and momentum. Here, new experimental data obtained in a similar setup are presented to study how quantum interference modifies particle propagation.

Detailed count rates for the transverse spatial distribution of photons in position, in momentum, and at the intermediate position where maximal inequality violation is observed were obtained. Contributions from the position state, the momentum state, and the interference between the two were identified. The state can be reconstructed from the experimental data, with an effective quasi-probability distribution of wL = 0.355 in the position state, wB = 0.493 in the momentum state, and winter = 0.152 in the interference term.

The interference term is responsible for an overall inequality violation of 0.060, with positive contributions of 15.2% to both P(L) and P(B), and an interference pattern contributing only 5.4% to P(M). This violation corresponds to negative values of the Wigner function in the regions outside intervals L and B, where the total negativity is obtained from integrals over the phase space regions. This negativity is a direct consequence of the simultaneous control of position and momentum expressed by the interference term’s contributions to P(L) and P(B). The results show how interference effects reshape the propagation of quantum particles in free space, providing important quantitative evidence for the failure of the classical particle picture in quantum mechanics. The remainder of this paper is organized as follows.

Section II introduces the concept of the experiment and explains the inequality. The relation between the inequality violation and the negativity of the Wigner function is also included. Section III explains the experimental setup and procedure, while Section IV discusses the measurement results and numerical analysis. Quantum interference appearing in spatial distributions is evaluated and isolated based on quasi-probability, and a comparison between the initial and intermediate times is discussed. This analysis enables a discussion of the quadratic dependence of the phase difference on position x. Section IV also presents the time-evolved wavefunction ⟨x| U(tM) |ψ⟩ of the superposition |ψ⟩ at time t = tM, from which the probability P(M) can be obtained by integration over the corresponding probability density, P(M) = ∫M/2’M/2 dx ⟨x | U(tM) | ψ⟩ ψ U†(tM) x. At a time tM with BtM/m = L, the wavefunctions of |L⟩ and |B⟩ have the same spatial envelope, and their interference is decided by the quadratic dependence of the phase difference on position x. Although the interference effect increases the probability density close to x = 0, these details are not fully elaborated in this excerpt.

Quantum interference violates position-momentum inequality and reveals non-classical photon

The inequality relating position and momentum probabilities was violated by 0.060, a departure from classical predictions previously considered impossible. This demonstrates that photons do not travel along straight lines as predicted by Newton’s first law; instead, quantum interference localises them within narrow ranges of both position and momentum. Detailed measurements using a Sagnac interferometer revealed contributions of 15.2% from both initial position and momentum states, alongside a 5.4% contribution from the interference pattern itself.

This experimental setup allowed for the reconstruction of the particle state, demonstrating a negative Wigner function, a mathematical concept indicating non-classical behaviour, outside the defined position and momentum intervals. This confirms a fundamental limit to classical descriptions of particle motion. Detailed analysis of photon distributions revealed contributions of 15.2% from the initial position state and 15.2% from the initial momentum state, both measured using a Sagnac interferometer, a device employing interference of light to measure rotation. While these results definitively demonstrate a departure from classical physics and the limitations of Newton’s first law, they currently describe photon behaviour in highly controlled laboratory conditions and do not yet translate into predictable manipulation of particles for practical technologies.

Photon behaviour illuminates quantum limits for massive particles

Scientists continue to refine our understanding of how quantum particles behave, and this work offers a precise demonstration of the interplay between position and momentum. The research acknowledges a significant gap, however; these observations are currently limited to photons, leaving open whether similar violations of classical physics occur in particles with mass. Bohmian mechanics offers alternative approaches to reconcile quantum behaviour with deterministic trajectories, but requires assumptions about hidden variables; this experiment instead focuses on directly observing the quantum state without invoking such concepts.

Acknowledging doubts about extending these findings beyond photons is crucial; particles possessing mass may exhibit different behaviours due to their inherent properties. Nevertheless, this detailed study of photon behaviour significantly advances our grasp of fundamental quantum principles, specifically the interplay between a particle’s position and momentum. A violation of Newton’s first law was demonstrated using photons in a Sagnac interferometer, which creates a superposition of position and momentum states.

These findings reveal how quantum mechanics governs individual particle behaviour, localising photons within specific position and momentum ranges. This experiment successfully demonstrated a simultaneous localisation of photons in both position and momentum, a feat previously considered incompatible with the uncertainty principle. By utilising a Sagnac interferometer, scientists observed a clear violation of Newton’s first law; photons did not follow predictable, straight-line paths. The resulting spread of the interference pattern at an intermediate point confirmed that quantum interference actively reshapes particle propagation, challenging classical notions of motion. The negativity of the Wigner function, a mathematical tool describing quasi-probability distributions, was experimentally verified outside the defined position and momentum ranges.

The research demonstrated that photons can be simultaneously localised in both position and momentum, seemingly defying the uncertainty principle. This is achieved by preparing photons in a superposition of position and momentum states using a Sagnac interferometer, resulting in an interference effect that localises the particles. Consequently, the experiment observed a violation of Newton’s first law as the interference pattern spread, confirming that quantum interference actively reshapes particle propagation. The data also allowed scientists to demonstrate the negativity of the Wigner function, providing further insight into quantum behaviour.