[Paper Review] Probing Planck-scale physics with quantum optics

Igor Pikovski, Michael R. Vanner+3 more|Nov 8, 2011

Noncommutative and Quantum Gravity Theories29 citations

TL;DR

This paper proposes a tabletop quantum optics experiment to probe quantum gravitational effects by testing modifications to the canonical commutator of a massive mechanical oscillator near the Planck scale. Using optomechanical interactions and high-precision optical interferometry, the scheme achieves sensitivity to Planck-scale deformations of the commutator—enabling tests of generalized uncertainty principles with current technology, including a 33-order-of-magnitude improvement over existing bounds for certain parameters.

ABSTRACT

One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Various approaches towards developing such a theory of quantum gravity are pursued, but the lack of experimental evidence of quantum gravitational effects thus far is a major hindrance. Yet, the quantization of space-time itself can have experimental implications: the existence of a minimal length scale is widely expected to result in a modification of the Heisenberg uncertainty relation. Here we introduce a scheme that allows an experimental test of this conjecture by probing directly the canonical commutation relation of the center of mass mode of a massive mechanical oscillator with a mass close to the Planck mass. Our protocol utilizes quantum optical control and readout of the mechanical system to probe possible deviations from the quantum commutation relation even at the Planck scale. We show that the scheme is within reach of current technology. It thus opens a feasible route for tabletop experiments to test possible quantum gravitational phenomena.

Motivation & Objective

• To develop a feasible experimental test for quantum gravitational modifications of the canonical commutation relation in massive systems.
• To overcome the limitations of current experiments, which lack sensitivity to Planck-scale effects due to insufficient position measurement precision.
• To enable direct probing of generalized uncertainty principles predicted by various quantum gravity approaches, such as string theory and doubly special relativity.
• To achieve experimental sensitivity to deformations of the commutator at the Planck scale using current or near-future technology.
• To provide empirical feedback for quantum gravity theories through high-precision measurement of the mechanical oscillator's commutator via optical field readout.

Proposed method

• The scheme uses a mechanical oscillator with mass near the Planck mass, coupled to a high-intensity optical field in an optical cavity via radiation pressure.
• A sequence of optomechanical interactions maps the commutator of the mechanical system's position and momentum onto the phase of a coherent optical pulse.
• The optical field's mean phase shift is measured using interferometric techniques, which are sensitive to deviations in the commutator due to quantum gravitational effects.
• The protocol non-linearly enhances sensitivity through high optical pulse intensity, enabling detection of small commutator deformations without requiring ultra-precise position measurements.
• The method is robust against noise, as it relies on measuring the optical field's mean, which can be isolated from decoherence and loss effects through parameter tuning.
• Deformations are modeled via modified commutators of the form [x,p] = iℏ(1 + β₀Lₚ²p² + γ₀Lₚ²p² + μ₀Lₚ²p²) or similar, with parameters β₀, γ₀, μ₀ quantifying deviations from standard quantum mechanics.

Experimental results

Research questions

• RQ1 Can quantum gravitational effects, such as a minimal length scale, be probed through deviations in the canonical commutator of a massive mechanical oscillator?
• RQ2 Is it possible to achieve experimental sensitivity to Planck-scale deformations of the commutator without requiring direct measurement of Planck-scale position uncertainties?
• RQ3 To what extent can current quantum optics and optomechanical technologies test generalized uncertainty principles predicted by quantum gravity models?
• RQ4 How do different types of commutator modifications (β₀, γ₀, μ₀) scale with experimental parameters like optical intensity and oscillator mass?
• RQ5 Can noise sources such as mechanical damping and optical loss be mitigated well enough to allow detection of Planck-scale signals?

Key findings

• The scheme achieves a sensitivity to β₀-modified commutators at δβ₀ ∼ 1, representing a 33-order-of-magnitude improvement over current experimental bounds.
• For γ₀-modified commutators, a precision of δγ₀ ∼ 1 is achievable with Np = 5×10¹⁰ photons, improving existing bounds by 10 orders of magnitude.
• For μ₀-modified commutators, a precision of δμ₀ ∼ 1 is reached with Np = 10⁸ photons in a single measurement run.
• The required experimental parameters—such as optical cavity finesse F = 4×10⁵, mass m = 10⁻⁷ kg, and λL = 532 nm—are within reach of current technology, including dilution refrigeration and optical stabilization.
• The method remains robust against decoherence and noise, provided the mechanical oscillator is cooled to a thermal occupation n̄ < 30 and the system is stabilized over timescales of seconds.
• Deviations from standard quantum mechanics due to quantum gravity can be distinguished from noise sources by varying optical intensity and oscillator mass, enabling unambiguous detection.