Optomechanical Sensing of Spontaneous Wave-Function Collapse

Quantum experiments with nanomechanical oscillators are regarded as a test bed for hypothetical modifications of the Schrödinger equation, which predict a breakdown of the superposition principle and induce classical behavior at the macroscale. It is generally believed that the sensitivity to these unconventional effects grows with the mass of the mechanical quantum system. Here we show that the opposite is the case for optomechanical systems in the presence of generic noise sources, such as thermal and measurement noise. We determine conditions for distinguishing these decoherence processes from possible collapse-induced decoherence in continuous optomechanical force measurements.

Figure 1

Sketch of an optomechanical setup for measuring macrorealistic noise forces. The harmonic motion $x(t)$ of a cantilever, monitored by means of an optical cavity field, is subject to thermal noise $f_T(t)$, optical amplitude noise $x_{\text{in}}(t)$, and a hypothetical collapse-induced noise force $f_{\mathrm{CSL}}(t)$. All three contributions are reflected in the noise spectrum of the phase quadrature $p_{\text{out}}(t)$ of the outgoing light field, as monitored by homodyne detection.

Figure 2

Lower bound ${\mathrm{\Lambda }}_T$ for the detectable CSL rate parameter ${\lambda }_{\mathrm{CSL}}$ due to thermal noise at 1 K, for varying mass $m$ and linewidth $\gamma$ of a cubic silicon cantilever; see Eq. (5). The side length of the cube is given on the top, the quality factor $Q$ of a 1 Hz oscillator on the right. The currently estimated upper bound for ${\lambda }_{\mathrm{CSL}}$ ($0.1\mathrm{nHz}-1\mu \mathrm{Hz}$) is indicated by the shaded area.

Figure 3

Lower bound ${\mathrm{\Lambda }}_{\text{SQL}}$ for the detectable CSL rates ${\lambda }_{\mathrm{CSL}}$ due to measurement noise at SQL, as a function of mass $m$ and measurement frequency $\omega$; see Eq. (10). We assume a cubic silicon cantilever (side length on the top) with frequency $\mathrm{\Omega }=1\mathrm{Hz}$ and quality factor $Q=10^6$. Relevant upper bounds for the CSL rate are indicated by the shaded area.