Prospects for near-field interferometric tests of collapse models

Near-field interferometry with large dielectric nanoparticles opens the way to test fundamental modifications of standard quantum mechanics at an unprecedented level. We showcase the capabilities of such platform, in a state-of-the-art ground-based experimental setup, to set stringent bounds on the parameter space of collapse models and highlight the future perspectives for this class of experiments.

Figure 1

Setup of the near-field interferometer with a levitated nanoparticle. The latter is initially trapped and cooled down in an optical cavity. After the cavity is switched off, the particle freely falls for a time $t_1$ before reaching an optical grating generated by a pulsed UV laser that is retroreflected by a mirror. The grating period is half the wavelength of the standing wave. At the optical grating, the particle's wave function is required to have a spatial coherence larger than, at least, the distance between two adjacent “slits” of the grating. After the grating, the particle freely falls for a time $t_2$ before being measured on the final screen.

Figure 2

Interference pattern for the proposed near-field interferometric experiments with nanoparticle of mass ${10}^7$ amu. (a) Shows the interference pattern obtained using Si particles at cryogenic temperature $T_{env}=4$ K and with $E_L/a_L=0.003\mathrm{J}{\mathrm{m}}^{-2}$. (b) Shows instead the analog result for ${\mathrm{SiO}}_2$ particles, with $E_L/a_L=0.009\mathrm{J}{\mathrm{m}}^{-2}$. In both cases the free-fall times are such that $t_1=2t_2=0.36$ s and the pulse energy to spot-area ratio is determined at the same value of the eikonal phase ${\varphi }_0=1.4\pi$ (cf. Refs. [15, 17] for further details on the connection between the eikonal phase and the energy to spot-area ratio). The blue dashed curves represent the “classical” shadow effect image, i.e., the figure that would be obtained from the deviation of the ballistic trajectory of classical particles; the black continuous curves represent the prediction of standard quantum mechanics; and the red dotted curves show the effect of accounting for CSL with $\lambda ={10}^{-12}{\mathrm{s}}^{-1}$ and $r_C={10}^{-7}$ m.

Figure 3

Exclusion plots for the CSL parameters with respect to the GRW's and Adler's theoretical values [9, 23, 29]. The red, solid line denotes the upper bound that can be obtained by the experiment proposed in Ref. [15] with ${\mathrm{SiO}}_2$ particles of mass of ${10}^6$ amu at cryogenic temperature. The blue, solid line denotes the upper bound that can be obtained by using a ${\mathrm{SiO}}_2$ particle with mass of ${10}^7$ amu and times $t_1=2t_2$ and $t_2=0.181s$ at cryogenic temperature. The green, solid line represents the upper bound that can be obtained by using a ${\mathrm{SiO}}_2$ particle with a mass of ${10}^7$ amu, times $t_1=t_2=9.95s$, and cryogenic temperature. The red, dotted-dashed line corresponds to the upper bound that can be obtained replacing the ${\mathrm{SiO}}_2$ particle with mass ${10}^6$ amu with a Si particle and working at room temperature. By using Si particles instead of ${\mathrm{SiO}}_2$, and working at cryogenic temperature, similar bounds to the ones shown in this picture can be achieved (not shown for clarity). The gray area at the bottom of the plot represents the theoretical bound given in Ref. [31], the dotted gray excluded areas represent the upper bounds given by current noninterferometric tests, as reported in Refs. [25, 32, 33, 34], and the dashed black lines represent the upper bounds given by current interferometric tests as reported in [11, 12, 35].