Metasurface-Assisted Quantum Nonlocal Weak-Measurement Microscopy

In standard quantum weak measurements, preselection and postselection of quantum states are implemented in the same photon. Here we go beyond this restrictive setting and demonstrate that the preselection and postselection can be performed in two different photons, if the two photons are polarization entangled. The Pancharatnam-Berry phase metasurface is incorporated in the weak measurement system to perform weak coupling between probe wave function and spin observable. By introducing nonlocal weak measurement into the microscopy imaging system, it allows us to remotely switch different microscopy imaging modes of pure-phase objects, including bright-field, differential, and phase reconstruction. Furthermore, we demonstrate that the nonlocal weak-measurement scheme can prevent almost all environmental noise photons from detection and thus achieves a higher image contrast than the standard scheme at a low photon level. Our results provide the possibility to develop a quantum nonlocal weak-measurement microscope for label-free imaging of transparent biological samples.

Figure 1

Quantum weak measurements for phase reconstruction of pure-phase objects. (a) The scheme of standard weak measurements. Preselection and postselection of quantum state are implemented in the same photon. (b) The scheme of nonlocal weak measurements. Preselection and postselection are performed in two polarization entangled photons, respectively. The PB phase metasurface performs the weak coupling, and introduces a pointer shift.

Figure 2

Experimental measurement of entangled weak value by controlling the nonlocal preselection in the heralding arm. (a) Experimental scheme. In the imaging arm, a dielectric metasurface is placed on the focus plane of a $4f$ system to introduce a pointer shift, the polarizer 2 is used to implement the postselection. The polarization of entangled photon pairs is $(1/\sqrt{2})(|HH⟩+|VV⟩)$. The polarizer 1 in the heralding arm performs the preselection state with $|H-\mathrm{\Delta }⟩$. (b) The experimental results of the entangled weak value by adjusting the preselection in the heralding arm. The insets show the experimental images of intensity for different preselection states.

Figure 3

Experimental setup of metasurface assisted quantum nonlocal weak-measurement microscope. Broadband dielectric mirror (BDM); periodically poled ${\mathrm{KTiOPO}}_4$ crystal (PPKTP); dual-wavelength polarization beam splitter (DPBS); polarization beam splitter (PBS); dichromatic mirror (DM); fiber coupler (FC); band-pass filter (BPF); dual-wavelength half wave plate (DHWP); half wave plate (HWP); quarter wave plate (QWP); single photon avalanche detector (SPAD); intensified charge coupled device (ICCD). The blue (red) light path presents the 405 nm (810 nm) photons. The imaging system is composed of an objectives ($(10\times ,\mathrm{NA}=0.25)$ and a $4f$ system. The PB phase metasurface performs a weak coupling and introduces a initial pointer shift. The preselection and the postselection are implemented by polarizer 1 and polarizer 2, respectively.

Figure 4

Nonlocal phase reconstruction of transparent glass plate sample (model: BK7). $\mathrm{\Psi }$ and $\mathrm{\Phi }$ shapes are etched on the glass surface with a 200 nm step using optical lithography. (a) and (d) The probability distribution $P^{|H-\mathrm{\Delta }⟩}(x,y)-P^{|H+\mathrm{\Delta }⟩}(x,y)$. (b) and (e) The deferential images of phase distribution $|\partial \phi (x,y)/\partial x+i\partial \phi (x,y)/\partial y|$. (c) and (f) The reconstructed phase distributions $\phi (x,y)$. Insets in (c) and (f) show the designed phase distributions.

Figure 5

Nonlocal switch of different imaging modes in the imaging arm based on the remote modulation of preselections in the heralding arm. (a) Bright-field image ($\mathrm{\Delta }=90°$). (b) Differential image ($\mathrm{\Delta }=0°$). (c) Phase reconstruction image ($\mathrm{\Delta }=3°$). (d)–(f) are taken along the white dashed lines in (a)–(c), respectively. Scale bar, $100\mathrm{\mu }\mathrm{m}$.