Fig. 1. Characteristics and preparation methods of the squeezed states and the entangled states. (a)–(d) Wigner functions of (a) the vacuum state, (b) the coherent state, (c) the quadrature amplitude squeezed vacuum state, and (d) the quadrature phase squeezed vacuum state. Insets show the edge distribution of Wigner function^[39]. (e) Parametric down-conversion based on degenerate optical parametric amplifier. (f) Parametric down-conversion based on non-degenerate optical parametric amplifier^[42]. (g), (h) Single-mode and two-mode squeezed state generated from the four-wave mixing process in the atomic ensemble^[44].

Fig. 2. (a) Preparation of entangled photon pairs^[49]. (b) Preparation of the two-photon NOON state^[50]. (c) Preparation of the multi-photon NOON state^[53].

Fig. 3. (a) Setup of the SRS microscope. (b) High-frequency modulation to suppress low-frequency noise. (c) SRL signal in the pump beam^[60].

Fig. 4. Preparation of the bright squeezed light. (a) The CW bright squeezed light is prepared by coupling a squeezed vacuum state with a coherent state on a beam splitter^[35]. (b) The pulsed bright squeezed light is prepared by using a seeded optical parametric amplifier^[36].

Fig. 5. (a) SNR of the polydimethylsiloxane (PDMS) at 2904.76 cm^–1 Raman shift measured with coherent (left side) and squeezed (right side) light, respectively^[35]. (b) A live yeast cell in an aqueous buffer at 2850 cm⁻¹ Raman shift imaged with coherent (left side) and squeezed (right side) light, respectively^[36].

Fig. 6. (a) Schematic of the SRS microscopy with QBD^[66]. (b) Classical and quantum balanced-detection SRS images at Raman shift 2118 cm⁻¹. Scale bar: 10 µm^[37].

Fig. 7. (a) Experimental setup of the entangled TPA microscope^[34]. (b) Images of breast cancer cells excited with the entangled two-photon (left) and the classical light (right), respectively.

Fig. 8. Classical and quantum-enhanced DIM^[38]. (a) Illustration of the classical DIM. (b) Illustration of the quantum-enhanced DIM. The red and blue lines represent different polarized light. (c) Image of the sample using a classical light. (d) Image of the sample using the two-photon entangled state. (e), (f) One-dimensional fine scan data for the area outlined in the red regions in (c) and (d) for the same photon number of 920.