Fig. 1. Strong IDS from the FWM process in rubidium vapor. (a) Experimental schematic. PBS, polarizing beam splitter; SA, spectrum analyzer. (b) Double-Λ energy level diagram. (c) Transmission for the probe beam as a function of the detuning from the ⁸⁵Rb D₁ line transition. The arrow indicates the pump detuning. (d) Experimentally measured noise power as a function of spectrum analyzer frequency with (A)–(D) electronic noise, squeezed noise between the probe and conjugate, SNL, and probe noise, respectively. Adapted from [72].

Fig. 2. (a), (b) Hyperfine levels in D₁ and D₂ line transitions of ⁸⁵Rb (a) and ⁸⁷Rb (b). (c), (d) Experimentally measured squeezing levels in the D₁ (red circles) and D₂ (blue triangles) lines of ⁸⁵Rb (c) and ⁸⁷Rb (d) versus pump detuning. Adapted from [73].

Fig. 3. IDS from the FWM process in potassium vapor, which is a strongly absorbing medium. (a) Experimental setup and double-Λ energy configuration. (b) Experimentally measured IDS with different intensity gain and probe transmissions (t). Adapted from [74].

Fig. 4. (a) Experimental details. (b) Energy level diagram of ⁸⁵Rb D₂ line transition. (c) Phase-matching conditions for the spontaneous FWM (c1), spontaneous SWM (c2), and spontaneous EWM (c3) processes. (d) Noise power as a function of spectrum analyzer frequency for SQL (c1), FWM (c2), E₃-dressed FWM (c3), E₄-dressed FWM (c4), and E₃- and E₄-dressed FWM (c5). (e) Noise power versus total optical power for SQL (A), FWM (B), E₃-dressed FWM (C), E₄-dressed FWM (D), and E₃- and E₄-dressed FWM (E). Adapted from [79].

Fig. 5. (a) Setup geometry. (b) Gain and IDS as a function of the angle $\theta$. (c) Mandel parameter for the probe only (left) and for the intensity difference (right) versus the transmission. Adapted from [86].

Fig. 6. (a) Experimental setup. (b) Experimental results of the effect of the size and spatial profile of the pump beam on the size of the coherence area and the number of spatial modes. Adapted from [87].

Fig. 7. (a) The masked and filtered probe beam is seeded into the center of the vapor cell. (b) Generation and detection of the squeezed vacuum beam with BLO. (c) Squeezing versus the width of the BLO. (d) Squeezing versus BLO position when it is translated along the x = y direction. The green squares and blue circles show the squeezing in a gain of four and two, respectively. (e), (f) Images of BLO corresponding to the green and blue data, respectively. (g)–(i) Similar to (d)–(f) as the BLO position translates along the x = −y direction. Adapted from [88].

Fig. 8. Entangled images from the FWM process. (a) Geometry of the multi-spatial-mode property of the FWM process. (b) Measured quadrature squeezing for T-shaped modes. Adapted from [93].

Fig. 9. (a) The probe (Pr) and the conjugate (C) beams are generated from the FWM process in the first rubidium cell. The second cell delays the probe beam. (b) EPR entanglement disappears for a delay of about 27 ns. Adapted from [95].

Fig. 10. (a) Experimental setup and double-Λ configuration. (b) Normalized amplitude of the amplified seeded pulse and the newly generated conjugate pulse for two different seeded pulse detunings. Adapted from [97].

Fig. 11. Advancement of bright intensity-difference squeezed light. (a) Experimental setup. (b) Measured delay of the cross-correlation function versus the detuning of the pump beam of the second FWM process and the observed IDS. Adapted from [98].

Fig. 12. Quantum mutual information of advanced and delayed entangled states. (a) Experimental setup. (b) Quantum mutual information versus relative delay for fast (red curve) and slow (green curve) light. Adapted from [99].

Fig. 13. (a) Experimental details for the FWM-based PSA. TA, tapered amplifier. (b) NF results versus spatially varying losses when cutting by a slit (red circles), cutting by a razor blade (green triangles), or attenuating by a neutral density filter (blue squares). (c) MTF of the PSA (MTF_PSA) measured along two directions. Adapted from [100].

Fig. 14. (a) The top panel shows the schematic of the PSA. The lower panel shows the double-Λ configuration in the D₁ transition of ⁸⁵Rb. Here ν₁ and ν₂ represent the pump beams, and ν_p represents the probe beam. (b) Experimental setup. (c) Quadrature squeezing measured by HD. Adapted from [101].

Fig. 15. (a) Configuration of PSA. $\widehat{a}$ and $\widehat{b}$ are the probe and conjugate beams, respectively. $\widehat{c}$ is the pump beam. (b) Detailed experimental setup. HWP, half-wave plate; rf, radio frequency; D₁ (D₂), photodetector; S, subtractor. Adapted from [102].

Fig. 16. IDS of two-beam PSA process (a), probe-seeded PIA process (b), conjugate-seeded PIA process (c), and probe-conjugate-seeded PIA process (d) under the same experimental situation. The inset of (d) shows the intensity profile of output fields of probe-conjugate-seeded PIA process. Adapted from [102].

Fig. 17. Experimental results of amplitude-quadrature-difference (a) and phase-quadrature-sum (b) entanglement; experimental results of amplitude-quadrature-sum (c) and phase-quadrature-difference (d) entanglement. Adapted from [103].

Fig. 18. (a) Experimental layout. (b) Noise powers of beams A–C, and their subtractions D–G. H is SNL of trace A–G. (c) Enhancement of quantum correlation. Adapted from [135].

Fig. 19. (a) Experimental setup. $\lambda$/2, half-wave plate. (b) Image of the output beams. Adapted from [136].

Fig. 20. (a) Noise power of different beams and their subtraction. (b) Enhancement of quantum correlation. Adapted from [136].

Fig. 21. (a) Detailed experimental layout. (b) Spatial structure of the output beams. (c) Image of the output beams. Adapted from [137].

Fig. 22. Measured IDS of the six quantum correlated beams. (a) Noise powers of beams ${\widehat{a}}_1$ (B), ${\widehat{a}}_3$ (C), ${\widehat{a}}_2$ (D), ${\widehat{a}}_4$ (E), and their SNL (A). (b) Noise powers of subtraction ${\widehat{a}}_1-{\widehat{a}}_3$ (B) and their SNL (A). (c) Noise powers of subtraction ${\widehat{a}}_1-{\widehat{a}}_2$ (B) and their SNL (A). (d) Noise powers of subtraction ${\widehat{a}}_1-{\widehat{a}}_4$ (B) and their SNL (A). (e) Noise powers of subtraction ${\widehat{a}}_1-{\widehat{a}}_2-{\widehat{a}}_3-{\widehat{a}}_4$ (B), ${\widehat{a}}_1-{\widehat{a}}_2-{\widehat{a}}_3-{\widehat{a}}_4+{\widehat{a}}_5+{\widehat{a}}_6$ (C) and their SNL (A). Adapted from [137].

Fig. 23. (a) Detailed experimental layout for generating hexapartite entanglement; (b) output beams; (c) 31 symplectic eigenvalues in the cases of different balanced pump powers. Adapted from [138].

Fig. 24. Reconfigurable hexapartite entanglement by tailoring the power ratio of the two pump beams. Adapted from [138].

Fig. 25. (a) Experimental layout; (b) output beams; (c) measurement of 10-beam quantum correlation. Adapted from [139].

Fig. 26. Effect of the angle between the two pump beams (a), one-photon detuning (b), and two-photon detuning (c) on the number of quantum correlated beams. Adapted from [140].

Fig. 27. (a) Unseeded, spontaneous FWM geometries for a circularly symmetric pump (left) and an asymmetrically structured pump (right). (b) Output image of FWM when seeded by a weak probe beam. (c) Output image in theory. (d) Experimental intensity images of the diffracting pump along the propagation direction. The theoretical pump profile in the center of the cell is also shown. (e) Measured IDS between beams 2 and 5. Adapted from [141].

Fig. 28. (a) Experimental diagram. (b) Top: images when the power ratio of P_A to P_B is changed. Bottom: total intensity of output light, excluding pump beams, as a function of ratio P_B/P_A. Adapted from [143].

Fig. 29. (a) Intensity distribution (upper) and phase interferogram (lower) when OAM beam serves as probe beam. (b) Mandel Q parameter of the intensity difference versus the transmittance as the two beams are attenuated equally. (c), (d) Similar to (a), (b) as the OAM beam serves as pump beam. Adapted from [149].

Fig. 30. (a) Detailed experimental setup. (b) Double-Λ energy level diagram of ⁸⁵Rb D₁ line transition. (c) OAM spectrum from the FWM process. (d) Dove prism is used to transfer LG_−l,pr to LG_l,pr. Adapted from [29].

Fig. 31. (a) Entanglement test between LG_l,pr and LG_−l,conj versus topological charge l. (b) Entanglement test between LG_l,pr and LG_l,conj versus topological charge l. Trace A is the intensity gain of probe beam and trace B is the symplectic eigenvalue. Adapted from [29].

Fig. 32. Entanglement meaurement of (a) $\sqrt{k}{\mathrm{LG}}_{1,\text{pr}}+\sqrt{1-k}{\mathrm{LG}}_{5,\text{pr}}$, (b) ${\mathrm{LG}}_{l,\text{pr}}+{\mathrm{LG}}_{-l,\text{pr}}$, and (c) ${\mathrm{LG}}_{1,\text{pr}}+e^{2i\theta }{\mathrm{LG}}_{-1,\text{pr}}$. Adapted from [29].

Fig. 33. (a) Detailed experimental setup. (b) Double-Λ energy level diagram. (c) Dove prism is used to transfer LG_−l,pr2 to LG_l,pr2. Adapted from [176].

Fig. 34. (a) Witnessing the OAM multiplexed tripartite entanglement. Traces A and B represent the gains of cell₁ and cell₂, respectively. Traces C, D, and E represent three symplectic eigenvalues. (b) Witnessing the OAM multiplexed bipartite entanglement. Traces F, G, and H represent three symplectic eigenvalues. Diagram of OAM multiplexed (c) tripartite and (d) bipartite entanglement. Adapted from [176].

Fig. 35. (a) Measurements of OAM multiplexed tripartite entanglement. (b)–(d) Measurements of the tripartite entanglement for coherent OAM superposition modes. Adapted from [176].

Fig. 36. (a) Principle for generating large-scale multipartite entanglement. (b) Detailed experimental setup. Adapted from [177].

Fig. 37. (a), (b) Measurements of large-scale multipartite entanglement for different topological charges l. (c), (d) Holograms loaded on the SLM and the six output LG beams. Adapted from [177].

Fig. 38. (a) Configuration of OAM multiplexed AOQT. (b) Detailed experimental setup of OAM multiplexed AOQT. (c) Fidelity of OAM multiplexed all-optical teleportation (AOT) with different OAM channels. Adapted from [199].

Fig. 39. (a)–(d) Fidelities of simultaneously teleported OAM superposition modes ${\widehat{a}}_{\text{in}}={\widehat{a}}_{\text{in},l}+{\widehat{a}}_{\text{in},-l}$. Adapted from [199].

Fig. 40. Detailed experimental setup of AOES. Adapted from [212].

Fig. 41. Experimental results of AOES. Variance of (a) amplitude-quadrature difference and (b) phase-quadrature sum between ${\widehat{a}}_1$ and ${\widehat{a}}_2^{\prime }$. (c), (e) are similar to (a) and (d), (f) are similar to (b) except that the states are EPR₁ and EPR₂. Adapted from [212].

Fig. 42. (a) Experimental setup of low-noise amplification. (b) Squeezing trace at 1 MHz for quadratures at two different amplifier gains. The left traces show the squeezing level with no amplification and no attenuation. The right traces show the squeezing with an amplification of 1.8 and an attenuation of 56%. (c) E₁₂ and I versus gain. Adapted from [213].

Fig. 43. Detailed experimental setup of all-optical optimal N → M quantum cloning. Adapted from [227].

Fig. 44. Fidelities of the quantum cloning machine. Adapted from [227].

Fig. 45. Experimental layout. Adapted from [233].

Fig. 46. (a)–(f) Experimental results when G = 2 and G = 16. (g) Fidelities versus G for all-optical quantum state transfer machine. Adapted from [233].

Fig. 47. (a) Experimental layout. OAM multiplexed bipartite entangled beams are utilized to implement the OAM MQDC protocol. Alice encodes classical signals on EPR1, and Bob decodes the signals by HDs. (b) Channel capacities of four schemes versus different topological charges l. Adapted from [241].

Fig. 48. Structure of MZI (a) and SU(1,1) interferometer (b). Adapted from [266].

Fig. 49. (a) Detailed experimental setup of MZI and SU(1,1) interferometer. (b) Phase sensitivity of SU(1,1) interferometer and SNL varying with N_s. Adapted from [266].

Fig. 50. (a) Cascaded FWM scheme. (b) Typical noise power spectra of measured joint quadrature squeezing. Trace i shows the noise power of ${\widehat{X}}_{-}$ for cascaded FWM processes; trace ii shows the noise power of ${\widehat{X}}_{-}$ for single FWM process; trace iii shows the corresponding SNL. (c) Measured quadrature squeezing versus the intensity gain of FWM processes. Adapted from [269].

Fig. 51. Effect of losses on the QNC of the SU(1,1) interferometer. p,c↓ (c,p↓) is the losses case in probe (conjugate) field when attenuation acts on the conjugate (probe) arm of the SU(1,1) interferometer; p,p↓ (c,c↓) is the losses case in probe (conjugate) field when attenuation acts on the probe (conjugate) arm of the SU(1,1) interferometer. Adapted from [275].

Fig. 52. Uncertainty of the phase estimation with internal loss for the SU(1,1) interferometer injected with vacuum fields (a) and coherent fields (b). Trace (i) shows the uncertainty in the lossless case. Trace (ii) shows the contribution from the internal losses. Trace (iii) shows the uncertainty with internal losses (1 − $\eta$₁ = 0.1). Adapted from [125].

Fig. 53. Configurations of conventional SU(1,1) interferometer and truncated SU(1,1) interferometer are shown in (a) and (b), respectively. i, ii, iii, and iv show different measurement schemes for SU(1,1) interferometer. NLO, nonlinear optical medium; HD, homodyne detector. (c) Theoretical results of the variance of the phase estimation versus gain in lossless case. (d) Measured SNR for truncated SU(1,1) interferometer (blue solid trace) and corresponding coherent scheme (red dashed trace). Adapted from [127].

Fig. 54. Schematic for the truncated SU(1,1) interferometer. $\lambda$ is the attenuation factor. Adapted from [278].

Fig. 55. (a) Theoretical noise power of ${\widehat{M}}_{\lambda Q}$ versus the attenuation factor $\lambda$ at different gains. (b) $\lambda$_opt versus the intensity gain of FWM process at different optical transmissions ($\eta$_c = $\eta$_p). (c) Experimental results of the noise power of ${\widehat{M}}_{\lambda Q}$ versus the attenuation factor $\lambda$ with an FWM gain of 1.67 in the case of 79% conjugate transmission and 76% probe transmission. (d) Experimental results of $\lambda$_opt versus FWM gain. Adapted from [278].

Fig. 56. Setup for ultrasensitive measurement of microcantilever displacement. Adapted from [40].

Fig. 57. Measurement results for sub-shot-noise microcantilever deflection detection. Adapted from [40].

Fig. 58. Experimental setup. MC, microcantilever. Adapted from [128].

Fig. 59. (a) Traces of microcantilever displacement when a weak probe is reflected from the microcantilever. Different lines correspond to different voltages of PZT on the AFM microcantilever. (b) SNR of the corresponding scheme. (c) Traces of microcantilever displacement when high-power LO beam is reflected from the microcantilever. (d) SNR of the corresponding scheme. Adapted from [128].

Fig. 60. (a) Experimental setup for the transduction of a squeezed state through an EOT medium. ND is a neutral density filter used to balance the classical intensity noise. (b) Scanning electron microscope image of triangle hole array of LSPs. (c) Measured squeezing levels versus transmissions. Adapted from [121].

Fig. 61. (a) Experimental setup. (b) Measured squeezing versus the reflectivity of the SPR sensor. (c) Measured squeezing versus the incident angle of the SPR sensor. Black, blue, and red lines represent squeezing with a refractive index of 1.3, 1.301, and 1.305, respectively. Adapted from [118].

Fig. 62. (a) Experimental setup. (b) Plasmonic resonance versus relative incidence angle and refractive index. (c) Quantum noise reduction versus incidence angle and refractive index. Adapted from [119].

Fig. 63. (a) Experimental setup. DLP, digital light processor; HJ, hybrid junction for simultaneously adding and subtracting the two signals. (b) Effect of EOT on spatial images coded on the correlated beams. Normalized noise of the amplitude-quadrature sum (blue trace) and phase-quadrature difference (red trace) of the entangled beams (c) before and (d) after the plasmonic films. Adapted from [122].

Fig. 64. (a) Experimental setup. (b) Measured power spectra for probing the sensor with coherent states and twin beams with Δn = 1.6 × 10⁻⁷ refractive index unit (RIU). (c) Measured power spectra with Δn = 8.2 × 10⁻⁹ RIU. (d) Normalized power versus the change in refractive index. (e) SNRs measured by probing the plasmonic sensor with coherent states (i) and with twin beams (ii). Adapted from [120].