Author Affiliations
1National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences, and School of Physics, Nanjing University, Nanjing 210093, China2Department of Physics, Nanjing Tech University, Nanjing 211816, China3Centre for Quantum Computation and Communication Technology, School of Engineering and Information Technology, University of New South Wales, Canberra, Australian Capital Territory 2600, Australia4Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA5e-mail: mxiao@uark.edushow less
Fig. 1. Representation of different states in the phasor diagram: (a) coherent state, (b) vacuum state, (c) vacuum-squeezed state, (d) phase-squeezed state, and (e) amplitude-squeezed state.
Fig. 2. Schematic of degenerate OPA and graph of dielectric polarization
P(E)=ε0(χ(1)E+χ(2)E2) representing the second-order nonlinear process in the crystal. Adapted with permission from Ref. [
68].
Fig. 3. (a) Schematic of balanced homodyne detection. PD, photodetector. (b) Setup of an MZI. M, mirror. Coherent light illuminates port a of the MZI, while a vacuum state (or squeezed state) is injected via port b.
Fig. 4. Square-wave phase signal is obtained with (a) vacuum and (b) squeezed vacuum. Adapted with permission from Ref. [
71].
Fig. 5. (a) Polarization interferometer. (b) Polarization rotation signal and noise. Adapted with permission from Ref. [
72].
Fig. 6. (a) Scheme of the experiment setup in one-dimensional displacement measurement. Adapted with permission from Ref. [
10]. (b) Scheme of the experiment setup in two-dimensional displacement measurement. The two squeezed modes are generated from two OPA cavities and mixed in a mode-mixing cavity. SHG, second harmonic generator; OPA, optical parametric amplifier; EOM, electro-optic modulator; ESA, electronic spectrum analyzer. Adapted with permission from Ref. [
34].
Fig. 7. TEM10 homodyne detection for beam displacement measurement. BS, 50/50 beam splitter; LO, local oscillator. The dashed line delineates the small displacement. Adapted with permission from Ref. [
78].
Fig. 8. (a) Schematic of squeezing-enhanced phase estimation. (b) Fisher information versus phase shift for a pure 6-dB squeezed-vacuum state. Adapted with permission from Ref. [
16].
Fig. 9. (a) Dependence of estimation variance on input phase. (b) Dependence of estimation variance on the number of homodyne samples. Adapted with permission from Ref. [
16].
Fig. 10. Quantum-enhanced homodyne phase tracking system. Adapted with permission from Ref. [
12].
Fig. 11. (a) Dependence of MSE on squeezing level. (b) Dependence of MSE on amplitude squared
|α|2. Adapted with permission from Ref. [
12].
Fig. 12. (a) Schematic of the mirror-motion estimation and (b) dependence of MSE on amplitude squared
|α|2. Adapted with permission from Ref. [
98].
Fig. 13. Example of a prepared-atom ensemble where the pump beam orients the spins of the ensemble. The pump beam, probe beam, and magnetic field are mutually orthogonal. Adapted with permission from Ref. [
108].
Fig. 14. Representation of quantum polarization states of bright coherent and bright amplitude-squeezed light on the Poincare sphere. Adapted with permission from Ref. [
114].
Fig. 15. (a) Simplified layout of Advanced LIGO. (b) Strain noise of each detector of Advanced LIGO. Adapted with permission from Ref. [
118].
Fig. 16. Simplified setup of the H1 interferometer with vacuum-squeezed-state injection. Adapted with permission from Ref. [
14].
Fig. 17. Strain sensitivity of H1 detector with and without squeezed-vacuum injection. Adapted with permission from Ref. [
14].
Fig. 18. Sagnac interferometer output signal. Adapted with permission from Ref. [
36].
Fig. 19. (a) Dependence of phase noise reduction on frequency for the quantum-enhanced fiber interferometer. (b)–(d) Demodulated noise spectra of the interferometer output at 30 kHz, 80 kHz, and 150 kHz. Adapted with permission from Ref. [
37].
Fig. 20. Time domain results of fiber-optic phase tracking. Adapted with permission from Ref. [
135].