Squeezed States of Light
Squeezed light is best understood by considering complex phasors for the representation of the state of light in one mode of the optical field. Classically, such a state can be represented by a certain phasor (or its end point in the complex plane). According to quantum optics, however, there is a quantum uncertainty, and any measurement of the complex amplitude of the light field can deliver different values within an uncertainty region. Moreover, there is an uncertainty relation for the quadrature components of the light field, saying that the product of the uncertainties in both components is at least some quantity times Planck's constant h.
Glauber's coherent states have circularly symmetric uncertainty regions, so that the uncertainty relation dictates some minimum noise amplitudes e.g. for the amplitude and phase. The area of that uncertainty region is independent of the average amplitude, i.e., it can not be reduced by attenuating the light. A further reduction in, e.g., amplitude noise is possible only by “squeezing” the uncertainty region, reducing its width in the amplitude direction while increasing it in the orthogonal direction, so that the phase uncertainty is increased. Such light is called amplitude-squeezed (see Figure 1, left). Conversely, phase-squeezed light (Figure 1, middle) has decreased phase fluctuations at the expense of increased amplitude fluctuations.
Of course, there are also squeezed states where the orientation of the uncertainty region is different from the cases shown, or where the shape of the uncertainty region is different from that of an ellipse. (An extreme case are Fock states, having a certain photon number.) In any case, some noise component is below the standard quantum limit.
There is also the so-called squeezed vacuum (Figure 1, right), where the center of the uncertainty region (corresponding to the average amplitude) is at the origin of the coordinate system, and the fluctuations are reduced in some direction. The mean photon number is larger than zero in this case; a squeezed vacuum is a “vacuum” only in the sense that the average amplitude (but not the average photon number) is zero. Squeezed light with a non-zero average amplitude is also called bright squeezed light.
Quantum noise also leads to fluctuations of the polarization, which are reduced in polarization-squeezed light.
Generation of Squeezed Light
Squeezed light is usually generated from light in a coherent state or vacuum state by using certain optical nonlinear interactions. For example, an optical parametric amplifier with a vacuum input can generate a squeezed vacuum with a reduction in the noise of one quadrature components by the order of 10 dB. A lower degree of squeezing in bright amplitude-squeezed light can under some circumstances be obtained with frequency doubling. The Kerr nonlinearity in optical fibers also allows the generation of amplitude-squeezed light. Semiconductor lasers can generate amplitude-squeezed light when operated with a carefully stabilized pump current. Squeezing can also arise from atom-light interactions.
Another possibility is to use optomechanical squeezing [20, 25]. Here, fluctuations of the radiation pressure, which are associated with the intensity noise, modulate the path length of light in an optical resonator and thus induce correlations between the amplitude and phase noise.
In principle, squeezed light can be used in a number of areas, as it allows for measurements with reduced quantum noise. An example is the ultraprecise measurement of lengths for the detection of gravitational waves with large-scale interferometers. In particular, the advanced LIGO Hanford setup has been equipped with that technology, which contributed a substantial enhancement of measurement sensitivity  before the first detection in 2015 succeeded .
So far, the use of squeezed light is not very widespread, basically because it is plagued with various difficulties. For example, any optical losses bring a squeezed state of light closer to a coherent state, i.e. tend to destroy the nonclassical properties. At least in fundamental quantum optics research, however, squeezed states of light play an important role.
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|||C. M. Caves, “Quantum limits on noise in linear amplifiers”, Phys. Rev. D 26 (8), 1817 (1982), doi:10.1103/PhysRevD.26.1817|
|||D. F. Walls, “Squeezed states of light”, Nature 306, 141 (1983), doi:10.1038/306141a0|
|||R. E. Slusher et al., “Observation of squeezed states generated by four wave mixing in an optical cavity”, Phys. Rev. Lett. 55 (22), 2409 (1985), doi:10.1103/PhysRevLett.55.2409|
|||S. Machida et al., “Observation of amplitude squeezing in a constant-current-driven semiconductor laser”, Phys. Rev. Lett. 58 (10), 1000 (1987), doi:10.1103/PhysRevLett.58.1000|
|||P. Grangier et al., “Squeezed light-enhanced polarization interferometer”, Phys. Rev. Lett. 59 (19), 2153 (1987), doi:10.1103/PhysRevLett.59.2153|
|||H. J. Kimble and D. Walls (eds.), special issue on squeezed light in J. Opt. Soc. Am B 4 (10) (1987)|
|||R. E. Slusher et al., “Pulsed squeezed light”, Phys. Rev. Lett. 59 (22), 2566 (1987), doi:10.1103/PhysRevLett.59.2566|
|||S. F. Pereira et al., “Generation of squeezed light by intracavity frequency doubling”, Phys. Rev. A 38 (9), 4931 (1988), doi:10.1103/PhysRevA.38.4931|
|||W. H. Richardson et al., “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser”, Phys. Rev. Lett. 66 (22), 2867 (1991), doi:10.1103/PhysRevLett.66.2867|
|||E. S. Polzik et al., “Spectroscopy with squeezed light”, Phys. Rev. Lett. 68 (20), 3020 (1992), doi:10.1103/PhysRevLett.68.3020|
|||R. Paschotta et al., “Bright squeezed light from a singly-resonant frequency doubler”, Phys. Rev. Lett. 72 (24), 3807 (1994), doi:10.1103/PhysRevLett.72.3807|
|||G. Breitenbach et al., “Squeezed vacuum from a monolithic optical parametric oscillator”, J. Opt. Soc. Am. B 12 (11), 2304 (1995), doi:10.1364/JOSAB.12.002304|
|||S. Schmitt et al., “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer”, Phys. Rev. Lett. 81 (12), 2446 (1998), doi:10.1103/PhysRevLett.81.2446|
|||M. Margalit et al., “Cross phase modulation squeezing in optical fibers”, Opt. Express 2 (3), 72 (1998), doi:10.1364/OE.2.000072|
|||Y. Li et al., “Sub-shot-noise-limited optical heterodyne detection using an amplitude-squeezed local oscillator”, Phys. Rev. Lett. 82 (26), 5225 (1999), doi:10.1103/PhysRevLett.82.5225|
|||Y. Takeno et al., “Observation of −9 dB quadrature squeezing with improvement of phase stability in homodyne measurement”, Opt. Express 15 (7), 4321 (2007), doi:10.1364/OE.15.004321|
|||H. Vahlbruch et al., “Observation of squeezed light with 10 dB quantum noise reduction”, Phys. Rev. Lett. 100 (3), 033602 (2008), doi:10.1103/PhysRevLett.100.033602|
|||C. F. McCormick et al., “Strong low-frequency quantum correlations from a four-wave-mixing amplifier”, Phys. Rev. A 78 (4), 043816 (2008), doi:10.1103/PhysRevA.78.043816|
|||M. Mehmet et al., “Squeezed light at 1550 nm with a quantum noise reduction of 12.3 dB”, Opt. Express 19 (25), 25763 (2011), doi:10.1364/OE.19.025763|
|||T. P. Purdy et al., “Strong optomechanical squeezing of light”, Phys. Rev. X 3, 031012 (2013), doi:10.1103/PhysRevX.3.031012|
|||J. Aasi et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light”, Nature Photonics 7, 613 (2013), doi:10.1038/nphoton.2013.177|
|||E. Oelker et al., “Ultra-low phase noise squeezed vacuum source for gravitational wave detectors”, Optica 3 (7), 682 (2016), doi:10.1364/OPTICA.3.000682|
|||H. Vahlbruch et al., “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency”, Phys. Rev. Lett. 117 (11-9), 110801 (2016), doi:10.1103/PhysRevLett.117.110801|
|||B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), “Observation of gravitational waves from a binary black hole merger”, Phys. Rev. Lett. 116 (6), 061102 (2016), doi:10.1103/PhysRevLett.116.061102|
|||N. Aggarwal et al., “Room-temperature optomechanical squeezing”, Nature Physics 16, 784 (2020), doi:10.5281/zenodo.3694290|
|||S. F. Tasker et al., “Silicon photonics interfaced with integrated electronics for 9 GHz measurement of squeezed light”, Nature Photonics 15, 11 (2021), doi:10.1038/s41566-020-00715-5|
|||P. Cutipa and M. V. Chekhova, “Bright squeezed vacuum for two-photon spectroscopy: simultaneously high resolution in time and frequency, space and wavevector”, Opt. Lett. 47 (3), 465 (2022), doi:10.1364/OL.448352|
See also: quantum optics, coherent states, intensity noise, phase noise, amplitude-squeezed light, nonclassical light, standard quantum limit
and other articles in the categories quantum optics, fluctuations and noise