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Squeezed States of Light

Definition: nonclassical states of light with noise below the standard quantum limit in one quadrature component

More general term: nonclassical states of light

More specific terms: amplitude-squeezed light, phase-squeezed light

Opposite term: classical light

German: gequetschte Lichtzustände

Categories: quantum opticsquantum optics, fluctuations and noisefluctuations and noise


Cite the article using its DOI: https://doi.org/10.61835/dcj

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Squeezed states of light (or squeezed light) are a kind of nonclassical light and constitute an interesting subject of quantum optics, the experimental investigation of which began in the 1980s.

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.

squeezed states of light
Figure 1: Different squeezed states of light, illustrated in phasor diagrams. The blue ellipses indicate the uncertainty regions.

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. For example, there are photon number squeezed states with a reduced uncertainty of the photon number but possibly complete phase uncertainty. (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 [22, 28]. 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 [23] before the first detection in 2015 succeeded [26].

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.

More to Learn

Encyclopedia articles:


[1]C. M. Caves, “Quantum limits on noise in linear amplifiers”, Phys. Rev. D 26 (8), 1817 (1982); https://doi.org/10.1103/PhysRevD.26.1817
[2]D. F. Walls, “Squeezed states of light”, Nature 306, 141 (1983); https://doi.org/10.1038/306141a0
[3]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); https://doi.org/10.1103/PhysRevLett.55.2409
[4]S. Machida et al., “Observation of amplitude squeezing in a constant-current-driven semiconductor laser”, Phys. Rev. Lett. 58 (10), 1000 (1987); https://doi.org/10.1103/PhysRevLett.58.1000
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[9]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); https://doi.org/10.1103/PhysRevLett.66.2867
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[12]R. Paschotta et al., “Bright squeezed light from a singly-resonant frequency doubler”, Phys. Rev. Lett. 72 (24), 3807 (1994); https://doi.org/10.1103/PhysRevLett.72.3807
[13]G. Breitenbach et al., “Squeezed vacuum from a monolithic optical parametric oscillator”, J. Opt. Soc. Am. B 12 (11), 2304 (1995); https://doi.org/10.1364/JOSAB.12.002304
[14]S. Schmitt et al., “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer”, Phys. Rev. Lett. 81 (12), 2446 (1998); https://doi.org/10.1103/PhysRevLett.81.2446
[15]M. Margalit et al., “Cross phase modulation squeezing in optical fibers”, Opt. Express 2 (3), 72 (1998); https://doi.org/10.1364/OE.2.000072
[16]Y. Li et al., “Sub-shot-noise-limited optical heterodyne detection using an amplitude-squeezed local oscillator”, Phys. Rev. Lett. 82 (26), 5225 (1999); https://doi.org/10.1103/PhysRevLett.82.5225
[17]V. V. Dodonov, “Nonclassical states in quantum optics: A squeezed review of the first 75 years”, J. Opt. B: Quantum Semiclassical Opt. 4 (1), R1–R33 (2002); https://doi.org/10.1088/1464-4266/4/1/201
[18]Y. Takeno et al., “Observation of −9 dB quadrature squeezing with improvement of phase stability in homodyne measurement”, Opt. Express 15 (7), 4321 (2007); https://doi.org/10.1364/OE.15.004321
[19]H. Vahlbruch et al., “Observation of squeezed light with 10 dB quantum noise reduction”, Phys. Rev. Lett. 100 (3), 033602 (2008); https://doi.org/10.1103/PhysRevLett.100.033602
[20]C. F. McCormick et al., “Strong low-frequency quantum correlations from a four-wave-mixing amplifier”, Phys. Rev. A 78 (4), 043816 (2008); https://doi.org/10.1103/PhysRevA.78.043816
[21]M. Mehmet et al., “Squeezed light at 1550 nm with a quantum noise reduction of 12.3 dB”, Opt. Express 19 (25), 25763 (2011); https://doi.org/10.1364/OE.19.025763
[22]T. P. Purdy et al., “Strong optomechanical squeezing of light”, Phys. Rev. X 3, 031012 (2013); https://doi.org/10.1103/PhysRevX.3.031012
[23]J. Aasi et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light”, Nature Photonics 7, 613 (2013); https://doi.org/10.1038/nphoton.2013.177
[24]E. Oelker et al., “Ultra-low phase noise squeezed vacuum source for gravitational wave detectors”, Optica 3 (7), 682 (2016); https://doi.org/10.1364/OPTICA.3.000682
[25]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); https://doi.org/10.1103/PhysRevLett.117.110801
[26]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); https://doi.org/10.1103/PhysRevLett.116.061102
[27]U. L. Andersen et al., “30 years of squeezed light generation”, Physica Scripta 91 (5), 053001 (2016); https://doi.org/10.1088/0031-8949/91/5/053001
[28]N. Aggarwal et al., “Room-temperature optomechanical squeezing”, Nature Physics 16, 784 (2020); https://doi.org/10.5281/zenodo.3694290
[29]S. F. Tasker et al., “Silicon photonics interfaced with integrated electronics for 9 GHz measurement of squeezed light”, Nature Photonics 15, 11 (2021); https://doi.org/10.1038/s41566-020-00715-5
[30]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); https://doi.org/10.1364/OL.448352

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Questions and Comments from Users


Is the 3-dB noise limit of an optical amplifier determined by the uncertainty range of the coherent state? If so, can the squeezed state reduce the noise to less than 3 dB?

The author's answer:

You probably mean the 3-dB noise figure. That is a property of an optical amplifier, not of the light field itself. Thus, the answer is no. Only a phase-sensitive amplifier – for example, an optical parametric amplifier – can possibly beat that 3-dB limit.

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