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Acta Physica Sinica

Quantum precision measurement based on squeezed light

Sun Heng-Xin, Liu Kui, Junxiang Zhang, Gao Jiang-Rui

Published Jan 1, 2015• 12 citations
Publisher

Abstract

According to the Heisenberg uncertainty principle, the precision of any physical quantity measurement is limited by quantum fluctuation in general, which leads to the so-called standard quantum limit (SQL). The SQL can be beaten by using squeezed light, hence enhancing the measurement accuracy. Squeezed light is a typical nonclassical light, it exhibits reduced noise in one quadrature component. Since Caves proposed the scheme of phase measurement enhancement with squeezing, squeezed light has been used to enhance measurement precision in many areas. This review focuses on the following four kinds of precision measurements based on squeezed light: the measurements of relative phase, small lateral displacement and tilt, magnetic field, and clock synchronization. For all of these measurements, vacuum squeezing has been used to enhance measurement precision, while the types of squeezing (squeezing angle, transverse mode, polarization etc.) are different. For phase measurement, quadrature squeezing is injected into the conventionally unused input port of Mach-Zehnder interferometer (MZI) or Michelson interferometer (MI). For displacement or tilt measurement, a vacuum squeezing beam of a special transverse mode is coupled into an intense coherent beam, yielding a spatial-squeezed light whose transverse position or tilt angle noise is lower than that of a classical light beam. Based on the Faraday effect of polarization rotation, the magnetic field can be detected precisely. The precision can be increased further by using the polarization squeezing. The polarization squeezing can be generated by coupling two orthogonal polarized beams together, a coherent beam and a vacuum squeezed beam. Various polarization squeezing can be illustrated on the Poincaré sphere. Finally, in the clock synchronization based on the optical frequency comb, squeezed light can be used to enhance the time measurement precision. A theoretical scheme with multimode squeezing of supermode (a kind of mode describing the frequency mode of a pulse laser beam) is introduced. The squeezing has extensively been applied into the quantum precision measurements such as gravitational wave detection as well as biological measurement and will play a more important role in the near future.

DOI
10.7498/aps.64.234210

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According to the Heisenberg uncertainty principle, the precision of any physical quantity measurement is limited by quantum fluctuation in general, which leads to the so-called standard quantum limit (SQL). The SQL can be beaten by using squeezed light, hence enhancing the measurement accuracy. Squeezed light is a typical nonclassical light, it exhibits reduced noise in one quadrature component. Since Caves proposed the scheme of phase measurement enhancement with squeezing, squeezed light has been used to enhance measurement precision in many areas. This review focuses on the following four kinds of precision measurements based on squeezed light: the measurements of relative phase, small lateral displacement and tilt, magnetic field, and clock synchronization. For all of these measurements, vacuum squeezing has been used to enhance measurement precision, while the types of squeezing (squeezing angle, transverse mode, polarization etc.) are different. For phase measurement, quadrature squeezing is injected into the conventionally unused input port of Mach-Zehnder interferometer (MZI) or Michelson interferometer (MI). For displacement or tilt measurement, a vacuum squeezing beam of a special transverse mode is coupled into an intense coherent beam, yielding a spatial-squeezed light whose transverse position or tilt angle noise is lower than that of a classical light beam. Based on the Faraday effect of polarization rotation, the magnetic field can be detected precisely. The precision can be increased further by using the polarization squeezing. The polarization squeezing can be generated by coupling two orthogonal polarized beams together, a coherent beam and a vacuum squeezed beam. Various polarization squeezing can be illustrated on the Poincaré sphere. Finally, in the clock synchronization based on the optical frequency comb, squeezed light can be used to enhance the time measurement precision. A theoretical scheme with multimode squeezing of supermode (a kind of mode describing the frequency mode of a pulse laser beam) is introduced. The squeezing has extensively been applied into the quantum precision measurements such as gravitational wave detection as well as biological measurement and will play a more important role in the near future.
Squeezed light, a prominent non-classical state of light, exhibits reduced quantum noise in one quadrature component below the standard quantum limit (SQL). The property enables quantum-enhanced precision measurements, surpassing the SQL in quantum sensing applications. This review comprehensively introduces the fundamental concepts, classifications, and experimental generation techniques of squeezed light. It further explores its pivotal role and recent advances in diverse quantum sensing domains, including interferometry, gravitational wave detection, magnetometry, force sensing, biomedical sensing, and quantum radar. The review covers theoretical foundations of squeezed states (including quadrature operators and classification schemes, experimental generation techniques in atomic ensembles, nonlinear crystals, and fibers), fundamentals of quantum sensing with squeezed light (from quantum noise theory to quantum-enhanced metrology), and quantum-enhanced sensing applications across the aforementioned domains. Finally, future challenges and opportunities in the field are discussed.
The ability to directly detect gravitational waves will open a completely new branch of astronomy to view the Universe, one that is inaccessible to electromagnetic-based astronomy. First generation ground-based interferometric gravitational-wave detectors have achieved strain sensitivities of order one part in ten to the twenty-one, at 100 Hz detection frequency. A new generation of detectors are under construction, designed to improve on the sensitivity of the first-generation detectors by a factor of 10. The quantum nature of light will broadly limit the sensitivity of these new instruments. This quantum noise will originate from the quantum vacuum fluctuations that enter the unused port of the interferometer. One of the most promising options for reducing the quantum noise impact and further increasing the sensitivity is applying quantum squeezed vacuum states. These squeezed states have lower noise in one quadrature than the vacuum state. By replacing the quantum vacuum fluctuations entering the interferometer with squeezed vacuum states, the quantum noise impact is reduced. This thesis firstly details the development of a squeezed light source that produces squeezed states applicable for enhancing interferometric gravitational-wave detectors. A doubly-resonant, travelling-wave bow-tie cavity squeezed light source is presented. For the first time, greater than 10 dB of quantum noise suppression across the gravitational-wave detection band is directly observed, and 11.6 dB of quantum noise suppression is observed above 200 Hz. This squeezing cavity design also has benefits with intrinsic isolation to backscattered light. Experiments that quantify this isolation are reported. The properties affecting squeezing magnitude and low-frequency squeezing measurement are discussed. In addition, a modified squeezing-ellipse-phase control technique for squeezed vacuum states is presented. This thesis secondly presents results from the LIGO Squeezed Light Injection Experiment, undertaken to test squeezed light injection into a 4 km interferometric gravitational-wave detector. The results of the experiment show the first measurement of squeezing-enhancement in a 4 km gravitational-wave detector, with 2.15 dB measured above 250 Hz. This represents the best sensitivity to gravitational waves yet achieved at these frequencies by any single gravitational-wave detector to date. An unknown area was whether the addition of a squeezer would introduce noise couplings that degrade the crucial low frequency sensitivity. The results demonstrate that injected squeezed states are compatible with low frequency gravitational-wave measurement. The characterisation of squeezing-injection optical losses and fluctuations of the squeezing angle are also reported. The knowledge and processes gained, from both the squeezed light source development work and the LIGO Squeezed Light Injection Experiment, will inform the design, planning and implementation of squeezed states in future gravitational-wave detectors.
Measurement of audio signal plays a significant role in many applications, such as gravitational wave detection, bio-particle imaging and magnetometer. In this paper, low-frequency squeezed light is generated by a non-degenerate optical parametric amplifier. In order to avoid the effect of injected light on low-frequency squeezing, an auxiliary laser is used to lock the length of non-degenerate optical parametric amplifier and a method of locking quantum noise is employed to lock the phase between the local light and the squeezed light. By isolating the vibration noises at low-frequency and reducing back action of parasitic interference, the squeezing of (7.1±0.1) dB takes place at 19 kHz. Then the squeezed light is injected into the Mach-Zehnder interferometer to measure an audio signal which drives a piezoelectric transducer to generate a small phase variation between two arms of Mach-Zehnder interferometer. According to the low-frequency squeezing, we realize experimentally the measurement of phase signal at audio frequency which exceeds the shot-noise limit of (3.0±0.4) dB. The experiment provides technical supports for the generation of low-frequency squeezed light and the measurement of audio signal. Furthermore it can be extended to other quantum measurements, such as high-precision magnetometer and measurement of small-displacement.
Introducing squeezed states of light into interferometers can increase the phase sensitivity of the device beyond the standard quantum limit (SQL). We discuss an SU(1,1) interferometer, where nonlinear optical elements replace the beam splitters in a Mach-Zehnder interferometer. A two-mode squeezed state of light is generated inside of such an interferometer. We talk about the phase sensitivities of an SU(1,1) interferometer with different detection schemes and their improvement over the SQL. We also discuss the concept of an optimal detection scheme for phase measurement in an interferometer. We describe a modification of the SU(1,1) interferometer which reduces the experimental complexities while giving the same phase sensitivity. We call the design a truncated SU(1,1) interferometer. We show our experimental results of 4 dB improvement in phase sensitivity over the SQL using a truncated SU(1,1) interferometer. We also compare the theoretical sensitivities of vacuum-seeded configurations of a conventional and a truncated SU(1,1) interferometer, and show our experimental results for the phase sensitivity of the truncated version. We explain the dependence of phase sensitivity on the measurement of squeezing. We talk about the methods to improve the measurement of squeezing in a 4-wave mixing experiment, and our efforts in implementing them. Finally, we mention our progress in measuring a big phase shift using an adaptive algorithm in the truncated SU(1,1) interferometer, and discuss the technicalities involved in big phase measurements.
Stable low-frequency squeezed vacuum states at a wavelength of 1550 nm were generated. By controlling the squeezing angle of the squeezed vacuum states, two types of low-frequency quadrature-phase squeezed vacuum states and quadrature-amplitude squeezed vacuum states were obtained using one setup respectively. A quantum-enhanced fiber Mach–Zehnder interferometer (FMZI) was demonstrated for low-frequency phase measurement using the generated quadrature-phase squeezed vacuum states that were injected. When phase modulation was measured with the quantum-enhanced FMZI, there were above 3 dB quantum improvements beyond the shot-noise limit (SNL) from 40 kHz to 200 kHz, and 2.3 dB quantum improvement beyond the SNL at 20 kHz was obtained. The generated quadrature-amplitude squeezed vacuum state was applied to perform low-frequency amplitude modulation measurement for sensitivity beyond the SNL based on optical fiber construction. There were about 2 dB quantum improvements beyond the SNL from 60 kHz to 200 kHz. The current scheme proves that quantum-enhanced fiber-based sensors are feasible and have potential applications in high-precision measurements based on fiber, particularly in the low-frequency range.
Generation of squeezed state at telecommunication wavelength has been recently a very interesting issue due to the lowest optical power attenuation of light at a wavelength of 1550 nm in a standard telecommunication fiber. The low-frequency vacuum squeezed state at 1550 nm in combination with fiber based interferometer offers the possibility to implement quantum precision measurement beyond standard quantum limit (SQL). In this paper, we experimentally realize a quantum-enhanced fiber Mach-Zehnder interferometer (FMZI) for measuring the low-frequency phase modulation signal by using low-frequency vacuum squeezing at 1550 nm. Firstly, the low-frequency vacuum squeezed state at the telecommunication wavelength of 1550 nm is generated by using a degenerate optical parametric oscillator (DOPO). The DOPO is a semi-monolithic construction based on a type I periodically poled KTiOPO4 (PPKTP) crystal and a concave mirror. The pump threshold of DOPO is 270 mW. When the pump power is 120 mW that is below the pump threshold of DOPO and the temperature of PPKTP is controlled at 34.8℃, a vacuum squeezing of 3 dB is generated at an analysis frequency range from 10 kHz to 500 kHz. The quadrature phase vacuum squeezing is obtained by locking the squeezed quadrature angle through using a coherent control scheme, in which two acousto-optic modulators are used to shift the frequency and produce the auxiliary beam acting as a coherent control field. Based on the constructed FMZI, a quantum-enhanced FMZI is realized by injecting the generated low-frequency vacuum squeezed state at 1550 nm into the vacuum channel of FMZI. The relative phase between two injected light fields is locked at π by using the Pound-Drever-Hall (PDH) locking technology, and the relative phase between light fields of its arms in FMZI is also locked at π/2 by using the PDH locking technology. When a phase modulation signal at the frequency of 500 kHz is loaded in the signal arm of FMZI, the noise power spectrum of the output from FMZI is measured by a balance homodyne detect system. A 2 dB quantum improvement beyond shot-noise-level at the frequency of 500 kHz is obtained experimentally by using the quantum-enhanced FMZI. The experimental results demonstrate a potential application in quantum precision measurement beyond the SQL based on fiber sensor technique.