quantum correlations PHOTONICS INSIGHTS
Figure 3. Left panel: Phase – amplitude quadrature representation of a coherent vacuum state( top) and a squeezed vacuum state( bottom). In the coherent case, uncertainties are equal in both quadratures, while in the squeezed case noise is reduced in one quadrature and increased in the other. Right panel( top): Quantum noise reduction achieved by injecting frequency-independent phase squeezing( blue) versus frequency-dependent squeezing( green). Frequency-independent squeezing reduces noise only at high frequencies, increasing it at low frequencies, while frequencydependent squeezing provides broadband noise suppression. Right panel( bottom): Rotation of the squeezing angle by 90 ° across the frequency spectrum, caused by optomechanical coupling with the interferometer’ s suspended test masses. This rotation misaligns the low-noise quadrature with the gravitational-wave signal when only frequency-independent squeezing is used.
for the vacuum. Since such fluctuations are responsible for quantum noise, we cannot limit ourselves to consider those that enter the interferometer with the laser from the bright port but we should also take into account those entering with the vacuum from the output port. Surprisingly enough, while the fluctuations from the laser cancel out when the two beams interfere at the beam splitter, those entering from the output port do not, they recombine with the laser power in the arms and become the ultimate responsible for the quantum noise( See Fig. 1). This insightful picture of interferometer quantum noise also enabled Caves to propose a fascinating solution: we should manipulate the vacuum fluctuations entering through the output port to“ reshape” them and reduce their harmful effects. We have to say“ reshape” and not just“ reduce” because in a coherent state, amplitude and phase fluctuations cannot be arbitrarily reduced. In fact, the Heisenberg principle dictates that the product of the uncertainty for two conjugate quadratures( as phase and amplitude in this case) cannot be lower than a given amount. What we can do is to reduce the fluctuation in one quadrature at the expenses of the other. Such a manipulated state, known as squeezed state, has uneven fluctuation in the two quadratures, and can be represented by an ellipse instead of that of a circle( See Fig 3, left panel). It is important to notice that since the interferometer measures phase changes, the uncertainty circle must be squeezed along the appropriate direction to reduce noise. In 1981, Caves proposed this groundbreaking approach to reduce quantum noise without increasing the laser power. In his paper,“ Quantum-Mechanical Noise in an Interferometer”, he wrote:“ Experimenters might then be forced to learn how to very gently squeeze the vacuum before it can contaminate the light in the interferometer.” It took nearly 40 years of experimental development before squeezing began to be routinely used in LIGO and Virgo. This squeezing is generated using an Optical Parametric Oscillator( OPO), which consists of a nonlinear crystal inside an optical cavity, pumped by a laser at twice the frequency of the light used for the interferometric detection. In the case
of LIGO and Virgo, which operate in the near infrared at 1064 nm, the pump laser for the OPO is a green light at 532 nm. The OPO is operated below threshold( meaning the pump power is too low to generate a bright output beam) and the nonlinear crystal inside it enables a process called parametric down-conversion, where energy from the pump can virtually split into pairs of lower-frequency photons. Although no real light is emitted, this interaction modifies the quantum fluctuations of the vacuum field exiting the OPO. The result is a squeezed vacuum state, where noise is reduced in one quadrature( e. g. the phase) and increased in the other one [ 3 ]. It sounds simple, but it is much more challenging in practice. Over the years, researchers have progressively increased the level of squeezing produced, that is the ratio between the reduced fluctuations and those of standard vacuum, usually expressed in dB( see Fig. 2). However, achieving a significant reduction of quantum noise in the detectors is made difficult by several reasons. One is that squeezed states are extremely fragile: any optical loss encountered by the squeezed beam reduces its squeezing level. In fact, quantum mechanics tells us that losses cause the squeezed vacuum to recombine with ordinary vacuum, degrading the effect proportionally to the importance of the loss. Optical losses occur everywhere in the interferometer: from transmission through Faraday isolators and anti-reflective mirror coatings, to scattering caused by surface imperfections, and the light picked off for extracting control signals. Minimizing these sources of loss as much as possible is essential to fully exploit the beneficial effect of squeezing on quantum noise. To give an idea, achieving high levels of quantum noise reduction( around 10 dB) requires keeping total optical losses below 8 % along the entire optical path. Another challenge concerns frequency. Virgo and LIGO operate at low frequencies( 10 Hz – 10 kHz), a range dominated by various disturbances such as electronic, acoustic, and laser frequency noise. Squeezing is far much easier to achieve at MHz frequencies, where these
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