Quantum Radiation Pressure Research Articles

Standard quantum limit of angular motion of a suspended mirror and homodyne detection of a ponderomotively squeezed vacuum field

Compared to the quantum noise in the measurement of the translational motion of a suspended mirror using laser light, the quantum noise in the measurement of the angular motion of a suspended mirror has not been investigated intensively despite its potential importance. In this article, an expression for the quantum noise in the angular motion measurement is explicitly derived. The expression indicates that one quadrature of the vacuum field of the first-order Hermite-Gaussian mode of light causes quantum sensing noise and the other causes quantum backaction noise, or in other words the first-order vacuum field is ponderomotively squeezed. It is also shown that the Gouy phase shift the light acquires between the mirror and the position of detection of the light corresponds to the homodyne angle. Therefore, the quantum backaction noise can be cancelled and the standard quantum limit can be surpassed by choosing the appropriate position of detection analogously to the cancellation of quantum radiation pressure noise by choosing an appropriate homodyne angle.

Observation of reduction of radiation-pressure-induced rotational anti-spring effect on a 23 mg mirror in a Fabry–Perot cavity

Although quantum radiation pressure noise could limit the sensitivity of the second-generation gravitational wave detectors, it has not been observed in a broad frequency band and its reduction methods have not been proven yet. A promising way to observe quantum radiation pressure noise is to store high power light in an optical cavity with a tiny mirror. However, anti-spring torque caused by radiation pressure of the light acting on the tiny mirror could make the system unstable, and it is generally difficult to attach actuators to the tiny mirror for stabilization. Hence a new method to overcome this anti-spring torque has been developed. In the new method, the other mirror of the cavity is controlled so that the position of the resonant light at the tiny mirror is fixed to decrease the anti-spring torque and stabilize angular motion of the tiny mirror. With the new method, it was successfully observed that the anti-spring torque caused by radiation pressure was suppressed in the present experiment with a 23 mg mirror, where resonant frequency of angular motion of the tiny mirror increased towards the mechanical resonant frequency.

Multidimensional optical trapping of a mirror

Alignment control in gravitational-wave detectors has consistently proven to be a difficult problem due to the stringent noise contamination requirement for the gravitational wave readout and the radiation-pressure-induced angular instability in Fabry-Perot cavities (Sidles-Sigg instability). We present the analysis of a dual-carrier control scheme that uses radiation pressure to control a suspended mirror, trapping it in the longitudinal degree of freedom and one angular degree of freedom. We show that this scheme can control the Sidles-Sigg angular instability. Its limiting fundamental noise source is the quantum radiation pressure noise, providing an advantage compared to the conventional angular control schemes. In the Appendix we also derive an exact expression for the optical spring constant used in the control scheme.

Displacement noise from back scattering and specular reflection of input optics in advanced gravitational wave detectors

The second generation of ground-based interferometric gravitational wave detectors are currently being built and installed. They are designed to be better in strain sensitivity by about a factor 10 with respect to the first generation. Light originating from the laser and following unintended paths, called stray light, has been a major problem during the commissioning of all of the first generation detectors. Indeed, stray light carries information about the phase of the emitting object. Therefore, in the next generation all the optics will be suspended in the vacuum in order to mitigate their associated stray light displacement noise. Despite this additional precaution, the challenging target sensitivity at low frequency which is partially limited by quantum radiation pressure combined with up-conversion effects, requires more detailed investigation. In this paper, we turn our attention to stray light originating from auxiliary optical benches. We use a dedicated formalism to compute the re-coupling of back-reflected and back-scattered light. We show, in particular, how much care should be taken in designing and setting requirements for the input bench optics.

Structural thermal noise in gram-scale mirror oscillators

The thermal noise associated with mechanical dissipation is a ubiquitous limitation to the sensitivity of precision experiments ranging from frequency stabilization to gravitational wave interferometry. We report on the thermal noise limits to the performance of 1 gm mirror oscillators that are part of a cavity optomechanics experiment to observe quantum radiation pressure noise. Thermal noise limits the observed cavity displacement spectrum from 80 Hz to 5 kHz. We present a calculation of the thermal noise, based on finite element analysis of the dissipation due to structural damping, and find it to be in excellent agreement with the experimental result. We conclude with the predicted thermal noise for an improved oscillator design, which should be capable of revealing the noise that arises from quantum backaction in this system.

Development of a high power optical cavity for optomechanical QND experiment

In order to observe quantum radiation pressure noise and reduce it by measuring the ponderomotively squeezed light on a table-top experiment, we are developing a laser interferometer with Fabry-Perot cavities with very small suspended mirrors. As a preliminary setup, we have constructed a Fabry-Perot cavity of finesse 1300 with a suspended mirror of 20 mg. The cavity was locked stably at low laser power for which the classical radiation pressure caused little effect on the dynamics of the small mirror. For the stable operation of this cavity with higher laser power, a technique to control the motion of the small mirror, especially its yaw motion, is necessary. We describe that the motion can be stabilized through the radiation pressure of light inside the cavity, by controlling the motion of the front mirror of a Fabry-Perot cavity properly.

Design of the 10 m AEI prototype facility for interferometry studies

The AEI 10 m prototype interferometer facility is currently being constructed at the Albert Einstein Institute in Hannover, Germany. It aims to perform experiments for future gravitational wave detectors using advanced techniques. Seismically isolated benches are planned to be interferometrically interconnected and stabilized, forming a low-noise testbed inside a 100 m^3 ultra-high vacuum system. A well-stabilized high power laser will perform differential position readout of 100 g test masses in a 10 m suspended arm-cavity enhanced Michelson interferometer at the crossover of measurement (shot) noise and backaction (quantum radiation pressure) noise, the so-called Standard Quantum Limit (SQL). Such a sensitivity enables experiments in the highly topical field of macroscopic quantum mechanics. In this article we introduce the experimental facility and describe the methods employed, technical details of subsystems will be covered in future papers.

Towards the experimental demonstration of quantum radiation pressure noise

Abstract Quantum radiation pressure noise has never been experimentally demonstrated, though it has been predicted for more than thirty years. It is, however, expected to limit the low-frequency sensitivity of second generation gravitational-wave interferometers. We have demonstrated classical radiation-pressure-induced correlations between two optical beams sent into the same high-finesse cavity with a moving mirror. Our two-beam scheme can be used to retrieve quantum noise embedded in an overwhelming classical noise, and has applications both in high-sensitivity measurements and in quantum optics.

Quantum noise of a Michelson-Sagnac interferometer with a translucent mechanical oscillator

Quantum fluctuations in the radiation pressure of light can excite stochastic motions of mechanical oscillators thereby realizing a linear quantum opto-mechanical coupling. When performing a precise measurement of the position of an oscillator, this coupling results in quantum radiation pressure noise. Up to now this effect has not been observed yet. Generally speaking, the strength of radiation pressure noise increases when the effective mass of the oscillator is decreased or when the power of the reflected light is increased. Recently, extremely light SiN membranes with high mechanical Q-values at room temperature have attracted attention as low thermal noise mechanical oscillators. However, the power reflectance of these membranes is much lower than unity which makes the use of advanced interferometer recycling techniques to amplify the radiation pressure noise in a standard Michelson interferometer inefficient. Here, we propose and theoretically analyze a Michelson-Sagnac interferometer that includes the membrane as a common end mirror for the Michelson interferometer part. In this new topology, both, power- and signal-recycling can be used even if the reflectance of the membrane is much lower than unity. In particular, signal-recycling is a useful tool because it does not involve a power increase at the membrane. We derive the formulas for the quantum radiation pressure noise and the shot-noise of an oscillator position measurement and compare them with theoretical models of the thermal noise of a SiN membrane with a fundamental resonant frequency of 75 kHz and an effective mass of 125 ng. We find that quantum radiation pressure noise should be observable with a power of 1 W at the central beam splitter of the interferometer and a membrane temperature of 1 K.

Fluctuations of quantum radiation pressure in dissipative fluid

Using the generalized Langevin equations involving the stress tensor approach, we study the dynamics of a perfectly reflecting mirror which is exposed to the electromagnetic radiation pressure by a laser beam in a fluid at finite temperature. Based on the fluctuation–dissipation theorem, the minimum uncertainty of the mirror's position measurement from both quantum and thermal noises effects including the photon counting error in the laser interferometer is obtained in the small time limit as compared with the “standard quantum limit”. The result of the large time behavior of fluctuations of the mirror's velocity in a dissipative environment can be applied to the laser interferometer of the ground-based gravitational wave detector.

Quantum radiation pressure on a moving mirror at finite temperature

We compute the radiation pressure force on a moving mirror, in the nonrelativistic approximation, assuming the field to be at temperature $T.$ At high temperature, the force has a dissipative component proportional to the mirror velocity, which results from Doppler shift of the reflected thermal photons. In the case of a scalar field, the force has also a dispersive component associated to a mass correction. In the electromagnetic case, the separate contributions to the mass correction from the two polarizations cancel. We also derive explicit results in the low temperature regime, and present numerical results for the general case. As an application, we compute the dissipation and decoherence rates for a mirror in a harmonic potential well.

Suppression of classic and quantum radiation pressure noise by electro-optic feedback

We present theoretical results that demonstrate a new technique that can be used to improve the sensitivity of thermal noise measurements: intracavity intensity stabilization. It is demonstrated that electro-optic feedback can be used to reduce intracavity intensity fluctuations, and the consequent radiation pressure fluctuations, by a factor of 2 below the quantum-noise limit. We show that this reduction is achievable in the presence of large classic intensity fluctuations in the incident laser beam. The benefits of this scheme are a consequence of the sub-Poissonian intensity statistics of the field inside a feedback loop and the quantum nondemolition nature of radiation pressure noise as a readout system for the intracavity intensity fluctuations.

Effect of quantum radiation pressure on the bubble dynamics in sonoluminescence

In the theoretical frame of quantum vacuum radiation (QVR), the effect of the QVR on the gas bubble dynamics in the single bubble sonoluminescence is studied. The dominated hydrodynamic equation of the gas bubble trapped in a liquid, Rayleigh–Plesset equation, has been modified by considering the reaction of the radiation force on the bubble surface and therefore causing a loss of energy. In the modified model the collapse and expansion of the bubble, especially near the turnaround at minimum radius, related to photon emission instead of independence on it. The numerical computation shows that the emission energy due to the QVR seems too low to explain the experimental data, if some present values of parameters, such as the ambient radius of the bubble and the sound pressure in liquid, are used. The radiation energy due to the QVR, however, can arise by changing those parameters. Based on this, it is concluded that the QVR may be a possible candidate for mechanisms of the sonoluminescence. [Work supported by NSF of China.]

O velikosti pohybu, který černý zářič koná vlivem kvantového tlaku záření

O velikosti pohybu, který černý zářič koná vlivem kvantového tlaku záření