Squeezing in a coupled two-mode optomechanical system for force sensing below the standard quantum limit

Abstract

Optomechanics allows the transduction of weak forces to optical fields, with many efforts approaching the standard quantum limit. We consider force-sensing using a mirror-in-the-middle setup and use two coupled cavity modes originated from normal mode splitting for separating pump and probe fields. We find that this two-mode model can be reduced to an effective single-mode model, if we drive the pump mode strongly and detect the signal from the weak probe mode. The optimal force detection sensitivity at zero frequency (DC) is calculated and we show that one can beat the standard quantum limit by driving the cavity close to instability. The best sensitivity achievable is limited by mechanical thermal noise and by optical losses. We also find that the bandwidth where optimal sensitivity is maintained is proportional to the cavity damping in the resolved sideband regime. Finally, the squeezing spectrum of the output signal is calculated, and it shows almost perfect squeezing at DC is possible by using a high quality factor and low thermal phonon-number mechanical oscillator.Dramatic progress in coupling mechanics to light [1][2][3][4] suggests that such devices may be used in a wide variety of settings to explore quantum effects in macroscopic systems. Furthermore, such systems can be exquisitely sensitive to small perturbations, such as forces induced either by acceleration as in accelerometer [5] or by, e.g., coupling to surfaces or fields as in atomic force microscopy [6]. For such force measurements, a high quality factor (Q) mechanical oscillator acts as a test mass, transducing a force into a time-dependent displacement of the oscillator [7,8]. By using interferometric techniques to monitor the position of the oscillator, one can infer the force via optical signals. However, the radiation pressure coupling between the mechanical mode and optical mode has three consequences: photon shot noise, quantum backaction and dynamical backaction [1,9]. The dynamical backaction modifies the oscillator dynamics [10] and makes laser cooling [11,12] or amplification of phonons [13] in the mechanical system possible. Photon shot noise and quantum backaction, the former decreases with increasing input laser power while the latter increases with increasing input laser power, introduce two sources of noise on the displacement readout of the oscillator motion. An optimal compromise between these two noise sources leads to the standard quantum limit (SQL) in force sensing [7].The SQL, however, is itself not a fundamental limit. By using squeezed states of light [14], employing quantum nondemolition (QND) measurement [15], or by cavity detuning [16], the SQL can be surpassed. Here we show that in a coupled two-mode optomechanical system, if we drive it appropriately, the interaction between cavity photons and the mechanical oscillator will generate squeezed states of the output light. Measuring an appropriate quadrature of the output light field, we would get fewer fluctuations than that of the vacuum state, which makes it possib...

Optomechanical force sensor in a non-Markovian regime

“…In the Markovian regime, this term is usually written as F m th g , where m g is the dissipation rate of the mechanics and F th is the noise operator. F ext is the external forces to be measured [13,14], which can be an accelerated mass [25], magnetostrictive material [26], atomic force [27], or gravitational waves [28]. Currently, most experimental realizations of cavity optomechanics are still in the single-photon, weak coupling with strong driving condition [29][30][31][32].…”

“…with D 2 i c k = D ¢ + , and the phase θ is introduced and can be optimized to enhance the sensitivity of the weakforce detection [14]. To obtain the relationship between the detecting force and the output signal, we can rewrite equation (7) as…”

“…Many schemes have been proposed to optimally compromise between photon shot noise and quantum back-action [8], which leads to the standard quantum limit (SQL) in weak force sensing [9,10]. Various approaches to beyond-SQL measurements have been proposed [11][12][13][14][15], including optical squeezing in the optomechanical system [5,14], atomic assistance in a separate cavity [13], mechanical modification by light [15], and so on. Up to now, most of the measurement schemes have been based on the Born-Markov approximation.…”

Gyroscope with two-dimensional optomechanical mirror

“…Optomechanical cavities [16,17] are very sensitive to any external forces acting on them, and hence they were extensively studied for gravitational wave detection [18,19], weak force detection [20][21][22][23][24][25], and displacement sensors [20,26,27]. In general, the freely oscillating mirror of the optomechanical cavity (OMC) is subject to the radiation pressure force [16,17,28] of the intra-cavity field.…”

Optimal quantum parameter estimation in a pulsed quantum optomechanical system

“…With the rapid advance of technology, quantum cavity optomechanics [17][18][19], in which the mechanical resonator is coupled to the optical field by radiation pressure or photothermal force, has excited a burst of interest [20] due to the following two reasons: On one hand, the cavity optomechanical system provides a new platform to investigate the fundamental questions on the quantum behavior of macroscopic system [21] and even the quantum-to-classical transition [22,23]; On the other hand, it brings a novel quantum device for applications in ultra-high precision measurement [24][25][26][27][28], gravitation-wave detection [29], quantum information processing [30] and quantum illumination [31]. Many interesting researches in cavity optomechanical systems, such as optomechanically induced transparency [32,33], ground-state cooling of the mechanical resonator [34][35][36][37][38], optomechanical entanglement [39,40], optimal state estimation [41], have been reported.…”