We show that optomechanical systems in the quantum regime can be used to demonstrate EPR-type quantum entanglement between the optical field and the mechanical oscillator, via quantum-state steering. Namely, the conditional quantum state of the mecha
nical oscillator can be steered into different quantum states depending the choice made on which quadrature of the out-going field is to be measured via homodyne detection. More specifically, if quantum radiation pressure force dominates over thermal force, the oscillators quantum state is steerable with a photodetection efficiency as low as 50%, approaching the ideal limit shown by Wiseman and Gambetta [Phys. Rev. Lett. {bf 108}, 220402 (2012)]. We also show that requirement for steerability is the same as those for achieving sub-Heisenberg state tomography using the same experimental setup.
We consider enhancing the sensitivity of future gravitational-wave detectors by using double optical spring. When the power, detuning and bandwidth of the two carriers are chosen appropriately, the effect of the double optical spring can be described
as a negative inertia, which cancels the positive inertia of the test masses and thus increases their response to gravitational waves. This allows us to surpass the free-mass Standard Quantum Limit (SQL) over a broad frequency band, through signal amplification, rather than noise cancelation, which has been the case for all broadband SQL-beating schemes so far considered for gravitational-wave detectors. The merit of such signal amplification schemes lies in the fact that they are less susceptible to optical losses than noise cancelation schemes. We show that it is feasible to demonstrate such an effect with the {it Gingin High Optical Power Test Facility}, and it can eventually be implemented in future advanced GW detectors.
For cavity-assisted optomechanical cooling experiments, it has been shown in the literature that the cavity bandwidth needs to be smaller than the mechanical frequency in order to achieve the quantum ground state of the mechanical oscillator, which i
s the so-called resolved-sideband or good-cavity limit. We provide a new but physically equivalent insight into the origin of such a limit: that is information loss due to a finite cavity bandwidth. With an optimal feedback control to recover those information, we can surpass the resolved-sideband limit and achieve the quantum ground state. Interestingly, recovering those information can also significantly enhance the optomechanical entanglement. Especially when the environmental temperature is high, the entanglement will either exist or vanish critically depending on whether information is recovered or not, which is a vivid example of a quantum eraser.
We propose a protocol for coherently transferring non-Gaussian quantum states from optical field to a mechanical oscillator. The open quantum dynamics and continuous-measurement process, which can not be treated by the stochastic-master-equation form
alism, are studied by a new path-integral-based approach. We obtain an elegant relation between the quantum state of the mechanical oscillator and that of the optical field, which is valid for general linear quantum dynamics. We demonstrate the experimental feasibility of such protocol by considering the cases of both large-scale gravitational-wave detectors and small-scale cavity-assisted optomechanical devices.
We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it requires a strong-coupling reg
ime -- the decay rate of external degrees of freedom is smaller than the parametric coupling rate. In the case for cavity-assisted optomechanical systems, e.g. the one proposed by Thompson et al., zero-point motion of the mechanical oscillator needs to be comparable to linear dynamical range of the optical system which is characterized by the optical wavelength divided by the cavity finesse.
As a pure quantum state is being approached via linear feedback, and the occupation number approaches and eventually goes below unity, optimal control becomes crucial. We obtain theoretically the optimal feedback controller that minimizes the uncerta
inty for a general linear measurement process, and show that even in the absence of classical noise, a pure quantum state is not always achievable via feedback. For Markovian measurements, the deviation from minimum Heisenberg Uncertainty is found to be closely related to the extent to which the device beats the free-mass Standard Quantum Limit for force measurement. We then specialize to optical Markovian measurements, and demonstrate that a slight modification to the usual input-output scheme -- either injecting frequency independent squeezed vacuum or making a homodyne detection at a non-phase quadrature -- allows controlled states of kilogram-scale mirrors in future LIGO interferometers to reach occupation numbers significantly below unity.
