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Register a new userGenerating mechanical and optomechanical entanglement via pulsed interaction and measurement
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Entanglement generation at a macroscopic scale offers an exciting avenue to develop new quantum technologies and study fundamental physics on a tabletop. Cavity quantum optomechanics provides an ideal platform to generate and exploit such phenomena owing to the precision of quantum optics combined with recent experimental advances in optomechanical devices. In this work, we propose schemes operating outside the resolved-sideband regime, to prepare and verify both optical-mechanical and mechanical-mechanical entanglement. Our schemes employ pulsed interactions with a duration much less than the mechanical period and, together with homodyne measurements, can both generate and characterize these types of entanglement. To improve the performance of our schemes, a precooling stage comprising prior pulses can be utilized to increase the amount of entanglement prepared, and local optical squeezers may be used to provide resilience against open-system dynamics. The entanglement generated by our schemes is quantified using the logarithmic negativity and is analysed with respect to the strength of the pulsed optomechanical interactions for realistic experimental scenarios including mechanical decoherence and optical loss. Two separate schemes for mechanical entanglement generation are introduced and compared: one scheme based on an optical interferometric design, and the other comprising sequential optomechanical interactions. The pulsed nature of our protocols provides more direct access to these quantum correlations in the time domain, with applications including quantum metrology and tests of quantum decoherence. By considering a parameter set based on recent experiments, the feasibility to generate significant entanglement with our schemes, even with large optical losses, is demonstrated.
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Observing a physical quantity without disturbing it is a key capability for the control of individual quantum systems. Such back-action-evading or quantum-non-demolition measurements were first introduced in the 1970s in the context of gravitational wave detection to measure weak forces on test masses by high precision monitoring of their motion. Now, such techniques have become an indispensable tool in quantum science for preparing, manipulating, and detecting quantum states of light, atoms, and other quantum systems. Here we experimentally perform rapid optical quantum-noise-limited measurements of the position of a mechanical oscillator by using pulses of light with a duration much shorter than a period of mechanical motion. Using this back-action evading interaction we performed both state preparation and full state tomography of the mechanical motional state. We have reconstructed mechanical states with a position uncertainty reduced to 19 pm, limited by the quantum fluctuations of the optical pulse, and we have performed `cooling-by-measurement to reduce the mechanical mode temperature from an initial 1100 K to 16 K. Future improvements to this technique may allow for quantum squeezing of mechanical motion, even from room temperature, and reconstruction of non-classical states exhibiting negative regions in their phase-space quasi-probability distribution.
We provide an argument to infer stationary entanglement between light and a mechanical oscillator based on continuous measurement of light only. We propose an experimentally realizable scheme involving an optomechanical cavity driven by a resonant, continuous-wave field operating in the non-sideband-resolved regime. This corresponds to the conventional configuration of an optomechanical position or force sensor. We show analytically that entanglement between the mechanical oscillator and the output field of the optomechanical cavity can be inferred from the measurement of squeezing in (generalized) Einstein-Podolski-Rosen quadratures of suitable temporal modes of the stationary light field. Squeezing can reach levels of up to 50% of noise reduction below shot noise in the limit of large quantum cooperativity. Remarkably, entanglement persists even in the opposite limit of small cooperativity. Viewing the optomechanical device as a position sensor, entanglement between mechanics and light is an instance of object-apparatus entanglement predicted by quantum measurement theory.
Precision measurement of non-linear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of non-linear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator by exploiting the intrinsic non-linearity of the radiation pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100~pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can be used to experimentally explore collapse models of the wavefunction and the potential for mechanical-resonator-based quantum information and metrology applications.
Utilizing the tools of quantum optics to prepare and manipulate quantum states of motion of a mechanical resonator is currently one of the most promising routes to explore non-classicality at a macroscopic scale. An important quantum optomechanical tool yet to be experimentally demonstrated is the ability to perform complete quantum state reconstruction. Here, after providing a brief introduction to quantum states in phase space, we review and contrast the current proposals for state reconstruction of mechanical motional states and discuss experimental progress. Furthermore, we show that mechanical quadrature tomography using back-action-evading interactions gives an $s$-parameterized Wigner function where the numerical parameter $s$ is directly related to the optomechanical measurement strength. We also discuss the effects of classical noise in the optical probe for both state reconstruction and state preparation by measurement.
We propose a scheme for the generation of a robust stationary squeezed state of a mechanical resonator in a quadratically coupled optomechanical system, driven by a pulsed laser. The intracavity photon number presents periodic intense peaks suddenly stiffening the effective harmonic potential felt by the mechanical resonator. These optical spring kicks tend to squeeze the resonator position, and due to the interplay with fluctuation-dissipation processes one can generate a stationary state with more than 13 dB of squeezing even starting from moderately pre-cooled initial thermal states.
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