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arXiv:2109.12796

Measurement-based preparation of non-Markovian and multimode mechanical states

Chao Meng, George A. Brawley, Soroush Khademi, Elizabeth M. Bridge, James S. Bennett, Warwick P. Bowen

Published Sep 27, 2021• 0 citations
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Abstract

Nanomechanical resonators are a key tool for future quantum technologies such as quantum force sensors and interfaces, and for studies of macroscopic quantum physics. The ability to prepare room temperature non-classical states is a major outstanding challenge. Here, we explore the use of measurement-based state conditioning to achieve this. We demonstrate conditional cooling of a nanomechanical resonator that has non-Markovian decoherence, and show theoretically that the non-Markovianity makes quantum squeezing significantly easier to achieve. We further show that collective measurement of multiple resonator modes improves the quality of state preparation. This allows us to achieve collective thermomechanical squeezing, in experiments that go beyond the validity of the rotating-wave approximation. Our modelling shows that non-Markovianity and multimode conditioning can both enable room temperature quantum squeezing with existing technology. Together, our results pave the way towards realising room temperature quantum nanomechanical devices and towards their application in quantum technology and fundamental science.

DOI
10.48550/arxiv.2109.12796

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Nanomechanical resonators are a key tool for future quantum technologies such as quantum force sensors and interfaces, and for studies of macroscopic quantum physics. The ability to prepare room temperature non-classical states is a major outstanding challenge. Here, we explore the use of measurement-based state conditioning to achieve this. We demonstrate conditional cooling of a nanomechanical resonator that has non-Markovian decoherence, and show theoretically that the non-Markovianity makes quantum squeezing significantly easier to achieve. We further show that collective measurement of multiple resonator modes improves the quality of state preparation. This allows us to achieve collective thermomechanical squeezing, in experiments that go beyond the validity of the rotating-wave approximation. Our modelling shows that non-Markovianity and multimode conditioning can both enable room temperature quantum squeezing with existing technology. Together, our results pave the way towards realising room temperature quantum nanomechanical devices and towards their application in quantum technology and fundamental science.
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We investigate theoretically the conditions under which a multimode nanomechanical resonator, operated as a purely mechanical parametric oscillator, can be driven into highly nonclassical states. We find that when the device can be cooled to near its ground state, and certain mode matching conditions are satisfied, it is possible to prepare distinct resonator modes in quantum entangled states that violate Bell inequalities with homodyne quadrature measurements. We analyze the parameter regimes for such Bell inequality violations, and while experimentally challenging, we believe that the realization of such states lies within reach. This is a re-imagining of a quintessential quantum optics experiment by using phonons that represent tangible mechanical vibrations.
We revisit quantum state preparation of an oscillator by continuous linear position measurement. Quite general analytical expressions are derived for the conditioned state of the oscillator. Remarkably, we predict that quantum squeezing is possible outside of both the backaction dominated and quantum coherent oscillation regimes, relaxing experimental requirements even compared to ground-state cooling. This provides a new way to generate nonclassical states of macroscopic mechanical oscillators, and opens the door to quantum sensing and tests of quantum macroscopicity at room temperature.
Why are classical theories often sufficient to describe the physics of our world even though everything around us is entirely composed of microscopic quantum systems? The boundary between these two fundamentally dissimilar theories remains an unsolved problem in modern physics. Position measurements of small objects allow us to probe the area where the classical approximation breaks down. In quantum mechanics, Heisenbergâ s uncertainty principle dictates that any measurement of the position must be accompanied by measurement induced back-action---in this case manifested as an uncertainty in the momentum. In recent years, cavity optomechanics has become a powerful tool to perform precise position measurements and investigate their fundamental limitations. The utilization of optical micro-cavities greatly enhances the interaction between light and state-of-the-art nanomechanical oscillators. Therefore, quantum mechanical phenomena have been successfully observed in systems far beyond the microscopic world. In such a cavity optomechanical system, the fluctuations in the position of the oscillator are transduced onto the phase of the light, while fluctuations in the amplitude of the light disturb the momentum of the oscillator during the measurement. As a consequence, correlations are established between the amplitude and phase quadrature of the probe light. However, so far, observation of quantum effects has been limited exclusively to cryogenic experiments, and access to the quantum regime at room temperature has remained an elusive goal because the overwhelming amount of thermal motion masks the weak quantum effects. This thesis describes the engineering of a high-performance cavity optomechanical device and presents experimental results showing, for the first time, the broadband effects of quantum back-action at room temperature. The device strongly couples mechanical and optical modes of exceptionally high quality factors to provide a measurement sensitivity ∼ ⁣104\sim\!10^4∼104 times below the requirement to resolve the zero-point fluctuations of the mechanical oscillator. The quantum back-action is then observed through the correlations created between the probe light and the motion of the nanomechanical oscillator. A so-called â variational measurementâ , which detects the transmitted light in a homodyne detector tuned close to the amplitude quadrature, resolves the quantum noise due to these correlations at the level of 10\% of the thermal noise over more than an octave of Fourier frequencies around mechanical resonance. Moreover, building on this result, an additional experiment demonstrates the ability to achieve quantum enhanced metrology. In this case, the generated quantum correlations are used to cancel quantum noise in the measurement record, which then leads to an improved relative signal-to-noise ratio in measurements of an external force. In conclusion, the successful observation of broadband quantum behavior on a macroscopic object at room temperature is an important milestone in the field of cavity optomechanics. Specifically, this result heralds the rise of optomechanical systems as a platform for quantum physics at room temperature and shows promise for generation of ponderomotive squeezing in room-temperature interferometers.
There has recently been a surge of interest in the study of mechanical systems near the quantum limit. Such experiments are motivated by both fundamental interest in studying quantum mechanics with macroscopic engineered systems and potential applications as ultra‐sensitive transducers, or even in quantum information processing. A particularly promising system is a microwave cavity optomechanical system, in which a nanomechanical resonator is embedded within (and capacitively coupled to) a superconducting microwave cavity. Here we discuss two schemes for the generation and measurement of quantum states of the nanomechanical resonator. A quantum squeezed state may be generated via mechanical parametric amplification, while a number state may be conditionally generated via continuous measurement and feedback control mediated by a superconducting qubit.
Nonclassical states of nano- and micro-mechanical motion enable measurements beyond the standard quantum limit and constitute a key resource for quantum sensing and metrology. The most strongly squeezed mechanical states to date have been generated with electromechanical platforms under cryogenic refrigeration and using reservoir engineering. To push mechanical systems deeper into the quantum-squeezed regime requires protocols that increase the rate at which squeezing is generated to more strongly overcome the decoherence rate at which state purity is lost. Here, we squeeze the 800 kHz libration mode of a silica nanoparticle optically levitated in vacuum at room temperature. We expose our mechanical oscillator to an optically generated inverted potential, where the squeezing operation proceeds at an exponentially accelerated rate. We reach a squeezed quadrature variance 11 dB below the vacuum fluctuations within 250 ns. Our protocol establishes a new paradigm for generating quantum squeezing of mechanical motion and offers a platform for quantum-enhanced sensing with massive oscillators.