The free particle is the most elementary dynamical system in quantum mechanics. Despite remarkable progress in quantum control of increasingly massive solid-state mechanical oscillators, the analogous control of the free-particle counterpart has remained elusive. Dissipation and environmental noise have prevented such control in the inherently low-frequency domain of free-particle dynamics---a regime of growing importance for quantum sensing and tests of fundamental physics. Here we realize a suspended 1-milligram rotor operating in the free-particle regime with exceptional environmental isolation. Combining this isolation with a low-noise measurement architecture, we directly resolve thermal fluctuations in the motion associated with a damping rate of only 7~nHz. Through continuous quantum measurement of the rotor, we localize its otherwise unconfined motion, obtaining conditional states with entropic temperatures as low as 140~nK as a quantitative measure of control in the free-particle regime. This is two orders of magnitude below temperatures previously achieved in tabletop optomechanical experiments. We demonstrate immediate utilities of the new operating regime, setting new constraints on modifications of quantum mechanics and benchmarking inferred entanglement-to-decoherence rate ratios nearly two orders of magnitude beyond the state of the art for tests of gravity at the quantum-classical interface.
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14-page main + 33-page supplement. 4 main figures + 13 supplementary figures
The free particle is the most elementary dynamical system in quantum mechanics. Despite remarkable progress in quantum control of increasingly massive solid-state mechanical oscillators, the analogous control of the free-particle counterpart has remained elusive. Dissipation and environmental noise have prevented such control in the inherently low-frequency domain of free-particle dynamics---a regime of growing importance for quantum sensing and tests of fundamental physics. Here we realize a suspended 1-milligram rotor operating in the free-particle regime with exceptional environmental isolation. Combining this isolation with a low-noise measurement architecture, we directly resolve thermal fluctuations in the motion associated with a damping rate of only 7nHz. Through continuous quantum measurement of the rotor, we localize its otherwise unconfined motion, obtaining conditional states with entropic temperatures as low as 140nK as a quantitative measure of control in the free-particle regime. This is two orders of magnitude below temperatures previously achieved in tabletop optomechanical experiments. We demonstrate immediate utilities of the new operating regime, setting new constraints on modifications of quantum mechanics and benchmarking inferred entanglement-to-decoherence rate ratios nearly two orders of magnitude beyond the state of the art for tests of gravity at the quantum-classical interface.
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 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.
The probing of the quantum nature of a macroscopic object is an open problem. Approaches in preparing quantum superposition towards a larger scale, which has been progressively accessible in a variety of experimental implementations, may detect new physics or extend the boundary of quantum theory. Development on a nano-mechanical system in the framework of quantum optics and information theory has opened new research directions. It paves ways to manipulate the wavefunction of a massive particle over a large spatial range and probe its quantum behavior to an unprecedented precision. In this thesis, quantum superposition on a mechanical system is studied theoretically in the light of possible implementations under current techniques in order to test superposition principle and the quantum nature of gravity in the mesoscopic region. The work includes two lines of study. In the first line, the motion of the center of mass (c.m.) of the mechanical system is coupled to its internal spin system magnetically, and a Ramsey scheme is developed based on coherent spin control. The wavepacket of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during the scheme. A remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling) and also a dynamical decoupling nature of the scheme itself is revealed. A careful examination of the perturbation effect due to setup imperfection and environment-induced decoherence is performed, which shows that the Ramsey fringes have a high tolerance on those unwanted faults under realistic experimental conditions. The scheme also facilitates a gravimetry protocol that potentially could be developed for a novel on-chip gravimeter with a precision of 10−6g/Hz. In the second line, an opto-mechanical experiment is proposed to entangle the motion of two mechanical oscillators through their mutual gravitational interaction. The feasibility of such an experiment is critically examined within the framework of cavity optomechanics. It is shown that within the decoherence time of mechanical noise and potentially gravitational induced state collapse, entanglement between mirrors could be obtained when the initial state of the cavity field is prepared in some particular states. Strategies that give enhancement to entanglement generation rate are studied in light of quantum estimation theory. It is shown that for a cavity initially in a coherent state, the resulting entanglement generation rate would be enhanced linearly with the amplitude of the coherent state. Lastly, it shows that in the proposed setup Casimir effect would significantly affect the gravity-induced entanglement. A proper shield can eliminate the detrimental effect of Casimir force, which, however, will constrain the closest distance between the mirrors in its implementation.
Pendulums are attractive for macroscopic quantum control because gravity dilution reduces mechanical loss, while the 1/f force-noise spectrum associated with structural damping allows nearly lossless trapping to suppress the thermal noise sampled at an upward-shifted resonance. The same 1/f spectrum, however, produces a low-frequency tail that penalizes entanglement. With 10% detection loss, we find that this tail raises the required back-action-to-thermal force-noise ratio by about 50%, corresponding to a required suspension gain Greq=1.49. To overcome this structural-noise penalty, we realize a 7-mg pendulum suspended by a stepped fused-silica fiber, with an energy-decay rate Γ/2π=361(39) nHz (Q≡ω0/Γ=7.3(8)×106) at ω0/2π=2.63 Hz. The reduction in ω0Γ yields a measured gain Gq≃2.5 relative to the previous monolithic device, exceeding the requirement.
Interferometers operating at or close to quantum limits of precision have found wide application in tabletop searches for physics beyond the standard model, the study of fundamental forces and symmetries of nature and foundational tests of quantum mechanics. The limits imposed by quantum fluctuations and measurement backaction on conventional interferometers (δϕ∼1/N) have spurred the development of schemes to circumvent these limits through quantum interference, multiparticle interactions and entanglement. A prominent example of such schemes, the so-called SU(1,1) interferometer, has been shown to be particularly robust against particle loss and inefficient detection, and has been demonstrated with photons and ultracold atoms. Here, we realize a SU(1,1) interferometer in a fundamentally new platform in which the interfering arms are distinct flexural modes of a millimeter-scale mechanical resonator. We realize up to 15.4(3) dB of noise squeezing and demonstrate the Heisenberg scaling of interferometric sensitivity (δϕ∼1/N), corresponding to a 6-fold improvement in measurement precision over a conventional interferometer. Our work extends the optomechanical toolbox for the quantum manipulation of macroscopic mechanical motion and presents new avenues for studies of optomechanical sensing and the nonequilibrium dynamics of multimode optomechanical systems.
In quantum mechanics, measurement can be used to prepare a quantum state. This principle is applicable even for macroscopic objects, which may enable us to see classical-quantum transition. Here, we demonstrate conditional mechanical squeezing of a mg-scale suspended mirror (i.e. the center-of-mass mode of a pendulum) near quantum regimes, through continuous linear position measurement and quantum state prediction. The experiment involved the pendulum interacting with photon coherent fields in a detuned optical cavity, which creates an optical spring. Futhermore, the detuned cavity allows us to perform linear position measurement by direct photo-detection of the reflected light. We experimentally verify the conditional squeezing using the theory combining prediction and retrodiction based on the causal and anti-causal filters. As a result, the standard deviation of position and momentum are respectively given by 36 times the zero-point amplitude of position qzpf and 89 times the zero-point amplitude of momentum pzpf. The squeezing level achieved is about 5 times closer to the zero-point motion, despite that the mass of the mechanical oscillator is approximately 7 orders of magnitude greater, compared to the previous study. Thus, our demonstration is the first step towards quantum control for massive objects whose mass-scale is high enough to measure gravitational interactions. Such quantum control will pave the way to test quantum mechanics using the center-of-mass mode of massive objects.
Thermal decoherence is a major obstacle to the realization of quantum coherence for massive mechanical oscillators. Although optical trapping has been used to reduce the thermal decoherence rate for such oscillators, it also increases the rate by subjecting the oscillator to stochastic forces resulting from the frequency fluctuations of the optical field, thereby setting a fundamental limit on the reduction. This is analogous to the noise penalty in an active feedback system. Here, we directly measure the rethermalization process for an initially cooled and optically trapped suspended mirror, and identify the current limiting decoherence rate as due to the optical trap. Our experimental study of the trap-induced decoherence rate will enable future advances in the probing of fundamental quantum mechanics in the bad-cavity regime, such as testing of deformed commutators.