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arXiv:1602.05955 · New Journal of Physics

Generation of mechanical interference fringes by multi-photon counting

Martin Ringbauer, Till J. Weinhold, L. A. Howard, A G White, Michael Ross Vanner

Published May 18, 2018• 31 citations
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Abstract

Exploring the quantum behaviour of macroscopic objects provides an intriguing avenue to study the foundations of physics and to develop a suite of quantum-enhanced technologies. One prominent path of study is provided by quantum optomechanics which utilizes the tools of quantum optics to control the motion of macroscopic mechanical resonators. Despite excellent recent progress, the preparation of mechanical quantum superposition states remains outstanding due to weak coupling and thermal decoherence. Here we present a novel optomechanical scheme that significantly relaxes these requirements allowing the preparation of quantum superposition states of motion of a mechanical resonator by exploiting the nonlinearity of multi-photon quantum measurements. Our method is capable of generating non-classical mechanical states without the need for strong single-photon coupling, is resilient against optical loss, and offers more favourable scaling against initial mechanical thermal occupation than existing schemes. Moreover, our approach allows the generation of larger superposition states by projecting the optical field onto NOON states. We experimentally demonstrate this multi-photon-counting technique on a mechanical thermal state in the classical limit and observe interference fringes in the mechanical position distribution that show phase super-resolution. This opens a feasible route to explore and exploit quantum phenomena at a macroscopic scale.

DOI
10.1088/1367-2630/aabb8d

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Exploring the quantum behaviour of macroscopic objects provides an intriguing avenue to study the foundations of physics and to develop a suite of quantum-enhanced technologies. One prominent path of study is provided by quantum optomechanics which utilizes the tools of quantum optics to control the motion of macroscopic mechanical resonators. Despite excellent recent progress, the preparation of mechanical quantum superposition states remains outstanding due to weak coupling and thermal decoherence. Here we present a novel optomechanical scheme that significantly relaxes these requirements allowing the preparation of quantum superposition states of motion of a mechanical resonator by exploiting the nonlinearity of multi-photon quantum measurements. Our method is capable of generating non-classical mechanical states without the need for strong single-photon coupling, is resilient against optical loss, and offers more favourable scaling against initial mechanical thermal occupation than existing schemes. Moreover, our approach allows the generation of larger superposition states by projecting the optical field onto NOON states. We experimentally demonstrate this multi-photon-counting technique on a mechanical thermal state in the classical limit and observe interference fringes in the mechanical position distribution that show phase super-resolution. This opens a feasible route to explore and exploit quantum phenomena at a macroscopic scale.
Summary form only given. One of the cornerstones of quantum mechanics is that matter can possess both particle- and wave-like properties. Since the inception of quantum mechanics, such wavelike behaviour has been observed in ever more massive systems - ranging from electrons, neutrons, ultracold atoms, and even large molecules comprising many hundreds of atoms. An exciting route to further extend the exploration of quantum phenomena to a macroscopic regime is through the study of quantum optomechanics, where optical fields are used to manipulate the motion of mechanical resonators using radiation pressure. We introduce a method for preparing non-classical states of motion for an optomechanical system which, using the non-linearity of single-photon measurements, is independent of the initial thermal occupation of the resonator and does not require strong single-photon coupling. We demonstrate this method in a thermal regime and observe interference fringes in the position quadrature distribution of a SiN membrane [1].
The investigation of macroscopic quantum phenomena is a current active area of research that offers significant promise to advance the forefronts of both fundamental and applied quantum science. Utilising the exquisite precision and control of quantum optics provides a powerful toolset for generating such quantum states where the types and 'size' of the states that can be generated are set by the experimental parameter regime available and the resourcefulness of the protocol applied. In this work we present a new multistep scheme to 'grow' macroscopic superposition states of motion of a mechanical oscillator via cavity quantum optomechanics. The scheme consists of a series of optical pulses interacting with a mechanical mode via radiation-pressure followed by photon-counting measurements. The multistep nature of our protocol allows macroscopic superposition states to be prepared with a relaxed requirement for the single-photon optomechanical coupling strength. To illustrate the experimental feasibility of our proposal, we quantify how initial mechanical thermal occupation and mechanical decoherence affects the non-classicality and macroscopicity of the states generated and show that our scheme is resilient to optical loss. The advantages of this protocol provide a promising path to grow non-classical mechanical quantum states to a macroscopic scale under realistic experimental conditions.
Precision measurement of nonlinear 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 nonlinear 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 nonlinearity 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.
Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices. Yet, the challenge of reconstructing and verifying the quantum state of mechanical systems has remained a major roadblock in the field. Here, we present a novel approach that allows for tomographic reconstruction of the quantum state of a mechanical system without the need for extremely high quality optical cavities. We show that, without relying on the usual state transfer presumption between light an mechanics, the full optomechanical Hamiltonian can be exploited to imprint mechanical tomograms on a strong optical coherent pulse, which can then be read out using well-established techniques. Furthermore, with only a small number of measurements, our method can be used to witness nonclassical features of mechanical systems without requiring full tomography. By relaxing the experimental requirements, our technique thus opens a feasible route towards verifying the quantum state of mechanical resonators and their nonclassical behaviour in a wide range of optomechanical systems.
Cavity quantum optomechanics has emerged as a new platform for quantum science and technology and has applications ranging from quantum-information processing to tests of the foundations of physics. Of crucial importance for optomechanics is the generation and verification of non-Gaussian states of motion and a key outstanding challenge is the observation of a canonical two-mode Schrodinger-cat state in the displacement of two mechanical oscillators. In this work, we introduce a protocol that utilizes the nonlinearity of the radiation-pressure interaction combined with photon-counting measurements to generate this bipartite non-Gaussian mechanical state. Our protocol employs short optical pulses to both generate the mechanical quantum state, and to then measure arbitrary mechanical quadrature moments, which we utilize to verify the non-Gaussian entanglement. Our entanglement-verification procedure can be used to evaluate an entire class of inseparability criteria and also provides a route for experimental characterisation of a broad range of single- and multi-partite mechanical states. Key experimental factors, such as optical loss and mechanical decoherence, are carefully analyzed and we show that the scheme is feasible with only minor improvements to current experiments that operate outside the resolved-sideband regime. Our scheme provides a new avenue for quantum experiments with entangled mechanical oscillators and offers significant potential for further research and development that utilizes such non-Gaussian states for quantum-information and sensing applications, and for studying the quantum-to-classical transition.
In this paper, we propose a feasible scheme for generating the Schr\"odinger-cat-like states of a macroscopic mechanical resonator in pulsed cavity optomechanics via photon detection. Starting with cooling the mechanical oscillator to its ground state, a red pulse and a blue pulse with different powers are simultaneously employed to dissipatively generate squeezed mechanical states. Subsequently, a second red pulse is utilized to achieve large-amplitude mechanical catlike states with high fidelities, conditioned on the multiphoton detection of cavity output and assisted by squeezing injection into the cavity. This combination effectively overcomes the difficulty that only a kitten can be produced by single-photon detection. Finally, after being stored in the resonator for a period of time during which thermal effect is analytically revealed, the mechanical quantum superpositions are mapped, with a third red pulse, to the cavity output field for state verification. Our scheme is generic and can also be used to produce other kinds of non-Gaussian mechanical states, such as optical-catalysis nonclassical states.