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arXiv:1807.03194 · npj Quantum Information

Proposal to test quantum wave-particle superposition on massive mechanical resonators

Wei Qin, Adam Miranowicz, Guilu Long, J. Q. You, Franco Nori

Published Jul 9, 2019• 40 citations
arXivHTMLPDF

Abstract

Abstract We present and analyze a proposal for a macroscopic quantum delayed-choice experiment with massive mechanical resonators. In our approach, the electronic spin of a single nitrogen-vacancy impurity is employed to control the coherent coupling between the mechanical modes of two carbon nanotubes. We demonstrate that a mechanical phonon can be in a coherent superposition of wave and particle, thus exhibiting both behaviors at the same time. We also discuss the mechanical noise tolerable in our proposal and predict a critical temperature below which the morphing between wave and particle states can be effectively observed in the presence of environment-induced fluctuations. Furthermore, we describe how to amplify single-phonon excitations of the mechanical-resonator superposition states to a macroscopic level, via squeezing the mechanical modes. This approach corresponds to the phase-covariant cloning. Therefore, our proposal can serve as a test of macroscopic quantum superpositions of massive objects even with large excitations. This work, which describes a fundamental test of the limits of quantum mechanics at the macroscopic scale, would have implications for quantum metrology and quantum information processing.

DOI
10.1038/s41534-019-0172-9

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Abstract We present and analyze a proposal for a macroscopic quantum delayed-choice experiment with massive mechanical resonators. In our approach, the electronic spin of a single nitrogen-vacancy impurity is employed to control the coherent coupling between the mechanical modes of two carbon nanotubes. We demonstrate that a mechanical phonon can be in a coherent superposition of wave and particle, thus exhibiting both behaviors at the same time. We also discuss the mechanical noise tolerable in our proposal and predict a critical temperature below which the morphing between wave and particle states can be effectively observed in the presence of environment-induced fluctuations. Furthermore, we describe how to amplify single-phonon excitations of the mechanical-resonator superposition states to a macroscopic level, via squeezing the mechanical modes. This approach corresponds to the phase-covariant cloning. Therefore, our proposal can serve as a test of macroscopic quantum superpositions of massive objects even with large excitations. This work, which describes a fundamental test of the limits of quantum mechanics at the macroscopic scale, would have implications for quantum metrology and quantum information processing.
We describe an experimentally feasible protocol for performing a variant of the quantum delayed-choice experiment with massive objects. In this scheme, a single nitrogen-vacancy (NV) center in diamond driven by microwave fields is dispersively coupled to a massive mechanical resonator. A double-pulse Ramsey interferometer can be implemented with the spin-mechanical setup, where the second Ramsey microwave pulse drives the spin conditioned on the number states of the resonator. The probability for finding the NV center in definite spin states exhibits interference fringes when the mechanical resonator is prepared in a specific number state. On the other hand, the interference is destroyed if the mechanical resonator stays in some other number states. The wavelike and particlelike behavior of the NV spin can be superposed by preparing the mechanical resonator in a superposition of two distinct number states. Thus a quantum version of Wheeler's delayed-choice experiment could be implemented, allowing fundamental tests of quantum mechanics on a macroscopic scale.
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/Hz10^{-6}g/\sqrt{\text{Hz}}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.
Micro-optomechanical systems are central to a number of recent proposals for realizing quantum mechanical effects in relatively massive systems. Here, we focus on a particular class of experiments which aim to demonstrate massive quantum superpositions, although the obtained results should be generalizable to similar experiments. We analyze in detail the effects of finite temperature on the interpretation of the experiment, and obtain a lower bound on the degree of non-classicality of the cantilever. Although it is possible to measure the quantum decoherence time when starting from finite temperature, an unambiguous demonstration of a quantum superposition requires the mechanical resonator to be in or near the ground state. This can be achieved by optical cooling of the fundamental mode, which also provides a method to measure the mean phonon number in that mode. We also calculate the rate of environmentally induced decoherence and estimate the timescale for gravitational collapse mechanisms as proposed by Penrose and Diosi. In view of recent experimental advances, practical considerations for the realization of the described experiment are discussed.
The toolbox of quantum optics allows to achieve coherent quantum control over massive mechanical resonators by using radiation pressure of light inside optical cavities. Only recently, cavity-assisted ground state cooling of mechanical motion has been achieved both in the micro- and in the nanomechanical domain [1, 2]. Together with the strong coupling regime [3], this opens up a new parameter regime for macroscopic quantum physics with respect to size and mass of the objects under investigation. I will discuss the prospects of generating macroscopic quantum superposition states [4] and quantum entanglement [5], both for micromechanical interfaces for quantum information processing and for new tests of the foundations of quantum physics.
The toolbox of quantum optics allows to achieve coherent quantum control over massive mechanical resonators by using radiation pressure of light inside optical cavities. Only recently, cavity-assisted ground state cooling of mechanical motion has been achieved both in the micro- and in the nanomechanical domain [1, 2]. Together with the strong coupling regime [3], this opens up a new parameter regime for macroscopic quantum physics with respect to size and mass of the objects under investigation. I will discuss the prospects of generating macroscopic quantum superposition states [4] and quantum entanglement [5], both for micromechanical interfaces for quantum information processing and for new tests of the foundations of quantum physics.
Quantum states of mechanical motion can be important resources for quantum information, metrology, and studies of fundamental physics. Recent demonstrations of superconducting qubits coupled to acoustic resonators have opened up the possibility of performing quantum operations on macroscopic motional modes, which can act as long-lived quantum memories or transducers. In addition, they can potentially be used to test for novel decoherence mechanisms in macroscopic objects and other modifications to standard quantum theory. Many of these applications call for the ability to create and characterize complex quantum states, putting demanding requirements on the speed of quantum operations and the coherence of the mechanical mode. In this work, we demonstrate the controlled generation of multi-phonon Fock states in a macroscopic bulk-acoustic wave resonator. We also perform Wigner tomography and state reconstruction to highlight the quantum nature of the prepared states. These demonstrations are made possible by the long coherence times of our acoustic resonator and our ability to selectively couple to individual phonon modes. Our work shows that circuit quantum acousto-dynamics (circuit QAD) enables sophisticated quantum control of macroscopic mechanical objects and opens the door to using acoustic modes as novel quantum resources.