Quantum entanglement of mechanical systems emerges when distinct objects move with such a high degree of correlation that they can no longer be described separately. Although quantum mechanics presumably applies to objects of all sizes, directly observing entanglement becomes challenging as masses increase, requiring measurement and control with a vanishingly small error. Here, using pulsed electromechanics, we deterministically entangle two mechanical drumheads with masses of 70 picograms. Through nearly quantum-limited measurements of the position and momentum quadratures of both drums, we perform quantum state tomography and thereby directly observe entanglement. Such entangled macroscopic systems are poised to serve in fundamental tests of quantum mechanics, enable sensing beyond the standard quantum limit, and function as long-lived nodes of future quantum networks.

Direct observation of deterministic macroscopic entanglement.

Developing the isolation and control of ultracold atomic systems to the level of single quanta has led to significant advances in quantum sensing, yet demonstrating a quantum advantage in real world applications by harnessing entanglement remains a core task. Here, we realize a many-body quantum-enhanced sensor to detect weak displacements and electric fields using a large crystal of $\sim 150$ trapped ions. The center of mass vibrational mode of the crystal serves as high-Q mechanical oscillator and the collective electronic spin as the measurement device. By entangling the oscillator and the collective spin before the displacement is applied and by controlling the coherent dynamics via a many-body echo we are able to utilize the delicate spin-motion entanglement to map the displacement into a spin rotation such that we avoid quantum back-action and cancel detrimental thermal noise. We report quantum enhanced sensitivity to displacements of $8.8 \pm 0.4~$dB below the standard quantum limit and a sensitivity for measuring electric fields of $240\pm10~\mathrm{nV}\mathrm{m}^{-1}$ in $1$ second ($240~\mathrm{nV}\mathrm{m}^{-1}/\sqrt{\mathrm{Hz}}$).

Quantum-enhanced sensing of displacements and electric fields with large trapped-ion crystals

Nanomechanics has brought mesoscopic physics into the world of vibrations. Because nanomechanical systems are small, fluctuations are significant, the vibrations become nonlinear already for comparatively small amplitudes, and new mechanisms of dissipation come into play. At the same time, the exquisite control of these systems makes them a platform for studying many problems of classical and quantum physics far from thermal equilibrium in a well-characterized setting. This review describes, at a conceptual level, basic theoretical ideas and explicative experiments pertaining to mesoscopic physics of nanomechanical systems. Major applications of nanomechanics in science and technology are also outlined. A broad range of phenomena related to the conservative as well as dissipative nonlinearity and fluctuations are discussed within a unifying framework. They include the linear response of single and coupled vibrational modes as well as nonlinear effects of periodic driving. Such driving breaks the continuous time-translation symmetry and the detailed balance, with conspicuous consequences for fluctuations, particularly in the presence of the driving-induced bi- and multistability. Mathematical techniques are described in the appendices to streamline the reading, but also to provide an introduction to the theory. The goal of the review is to show the richness of the physics at work. The continuous experimental and theoretical advances make nanomechanical systems a vibrant area of research, with many new phenomena to discover.

Mesoscopic physics of nanomechanical systems

Observing quantum mechanics at the macroscopic scale has captured the attention of scientists and the imagination of the public for more than a century. While quantum mechanics was conceived in the context of electrons and atoms, the ability to observe its properties on ever more macroscopic systems holds great promise for fundamental research and technological applications. Therefore, researchers have been preparing larger material systems in interesting quantum states and, in particular, entangled states of separate mechanical oscillators[1-3]. As these quantum devices move from demonstrations to applications, their full potential can only be realized by combining entanglement generation with an efficient measurement of the joint mechanical state. Unfortunately, such a high level of control and measurement can expose the system to undesired interactions with its environment, a problem that becomes more pronounced at the macroscopic scale. Here, using a superconducting electromechanical circuit and a pulsed microwave protocol, we ground-state cool, entangle and perform state tomography of two mechanical drumheads with masses of 70 pg. Entanglement is generated deterministically and is followed by a nearly quantum-limited measurement of the positions and momentums of both mechanical oscillators. From these efficient measurements, the resulting tomography demonstrates entanglement without noise subtraction. Highly entangled, massive quantum systems, as demonstrated here, are uniquely poised to address fundamental tests of quantum mechanics[4,5], enable force sensing beyond the standard quantum limit[6], and possibly serve as long-lived nodes of a future quantum network[7,8].

Tomography of Entangled Macroscopic Mechanical Objects

We report the results of back-action evading experiments utilizing a tightly coupled electro-mechanical system formed by a radio frequency micromechanical resonator parametrically coupled to a NbTiN superconducting microwave resonator. Due to excess dissipation in the microwave resonator, we observe a parametric instability induced by a thermal shift of the mechanical resonance frequency. In light of these measurements, we discuss the constraints on microwave dissipation needed to perform BAE measurements far below the zero-point level.

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Thermally induced parametric instability in back-action evading measurement of micromechanical quadrature near the zero-point level

Superconducting-qubit readout via low-backaction electro-optic transduction

Through simultaneous but unequal electromechanical amplification and cooling processes, we create a method for a nearly noiseless pulsed measurement of mechanical motion. We use transient electromechanical amplification (TEA) to monitor a single motional quadrature with a total added noise -8.5±2.0  dB relative to the zero-point motion of the oscillator, or equivalently the quantum limit for simultaneous measurement of both mechanical quadratures. We demonstrate that TEA can be used to resolve fine structure in the phase space of a mechanical oscillator by tomographically reconstructing the density matrix of a squeezed state of motion. Without any inference or subtraction of noise, we directly observe a squeezed variance 2.8±0.3  dB below the oscillator's zero-point motion.

Measurement of Motion beyond the Quantum Limit by Transient Amplification.

Quantum state tomography of a mechanical oscillator

Efficient anti-dissipative measurement of mechanical motion

Entangling superconducting quantum processors via light would enable new means of secure communication and distributed quantum computing. However, transducing quantum signals between these disparate regimes of the electromagnetic spectrum remains an outstanding goal, and interfacing superconducting qubits with electro-optic transducers presents significant challenges due to the deleterious effects of optical photons on superconductors. Moreover, many remote entanglement protocols require multiple qubit gates both preceding and following the upconversion of the quantum state, and thus an ideal transducer should leave the state of the qubit unchanged: more precisely, the backaction from the transducer on the qubit should be minimal. Here we demonstrate non-destructive optical readout of a superconducting transmon qubit via a continuously operated electro-optic transducer. The modular nature of the transducer and circuit QED system used in this work enable complete isolation of the qubit from optical photons, and the backaction on the qubit from the transducer is less than that imparted by thermal radiation from the environment. Moderate improvements in transducer bandwidth and added noise will enable us to leverage the full suite of tools available in circuit QED to demonstrate transduction of non-classical signals from a superconducting qubit to the optical domain.

Robert D. Delaney

Papers

Superconducting-qubit readout via low-backaction electro-optic transduction

Measurement of Motion beyond the Quantum Limit by Transient Amplification.

Quantum state tomography of a mechanical oscillator

Efficient anti-dissipative measurement of mechanical motion

Non-destructive optical readout of a superconducting qubit