Stabilized entanglement of massive mechanical oscillators

Abstract

Quantum entanglement is a phenomenon whereby systems cannot be described independently of each other, even though they may be separated by an arbitrarily large distance . Entanglement has a solid theoretical and experimental foundation and is the key resource behind many emerging quantum technologies, including quantum computation, cryptography and metrology. Entanglement has been demonstrated for microscopic-scale systems, such as those involving photons, ions and electron spins , and more recently in microwave and electromechanical devices. For macroscopic-scale objects, however, it is very vulnerable to environmental disturbances, and the creation and verification of entanglement of the centre-of-mass motion of macroscopic-scale objects remains an outstanding goal. Here we report such an experimental demonstration, with the moving bodies being two massive micromechanical oscillators, each composed of about 10 atoms, coupled to a microwave-frequency electromagnetic cavity that is used to create and stabilize the entanglement of their centre-of-mass motion. We infer the existence of entanglement in the steady state by combining measurements of correlated mechanical fluctuations with an analysis of the microwaves emitted from the cavity. Our work qualitatively extends the range of entangled physical systems and has implications for quantum information processing, precision measurements and tests of the limits of quantum mechanics.

Nano‐Cavity QED with Tunable Nano‐Tip Interaction

“…Finally, the field of cavity optomechanics has recently emerged, employing a complementary approach to cQED by focusing on controlling the interaction of light with vibrational modes of solid state resonators . However, to achieve the few vibrational quanta interaction regime in mesoscale resonators with characteristic frequencies in the MHz–GHz range, deep cryogenic conditions are required . On the other hand, scaling the mass of a mechanical oscillator to the atomic scale in the form of a molecular bond leads to an increase in vibrational frequency into the THz–PHz regime, where the vibrational ground state can be reached at room temperature .…”

“…[106][107][108] However, to achieve the few vibrational quanta interaction regime in mesoscale resonators with characteristic frequencies in the MHz-GHz range, deep cryogenic conditions are required. [109][110][111][112][113] On the other hand, scaling the mass of a mechanical oscillator to the atomic scale in the form of a molecular bond leads to an increase in vibrational frequency into the THz-PHz regime, where the vibrational ground state can be reached at room temperature. [114,115] This enables a new regime of room temperature molecular cavity optomechanics and indeed, the coherent interaction regime of strong coupling has been reached in micro-cavities for ensemble measurements.…”

Measurement of Motion beyond the Quantum Limit by Transient Amplification

“…Much of this progress results from advances in the parametric coupling of these oscillators to optical cavities or resonant electrical circuits. These related fields of optomechanics and electromechanics have demonstrated the ability to cool mechanical oscillators to near their motional ground state [1], entangle mechanical oscillators with each other [2, 3] or with other degrees of freedom [4], and create squeezed states of motion [5][6][7]. To verify the successful creation of these non-classical states, electromechanical and optomechanical methods have also enabled measurements of mechanical motion with near 50% quantum efficiency [8, 9], or equivalently an added noise equal to the zero-point motion of the oscillator, the quantum limit for simultaneous measurement of both mechanical quadratures [10].These advances have encouraged notions of using nonclassical states of motion to test quantum mechanics at larger scales, sensing forces with quantum enhanced precision, and enabling quantum transduction between disparate physical systems [11].…”

“…Specializing to the case δ m = 0 and ω ± = ω c ± ω m (as in [2]) the linearized Heisenberg-Langevin equations can be calculated in the rotating wave approximation:…”

Arbitrary multimode Gaussian operations on mechanical cluster states

“…Additionally, recent experiments demonstrated the possibility to coherently couple multiple mechanical resonators to a single cavity field [37][38][39][40]. In fact, various theoretical analyses of multiple resonators coupled to radiation pressure have been put forward [41][42][43][44][45][46][47][48][49][50][51][52].…”