Measurement-Induced Macroscopic Superposition States in Cavity Optomechanics

Abstract

A novel protocol for generating quantum superpositions of macroscopically distinct states of a bulk mechanical oscillator is proposed, compatible with existing optomechanical devices operating in the badcavity limit. By combining a pulsed optomechanical quantum nondemolition (QND) interaction with nonclassical optical resources and measurement-induced feedback, the need for strong single-photon coupling is avoided. We outline a three-pulse sequence of QND interactions encompassing squeezingenhanced cooling by measurement, state preparation, and tomography. DOI: 10.1103/PhysRevLett.117.143601 Introduction.-Elusive as they are, Schrödinger cat [1] states remain some of the hardest to tame in the quantum world, yet also among the ones most strived for. That is due to their quintessential embodiment of the manifestly nonclassical properties of quantum mechanics, by simultaneously occupying two macroscopically distinct states-dead and alive. Successful creation of such coherent state superpositions have so far been limited exclusively to isolated microscopic quantum systems, e.g. in ion traps [2,3] and microwave cavity and circuit quantum electrodynamics [4][5][6][7], while closely related variants, colloquially termed Schrödinger kittens, have been demonstrated in propagating optical fields [8][9][10]. However, an intriguing and long-standing question is whether also macroscopic objects can be prepared in quantum superpositions of being here and there?A vast number of proposals for optomechanical generation of non-Gaussian mechanical states, such as cat states, exist in the literature [11][12][13][14][15][16]. Non-Gaussian states of light can be directly mapped onto the mechanical motional states either via a swapping operation [17][18][19] or by teleportation [20,21], but this can be achieved only in the highly challenging sideband resolved regime in which the mechanical frequency lies outside the resonance of a narrow-banded cavity (good cavity limit). Mechanical non-Gaussian states can also be generated in the much simpler bad cavity regime (where the sidebands are unresolved) by using a broadband cavity and either single photon [22] or coherent state resources [23]. However, these protocols rely on an extremely strong non-Gaussian interaction between light and mechanics and are thus of limited practical feasibility due to the insufficient optomechanical interaction strengths currently achievable.As suggested in recent works [24][25][26][27], quantum nondemolition (QND) state transfer [28,29] induced by pulsed optomechanical interaction [30][31][32] offers a more feasible route. Extending this framework, we propose a novel squeezing-enhanced protocol for preparation of macroscopic

Arbitrary multimode Gaussian operations on mechanical cluster states

“…This will necessitate involving a non-Gaussian element in the network, whether taking advantage of a non-Gaussian measurement, a non-linear optomechanical dynamics, or an already prepared nonGaussian resource. Promisingly in this direction, it has been shown that opto-and electro-mechanical systems can intrinsically host non-linearities in various settings [33,36,76,77], and this possibility has been suggested for engineering non-Gaussian states, dynamics, and measurements [32,[78][79][80][81][82][83][84][85]. The latter could potentially be exploited to unlock the universality of computation and this shall be the topic of future work.…”

Extracting work from quantum states of radiation

“…Recently, quantum entanglement between radiation and mechanical systems and also quantum squeezing of mechanical uncertainty have been demonstrated [14,16,17]. These experiments can be extended to prepare various quantum states of mechanical system [38][39][40][41][42][43][44][45]. To reach a high quality of transfer for any state of light to mechanical systems, universal interfaces have been proposed as well [46][47][48][49].…”

Nonclassical-state generation in macroscopic systems via hybrid discrete-continuous quantum measurements

“…Indeed, using a singlephoton detection event, entanglement between the vibrational states of two diamond crystals has been generated [38], and techniques for mechanical NOON state generation have been proposed [39,40], as well as schemes to entangle atomic ensembles with mechanical motion [41,42]. In addition, a scheme has been recently proposed that utilizes an optomechanical interaction with a nonclassical optical field prepared via photon subtraction to conditionally generate nonclassical mechanical states [43].…”