Engineering single-phonon number states of a mechanical oscillator via photon subtraction

Abstract

We introduce an optomechanical scheme for the probabilistic preparation of single-phonon Fock states of mechanical modes based on photo-subtraction. The quality of the produced mechanical state is confirmed by a number of indicators, including phonon statistics and conditional fidelity. We assess the detrimental effect of parameters such as the temperature of the mechanical system and address the feasibility of the scheme with state-of-the-art technology.Recent developments in quantum optomechanics [1] have shown the promises for quantum state engineering held by various experimental platforms. Squeezing of the quantum noise of a micromechanical resonator has been recently demonstrated in at least two experimental settings [2,3], while the first steps towards optomechanical entanglement have been reported in some noticeable experiments [4,5].Although the investigations performed so far have focused on Gaussian operations [6] and states, including the engineering of universal resources for quantum computation [7], similar attention has been paid to the preparation of non Gaussian states [8][9][10][11][12][13][14][15][16][17]. In this respect, the preparation of phononic number states is a particularly important goal in light of the possibility to use optomechanical devices as memories and on-demand singlephoton sources [18]. Such states have been realized experimentally by coupling the mechanical mode to a superconducting qubit [19].In this paper, we propose a novel scheme for the preparation of single-phonon number states (SPNS) that combines the features offered by the linearized optomechanical interaction and the potential for effective nonlinear effects made available by photon subtraction. In Ref. [11], one of us has demonstrated the effectiveness of photon subtraction for the preparation of non-classical states of mechanical modes: The non-classical correlations established between mechanical and optical oscillators in an optomechanical cavity, complemented by the subtraction of a single photon from the optical field, are sufficient to prepare the mechanical mode in a highly non-classical (non-Gaussian) state. Here, we extend such scheme showing the possibility to engineer a state that is very close to an ideal SPNS in both a dynamical way and at the steady-state of the optomechanical evolution. We characterize the quality of the resource thus achieved * Electronic Address: mmiskeenk16@hotmail.com † Electronic Address: mjakram@qau.edu.pk ‡ Electronic Address: m.paternostro@qub.ac.uk § Electronic Address: farhan.saif@qau.edu.pk using both state fidelity and the phonon-number statistics. The remainder of this paper is organized as follows: In Sec. I, we introduce the system under scrutiny and its equations of motion. In Sec. II, we provide the analytical form of the conditional mechanical state achieved after a single-photon subtraction on the optical field. Sec. III is devoted to the characterisation of such conditional state. Sec. IV addresses the steady-state version of the scheme put forward here, while S...

Unconditional preparation of nonclassical states via linear-and-quadratic optomechanics

“…Conditional strategies have also been developed, e.g. based on photon-subtraction or pulsed interactions, which however suffer from being probabilistic and/or having a low efficiency [22][23][24][25][26][27]. In contrast, reservoir engineering guarantees the stable and unconditional preparation of the desired state.…”

Linear and quadratic reservoir engineering of non-Gaussian states

“…In cavity optomechanics, proposals for the preparation of mechanical nonclassical states usually rely on either the singlephoton strong coupling [64,65], which is still extremely weak in current experimental platforms, or on conditional operations (e.g. photon-subtraction or pulsed schemes), which are probabilistic and suffer from low efficiency [66][67][68][69][70][71]. In contrast, the optomechanical implementation of our scheme guarantees the unconditional preparation of nonclassical states and only requires weak coupling.…”

Macroscopic nonclassical-state preparation via postselection

“…We have proposed a feasible probabilistic method to generate a macroscopic mechanical qubit, as well as Schrödinger's cat and single Fock number states (n = 1) for the oscillator. As opposed to previous works [58][59][60], we studied an open dispersive spin-mechanical system without any spin and/or mechanical driving, but on non-ideal spin post-selection measurements in the weak/moderate coupling regime.…”

“…To realize this, we have considered an open spin-mechanical quantum system via a conditional displacement Hamiltonian in the dispersive regime without any need for adjusting resonances. Therefore, in comparison with previous works on the matter [58][59][60], our proposal does not rely on any non-linearity, energy exchange nor external pumpingwhich might be an advantage for scalability purposes. Moreover, in contrast to cavity photons, spin systems exhibit both long coherence as well as depolarization times at room temperature, and also they can be easily prepared and readout [61,62].…”