Elsevier

Optics Communications

Volume 482, 1 March 2021, 126604
Optics Communications

Continuous-mode photon–phonon entanglement effects in optomechanical resonator–waveguide system

https://doi.org/10.1016/j.optcom.2020.126604Get rights and content

Highlights

  • Two-mode optomechanical resonator–waveguide system is employed to generate entangled traveling photon–phonon fields.

  • Generation efficiency of entangled traveling photon–phonon pairs is drastically enhanced.

  • Continuous-mode photon–phonon squeezing operations can be implemented.

  • Entanglement of photon–phonon pairs and characteristics of photon–phonon squeezing operations can be controlled by pump spectra.

Abstract

We study the quantum effects of entanglement between continuous-mode photon and phonon fields in waveguide channels that are coupled to an optomechanical resonator structure with two optical modes. We show that such optomechanical resonator–waveguide system can drastically enhance the efficiency for generating entangled traveling photon–phonon single pairs, and can serve to implement controllable continuous-mode photon–phonon squeezing of weak input signals. The effectiveness of the generation-efficiency enhancement and the quantum squeezing operation is attributed to the resonance between the normal-mode photon transition and the phonon mode in the optomechanical resonator structure.

Introduction

Optomechanics explores interaction between mechanical objects and electromagnetic fields [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], and offers promising opportunities for test of macroscopic quantum mechanics, measurement of extremely small forces or displacements, and application in quantum information processing [14], [15], [16], [17], [18], [19], [20]. A unique feature arising from optomechanical coupling is quantum entanglement between light and mechanics, which, other than inspiring fundamental insight into quantum physics, could be essential in combining the potential virtues of photons (e.g., suitable for long-distance propagation) and phonons (e.g., suitable for long-time storage) as quantum-information carriers. Although light-mechanics entanglement has been intensely studied in literature  [21], [22], [23], [24], [25], [26], [27], the efforts were mainly devoted to entangled states of localized (resonator-mode) photons and phonons, and reports on entangled traveling continuous-mode photon–phonon fields (in photonic and phononic waveguides [28], [29], [30], [31]) have been relatively rare. Compared to the localized resonator modes, the traveling quantum fields not only allows for constructing photon–phonon single pairs of continuous-variable entanglement, but also are necessary in transmitting or distributing the entanglement to different locations. Therefore, it is of great interest to investigate the light-mechanics entanglement in traveling continuous-mode fields, which, as just mentioned, has attracted much less attention than the localized-mode aspects in optomechanics.

In this paper, we study the effects of quantum entanglement between continuous-mode photon and phonon fields in waveguide channels that are coupled to a two-mode (two optical modes and one mechanical mode) optomechanical resonator structure. We show that, as the optical and mechanical resonator-modes satisfy appropriate resonance conditions, entangled traveling photon–phonon single pairs in the waveguide channels can be generated with drastically enhanced efficiency compared to that in the single-mode (one optical and one mechanical resonator-mode) optomechanical resonator–waveguide system [32], and more importantly, the current two-mode optomechanical resonator–waveguide system can serve to implement controllable continuous-mode photon–phonon squeezing operation on weak input signal states. The physical mechanisms underlying the generation-efficiency enhancement and the quantum photon–phonon squeezing operation are analytically explained, and the entanglement of the traveling photon–phonon pair and the coherence in the continuous-mode photon–phonon squeezed vacuum state are investigated. Here, for comparison with previous work in literature, we remark that the design and characterization of phononic or photonic–phononic waveguides and their respective coupling to optomechanical resonators were investigated in Refs. [28], [29], [30], conversion of traveling phonon to photon states (and vice versa) was proposed in Ref. [31], and entangled traveling photon fields (without waveguides) were studied in Refs. [33], [34], [35].

The paper is organized as follows. In Section 2, we study the generation of entangled traveling photon–phonon single pairs in the two-mode optomechanical resonator–waveguide system, and show that the generation efficiency can be substantially enhanced. In Section 3, via an effective three-wave-mixing Hamiltonian that reveals the resonant characteristic of the optomechanical system, we analyze the generation-efficiency enhancement in a more physically-intuitive way, and further demonstrate that the optomechanical system can be employed to implement controllable continuous-mode photon–phonon squeezing of weak input signals. A brief summary is given in Section 4.

Section snippets

Enhanced generation of entangled traveling photon–phonon pairs

The quantum system under our current study is sketched in Fig. 1(a), where the optomechanical resonator y couples to the auxiliary optical resonator x and the waveguide that supports both photonic and phononic channel fields. The implementation of optical and mechanical channels in a single waveguide is not essential, i.e., the analysis and conclusions in this paper are equally valid for systems with separate optical and mechanical waveguides. We start from the following Hamiltonian (ħ=1) that

Normal-mode-basis effective Hamiltonian and continuous-mode photon–phonon squeezing

In Section 2, our study of the photon–phonon pair generation is based on the original Hamiltonian (1), but the mechanism for the efficiency enhancement is more intuitively understood in the normal-mode basis (10) that directly reveals the resonant characteristic of the generation process. In this section, we explore further quantum light-mechanics entanglement effects in the optomechanical system via an effective Hamiltonian in the normal-mode basis.

With ω0m=2|J| and γe,m being independent of k

Summary

We have studied the continuous-mode photon–phonon entanglement effects in an optomechanical resonator–waveguide system with two optical resonator-modes. We found that the efficiency for the generation of entangled traveling photon–phonon single pairs can be drastically enhanced due to the resonance between the mechanical mode and the normal-mode photon transition in the resonator structure, while the entanglement characteristics are essentially preserved, in comparison to those of the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Funding

Natural Science Foundation of Shandong Province (ZR2018MA044, ZR2013AL007); National Natural Science Foundation of China (61501214, 11404156); Start-up Fund of Liaocheng University .

References (40)

  • KharelP. et al.

    High-frequency cavity optomechanics using bulk acoustic phonons

    Sci. Adv.

    (2019)
  • MalzD. et al.

    Quantum-limited directional amplifiers with optomechanics

    Phys. Rev. Lett.

    (2018)
  • YinT.S. et al.

    Nonlinear effects in modulated quantum optomechanics

    Phys. Rev. A

    (2017)
  • NorteR.A. et al.

    Mechanical resonators for quantum optomechanics experiments at room temperature

    Phys. Rev. Lett.

    (2016)
  • DengZ.J. et al.

    Entanglement rate for Gaussian continuous variable beams

    New J. Phys.

    (2016)
  • PirkkalainenJ.M. et al.

    Cavity optomechanics mediated by a quantum two-level system

    Nature Commun.

    (2015)
  • AspelmeyerM. et al.

    Cavity optomechanics

    Rev. Modern Phys.

    (2014)
  • LiaoJ.Q. et al.

    Entangling two macroscopic mechanical mirrors in a two-cavity optomechanical system

    Phys. Rev. A

    (2014)
  • AspelmeyerM. et al.

    Quantum optomechanics

    Phys. Today

    (2012)
  • WingerM. et al.

    A chip-scale integrated cavity-electro-optomechanics platform

    Opt. Express

    (2011)
  • KippenbergT.J. et al.

    Cavity optomechanics: back-action at the mesoscale

    Science

    (2008)
  • KippenbergT.J. et al.

    Cavity opto-mechanics

    Opt. Express

    (2007)
  • MarquardtF. et al.

    Quantum theory of cavity-assisted sideband cooling of mechanical motion

    Phys. Rev. Lett.

    (2007)
  • BernierN.R. et al.

    Nonreciprocal reconfigurable microwave optomechanical circuit

    Nature Commun.

    (2017)
  • BalramK.C. et al.

    Coherent coupling between radiofrequency, optical and acoustic waves in piezo-optomechanical circuits

    Nature Photonics

    (2016)
  • ChenY.

    Macroscopic quantum mechanics: theory and experimental concepts of optomechanics

    J. Phys. B: At. Mol. Opt. Phys.

    (2013)
  • StannigelK. et al.

    Optomechanical quantum information processing with photons and phonons

    Phys. Rev. Lett.

    (2012)
  • SchmidtM. et al.

    Optomechanical circuits for nanomechanical continuous variable quantum state processing

    New J. Phys.

    (2012)
  • StannigelK. et al.

    Optomechanical transducers for quantum-information processing

    Phys. Rev. A

    (2011)
  • RugarD. et al.

    Single spin detection by magnetic resonance force microscopy

    Nature

    (2004)
  • Cited by (1)

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