Stimulated Raman Adiabatic Passage in Optomechanics

Vitaly Fedoseev, Fernando Luna, Ian Hedgepeth, Wolfgang Löffler, and Dirk Bouwmeester

Phys. Rev. Lett. 126, 113601 – Published 19 March 2021

Abstract

In multimode optomechanical systems, the mechanical modes can be coupled via the radiation pressure of the common optical mode, but the fidelity of the state transfer is limited by the optical cavity decay. Here we demonstrate stimulated Raman adiabatic passage (STIRAP) in optomechanics, where the optical mode is not populated during the coherent state transfer between the mechanical modes avoiding this decay channel. We show a state transfer of a coherent mechanical excitation between vibrational modes of a membrane in a high-finesse optical cavity with a transfer efficiency of 86%. Combined with exceptionally high mechanical quality factors, STIRAP between mechanical modes can enable generation, storage, and manipulation of long-lived mechanical quantum states, which is important for quantum information science and for the investigation of macroscopic quantum superpositions.

Received 27 July 2020
Accepted 12 February 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.113601

Physics Subject Headings (PhySH)

Entanglement production Optomechanics Quantum state transfer

Atomic, Molecular & Optical

Authors & Affiliations

Vitaly Fedoseev ^1,*, Fernando Luna², Ian Hedgepeth², Wolfgang Löffler ¹, and Dirk Bouwmeester^1,2

¹Huygens-Kamerlingh Onnes Laboratorium, Leiden University, 2333 CA, Leiden, Netherlands
²Department of Physics, University of California, Santa Barbara, California 93106, USA

^*vfedoseev@physics.leidenuniv.nl

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Issue

Vol. 126, Iss. 11 — 19 March 2021

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Images

Figure 1
STIRAP scheme in optomechanics. (a) Energy levels diagram. (b) Coupling strengths of the pulse sequence for the driving fields. (c) The resulting energy eigenvalues for the instantaneous Hamiltonian eigenstates. STIRAP explores the properties of $Φ_{0} (t)$ given in Eq. (2). (d) The optomechanical implementation contains a cavity mode at frequency $ω_{cav}$ , two driving fields at $ω_{L 1}$ and $ω_{L 2}$ and eight motional sidebands due to the mechanical modes at $ω_{1}$ and $ω_{2}$ on the driving fields, red bars corresponding to the sidebands on $ω_{L 1}$ and blue bars corresponding to the sidebands on $ω_{L 2}$ . Two sidebands match $ω_{cav}$ . In the case of $Φ_{0} (t)$ the states $ψ_{1}$ and $ψ_{3}$ are out of phase leading to destructive interference of the sidebands that overlap with $ω_{cav}$ .
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Figure 2
Optomechanical setup. (a) A transparent dielectric membrane patterned with a phononic crystal is placed in the middle of a high-finesse optical cavity. Shift of the membrane along the axis of the cavity changes the cavity resonance frequency, causing coupling of light in the cavity to vibrational modes of the membrane. (b) Simulated displacement of a mechanical mode of the defect of the phononic crystal. The mode is localized as its frequency lies in the band gap (mode 1, initially excited). (c) Simulated displacement of the 3,3 drumhead mode of the full membrane (mode 2). This second mode was selected because it has an appropriate mechanical frequency and quality factor and has a maximum amplitude at the center. This allows both modes to be aligned for optimal coupling to the same cavity mode.
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Figure 3
Experimental optomechanical STIRAP. (a) Left scale: phonon number as a function of time, red dots correspond to averaged measurements for mode 1 ( $ψ_{1}$ ), blue dots for mode 2 ( $ψ_{3}$ ). The prefactor $10^{9}$ is a rough estimate. Light red and light blue regions represent the phonon populations with statistical uncertainties (1 standard deviation) obtained from simulations without free fit parameters. Right scale: multiphoton optomechanical coupling strengths, calculated from measured pulse intensities. The driving field pulses have a nearly Gaussian profile with the standard deviation parameter $σ$ and separation $Δ t$ , but their beginning and ending are smoothly truncated to zero. Black stars correspond to the phonon populations used to calculate transfer efficiency (5% of the peak voltage sent to the AOM). (b) Measured phases of mode 1 (red) and mode 2 (blue) in the rotating frame.
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Figure 4
Transfer efficiencies under different parameters of the optical pulses. (a) The transfer efficiency as a function of the ratio of the delay between the pulses $Δ t$ and the Gaussian pulse width $σ$ . Positive values of $Δ t$ correspond to the case that the field at $ω_{L 2}$ is applied before the field at $ω_{L 1}$ . (b) Maximal transfer efficiencies as a function of $σ$ . In (a) and (b) the red dots show measured efficiencies in individual runs, black dots are the simulated efficiencies, and the black lines are guides to the eye. The increasing error bars for larger $σ$ in (b) are due to observed but not accounted for small nonlinear and heating effects, see Supplemental Material. (c) and (d) show the experimental (c) and predicted (d) transfer efficiency as a function of the Gaussian parameter $σ$ and separation $Δ t$ . The horizontal row of dots in (c) and (d) correspond to the data shown in (a), while the vertical row of dots correspond to the data shown in (b). The transfer process for the parameters corresponding to the open circle in (c) and (d) is shown in Fig. 3. (e) The efficiency as a function of the two-photon detuning $Δ_{2 ph}$ with zero single-photon detuning. (f) The efficiency as a function of the single-photon detuning $Δ_{1 ph}$ with zero two-photon detuning. In (e) and (f) the red circles are measured efficiencies in individual runs, and the shaded regions are simulated efficiencies with statistical uncertainties. The simulated curve in (e) has a frequency correction of 4 Hz caused by small nonlinear and heating effects, see Supplemental Material.
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