Room-Temperature Mechanical Resonator with a Single Added or Subtracted Phonon

Rishi N. Patel, Timothy P. McKenna, Zhaoyou Wang, Jeremy D. Witmer, Wentao Jiang, Raphaël Van Laer, Christopher J. Sarabalis, and Amir H. Safavi-Naeini

Phys. Rev. Lett. 127, 133602 – Published 20 September 2021

Abstract

A room-temperature mechanical oscillator undergoes thermal Brownian motion with an amplitude much larger than the amplitude associated with a single phonon of excitation. This motion can be read out and manipulated using laser light using a cavity-optomechanical approach. By performing a strong quantum measurement (i.e., counting single photons in the sidebands imparted on a laser), we herald the addition and subtraction of single phonons on the 300 K thermal motional state of a 4 GHz mechanical oscillator. To understand the resulting mechanical state, we implement a tomography scheme and observe highly non-Gaussian phase-space distributions. Using a maximum likelihood method, we infer the density matrix of the oscillator, and we confirm the counterintuitive doubling of the mean phonon number resulting from phonon addition and subtraction.

Received 24 February 2021
Accepted 19 July 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.133602

Physics Subject Headings (PhySH)

Optomechanics Quantum fluctuations & noise Quantum measurements Quantum optics Quantum state engineering

Quantum cavities

Atomic, Molecular & Optical

Authors & Affiliations

Rishi N. Patel ^*, Timothy P. McKenna , Zhaoyou Wang , Jeremy D. Witmer, Wentao Jiang , Raphaël Van Laer, Christopher J. Sarabalis, and Amir H. Safavi-Naeini^†

Department of Applied Physics, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

^*rishipat@stanford.edu
^†safavi@stanford.edu

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Vol. 127, Iss. 13 — 24 September 2021

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Images

Figure 1
Concept and principal components of experimental setup: (a) Concept showing, on left (right), how a Raman scattered photon on cavity resonance at frequency $ω_{c}$ heralds addition (subtraction) of a phonon at mechanical frequency $ω_{m}$ . Insets from left to right show simulated mechanical and optical mode profiles, respectively. (b) Diagram showing main components of setup. A tunable laser is stabilized to a Fabry-Perot cavity (FP) and frequency upshifted using an acousto-optic modulator (AOM). Resulting signal polarization is set using a fiber polarization controller (FPC) and sent into the optomechanical crystal device (OMC) whose temperature is stabilized near 300 K. Reflected light is incident on a beam splitter and split into two paths. On the bottom, we reject pump light with two FP filers, followed by single-photon detection using a superconducting nanowire single-photon detector. To the left, we perform balanced heterodyne detection (BHD), where the resulting signal is further digitally down-converted from 20 MHz and filtered using a digitizer and graphics processing unit. A schematic of the decaying cavity field is shown in inset. $τ$ denotes time lag between when a click occurs and when heterodyne data collection starts.
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Figure 2
Measurement of quadrature histograms for thermal and phonon-added thermal state. (a) Experimental result showing histogram of $1.5 \times 10^{7}$ quadrature samples. Data are binned into 101 bins along the $X$ and $P$ axes. Color bars show counts per bin. Statistics are Gaussian, corresponding to a mechanical thermal state. (b) Postselected results, triggered by single-photon clicks. Observed statistical distribution now corresponds to a phonon-added state and is non-Gaussian. (c) and (d) Corresponding theory plots to Figs. 2 and 2, obtained by binning and fitting analytically determined Husimi $Q$ functions via two parameters. Dotted black circles with radii $r = \sqrt{{\bar{n}}_{th}}$ are shown for reference. ${\bar{n}}_{th} \approx 1580$ phonons, corresponding to mean occupancy of 3.96 GHz oscillator at room temperature. Solid black circle shows length scale for added noise. (e) Blue (red) bars correspond to linecut of 2D experiment histograms at $P = 0$ for thermal (postselected) datasets. The theory fits for thermal (postselected) results are shown in solid (dotted) black lines.
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Figure 3
Reconstructed density matrix elements. (a) Radial histogram of measurement results for thermal state (filled blue points), phonon-added thermal state (open red circles), and phonon-subtracted thermal state (green triangles). Respective dotted lines show theory fits. (b) Diagonal density matrix elements reconstructed from experimental data. Estimates for gain and added noise provided by fits to quadrature histogram data. Black dotted lines show result of theory for thermal and phonon-added states with thermal bath occupancy set to ${\bar{n}}_{th} = 1578$ phonons ( $\approx 300 K$ mode temperature). (c) Experimentally reconstructed density matrix elements for a phonon-subtracted thermal state.
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