Microwave-to-optics conversion using a mechanical oscillator in its quantum groundstate

Abstract

Conversion between signals in the microwave and optical domains is of great interest both for classical telecommunication, as well as for connecting future superconducting quantum computers into a global quantum network. For quantum applications, the conversion has to be both efficient, as well as operate in a regime of minimal added classical noise. While efficient conversion has been demonstrated using mechanical transducers, they have so far all operated with a substantial thermal noise background. Here, we overcome this limitation and demonstrate coherent conversion between GHz microwave signals and the optical telecom band with a thermal background of less than one phonon. We use an integrated, on-chip electro-opto-mechanical device that couples surface acoustic waves driven by a resonant microwave signal to an optomechanical crystal featuring a 2.7 GHz mechanical mode. We initialize the mechanical mode in its quantum groundstate, which allows us to perform the transduction process with minimal added thermal noise, while maintaining an optomechanical cooperativity >1, so that microwave photons mapped into the mechanical resonator are effectively upconverted to the optical domain. We further verify the preservation of the coherence of the microwave signal throughout the transduction process.

FIG. 1.. Device layout and room temperature characterization.

(A) Microscope image of the transducer devices: Our structures are comprised of an interdigital transducer (IDT, in gold, cf. upper inset), which spans several optomechanical devices for ease of fabrication. The bottom side of the chip is directly accessible with a lensed fiber, allowing for optical access to the devices. The lower inset contains a scanning electron microscope image of an optomechanical resonator. The waveguide (right) is used for evanescently coupling light in and out of the device using the lensed fiber (accessed from the bottom, not shown). (B) Finite element simulations of the optomechanical device. The E_y component of the fundamental optical mode is shown (top) alongside the displacement field of the co-localized mechanical mode oscillating around 2.7 GHz (bottom). (C) Schematic of the room temperature characterization setup. A laser is used to address the device optically. The reflected light is then measured on a high-speed photodiode to resolve the noise spectrum around the mechanical frequency while an RF source is used to drive the IDT. (D) (Upper Panel) S₁₁ reflection measurement of the IDT device with a resonance at 2.76 GHz. (Lower Panels) Optical measurements of the GHz-frequency noise of the reflected light with (bottom) and without (center) the RF drive tone applied to the IDT, which results in a narrow, coherent peak in the spectrum on top of the thermal peak. The laser in these measurements is blue-detuned from cavity resonance by the mechanical frequency, ω_m.

FIG. 2.. Device characterization at Millikelvin temperatures.

(A) Schematic of the cryogenic experimental setup. The sample with the OMC and IDT, as well as a pair of superconducting nanowire single photon detectors (SNSPDs) are placed inside the dilution refrigerator (at 20 mK and ∼1 K, respectively). We lock the laser on the red sideband of our cavity and filter residual reflected pump light from the cavity, detecting photons scattered on the cavity resonance. (B) Sideband thermometry to extract the thermal occupation of the mechanical resonator. We find an occupancy n_th = 0.9±0.01, confirming the initialization of the device close to its quantum groundstate. The bar graph shows the integrated counts for the red and blue sideband drives as well as the corresponding histograms (inset). Errors are one standard deviation, owing to the shot noise resulting from photon counting. (C) Mechanical characterization and initial RF to telecom-band conversion at mK temperatures. We sweep the RF drive frequency with the laser locked at ω_c − ω_m and monitor the count rate. The solid curve is a Lorentzian fit to the data, from which we extract a mechanical linewidth of 197 kHz, corresponding to a mechanical lifetime of ∼0.8 μs. (D) Hanbury Brown and Twiss-type measurement of the photons emitted from our cavity with 7 nW of optical input power. The second order correlations g⁽²⁾(τ) are shown for a selection of the measured RF powers alongside a reference measurement with no RF drive, but high optical power (4.5 μW, bottom curve). The curves are offset for clarity. The bunching in the reference measurement results from absorption heating due to the laser drive, yielding a large thermal state of the mechanical resonator.

FIG. 3.. Correlation measurements of the microwave-to-optical transducer in the pulsed regime.

(A) The transducer is operated such that RF drive pulses are upconverted to the optical domain using optical readout pulses. Shown are the correlations between coinciding detection events on the two single-photon detectors for photons emerging from the same Δi = 0 or different Δi ≠ 0 pulse sequences. The panels correspond to various coherent phonon populations. (B) The full set of g⁽²⁾(0) values is shown as a function of RF power applied to the IDT. The dashed curve displays the expected value of g⁽²⁾(0) for a displaced thermal state with the corresponding extracted coherent phonon number n_coh (see SI). The inset shows the relative increase in the count rate as a function of RF power with a linear fit. We use this to extract the ratio of n_coh/n_th, which allows us to demonstrate the conversion at the single coherent phonon level for the lowest powers. We can see a clear transition from a bunched (low RF power) towards a not-bunched (high RF power) second order correlation.

FIG. 4.. Preservation of phase coherence during transduction.

(A) Interference patterns taken at different values of n_coh. The solid curves are sinusoidal fits to the data, from which we extract the visibility. (B) Visibility as a function of the coherent phonon occupation in the mechanical resonator. The error in the visibility for the lower values of n_coh are smaller than the data point size. The data is overlaid with the expected visibility from the coherent and noise contributions $\sqrt{n_{\text{coh}}/\left(n_{\text{coh}}+n_{\text{noise}}\right)}$. The solid line considers thermal noise only (n_noise = n_th), while the dashed line also takes any other sources into account (n_noise = n_th + n_other), while both are scaled by the maximum available visibility in our setup.