How to Couple a Single Phonon to a Single Atomic Spin: A Step-by-Step Guide for Quantum Researchers

Introduction

In a groundbreaking experiment at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS), researchers achieved the first-ever coupling between a single quantum of vibrational energy—a phonon—and a single atomic spin. This milestone opens new possibilities for quantum technologies that use sound as an information carrier, potentially complementing or replacing light and electricity. While the original study (published in Nature) details the precise laboratory methods, this guide translates those techniques into a step-by-step protocol for researchers aiming to replicate or adapt the experiment. You will learn how to prepare a diamond crystal with nitrogen-vacancy (NV) centers, construct a surface acoustic wave resonator, and perform coherent control over a single spin-phonon system.

What You Need

• Diamond sample (high-purity, single-crystal, with naturally occurring or implanted NV centers)
• Surface acoustic wave (SAW) resonator (lithographically patterned interdigitated transducers on a piezoelectric substrate, e.g., lithium niobate)
• Confocal microscopy setup (for optically detecting single NV centers)
• Microwave generator and amplifier (to drive spin transitions at ~2.87 GHz)
• Radio-frequency (RF) signal generator (to excite SAW resonances at ~10–100 MHz)
• Cryostat (operating at ~4 K to reduce thermal phonon noise)
• Pulsed laser (532 nm for spin initialization and readout)
• Photon counting detector (avalanche photodiode or single-photon counter)
• Time-resolved measurement electronics (for Rabi oscillations and Ramsey interferometry)
• Optical cryostat window (to allow laser access while maintaining low temperature)
• Magnetic field source (permanent magnet or electromagnet for spin splitting)

Step-by-Step Procedure

Step 1: Prepare the Diamond Sample with NV Centers

Start with a high-purity diamond slab (typically 50–100 µm thick). If your diamond lacks sufficient native NV centers, implant nitrogen ions at a low dose (e.g., 10¹² ions/cm²) and anneal at 800°C to form NV centers. Polish the surface to optical quality to minimize scattering. Characterize the density of NV centers using confocal fluorescence microscopy—aim for sparse ensembles so that single centers can be isolated.

Step 2: Fabricate the Surface Acoustic Wave (SAW) Resonator

On a piezoelectric substrate (lithium niobate, cut for efficient SAW excitation), pattern interdigitated transducers (IDTs) using electron-beam lithography and metal deposition (e.g., aluminum). Design the IDT period to match the desired SAW resonance frequency (e.g., 2.4 GHz for coupling to NV spin transitions). Include a focusing structure to concentrate acoustic energy into a small spot. Characterize the resonator with a vector network analyzer to measure the quality factor (Q) and ensure a single resonant mode.

Step 3: Align the Diamond with the SAW Resonator

Place the diamond sample directly on top of the SAW resonator, with the NV-containing face closest to the acoustic field. Use a transfer technique: first, pick up the diamond using a micromanipulator and a polymer stamp (e.g., PDMS), then gently lower it onto the resonator. Apply slight pressure to ensure good mechanical contact, as the phonon coupling depends on the acoustic wave penetrating the diamond. Use a microscope to verify alignment—the NV center of interest should sit within 1 µm of the acoustic hotspot.

Step 4: Calibrate the Spin Initialization and Readout

Cool the assembly to cryogenic temperature (≈4 K) in the cryostat. Use a confocal microscope to locate a single NV center. Apply a 532 nm laser pulse (≈1 µs) to initialize the spin into the m_s = 0 state via spin-selective excitation. Measure the fluorescence count rate during a subsequent laser pulse: a dark state indicates the spin is in m_s = 0, while a bright state indicates m_s = ±1. Apply an external magnetic field (≈100 G) to split the degenerate ±1 states and enable selective microwave driving.

Step 5: Drive Spin Transitions with Microwaves

Use a microwave generator tuned to the spin resonance frequency (≈2.87 GHz ± Zeeman shift). Deliver the microwaves via a coplanar waveguide or a wire loop near the diamond. Perform Rabi oscillations by varying the microwave pulse length: observe coherent spin flips as a function of pulse duration. Adjust the microwave power to achieve a π-pulse time of ~50–100 ns. This step verifies that you can control the single spin coherently.

Step 6: Excite the SAW Resonator and Measure Phonon Coupling

Apply a resonant RF pulse to the IDTs (using the same frequency as the SAW resonance). This generates a coherent phonon population in the resonator. To detect single-phonon coupling, perform a Ramsey-type experiment: first apply a π/2 microwave pulse to put the spin into a superposition state. Then, after a variable delay (during which the SAW is pulsed), apply a second π/2 pulse and read out the spin state. Any modulation of the final spin population as a function of SAW pulse amplitude and duration indicates phonon coupling. For direct evidence of single-phonon coupling, reduce the SAW power until the average phonon number is much less than 1, and observe discrete jumps in spin probability corresponding to 0, 1, or 2 phonons.

Step 7: Verify Coherent Control and Estimate Coupling Strength

Repeat the experiment with different SAW pulse lengths to observe phonon Rabi oscillations—the spin state will oscillate between m_s = 0 and m_s = −1 at a frequency proportional to the spin-phonon coupling strength g. Fit the data to extract g. Also measure the phonon lifetime (coherence time) by varying the delay between phonon generation and readout. Compare with the spin coherence time to assess the potential for quantum information storage.

Tips for Success

• Cryogenic stability: Fluctuations in temperature can shift both the SAW resonance and the spin transition frequency. Use active temperature control and allow ample thermalization time.
• Minimize strain: The mechanical contact between diamond and SAW resonator must be intimate but not so strong that it induces unwanted strain in the diamond, which broadens the spin linewidth.
• Optimize acoustic focusing: The SAW resonator should focus acoustic energy to a spot size comparable to the diffraction limit of the optical setup. Test with a test sample before using the precious NV-containing diamond.
• Use pulsed measurements: Continuous-wave operation can heat the sample; prefer short (ns–µs) RF and optical pulses to avoid thermal drift.
• Cross-check with simulations: Finite-element modeling of the SAW resonator and acoustic propagation in diamond can predict coupling strengths and help design the geometry.
• Document everything: Small changes in sample position or power lead to large variations—keep detailed logs of alignment and calibration.

By following these steps, you can replicate the Harvard SEAS experiment and explore the emerging field of quantum acoustics. For further details, consult the original Nature paper and supplementary materials.