Sustained macroscopic quantum coherence in a superradiant solid under ambient conditions

AI summary

Overview

Research area: Quantum physics — solid-state quantum optics, superradiance and many-body nonequilibrium dynamics in spin ensembles.

Technical level: Intermediate. The core ideas (collective emission, coherence, phase diagrams) are accessible, but the paper relies on cavity QED language, mean-field theory and Bloch-sphere dynamics that assume some quantum mechanics background.

Scope: The paper reports a room-temperature diamond maser in which about 10^14 nitrogen-vacancy (NV) spins and about 10^9 microwave cavity photons sustain collective coherence, and maps how that coherence reorganizes into three distinct phases as the optical pump, cavity quality factor and spin-cavity detuning are varied.

What This Paper Is About

Macroscopic quantum coherence — many particles sharing a definite phase relation — is the basis of lasers, Bose-Einstein condensates, superfluids and superconductors, but it is hard to keep alive in solids at room temperature because disorder and environmental coupling destroy the phase relation. Superradiance, in which many emitters synchronize into one collective dipole, offers a route to building such coherence, yet previous demonstrations relied on dilute atomic gases, small emitter numbers, cryogenic cooling, or short transient pulses. The goal here is to show that superradiant coherence among a genuinely macroscopic number of solid-state spins can be generated and sustained continuously under ambient conditions, and to characterize the different collective states it can take.

Key Contributions

1. A room-temperature, continuous solid-state superradiant maser. Approximately 10^14 NV center spins in an isotopically purified diamond are synchronized with about 10^9 intra-cavity microwave photons in a cavity resonating at 9.360 GHz, with no cryogenic cooling.

2. Discovery and identification of three distinct superradiant phases. By tuning the optical pump rate, cavity quality factor and spin-cavity detuning, the authors observe continuous-wave (CW) masing, periodically amplitude-modulated (PAM) masing, and sequences of superradiant bursts — interpreted respectively as synchronized fixed-frequency macroscopic spin coherence, a coherent continuous time crystal, and unsynchronized transients.

3. Experimental evidence that the coherence lives in the spins, not the cavity. After the pump laser is switched off, emission persists for more than 40 µs — far longer than the cavity photon lifetime (0.66 µs) and the spin dephasing time T2 = 5.7 µs, but far shorter than the spin relaxation time T1 ≈ 4.3 ms — with a Sech-shaped envelope characteristic of superradiance.

4. A measured and numerically reproduced phase diagram. The boundaries between the three phases are mapped as functions of pump rate, cavity quality factor Q and detuning, with mean-field simulations (321 spin sub-ensembles) agreeing well with the data.

Main Findings

• System parameters: Diamond of 3 × 3 × 0.5 mm^3, ^12C purified to 99.99%; TE01δ cavity mode at ω_c/2π = 9.360 GHz; mode linewidth κ_c/2π tunable from 0.23 MHz to 0.56 MHz, corresponding to Q from 17,000 to 40,000; spin longitudinal relaxation γ/2π = 37 Hz, inhomogeneous broadening σ/2π = 0.42 MHz, single-spin dephasing γ_φ/2π = 0.056 MHz; collective spin-cavity coupling G/2π = 0.32 MHz; estimated N = 1.40 × 10^14 pumped NV^- centers.

• Frequency dragging: Varying the magnetic field by 0.35 Gs shifts the spin-transition frequency by 0.98 MHz but the maser frequency by only 0.27 MHz. For the CW case shown, the maser is displaced 0.10 MHz from the cavity mode while the spin-cavity detuning is 0.50 MHz.

• CW maser performance: Output power P_out ≈ −67 dBm with a full width at half maximum of 128 Hz; maximum measured CW output P_out^max ≈ −52.3 dBm, corresponding to about 1.45 × 10^9 intra-cavity photons under 1.7 W optical pump power. In a separate measurement (Q ≈ 24,580), the CW peak has an FWHM of 164 Hz, implying a coherence time of 1.94 ms.

• CW phase (just above threshold): All spin sub-ensembles are driven to fixed points in the frame rotating at the maser frequency, and the summed collective transverse spin is of order N — sustained macroscopic spin coherence. Simulations at W/W_th = 2.21 reproduce this.

• PAM phase (well above threshold): A modulation period of 0.2 ms in the time domain, and a frequency comb with 5 kHz spacing between sharp lines of FWHM ~145 Hz in the spectrum. Simulations at W/W_th = 2.54 show all sub-ensembles following closed trajectories with the same period and phase — a limit cycle. Because coherence persists throughout the cycle, the authors describe this as a quantum-coherent continuous time crystal in a solid at ambient conditions.

• Burst phase (deep above threshold): A plateau-shaped spectrum with no resolved lines, and well-separated multi-peak bursts with no coherent oscillation between them. Simulations at W/W_th = 7.36 show sub-ensembles following trajectories with different shapes, periods and phases, including segments along the z-axis where transverse polarization and emission vanish. Higher burst amplitudes correlate with longer waiting times.

• Residual emission depends on switch-off timing: Emission persists 40–50 µs in all three regimes. Switching off at a cycle peak preserves amplitude, shape and phase until the cycle completes; switching off at cycle end gives small (PAM) or nearly vanishing (burst) residual emission; switching off during the interval produces a ramp-up followed by decay, with shorter waiting time and larger peak amplitude for longer delay. Pump rates for these tests were W/W_th = 2.21, 2.54 and 13.4.

• Phase diagram and threshold: At resonance (Δ = 0), intra-cavity power reaches a maximum of 12 nW at 256 mW pump power; the minimum pump rate W/W_th = 1 corresponds to 33 mW. The threshold pump power is roughly an order of magnitude lower than previously reported values, attributed to larger cooperativity. Period or burst interval decreases with pump power, but shows a non-monotonic increase at the PAM-to-burst boundary.

• Sample characterization: Initial nitrogen concentration 13 ppm, NV^- approximately 4.5 ppm after treatment, measured [NV^-] of 2.7 ± 0.1 ppm by XY8-N dynamical decoupling; T2* = 754 ns; magnetic field inhomogeneity below 0.064 Gs; N ≈ N_NV(π/4)(1/4)(1/3) ≈ (1.40 ± 0.05) × 10^14.

Methodology in Plain English

The team placed a small diamond chip full of NV color centers inside a tunable microwave cavity made of copper with a sapphire ring resonator, and applied a magnetic field along the diamond's [111] axis to bring the spin transition into resonance with the cavity. A 532 nm green laser optically pumps the spins into an inverted state; the pump rate is controlled by rotating the laser polarization rather than changing laser power, so laser heating stays constant across measurements. Gas-flow cooling stabilizes the sample temperature.

The emitted microwave signal is picked up by a loop antenna and recorded in both time and frequency domains with an oscilloscope and spectrum analyzer, while a vector network analyzer measures the cavity Q factor and the spin-cavity anti-crossing. The key experiment is to sweep the magnetic field, pump rate and Q factor and watch how the emission spectrum changes — a single sharp peak, a frequency comb, or a flat plateau.

To explain the observations, the authors model the system with a Dicke-type Hamiltonian including cavity leakage, spin relaxation, spin dephasing and incoherent pumping, and solve it in a mean-field framework. Because the spin ensemble is inhomogeneously broadened, they divide it into 321 sub-ensembles of nearly identical frequency and track each collective spin on a Bloch sphere, using a mean thermal photon number of 670.

Why This Matters

Impact on research: The work shows that macroscopic quantum coherence need not be confined to ultracold gases or cryogenic solids. It reframes inhomogeneous broadening — normally treated purely as a decoherence problem — as something that actively shapes collective dynamics, and it realizes a continuous time crystal in a solid under ambient conditions, a regime previously demanding cold atoms or cryogenics.

Real-world applications (as framed in the paper):

• Quantum-enhanced sensing and metrology, including precise clocks that exploit macroscopically correlated spins.
• Quantum communications, leveraging bright, coherent microwave emission with collective correlations.
• Quantum nonlinear spectroscopy, using many-body correlations imprinted on the emitted field.
• Bright quantum microwave sources for quantum computing hardware and for generating light with collective quantum correlations.

Industry relevance: Room-temperature operation and a compact diamond-plus-cavity footprint remove the cryogenic infrastructure that dominates the cost of most solid-state quantum hardware. The roughly order-of-magnitude reduction in threshold pump power relative to earlier diamond masers (33 mW versus prior values) matters for practical microwave sources, and tunable Q and pump parameters give straightforward electronic control over which emission regime is accessed.

Future Directions

• Engineering spin-spin interactions. The authors propose adding direct and cavity-mediated interactions to generate genuine many-body correlations within the ensemble, which could then be imprinted on the emitted microwave field through collective emission.

• Accessing higher-order correlations. Shaping the spin-frequency distribution and collective interactions could open access to higher-order many-body correlations for sensing and spectroscopy.

• Understanding multi-peak structure. Multi-peak bursts are observed even in the PAM phase, indicating the ensemble self-organizes into several individually synchronized groups rather than one; the paper points to numerical work in its Supplementary Information and leaves the full characterization open.

• Independent replication and comparison. The authors note a preprint by Zollitsch et al. (2026) reporting similar results, which invites direct comparison of the two platforms.

Target Audience

Quantum physicists working on superradiance, masers, spin ensembles and nonequilibrium many-body dynamics; cavity QED and quantum-optics experimentalists; diamond-NV researchers interested in room-temperature collective effects; and quantum-technology engineers looking for ambient-condition microwave sources with collective correlations. Readers without some background in collective spin dynamics and cavity parameters will find the phase-diagram and Bloch-sphere sections demanding, but the experimental narrative and the three-regime classification are approachable.

Authors’ abstract

Macroscopic quantum coherence, such as in laser, Bose-Einstein condensates, superfluids, and superconductors, is important to fundamental physics and useful for quantum technologies. Superradiance provides a mechanism to produce coherence among a large number of particles and photons. Its implementation, however, has been limited to gaseous systems, solids at very low temperature, or short pulses. Here we demonstrate a solid-state superradiant maser under ambient conditions, which establishes long-lived coherence among about $10^{14}$ nitrogen-vacancy center spins in diamond and about $10^9$ photons in a microwave cavity. By varying the system parameters to access the above-threshold, well-above-threshold, and deep-above-threshold regimes, we observed continuous-wave masing, periodic amplitude modulation, and sequences of superradiant bursts, which are attributed, correspondingly, to macroscopic spin coherence synchronized at a fixed frequency, a coherent time crystal of large spins, and unsynchronized superradiant transients. This work demonstrates that macroscopic quantum coherence can be spontaneously generated and maintained in solids under ambient conditions and provides a solid-state platform for exploring bright quantum lights with many-body correlations.