I remember around the time I started my MSc that there was some chatter about masing with NVs. I've finally caught up.

In this post I am going to record my learning about masing with solid state spins. All of the info will come from three Jonathan Breeze articles^{1 2 3}.

Introduction to Masers

The maser is, obviously, the microwave analogue (or prelogue) of the laser. Apparently they are usually used in communications and astronomy on the detection side as low-noise amplifiers of very small radio signals. The principle, if you're familiar with NV defects, is quite simple to understand: optically pump some two-level system to create a population inversion, and tune the bias field to create the splitting (and thus operation frequency) you require. Then you just... mase. Okay, sorry, you also want a nice cavity. Reading through Breeze's review³, you of course see there is some nutty physics to enjoy.

State-of-the-art

The platforms used for MW amplification are currently solid-state 'conventional' (MW-pumped paramagnetic ions in dielectric material) masers (e.g. Ruby), atomic/free-electron masers, and High-Electron-Mobility Transistors (HEMTs). HEMTs are I understand the default choice, though Ruby lasers have been used in deep-space communication and astronomy. Atomic/free-electron masers require complex bulk vacuum apparatus, so are uncommon outside of laboratory settings. HEMTs and conventional masers require subkelvin temperatures, but HEMTs usually win out as the lowest noise amplifier. Most realizations of masers also require strong magnets, magnetic shielding or both. There is general interest for a low-noise maser working in ambient conditions.

As research focused on lasers, masers found application only in niche areas where their ultralow noise amplification was essential such as radio astronomy and frequency standards. Given the ubiquity of microwave devices in modern communications infrastructure, it is nevertheless interesting to consider in greater detail the technological barriers that prevented masers from gaining the widespread adoption of laser.³

Why can't conventional masers work at room temperature?:

It is known why conventional solid-state masers cannot be made to work at room temperature. The most serious problem is that the rate of spin–lattice relaxation (T_1), and, thus, the microwave power required to saturate the maser’s pump transition and, in turn, the required thermal cooling power of the maser’s refrigerator, increase extremely rapidly with the absolute (lattice) temperature, T, of the maser crystal. For two-phonon (Raman) scattering off Kramers-type paramagnetic ions in a three-dimensional lattice well below its Debye temperature, this relaxation rate scales as T. A second problem is that, even if the maser’s pump transition can be saturated by pumping hard, the population inversion and, hence, the maser crystal’s gain scale as f_pump / kB T. The residual noise temperature of a conventionally pumped solid-state maser amplifier thus scales as T, so nullifying the maser’s low-noise advantage at higher operating temperatures. It was realized very early on that, at the expense of energy efficiency, larger population inversions and, thus, lower noise temperatures and somewhat higher sustainable operating temperatures can be obtained by increasing f_pump — in the extreme case by driving optical pump transitions with light, which can often be supplied by a laser. But optical pumping alone does not obviate the first problem, that is, the rapid increase in the rate of spin–lattice relaxation with temperature.¹

I'll also note that RF masers are not particularly sought after as RF electronics are sufficient:

It is noteworthy that a radio-frequency amplifier, based upon nuclear polarization at room temperature was suggested in the past. However, this approach is restricted to low radio frequency (<50 MHz and magnetic fields of ~10-20kG), where existing solid-state electronics provides better noise performances. ⁴

One answer to room-temperature maser operation is using paramagnetic centres with an inter-system crossing that generates high electron spin polarisation.

The Pentacene Maser

The first room-temperature solid state maser¹, from Breeze & co. was based on an organic mixex molecular crystal, p-terphenyl doped with pentacene. This system mases at 1.42 GHz under ambient conditions (including zero field!), though only in a pulsed mode.

The optical pump threshold power was determined to be about 230 W with a peak microwave power output of -10 dBm -- (100e6 times greater than the hydrogen maser -- achieved when the pump power was increased further.³

Why only pulsed mode?

To date, maser action in the pentacene-based system has only been observed for brief durations, typically of the order of milliseconds. This is mainly due to two factors: (i) the relatively long lifetime of Z, the lowest triplet-state sub-level, reduces the number of pentacene molecules available for optical pumping, creating a “bottleneck” that quenches the population inversion and (ii) the organic gain medium host (para-terphenyl) cannot withstand continuous optical pumping due to its poor thermal conductivity and low melting point. Recent measurements of the spin-lattice relaxation and triplet-singlet decay rates have revealed that rapid spin-lattice relaxation between the Y and Z sub-levels can lift the bottleneck, but gain medium heating is still an obstacle.³

Apparently the cavity design was instrumental in this advance

This discovery can be traced back to earlier work on microwave dielectric ceramics. The development of a distributed Bragg-reflector resonator analogous to a photonic crystal, constructed from concentric cylindrical sapphire rings and plates but departing from conventional quarter-wave thicknesses, demonstrated a Q-factor of 6e5 at 30 GHz. The question was posed of what other applications could be found for such a high Q-factor at room-temperature instead of the obvious: the frequency discriminating component of low phase-noise oscillators and frequency standards.³

The NV-diamond Maser

Diamond is a nice choice: well understood optically-pumped defects in the nitrogen-vacancy (NV) centre and critically the highest known thermal conductivity. The NV also has fantastic spin relaxation and spin decoherence times at room temperature - perfect for masing. Population inversion can be produced by a sufficiently high field pushing the |-1> state below the |0> state (and pumping with 532nm).

I don't have much to say about the CW NV maser paper, except that it worked. So what are its limitations?

Before practical devices based on the diamond maser can be developed, there are certain challenges that must be overcome. The applied magnetic field needs to be highly uniform across the diamond sample to prevent inhomogeneous broadening of the NV center spin transition—for example, a 10 part-per-million inhomogeneity in the field at 430 mT would result in an additional 0.8 MHz increase in the spin dephasing rate. The temperature stability of any magnets employed will also be an important factor in this regard. Halbach arrays of rare-earth permanent magnets have been shown to provide fields of this magnitude with a high degree of homogeneity, but variance in the properties of permanent magnets necessitates careful shimming of the magnet arrays. There is also the issue of sensitivity to extrinsic and intrinsic sources of magnetic noise, which could explain the observed instability of the emission line for zero spin-cavity detuning. For a linewidth of 0.1 Hz, the sensitivity of the maser frequency to magnetic fields is of the order of 10 pT/ root Hz. Meanwhile, naturally abundant carbon-13 nuclei (1.2% of carbon atoms) and nitrogen donor impurities (P1 centers), the latter with typical concentrations in the region of 1–100 ppm depending on the diamond sample, will form significant sources of intrinsic magnetic noise.³

Lasing without inversion - a very interesting concept I need to read more about:

For the other hurdles, it is worth exploring whether masers based on different operating principles might offer advantages. One such approach might exploit the exquisite control over the quantum states and the long coherence times of NV centers in diamond to prepare the spins in a coherent superposition of two energy levels, |a> and |b>, whose transitions to a third state |c> are coupled to a detuned pair of lasers, giving transition probability amplitudes A_ca and A_cb . Since for absorption, the transition is from a coherent superposition to a common final state, the amplitudes are summed before squaring and can destructively interfere. In contrast, amplitudes of stimulated emission from |c> to |a> or |b> are summed in square |A_ca|² + |A_cb|² so cannot cancel each other out. In this way, it is possible to achieve stimulated emission of coherent light even from relatively small populations of spins excited to |c>, known as lasing without inversion (LWI). This inversionless approach has already been realized in lasers with atomic vapors as gain media and would remove the requirement for high pump powers necessary to achieve inversion. The demonstration of zero-field coherent population trapping for NV centers in diamonds strained along the [100] direction suggests that this approach could also eliminate the need for an external magnetic field.³

There are some more exotic suggestions in that same review (superradiance, Floquet engineering), as well as other paramegnetic systems: Rydberg excitons, the silicon vacancy in SiC and the boron vacancy in hBN, the latter unlikely given the quantum efficiency IMO.

Outstanding Questions

• What's next? I don't know where Breeze and co. are going next, but I'm keen to read it. Most likely CW pentacene operation, or silicon vacancies.
• Will we see any proof-of-principle applications with room-temperature masers?

References