Perspective on room-temperature solid-state masers of multi-stage infrared photodetectors

The ﬁrst solid-state masers to operate at room-temperature and ambient air-pressure were recently demonstrated using optically pumped spin-triplet states as the gain medium. In this Perspective, we brieﬂy review the previous state-of-the-art in cryogenic solid-state masers and then discuss the development of the room-temperature solid-state maser: from the organic pentacene pulsed maser to the diamond nitrogen-vacancy continuous-wave maser. We characterize the operation of these masers as coherent microwave sources and ultra-low noise ampliﬁers before outlining how they can be adapted to act as model systems in which to explore room-temperature cavity quantum electrodynamics. After discussing challenges facing current embodiments of the room-temperature solid-state maser, we explore how they might be addressed or by-passed altogether through the development of alternative materials and masing mechanisms. Finally, we speculate on how the advent of masers that can operate in ambient conditions might lead to novel applications in metrology and quantum technologies.


I. BACKGROUND
The maser is the microwave analog of the laser, employed in communications and radio astronomy due to its ability to amplify microwave signals with exceptionally low levels of noise. Using atomic beams, vapors, or defects in solid-state systems as gain media, population inversions allow the stimulated emission of high-intensity, coherent radiation from excited states.
The theoretical principles underpinning the operation of the MASER (microwave amplification by stimulated emission of radiation) were first proposed independently by Weber 1 and by Basov and Prokhorov 2 in the early 1950s. This led to the first working maser, based on ammonia, being demonstrated in 1954 by Gordon et al. 3 Following this demonstration, there was a period of rapid development with work on atomic masers culminating in the demonstration of the hydrogen maser in 1960. 4,5 In parallel to the work on atomic masers, Bloembergen launched an equally fruitful wave of investigations into solid-state masers by proposing a simple three-level system in 1956. 6 This led to the development of relatively compact solid-state masers based on paramagnetic salts and Cr 3þ impurities in ruby 7-10 that quickly found applications in radar 11 and radio astronomy, where it facilitated the first measurement of the (surprisingly high) temperature of Venus. 12,13 The laser, first reported by Maiman in 1960 14 as an optical version of the maser, went on to enable many innovations in spectroscopy, manufacturing, communications, medicine, and metrology. The maser, however, was compromised by the challenging experimental conditions required for its operation. Atomic 15 and free-electron masers 16 require ultra-high vacuum with associated bulky equipment such as chambers and pumps to achieve and maintain population inversion. In contrast, certain optically pumped solid-state masers 17 could escape the requirement for ultra-high vacuum but still needed cryogenic refrigeration, strong magnetic fields, and magnetic shielding. The key barrier of requiring cryogenic temperatures was particularly difficult to overcome since in order to achieve significant population inversions in solid-state systems, either the energy gap of the maser transition should significantly exceed the system temperature ( hx l ) k B T), so that there is a large ground-state population to pump, or the spinlattice relaxation rate must be slow enough to allow an appreciable excited-state population to build up. Since for any microwave transition (k > 1 mm), the transition energy must satisfy hx l < 14:4 K and the spin-relaxation rate increases sharply with temperature, this typically rules out maser operation at room temperature. For these reasons, soon after the discovery of the maser, attention switched to the laser and newly discovered semiconductor devices, whose larger energy gaps allowed them to operate at roomtemperature and in Earth's magnetic field. As research focused on lasers, masers found application only in niche areas where their ultralow noise amplification was essential such as radio astronomy 12 and frequency standards. 18 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 lasers.
The cornerstone of both masers and lasers is the gain medium which, through a variety of pumping schemes (including electrical, 19 chemical, 20 optical, 21 and state selection 22 ) requires the population of two of its energy levels to be inverted-a higher energy state is more populated than a lower energy state. Through stimulated emission, the photon population within a maser or laser resonant cavity or waveguiding structure can grow exponentially at a rate exceeding any photon loss mechanisms, thus coherently amplifying any input photons with high gain and low-noise or providing a coherent source of radiation.
Atomic masers, such as the hydrogen maser, can operate at room-temperature, but their output power is weak due to the typically low hydrogen density and inefficient state selection. 22 They are also complex to engineer: gaseous H 2 is disassociated into atomic hydrogen via radio frequency plasma discharge then fed through a state selector and finally into a PTFE (polytetrafluoroethylene)-coated high qualityfactor microwave cavity resonant with the frequency of the hydrogen emission line at 1.42 GHz. Traditional solid-state masers employ a multi-level pumping scheme, the simplest consisting of three levels as proposed by Bloembergen. The transition between the lowest and highest levels is saturated by a microwave pump, establishing a population inversion between the highest state and a less populated intermediate state [ Fig. 1(a)]. To make the pump process more efficient, cryogenic cooling with liquid helium to a temperature $4 K is necessary to increase the relative population of the lowest state according to Boltzmann statistics, from which the levels are populated as n low =n high ¼ exp ð hx p =k B TÞ at equilibrium where hx p is the energy gap between the lowest and highest levels. This pumped three-level system operating at cryogenic temperatures forms the basis of state-ofart solid-state masers such as the ruby maser [Cr-doped Al 2 O 3 , Fig.  1(b)]. Alternatively, increasing the pump frequency x p to millimeterwave and even up to optical frequencies can further increase the inversion. Nevertheless, cryogenic operation has remained necessary for masers based on paramagnetic impurities, such as Cr 3þ and Fe 3þ , in ruby even where large ground-state populations can be achieved at higher temperatures, because the transverse spin decoherence rates and longitudinal spin-lattice relaxation rates are too rapid at roomtemperature, enhanced by the immersion of the impurities within a spin-bath of Al 3þ ions with nuclear spin I ¼ 5/2 and spin-phonon interactions such as two-phonon Raman scattering with a T 7 to T 9 temperature dependence.
A more recent update on the three-level solid state maser exploited the very high quality factors (Q > 10 9 ) that can be achieved in whispering-gallery mode resonators at low temperatures. 23 By designing a sapphire resonator so that one of its whispering gallery modes had a frequency coincident with the 12.04 GHz zero-field EPR transition between the j1=2i and j3=2i states of Fe 3þ impurities in the sapphire and pumping the j1=2i $ j5=2i transition at 31.3 GHz, Bourgeois et al. 24 demonstrated successful maser oscillation. The whispering-gallery maser oscillator was subsequently developed further 25,26 to achieve power outputs as high as 2.5 nW-four orders of magnitude beyond the power output achieved with hydrogen masers. 27 Since the Schawlow-Townes limit 28 on the frequency stability depends inversely on the output power, this makes these systems Crystal environment of a Cr 3þ impurity ruby in Cr-doped Al 2 O 3 , used in state-ofthe-art ruby masers. (c) Pumping mechanism for the pentacene maser. Electrons in pentacene molecules are efficiently pumped from the ground-state singlet into longlived metastable triplet states through photoexcitation and intersystem crossing, leading to a population inversion between the X and Z triplet-state sub-levels. (d) A pentacene molecule in the para-terphenyl crystal environment used as a gain medium for the pentacene maser. (e) Pumping scheme for the diamond maser. By applying an external magnetic field along the nitrogen-vacancy center (NV) axis, the energy of the triplet S ¼ À1 state is pushed below that of the spin-singlet state by Zeeman splitting, allowing an inversion to be achieved through spin-selective intersystem crossing. (f) Crystal environment of a NV center in diamond, used as a gain medium in the diamond maser.
highly promising as frequency standards with a potential frequency stability of order 10 À16 s À1=2 , where s is the integration time. Nevertheless, while the whispering-gallery maser oscillator operates at zero-field, it still relies on cryogenic (< 5 K) temperatures to achieve the inversion and low dielectric losses required to operate.
The capacity for solid-state masers to operate as compact, highoutput, and low-noise microwave amplifiers was, thus, wellestablished with a final obstacle to broader employment in microwave devices being the necessity for cryogenic temperatures.

II. REVIEW OF ROOM-TEMPERATURE MASERS
In 2012, the first solid-state maser to operate at room-temperature was reported, 29 using photoexcited triplet-states in organic pentacene molecules as the gain medium. This discovery can be traced back to earlier work on microwave dielectric ceramics. These materials, used in microwave communications, rely on three key properties-relative permittivity e r , dielectric loss tan d, and temperature coefficient of permittivity s e . The development of a distributed Bragg-reflector resonator 30 analogous to a photonic crystal, constructed from concentric cylindrical sapphire rings and plates but departing from conventional quarterwave thicknesses, demonstrated a Q-factor of 6 Â 10 5 at 30 GHz. 31,32 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.
The idea of using photoexcited triplet-states in organic molecules as maser gain media had previously been proposed by Brock et al. 33 in 1961 who wrote that "coherent stimulated emission at microwave or millimeter wavelengths may prove feasible using the population in the Zeeman levels of the first triplet state. Such an emission process would permit the realization of organic molecular crystal masers having the unique property of being active only when optically excited." This proposal was pursued experimentally by Blank et al. [34][35][36] using inverted populations within photoexcited triplet-state sub-levels of organic paramagnetic molecules. In an ensemble of C 60 dissolved in toluene they observed 34 spin-lattice relaxation times of T 1 $ 10 ls at 253 K, leading them to conclude that the triplet mechanism was incapable of generating sufficiently long coherence times for maser operation. Subsequent work took place on a solution of trityl radicals and etioporphyrin triplets with a more complicated inversion process, in which photoexcited triplets led to chemically induced population inversion in the radicals, 20,37 allowing the spin-lattice relaxation time to be extended further to T 1 $ 100 ls at room temperature. 35 However, Blank and Levanon were ultimately not able to overcome cavity losses sufficiently to allow their triplet-radical system to operate as a maser. 36 To realize the first room-temperature solid-state maser, Oxborrow et al. doped a single-crystal of para-terphenyl with 0.01% of pentacene to produce the gain medium [ Fig. 1(d)]. Through photoexcitation and intersystem crossing (ISC), electrons in singlet groundstates within pentacene molecules can populate long-lived (mean lifetime $45 ls) metastable triplet states with a high quantum yield of $65%. 38 Intramolecular electronic dipole-dipole interactions at zero magnetic field lift the degeneracy of the triplet sub-level energies, resulting in three non-degenerate sub-levels, X, Y, and Z, in the order of decreasing energy, populated in the ratio 9.5:2:1 as shown in Fig. 1(c). The maser exploited a population inversion between the X and Z triplet-state sub-levels with an energy difference equivalent to approximately 1.45 GHz. The pentacene:para-terphenyl crystal was placed within the bore of a cylindrical sapphire ring which formed part of a microwave cavity supporting a TE 01d mode with resonant frequency matching the X-Z transition at 1.45 GHz and unloaded Q-factor 180 000. The magnetic energy distribution of the TE 01d mode has an antinode at the center of the sapphire ring, where there is an axial magnetic dipole that induces transitions between the X and Z sublevels when it is aligned with the molecular y-axis of pentacene. The pentacene molecules were optically pumped by a pulsed dye laser with wavelength $585 nm and duration 1 ms, resulting in a maser emission burst of duration 450 ls [ Fig. 2(a)]. The optical pump threshold power was determined to be about 230 W with a peak microwave power output of À10 dBm-100 Â 10 6 times greater than the hydrogen maserachieved when the pump power was increased further. 29 The pentacene maser was subsequently miniaturized by replacing the sapphire (Al 2 O 3 ) dielectric resonator material with a relative permittivity of e r % 9, by strontium titanate (SrTiO 3 ) with relative permittivity e r % 318, resulting in over two orders of magnitude reduction in the mode volume, 40 which scales with the permittivity as V m / e À3=2 r . Although the SrTiO 3 resonator had a lower unloaded Qfactor of $8000, it was nevertheless possible to achieve maser action due to the increased rate of stimulated emission resulting from the increased density of photonic states in the cavity, known as Purcell enhancement 41 and characterized by the Purcell factor F P / Q=V m . The miniaturized maser produced a microwave pulse of stimulated emission when optically pumped by a xenon flashlamp with 70 W peak power and an estimated pump threshold power of $20 W. Further work on this device, using nanosecond laser pulses enabled the temporal response of maser emission to be measured as a function of optical excitation energy and explained using the Lotka-Volterra (predator-prey) model, 42 recently interpreted as an example of superradiance. 43 A pentacene:para-terphenyl sample with increased concentration of pentacene revealed an unexpected phenomenon under nanosecond optical pumping-vacuum Rabi oscillations and normalmode splitting 39 [Figs. 2(b) and 2(c)], indicating that the device was operating in the strong-coupling regime of cavity quantum electrodynamics (cQED). Strong-coupling is generally assumed to occur when the normal-mode splitting X is greater than both spin and photon mode decay rates but is more accurately defined as when it exceeds the mean of the spin decoherence/dephasing and cavity decay rates, the dephasing time, and j c ¼ x c =Q is the cavity decay rate where x c is the angular frequency of the cavity resonance and Q is its qualityfactor. The normal-mode splitting for an ensemble of spins is given by where g e is the collective spin-photon coupling, itself proportional to the single spin-photon coupling g e ¼ g ffiffiffiffi N p , where N is the number of spins or quantum emitters. The single spin-photon coupling is given by where c e is the electron gyromagnetic ratio, l 0 is the permeability of free space, and V m is the magnetic mode volume. 39 Strong-coupling was achieved in the STO:pentacene maser by increasing the number of spins to N $ 10 14 by increasing the concentration of pentacene molecules to $0.1% and boosting the spin-photon coupling by reducing the mode volume to V m $ 0:25 cm 3 . A key parameter in cQED is the "cooperativity" C ¼ 4g 2 N=j s j c , a figure of merit for the efficiency of coherent quanta transfer between different systems, in this case, a spin ensemble and a microwave cavity. The cavity contributes a factor g 2 =j c $ Q=V m to the cooperativity, which is proportional to the Purcell factor 41 and again reflects the relative density of photonic states.
To date, maser action in the pentacene-based system has only been observed for brief durations, typically of the order of milliseconds. 44 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 45 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. Alternatively, it has been suggested 46 that replacing pentacene with other polyacenes, especially molecules based on anthracene and tetracene, is a promising route to continuous-wave masing, though this approach would rely on finding suitable host crystals to fill the role that para-terphenyl plays in the pentacene maser. Even with continuous-wave operation of the pentacene maser yet to be achieved, pulsed masing at room temperature and using only the Earth's magnetic field opens new avenues of investigation, and there will undoubtedly be further developments in this area.
Outside of organic gain media, attention in the pursuit of continuous-wave maser action at room temperature was naturally drawn to the long coherence times observed for spin defects in widebandgap materials. 47 Charged nitrogen-vacancy (NV) color centers in diamond [ Fig. 1(f)] have ground-state triplets (S ¼ 1) with remarkably long spin-lattice relaxations times (T 1 $ 5 ms), (inhomogeneous) spin dephasing times (T Ã 2 $ 0:1 ls), and (homogeneous) spin decoherence times (T 2 $ 10 ls) at room-temperature. At zero magnetic field, the ground-state triplet consists of a pair of quasi-degenerate sub-levels j61i at an energy hÁ 2.87 GHz above the j0i sub-level. NV centers have been the subject of intense research due to their spin-dependent photoluminescence (PL), allowing spin states to be initialized and readout optically. The j0i triplet sub-level can be preferentially populated by pumping the NV centers with green ($532 nm) laser light, resulting in a spin-polarized multi-level system. This occurs through spin-selective intersystem crossing of electrons from the photoexcited triplet state j61i sub-levels into a metastable singlet-state, which then mostly decay into the ground-state triplet sub-level j0i [ Fig. 1(e)].
The idea of using charged nitrogen-vacancy (NV) defects in diamond as a gain medium for room-temperature masers was first proposed in 1977 by Loubser and Van Wyk 48 and studied in more detail recently by Jin et al. 49 If an external magnetic field is applied along a h111i crystal axis direction, collinear with an NV axis, the j61i sublevel energies split via the Zeeman interaction, leaving the j0i sub-level energy unchanged. If the field applied is greater than the zero-field splitting D-parameter (2.87 GHz or 102.5 mT), the j-1i sub-level energy drops below the populated j0i sub-level, resulting in a population inversion.
To achieve maser oscillation, the threshold pump rate per spin-defect can be shown 50 to be equal to w thr ¼ c=KðC À 1Þ, where K < 1 is a pump efficiency parameter that accounts for the likelihood of an electron being promoted into the j0i sub-level and c is the spinlattice relaxation rate. Having a cooperativity C ! 1 is, therefore, a necessary condition for masing to be feasible. Considering the ideal situation of the pump efficiency being unity K ¼ 1 and a cooperativity much greater than unity C ) 1 reveals a counter-intuitive observation, that the pump threshold per spin defect is less than the spinlattice relaxation rate, i.e., w thr $ c=C. This occurs because the inversion per spin is clamped to r z ¼ 1=C above threshold, so only this fraction of the total number of spins participates in the maser action. This shows that the cooperativity C is also a measure of the collective nature of the maser process.
The first continuous-wave room-temperature solid-state maser was demonstrated in 2018 using NV À color centers in diamond 50 (Fig. 3). The diamond, a 2 mm cube grown by chemical vapor deposition, was supplied by Element Six and contained $4 Â 10 13 NV centers. The NV spin properties were characterized using pulsed and continuous electron spin resonance (ESR) spectroscopy at 9.2 GHz, yielding a spin-lattice relaxation time T 1 ¼ 4:8 ms, spin decoherence time T 2 ¼ 22 ls, and spin dephasing time T Ã 2 ¼ 0:5 ls. A sapphiredielectric loaded microwave resonator was designed with an optimized Applied Physics Letters PERSPECTIVE scitation.org/journal/apl Purcell factor F P / Q=V m with a loaded Q-factor of 30 000 (unloaded 55 000) and a magnetic mode volume V m of 0.15 cm 3 .
Combined with the diamond sample, this system yielded a cooperativity C % 11. With an externally applied magnetic field of 430 mT aligned with one of the four h111i axes of the diamond and a modest 400 mW of optical pump power at 532 nm supplied by a Nd:YAG frequency-doubled laser, continuous maser emission was observed at 9.2 GHz with a peak power of À90 dBm (comparable with a hydrogen maser) and linewidth 50 Hz which agreed with the Schawlow-Townes limit of 10 Hz [ Fig. 3(b)]. The mean pump rate per NV À center was estimated to be w ¼ 410 s À1 . Scanning the magnetic field in small increments of 1 lT revealed three emission peaks separated by $2.7 MHz ($0.1 mT), due to the hyperfine interaction of the NV À electron spin with the 14 N (I ¼ 1) nucleus. ESR measurements confirmed a predicted inversion per NV center of r z ¼ 0:1, corresponding to a negative spin-temperature of jT s j ¼ 2:1 K. This spin temperature represents the intrinsic noise temperature that may be expected when operating the diamond maser as a microwave amplifier and is comparable to the $1 K noise temperatures found in state-ofthe-art ruby masers. However, by optimizing the cavity coupling and material properties of the diamond, it is expected that the noise temperatures could be reduced by a further order of magnitude to jT s j $ 0:1 K in ambient conditions. 49,51 Such low noise temperatures suggest that diamond masers will become especially valuable for applications, in which low phase noise is essential such as radar. 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 j s . 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, 52 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/ ffiffiffiffiffiffi Hz p . Meanwhile, naturally abundant 13 C 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. 53,54

III. CHALLENGES AND FUTURE DEVELOPMENTS
While the realization of a diamond maser that operates at room temperature is a significant step toward broader technological adoption of masers, there remain certain challenges that must be overcome before broadly applicable devices become a reality. The most important of these are softening the requirement for a strong, spatially and temporally homogeneous magnetic field and reducing the effect of temperature fluctuations due to heating from the pump laser, while improving the efficiency with which the pump power is converted to output power (Jin et al. 49 suggest that it should be possible to attain output powers exceeding À50 dBm with an absorbed pump power of 1 W) and reducing the size of the cavity are further important steps. The latter two challenges might be addressed by fine-tuning the diamond crystal composition 51 and by using dielectric cavities with a high relative permittivity to reduce the mode volume and required pump power. 40 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, jai and jbi, whose transitions to a third state jci 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 FIG. 3. Output power of the diamond maser as a function of the magnetic field and the microwave pump frequency with an optical pump power of 400 mW. (a) The system shows three regions of maser oscillation, corresponding to hyperfine transitions in the diamond nitrogen-vacancy centers. The white trace shows the power integrated over the frequency range at each field. 50 The central emission region (magnified at the top of the figure) shows a narrow ($50 Hz) linewidth at its edges (b) in agreement with the Schawlow-Townes limit of $10 Hz, though at its center the peak is broadened due to limit cycles in the inversion-photon-population phase space. Adapted from Breeze et al.

PERSPECTIVE
scitation.org/journal/apl common final state, the amplitudes are summed before squaring and can destructively interfere. In contrast, amplitudes of stimulated emission from jci to jai or jbi are summed in square jA ca j 2 þ jA cb j 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 jci, known as lasing without inversion (LWI). 55,56 This inversionless approach has already been realized in lasers with atomic vapors as gain media [57][58][59][60] 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 61 suggests that this approach could also eliminate the need for an external magnetic field. Another operating principle that might reduce the sensitivity of the emission frequency to thermal fluctuations in the gain medium is to develop masers based on superradiant emission, 43,62 in which stimulated emission from independent NV centers is replaced by coherent spontaneous emission from a collective excitation of the entire ensemble. This process may be qualitatively understood within the Dicke model, 63,64 which describes a system of N two-level atoms interacting with a single mode of the radiation field. When the strength of the atom-field interaction significantly exceeds the energy of the electromagnetic mode and the energy difference of the two atomic energy levels, there is a spontaneous phase-locking of the atomic dipoles. In this superradiant state, a large number of electromagnetic excitations are stored coherently in the atoms rather than in the radiation field and the system rapidly radiates with an intensity proportional to N 2 .
Experimentally, the collective states required for superradiance are achieved by allowing emitters to interact with a single cavity mode in the "bad cavity" regime, where the cavity-mode decay rate is much faster than the rate at which emitters decohere or dephase. Since in such states information about the phase and amplitude is stored in the ensemble of emitters, the superradiant emission becomes insensitive to small fluctuations in the cavity length that might lead to the dephasing of optical modes and has been used as the basis for ultrastable superradiant lasers, 65,66 in which a repumping laser maintains the collective excited state to allow continuous superradiant emission. Since superradiance has already been observed from diamond NV centers at low temperatures 67,68 and it has been demonstrated in the pentacenebased system that the collective spin-photon states required can be generated 39 even at room temperature (with possible signs of superradiance 42,43 ), it seems likely that a similar tactic may stabilize diamondbased room-temperature masers against thermal fluctuations in the cavity. A recent theoretical study 69 further suggests that if diamond NV center-based superradiant masers are realized, it should be possible to reduce linewidths to the order of millihertz.
A more exotic prospect is to take advantage of recent advances in Floquet engineering 70,71 to develop a diamond-based Floquet maser. Working with a 129 Xe vapor cell, a recent work by Jiang et al. 72 has demonstrated that it is possible to operate a maser based on transitions between Floquet states stabilized by an oscillating magnetic field B ac ðtÞ ¼ B cos ðx ac ) that periodically drives the Zeeman sub-levels of the 129 Xe nuclear spins. The Floquet states j6i n appear as sidebands offset from a central Larmor frequency x 0 by integer-multiples of the driving frequency (i.e., at x 0 6 x ac ), and population inversion into a majority jþi n state is driven by spin-exchange collisions with a small admixture of optically pumped 87 Rb atoms. In place of a resonant cavity, the spin polarization is monitored directly via optical rotation of a probe laser and used to drive a feedback field B f . In this way, it is possible to generate steady-state superradiant emission from the transition between jþi n and j-i n Floquet states. Such a maser can be used as a magnetometer where the field to be measured is used as the driving field, so that its amplitude and frequency may be determined by the properties of the Floquet sidebands. Interestingly, such a magnetometer appears to have a sensitivity that increases as the frequency of the measured field decreases, in contrast to SQUID magnetometers whose low-frequency response is hampered by 1=f noise. The sensitivity of the 129 Xe Floquet maser is limited to $700 fT/Hz 1/2 at 60 mHz due to field fluctuations from the 87 Rb atoms used to achieve inversion, though if these fluctuations can be overcome, it is expected that greater sensitivity can be achieved at even lower frequencies. It is here that a Floquet maser based on spin defects might offer an advantage through the relative ease with which they may be driven into specific quantum states.
An alternative approach to developing further solid-state roomtemperature masers is to explore different gain media. As new host materials for spin defects are explored 73,74 and control over defect implantation improves, we anticipate that further defect-based roomtemperature masers will emerge. Significant progress has already been made in this regard using silicon vacancies (V Si ) in silicon carbide (SiC), whose S ¼ 3/2 ground state may be spin-polarized via intersystem crossing through optical pumping at $800 nm. Previous work 75 has demonstrated T 2 $ 100 ls coherence times and achieved population inversion leading to continuous microwave emission at room temperature, but in systems explored so far the gain factors have not exceeded losses in the cavity. A recent work by Fischer et al. 76 has explored in detail the conditions under which a continuous-wave maser using SiC as a gain medium at room temperature might be realized. It is convenient here to express the masing condition in terms of the gain medium quality factor 77 where D is the resonance linewidth of the gain medium, N is the defect volume density, b 2 is the matrix element for the transition, g is the cavity filling factor, Dp is the population difference between the lower and higher energy level (taken by Fischer et al. to be À1.5%), and K is a constant equal to g 2 e l 2 B l 0 =h. The condition for masing is then simply that the cavity quality factor should be greater than the gain medium quality factor Q c > Q m .
A further requirement is that the pump power required to achieve a population inversion should not heat the system to an extent that degrades its performance as a gain medium, determined to be $30 W/cm 2 for SiC. Fischer et al. estimate the necessary pump power in a cylindrical cavity of radius r and length L as whereP 0 ¼ 3:9 W/cm 2 is a characteristic pump power for SiC and r ¼ 6:1 Â 10 À15 cm 2 is the mean absorption cross section of the defects in their SiC sample. Since N is a common parameter of the two conditions, it must be carefully tuned to minimize Q m while keeping P < 30 W/cm 2 .
Using the sample parameters obtained from the sample of Fischer et al. and assuming a cavity with Q c % 2 Â 10 5 , we, therefore, expect masing to occur for 6:0 Â 10 14 cm À3 < N < 2:3 Â 10 15 cm À3 . The upper bound on the defect density may be increased further to 9:2 Â 10 16 if the mean absorption cross section of defects in the system can be brought closer to the r % 1:5 Â 10 À16 observed for individual V Si defects. 78 The excess cross section is presumed to come from other types of defects such as neutral divacancies, so deterministic defect-implantation methods [79][80][81] should be able to achieve this by decreasing the relative concentrations of non-V Si defects.
Since the defect densities required are within the range of densities that have already been achieved experimentally, 82 it seems that continuous-wave SiC masers that operate at room temperature are within reach.
Another host for spin defects that have shown promise is the van der Waals crystal hexagonal boron nitride (hBN), in which ensembles of negatively charged boron vacancies (V À B ) with S ¼ 1 have been successfully prepared in coherent quantum states with T 2 % 10 ls spin coherence times at room temperature using optically-detected magnetic resonance (ODMR). [83][84][85][86] While the exact decoherence mechanism is not yet well understood, experimental 87 and theoretical 88 works suggest that the spin coherence time can be significantly improved by increasing the relative concentrations of 10 B (with nuclear spin I ¼ 3) with respect to 11 B (I ¼ 3/2), so that isotopically purified hBN might extend the range of defect-based gain media for room-temperature masers to include 2D materials. If significant population inversions and masing can be achieved for hBN, it will form an attractive system for lowvolume, low-power devices analogous to nanolasers based on transition metal dichalcogenides. 89 The very large Stark shifts observed for defects in hBN 90 further offer the enticing possibility that the maser frequency in such devices could be tuned using electric fields and eliminate the need for magnetic fields altogether.
Aside from spin defects, an interesting recent proposal suggests that hydrogenic bound states of electrons and holes in semiconductors, known as Rydberg excitons, could form the basis of an electrically tunable continuous-wave maser 91 comparable to atomic Rydberg masers. 92 Rydberg states with a large principal quantum number n can be longlived since their lifetime scales as n 2 , though the $n À3 energy difference between successive states typically makes it difficult to resolve high-n Rydberg excitons experimentally. For the semiconducting copper oxide Cu 2 O, however, it has been possible 93 to observe excitons excited up to n ¼ 25. Ziemkiewicz and Ziel ınska-Racz ynska propose that by placing a mm-sized sample of Cu 2 O in a cavity and using the Stark shifts induced by an external electric field to match the transition between different Rydberg states to a 571 nm optical pump, it will be possible to selectively pump between specific Rydberg states. There are 2300 three-level subsets {n 1 ; n 2 ; n 3 } that can be selected from the 25 available Rydberg states, allowing the maser transition to be broadly tuned over wavelengths from 0:1-10 mm. Although milliKelvin temperatures are required to access the 25 Rydberg states modeled by Ziemkiewicz and Ziel ınska-Racz ynska, it will be interesting to explore whether this approach can be realized at room temperature. Recent work 94 on synthetic Cu 2 O with very low levels of defects and impurities reported the observation of excitonic Rydberg states at room temperature. Aside from Cu 2 O, room-temperature Rydberg states up to n ¼ 4 have also been observed in monolayers of transition metal dichalcogenides such as MoS 2 and WS 2 . 95 These would provide another route to a two-dimensional room-temperature nanomaser.
As the range of gain media and operating principles for roomtemperature solid-state masers continues to grow, it is interesting finally to speculate what applications might open up as practical devices become available. Masers have historically been important in metrology, where their ultra-low-noise amplification has allowed the detection of very weak electromagnetic signals. For this reason, we anticipate that room-temperature masers will find ready use in deepspace communications and as sensitive magnetometers. For the latter, the diamond maser has already shown sensitivities of order 10 pT/ ffiffiffiffiffiffi Hz p and might be made more sensitive still by masing between Floquet states, as discussed above.
Another prominent application of masers has been as frequency standards 18 with the hydrogen maser recently employed in the Galileo 96 and BeiDou 97 satellite navigation systems. An attractive use for masers that operate at ambient temperature and pressure might, therefore, be as highly portable precision clocks that could maintain local synchronization with a satellite navigation system when satellite signals are obstructed. Over short (seconds to minutes) timescale clock stability is largely determined by the clock signal Q factor, so we may expect the diamond maser (Q $ 10 8 -10 11 ) to be highly competitive with quartz resonators (Q $ 10 6 and with non-masing diamond NV center clocks (Q $ 100) based on zero-field transitions between the j61i and j0i ground states. 98 The key challenge to realizing a practical chip-based diamond maser clock will lie in overcoming the sensitivity to temperature fluctuations either by employing one of the alternative maser operating principles discussed above or by introducing ways to compensate the temperature-dependence of the masing frequency. 98 We further anticipate that the arrival of masers that operates in ambient conditions will extend the benefits of lasers in spectroscopy (e.g., low linewidths and high spatial coherence) to microwave wavelengths, leading to new developments in microwave spectroscopy 99,100 and sensing applications. 101 A key step in this direction will be to increase the output power that can be achieved by room-temperature solid-state masers.
It is finally interesting to speculate whether room-temperature masers may contribute to the suite of applications in quantum technology currently being explored more generally for spin defects in widebandgap materials. [102][103][104] The observation of strong coupling and highly entangled Dicke states in the pentacene maser are promising in this regard 105 with Dicke states playing an important role in quantum metrology 106,107 and quantum computing. 108,109 Alternatively, the coherent radiation generated using room-temperature solid state masers might be employed 110 in microwave quantum illumination systems 111,112 to achieve a form of quantum radar that uses photon correlations to outperform classical systems in the detection of low-reflectivity targets in a noisy environment. 113 Finally, the formal analogy between three-level masers and heat engines 114 suggests that solid-state roomtemperature masers may be employed as quantum heat engines, whose coherence enables them to deliver a greater power output than their classical counterparts. 115 A population-inverted diamond NV center system was recently operated as a quantum heat engine to demonstrate that such quantum advantages can be realized experimentally. 116 Room-temperature solid state masers, thus, offer attractive systems with which to explore fundamental questions in quantum optics as well as challenges in metrology and quantum technologies. In the coming years, we expect to see ever more materials and device concepts exploited to further develop masers and address these challenges.