news & views wrong (spin-non-conserving) path, the ion emission, and have measured spin relaxation spin–photon and entanglement of remote is able to emit on average 700 photons while using the coupled spin–cavity system, REIs remain out of reach for now. However, keeping its electron spin state. Kindem and colleagues went one step owing to the diversity of REI species, the Finally, the two spin-conserving beyond — measuring spin dephasing and possibility of their tight packing into optical transitions have different optical even exploring the spin dephasing limits in the crystal and the ultra-long and can be addressed separately YVO with spin decoupling techniques. times, the future of REI-based quantum by a narrow-band single-mode . Besides the intriguing and hardware looks bright. ❐ If, say, the electron is in the ground engineering achievements behind the state and one shines the laser in observation of spin quantum jumps, the Roman Kolesov and Jörg Wrachtrup "j i resonanceI with the transition, the ability to read out the quantum state of 3. Physikalisches Institut, Universität Stuttgart, "j i � "j i erbium ion keeps emittingI the spin is of fundamental importance for Stuttgart, Germany. photons until it accidentally jumps into the quantum information processing. Certain e-mail: [email protected]; |↓〉 state. By observing this fluorescence, algorithms that are critical for scalability, [email protected] one can immediately say that the spin is such as error correction, rely on single- in state . However, if there is no shot readout. While the detection and Published online: 30 March 2020 "j i fluorescenceI emitted, one concludes that coherent control of REI has been elusive https://doi.org/10.1038/s41567-020-0871-3 the spin is in state . This simple but for a long time, with the invention of #j i elegant strategy allowsI the observation of efficient resonators for REI-based systems References quantum jumps of erbium electron spin published now, REIs are quickly catching 1. Afzelius, M., Gisin, N. & de Riedmatten, H. Phys. Today 68, 42 (2015). in real time — with very far reaching up with the leading contenders in the 2. Zhong, M. et al. Nature 517, 177–180 (2015). implications for quantum computing field. Starting from the first detection of 3. Raha, M. et al. Nat. Commun. https://doi.org/10.1038/s41467- architectures based on REIs. single REI reported eight years ago5, most 020-15138-7 (2020). 4. Kindem, J. M. Nature https://doi.org/10.1038/s41586-020-2160-9 While both groups of authors have basic qubit functionalities have now been (2020). used similar methods for cavity-enhanced shown, although some key steps such as 5. Kolesov, R. et al. Nat. Commun. 3, 1029 (2012).

LASER PHYSICS Mode-locking dissected Despite the wide use of mode-locked , no general theory for mode-locking exists. An attractor dissection approach provides some intuitive understanding of the complex dynamics in one type of mode-locking. F. Ömer Ilday

ode-locked lasers have ability to focus its beam is limited. From the oscillation of the modes enables their extraordinarily diverse humble laser pointer to ultra-high-power coherent superposition to generate Mscientific, medical and industrial lasers for cutting metal sheets, multimode ultrashort pulses, which have found a applications, and have directly enabled three lasers are widely used. The straightforward diverse range of scientific and industrial Nobel Prizes. Until recently, mode-locking — although technically challenging — applications. The recent demonstration was restricted to longitudinal modes only alternative is to restrict the cavity to a single of spatiotemporal mode-locking — the and required laser cavities with a single transverse and, less commonly, a single simultaneous locking of longitudinal and transverse mode. But simultaneous locking longitudinal mode. A single-mode laser transverse modes of a laser2 — came as a of longitudinal and spatial modes of a laser can produce a truly constant output, and surprise. This advance has created much — spatiotemporal mode-locking — is also its beam can be focused to the diffraction excitement in the laser community; possible. Writing in Nature Physics1, Logan limit. These lasers are the workhorses of thanks to the increased dimensionality, Wright and co-workers have now taken many scientific applications, including we are likely to witness an explosion in a first and bold step towards a theory of gravitational wave detection and laser- the richness of self-organization that lasers spatiotemporal mode-locking. cooling of atoms. can exhibit. A laser cavity (Fig. 1a) generally supports The not-so-straightforward but However, this richness is also a challenge many distinct electromagnetic modes, fascinating alternative is mode-locking. — without theoretical guidance, exotic both in the longitudinal and transverse Under the right conditions, thousands mode-locking states may turn into the directions. Most commonly, these modes of longitudinal modes of a cavity can proverbial needle in a haystack. For example, oscillate independently of each other. spontaneously self-organize to oscillate in one trustworthy tool to build intuition about The laser’s output can be nearly constant in perfect synchrony with each other, like an mode-locking is numerical simulation time, but with large fluctuations, and the enormous orchestra. The synchronized of the laser’s operation. In spatiotemporal

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a ˆ ˆ ˆ b c O1 O2 O3 ˆ Oˆ Δλ O4 4 Spatial Saturable Spectral O'ˆ ˆ ˆ 1 filter absorber filter ˆ R O1 ˆ ˆ O1 ˆ ˆ O3 O2 O3 O2

ˆ Optical fiber O4

Fig. 1 | Spatiotemporal mode-locking in phase space. a, A mode-locked laser’s cavity contains multiple optical elements, each described by a nonlinear operator (Ô1, Ô2, Ô3, Ô4). b, Evolution of the pulse through the laser cavity constitutes a closed trajectory in phase space, described by the operators Ô1, Ô2, Ô3 and Ô4. c, An attractor dissection approach produces a highly simplified model by retaining one or two dominant operators (Ô1′) and replacing the others with a simple rescaling operation (Ȓ). mode-locking, one has to solve as many various possible scenarios, the team was able limitations. However, this is a limited level coupled equations as there are spatial to predict previously unknown regimes of of understanding for a self-organized system modes. Each of these equations is as rich and spatiotemporal mode-locking, which they where the final state is an emergent one. complicated as the single one used to model subsequently demonstrated experimentally. None can dissect the requirements to a new regular mode-locking — which is itself still This theory is not the final word mode-locking state with desired features not fully understood — not to mention on spatiotemporal mode-locking. The and translate them to a sequence of cavity the superlinear increase of the number of occasionally non-rigorous but beautifully elements with appropriate parameters. parameters with the number of modes. insightful attractor dissection approach Consequently, laser design involves Even regular mode-locking does not have will surely stimulate new work. Besides laboriously searching the vast parameter a general formulation, so the task Wright several more specialized questions, one space or trying to adopt a previously known and co-workers have accomplished may look fundamental question remains unanswered: mode-locking state. A satisfactory solution impossibly difficult. But sometimes a more the well-known dictum that a laser evolves to this inverse problem could revolutionize general problem can yield more insight towards lowest loss generally holds, but the development of mode-locked lasers. than its more restricted version. Indeed, even for regular mode-locking there is The recent proposal of a thermodynamic their method — which they call attractor no rigorous proof. It is far from clear treatment of nonlinear propagation of dissection — allows them to break down how well it holds in complex situations in optical fibres with a large number overwhelmingly complicated dynamics into like spatiotemporal mode-locking, with of transverse modes4 may hold clues to a simpler scenarios. higher-dimensional phase space. For radically different approach. Unfortunately, A laser evolves towards the state that example, the laser can have access to this thermodynamic formulation is minimizes its losses1,3. Various distinct multiple steady states that extract with restricted to light propagation without effects are acting on the pulse as it traverses sufficiently similar efficiencies for noise- loss or gain, without which mode-locking the cavity (Fig. 1b). A suitable nonlinear induced transitions to occur between them. is impossible. But a generalization of the operator can describe each effect. But, Interestingly, the authors already appear attractor dissection method guided by if all of them are considered at once, to have encountered signs of limitations thermodynamics may be able to solve the figuring out which final state minimizes when none of the effects in the cavity is inverse problem of mode-locking. ❐ the losses is often impossible. The attractor dominant. Looking beyond laser physics dissection method simplifies finding this and considering the remarkable success F. Ömer Ilday state. Crucially, Wright and co-workers of the lowest-loss dictum, any significant Department of Physics, Department of Electrical intuited that the ultimate selection of a progress towards understanding it more and Electronics Engineering, UNAM – National specific mode-locked state by the lowest- deeply may be relevant to a large class of Nanotechnology Research Center, Bilkent University, loss principle is often, but not always, self-organizing systems that have no evident Ankara, Turkey. dominated by one or two of these effects. connection to lasers. e-mail: [email protected] For the parameter ranges where this is true, The advance made by Wright and they focused on the dominant operator and co-workers gives us reason to be optimistic Published online: 10 February 2020 lumped together the remaining effects into that it is possible to develop a general https://doi.org/10.1038/s41567-020-0811-2 a simple rescaling operator (Fig. 1c). This theory of mode-locking. Presently, there are References highly simplified model can be analysed various theoretical formulations for regular 1. Wright, L. G. et al. Nat. Phys. https://doi.org/10.1038/s41567-020- and understood intuitively. For example, the mode-locking, and now a preliminary 0784-1 (2020). spatial filter alone may be dominant for a formulation for spatiotemporal mode- 2. Wright, L. G., Christodoulides, D. N. & Wise, F. W. Science 358, given set of cavity parameters. For another locking. Each of these predicts the overall 94–97 (2017). 3. Haken, H. Light: Laser Light Dynamics (North-Holland, 1985). set, the saturable absorber together with the characteristics of the mode-locked state 4. Wu, F. O., Hassan, A. U. & Christodoulides, D. N. Nat. Photon. 13, gain may dominate. By playing around with for a given cavity layout — within certain 776–782 (2019).

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