Colloquium: Nonthermal pathways to ultrafast control in quantum materials

Recent progress in utilizing ultrafast light-matter interaction to control the macroscopic properties of quantum materials is reviewed. Particular emphasis is placed on photoinduced phenomena that do not result from ultrafast heating effects but rather emerge from microscopic processes that are inherently nonthermal in nature. Many of these processes can be described as transient modifications to the free energy landscape resulting from the redistribution of quasiparticle populations, the dynamical modification of coupling strengths, and the resonant driving of the crystal lattice. Other pathways result from the coherent dressing of a material’s quantum states by the light field. A selection of recently discovered effects leveraging these mechanisms, as well as the technological advances that led to their discovery, is discussed. A road map for how the field can harness these nonthermal pathways to create new functionalities is presented.

Figure 1

Overview of the main experimental tools available to investigate ultrafast phenomena in quantum materials. The upper central panel illustrates the broad spectral and temporal ranges from which tailored short laser pulses can be created to photoexcite (pump) materials out of equilibrium. The surrounding panels show categories of ultrafast time-resolved probes and their capabilities.

Figure 2

Illustration of nonthermal pathways triggered by laser excitation. All panels show a potential or free energy landscape as a function of a system coordinate, such as an electronic order parameter or a lattice displacement. (a) Weak excitations around a stable minimum (ground state) permit one to probe collective modes and their mutual couplings. (b) With a short, more intense laser pulse, one can switch between degenerate ground states ($A$ and $B$) or drive the material to a nonthermal, metastable excited state $C$. (c) Nonequilibrium critical behavior can be induced by a short, even more intense excitation that transiently modifies the free energy landscape itself. (d) With a strong excitation, the system can also be driven into anharmonic regimes with deviations from parabolic behavior, which allows one to probe nonlinear effects and change effective couplings in the material.

Figure 3

Multimessenger probing of disentangled microscopic degrees of freedom. (a) A portfolio of ultrafast techniques has been used to investigate photoinduced melting of charge-density wave order in the materials $(\mathrm{La}/\mathrm{Tb}){\mathrm{Te}}_3$, including time-resolved x-ray diffraction (tr-XRD), time- and angle-resolved photoemission spectroscopy (tr-ARPES), transient optical spectroscopy (TOS), and ultrafast electron diffraction (UED). The signals obtained can be qualitatively and quantitatively different since distinct degrees of freedom are probed. From [449]. (b) Se atoms in FeSe are coherently displaced following photoexcitation by an ultrafast IR pulse, which can be directly measured by tr-XRD (blue, top). At the same time, corresponding energy shifts of electron bands are revealed by tr-ARPES (orange, middle; green, bottom). The schematic on the right depicts the $A_{1g}$ phonon mode that induces the periodic modulation of the lattice and electronic bands. From [116].

Figure 4

Ultrafast switching. (a) At equilibrium $1T\text{−}{\mathrm{TaS}}_2$ goes through successive charge-density wave (CDW) transitions as a function of temperature, resulting in an insulating low-temperature state that is characterized by strong correlations (blue circles, red up triangles). Upon photoexcitation with a single 35 fs optical pulse, a long-lived metallic state emerges (green down triangles). Adapted from [405]. (b) Photoexcitation of electrons in bismuth changes the local nuclear potential energy. For excitation densities above 2% the amplitude of the initiated $A_{1g}$ mode drives a transition to a higher-symmetry phase. The $A_{1g}$ phonon mode, characteristically for the low-symmetry phase, gets damped as the new phase is reached. Adapted from [386].

Figure 5

Nonthermal critical behavior. (a) Nonequilibrium phase diagram as a function of $U_{\mathrm{i}}$ and size of the quench $U_{\mathrm{f}}-U_{\mathrm{i}}$. A splitting of the critical point into thermal and nonthermal antiferromagnetic (AFM) critical points is observed. (b) Time evolution of the magnetization for a quench of the electron-electron interaction $U_{\mathrm{i}}\to U_{\mathrm{f}}$ in the antiferromagnetic phase of the Hubbard model. Each color represents a different value of $U_{\mathrm{f}}$ (left panel: $U_{\mathrm{f}}=1.0,1.1,\dots ,1.9$ and right panel: $U_{\mathrm{f}}=1.5,1.6,\dots ,2.4$ from bottom to top). Adapted from [400].

Figure 6

Dynamically screened Hubbard $U$ interaction in laser-driven quantum materials. (a) Screening is typically enhanced when a material is excited by an optical laser pulse, which creates electronic excitations, resulting in a dynamically reduced time-dependent $U$ ([382]; [126]). In charge-transfer insulators this results in a narrowing of the Mott-Hubbard gap between the upper and lower Hubbard bands (UHB and LHB, respectively), as well as the charge-transfer gap $\mathrm{\Delta }$ ([383]). (b) For a mid-IR laser excitation that is resonant with an IR-active phonon mode, the dynamical $U$ can parametrically depend on the phonon-mode coordinate $Q_{\mathrm{IR}}$ via a nonlinear electron-phonon interaction ($Q_{\mathrm{IR}}^{2}U$). Whether $U$ increases or decreases on average depends on the sign of this nonlinearity.

Figure 7

Transient crystal structure from nonlinear phononics. (a) Oscillatory dynamics of an IR-active phonon-mode coordinate $Q_{\mathrm{IR}}$ is induced under resonant driving by a mid-IR laser pulse. (b) Owing to nonlinear phonon-phonon coupling to a Raman mode (coordinate $Q_{\mathrm{R}}$) of the form $Q_{\mathrm{IR}}^2{Q}_{\mathrm{R}}$, the potential energy of the Raman mode is transiently shifted to a new minimum following the squared amplitude $Q_{\mathrm{IR}}^2$. (a),(b) Adapted from [234]. Accordingly, the Raman mode is displaced toward its transient potential minimum, which remains as long as the dynamics of the IR-active mode is coherent. (c) For ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$, the motion of the optically excited coherent $B_{1u}$ mode leads to a transiently modified crystal structure that was measured using time-resolved x-ray diffraction ([236]) and is compatible with light-induced superconducting behavior. (d) Time-resolved relative change of intensity $\mathrm{\Delta }I/I$ of two representative Bragg peaks. Solid curves show the ab initio calculated structure based on nonlinear phonon-mode coupling. (e) Transient change in the Cu-O distance $d$ obtained from the calculation. (c)–(e) Adapted from [42].

Figure 8

Versatile functionalities enabled by Floquet engineering. (a) Periodic driving using optical fields can steer the macroscopic properties of quantum materials by dressing their microscopic degrees of freedom, such as electronic hopping parameters. (b) Examples include proposals and experimental realizations of new electronic band structures ([420]; [231]), the manipulation of band topologies ([284]; [190]; [217]; [246]), and the observation of excitonic Stark shifts caused by the creation of strong synthetic magnetic fields ([183]; [356]). Additional proposals include the optical control of magnetic correlations ([248]; [61]; [177]) that have been experimentally observed in quantum simulation settings ([127]), the creation of fractionized quasiparticles obeying non-Abelian statistics ([209]), and forms of photon-dressed superconductivity ([193]; [265]; [175]; [390]).

Figure 9

Dynamical localization in an atomic chain and Floquet sidebands. (a) Illustration of dynamical localization in an atomic chain visualized in real (upper row) and momentum space (lower row). The two columns represent the real-time picture (left panel) as well as the effective, time-averaged picture (right panel) of the periodically driven system. When the equilibrium band dispersion (black, lower left panel) is driven back and forth in momentum space by the light field (red), the total bandwidth is reduced in the effective dressed picture (blue, lower right panel). This corresponds to a decrease in the effective hopping amplitude in real space, described by the Bessel function $t_{\mathrm{eff}}=t_0{J}_0(F)$, shown in the upper right panel. (b) Visual representation of Floquet replicas according to Eq. (6). At high frequency ($\omega \to \infty$) the effective Hamiltonian is given by the time average $H^0$. At finite frequency Floquet sidebands at energy distance $\omega$ become accessible via the higher moments $H^1,H^2,\dots$ of the Fourier series of the time-dependent Hamiltonian $H(t)$.

Figure 10

Topological Floquet engineering in Dirac systems. (a) A coherent interaction with circularly polarized light was predicted to induce a photon-dressed topological band structure in graphene that is characterized by protected chiral edge states ([284]; [190]). (b) When the Floquet sidebands form, they hybridize at their crossing points, opening band gaps (${\mathrm{\Delta }}_1$, ${\mathrm{\Delta }}_2$). A gap also opens at the Dirac point (${\mathrm{\Delta }}_0$) due to a two-photon absorption-emission process that breaks time-reversal symmetry. The resulting Floquet-Bloch bands are fully gapped and possess a nonzero total Berry curvature and Chern number. (c) Real-space schematic of the two-photon absorption-emission hopping process that induces a gap at the Dirac point in graphene. (d) tr-ARPES data of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ detecting the formation of Floquet-Bloch bands from the Dirac surface states. From [231]. (e) Nonequilibrium anomalous Hall conductance of graphene driven by circularly polarized light as a function of the equilibrium Fermi level ($E_F$). Red and blue shading corresponds to $E_F$ being gated to the regions where the gaps ${\mathrm{\Delta }}_0$ and ${\mathrm{\Delta }}_1$ were predicted to appear. From [246].

Figure 11

Routes to avoid runaway heating. (a) Generic interacting systems heat up upon applying a continuous drive, which is detrimental to coherent control. However, when the drive frequency is tuned to a spectral gap in the system, this heating can in principle be pushed to exponentially large times. Control of prethermal states can then be achieved on intermediate to long timescales until thermalization sets in. (b) Examples of condensed matter systems for which such a strategy could be applied. The upper two and bottom left panels show Mott and charge-transfer insulators (LHB and UHB denote the lower and upper Hubbard bands, respectively). Another example involves quantum Hall insulators (lower right panel). Between the different Landau levels (LLs) energy gaps proportional to the externally applied magnetic field emerge. Frequency detuning to the sharp resonances between LLs could in principle allow for prethermal state Floquet control of the system.

Figure 12

Floquet engineering of magnetic interactions. (a) Schematic of manipulation of magnetic degrees of freedom via irradiation of quantum magnets with light. (b) In Mott insulators, pumping below the charge gap suppresses charge excitations on short timescales while renormalizing the magnetic interactions at low energies. (c) Irradiation with light can alter conventional spin-exchange interactions by reducing the energy cost of intermediate virtual states of electronic tunneling. (d) Circularly polarized light can induce new types of magnetic interactions, such as $\mathrm{SU}(2)$-symmetric chiral three-spin-exchange interactions due to dynamical time-reversal symmetry breaking, which are absent at equilibrium.