Two-Dimensional Coherent Spectroscopy

• Two-dimensional coherent spectroscopy is a nonlinear technique that employs coherent pulse sequences to correlate excitation and emission frequencies.
• It uses advanced methods like non-collinear box geometries and frequency-tagged collinear setups to isolate and enhance specific quantum pathways.
• 2DCS reveals key material properties by distinguishing homogeneous dephasing from inhomogeneous broadening and mapping coupling mechanisms in diverse systems.

Two-dimensional coherent spectroscopy (2DCS) is a family of phase-sensitive nonlinear spectroscopies in which a material is driven by a sequence of coherent pulses and the response is resolved along two independent time variables and, after Fourier transform, two conjugate frequency axes (Huang et al., 2 Jul 2025). In the broad 2DCS tradition established in NMR, optical 2D Fourier-transform spectroscopy, and 2D IR, the central idea is to correlate how a system is excited with how it later emits or is detected (Huang et al., 2 Jul 2025). In practice, 2DCS spans heterodyne-detected optical four-wave mixing, fluorescence-detected collinear implementations, THz electric- and magnetic-field protocols, and condensed-matter formulations that directly access two-frequency nonlinear conductivity or susceptibility tensors (Munoz et al., 2020, Revesz et al., 2024, Froese et al., 5 Jun 2025). Its distinctive value is that different quantum pathways that overlap in one-dimensional spectra often separate in the 2D frequency plane, allowing direct analysis of couplings, broadening mechanisms, collective modes, and multi-particle continua (Huang et al., 2 Jul 2025, Alfrey et al., 6 Jul 2026).

1. Fundamental observables and spectral organization

In the standard time-domain formulation, two or more coherent pulses prepare and probe a nonlinear signal that depends on two delays, commonly denoted $t$ and $\tau$, and the measured field or demodulated observable is Fourier transformed to $(\omega_t,\omega_\tau)$ (Huang et al., 2 Jul 2025, Revesz et al., 2024). In THz implementations the nonlinear emitted field is often defined by subtraction,

$$E_{\mathrm{NL}}=E_{\mathrm{A+B}}-E_{\mathrm{A}}-E_{\mathrm{B}},$$

so that one isolates the part generated by pulse-pair interactions rather than by either pulse alone (Huang et al., 2 Jul 2025). In collinear optical implementations the same logic appears in the complex lock-in observable $Z(t,\tau)$, with the 2D spectrum reconstructed as $S(\omega_t,\omega_\tau)=FFT[Z(t,\tau)]$ (Revesz et al., 2024).

Many optical implementations measure a third-order response. In the notation used for excitonic order in Ta$_2$NiSe$_5$, the signal is organized by a response function of the form

$$P^{(3)}(t)\sim \iiint dt_3dt_2dt_1\, R^{(3)}(t_3,t_2,t_1)\, E(t-t_3)E(t-t_3-t_2)E(t-t_3-t_2-t_1),$$

with pathway classes sorted into rephasing, nonrephasing, and pump-probe sectors (Chen et al., 22 Dec 2025). THz-2DCS reviews use closely related nested-commutator expressions for $\chi^{(2)}$ and $\tau$0, but emphasize that the measured operator $\tau$1 can be polarization, current, magnetization, or another collective observable rather than only an optical dipole (Huang et al., 2 Jul 2025). This makes 2DCS a spectroscopy of multi-time quantum correlation functions rather than only of static resonances (Huang et al., 2 Jul 2025).

The 2D frequency plane is typically read geometrically. Diagonal peaks indicate correlated excitation and detection frequencies; off-diagonal cross peaks indicate coupling, coherence transfer, or multi-state connectivity; anti-diagonal structures are characteristic of rephasing and echo phenomena (Huang et al., 2 Jul 2025, Watanabe et al., 2024). In perturbative THz language, the spectrum can contain pump-probe, nonrephasing, rephasing, two-quantum, third-harmonic, rectification, and second-harmonic features, depending on symmetry and pulse ordering (Huang et al., 2 Jul 2025). A different but related organization appears in second-order condensed-matter formulations, where the fully symmetrized susceptibility $\tau$2 lives in the plane of two input frequencies; the diagonal $\tau$3 is the SHG line, while the antidiagonal $\tau$4 is the galvanoelectric-effect line (Brenig et al., 2024). This coexistence of third-order and second-order 2D formalisms is a defining feature of the field rather than an inconsistency: the common structure is resolution of nonlinear response along two independent frequency axes (Brenig et al., 2024, Froese et al., 5 Jun 2025).

2. Experimental implementations and signal isolation

A canonical optical realization is the non-collinear box geometry. In the MONSTR-style implementation discussed for fast phase cycling, four phase-locked pulses occupy the corners of a square; three pulses $\tau$5, $\tau$6, and $\tau$7 generate a transient four-wave-mixing signal, while the fourth pulse acts as reference or local oscillator (Munoz et al., 2020). For the rephasing sequence, $\tau$8 arrives first, $\tau$9 second after delay $(\omega_t,\omega_\tau)$0, $(\omega_t,\omega_\tau)$1 third after waiting time $(\omega_t,\omega_\tau)$2, and the signal is emitted during time $(\omega_t,\omega_\tau)$3 and detected by spectral interferometry in the phase-matched direction of the reference pulse (Munoz et al., 2020). In this geometry, many unwanted pathways are already rejected by phase matching, but scattered excitation light and isotropic fluorescence can still contaminate the detected signal (Munoz et al., 2020).

Collinear implementations replace spatial phase matching by frequency tagging and demodulation. In a 5 kHz fluorescence-detected optical 2DCS spectrometer, four collinear pulses $(\omega_t,\omega_\tau)$4 are produced by nested Mach-Zehnder interferometers, each pulse acquires an acousto-optic-modulator tag, and the rephasing one-quantum signal is selected by lock-in detection at

$(\omega_t,\omega_\tau)$5

(Revesz et al., 2024). Because the signal is sampled once per laser shot, the paper states the practical Nyquist-style constraint

$(\omega_t,\omega_\tau)$6

which at $(\omega_t,\omega_\tau)$7 kHz forces operation below $(\omega_t,\omega_\tau)$8 kHz and, in the reported apparatus, below about $(\omega_t,\omega_\tau)$9 kHz after filtering (Revesz et al., 2024). The same general architecture was used in broadband rubidium vapor spectroscopy, where AOM-tagged collinear fluorescence detection yielded a complete set of single-quantum, zero-quantum, and double-quantum spectra involving both $$E_{\mathrm{NL}}=E_{\mathrm{A+B}}-E_{\mathrm{A}}-E_{\mathrm{B}},$$0 and $$E_{\mathrm{NL}}=E_{\mathrm{A+B}}-E_{\mathrm{A}}-E_{\mathrm{B}},$$1 lines (Yan et al., 2022).

A major optical instrumentation development is fast phase cycling in non-collinear 2DCS. By inserting liquid-crystal phase retarders into the $$E_{\mathrm{NL}}=E_{\mathrm{A+B}}-E_{\mathrm{A}}-E_{\mathrm{B}},$$2 and $$E_{\mathrm{NL}}=E_{\mathrm{A+B}}-E_{\mathrm{A}}-E_{\mathrm{B}},$$3 beams, electronically toggling $$E_{\mathrm{NL}}=E_{\mathrm{A+B}}-E_{\mathrm{A}}-E_{\mathrm{B}},$$4 and $$E_{\mathrm{NL}}=E_{\mathrm{A+B}}-E_{\mathrm{A}}-E_{\mathrm{B}},$$5 phase shifts, and combining four interferograms,

$$E_{\mathrm{NL}}=E_{\mathrm{A+B}}-E_{\mathrm{A}}-E_{\mathrm{B}},$$6

the scattered fields from all three excitation pulses cancel while the desired third-order transient four-wave-mixing field adds constructively (Munoz et al., 2020). In potassium vapor this four-step combination removed the diagonal scatter background to the point that no background was visibly present along the diagonal line in the displayed spectrum, and the reported signal-to-noise ratio was enhanced by a factor of 5 relative to acquisition without phase cycling (Munoz et al., 2020). The method is explicitly designed as an add-on to existing non-collinear platforms and is faster and more exact than mechanically generated phase steps constrained by HeNe stabilization (Munoz et al., 2020).

Broadband excitation expands the accessible state space. In rubidium, a Ti:sapphire oscillator with 67.45 nm FWHM bandwidth centered at 810.89 nm simultaneously covers both $$E_{\mathrm{NL}}=E_{\mathrm{A+B}}-E_{\mathrm{A}}-E_{\mathrm{B}},$$7 and $$E_{\mathrm{NL}}=E_{\mathrm{A+B}}-E_{\mathrm{A}}-E_{\mathrm{B}},$$8 transitions, enabling single-quantum cross peaks, zero-quantum Raman-like coherences, and double-quantum collective resonances such as $$E_{\mathrm{NL}}=E_{\mathrm{A+B}}-E_{\mathrm{A}}-E_{\mathrm{B}},$$9 in one experiment (Yan et al., 2022). This illustrates a general point: geometry, phase selection, and spectral bandwidth are not secondary implementation details, but determine which coherence manifolds a given 2DCS experiment can access (Yan et al., 2022, Munoz et al., 2020).

3. Lineshapes, broadening, and inverse problems

One of the most established uses of 2DCS is separating homogeneous dephasing from inhomogeneous broadening. In the MoSe$Z(t,\tau)$0 exciton study, the central geometric intuition is that static distributions of transition energies elongate peaks along the diagonal, whereas homogeneous dephasing broadens the peak perpendicular to the diagonal (Alfrey et al., 6 Jul 2026). This directly reduces the degeneracy that plagues one-dimensional Voigt fits, where Gaussian width $Z(t,\tau)$1 and Lorentzian width $Z(t,\tau)$2 trade off against each other along shallow $Z(t,\tau)$3 valleys (Alfrey et al., 6 Jul 2026). Across many sample locations, the reported Pearson correlation coefficient magnitude decreased from $Z(t,\tau)$4 for linear Voigt analysis to $Z(t,\tau)$5 for 2DCS, while the confidence-ellipse axis ratio shrank from $Z(t,\tau)$6 to $Z(t,\tau)$7 (Alfrey et al., 6 Jul 2026). This does not eliminate covariance, but it makes the homogeneous/inhomogeneous decomposition substantially more identifiable (Alfrey et al., 6 Jul 2026).

The same study illustrates how 2DCS can alter extracted linewidth partitions even when the underlying sample is unchanged. On the same hBN-encapsulated MoSe$Z(t,\tau)$8 flake, photoluminescence fits gave

$Z(t,\tau)$9

whereas 2DCS yielded

$S(\omega_t,\omega_\tau)=FFT[Z(t,\tau)]$0

(Alfrey et al., 6 Jul 2026). The paper interprets this difference as physically plausible because photoluminescence probes an incoherently relaxed population, while 2DCS probes the coherent nonlinear optical response directly (Alfrey et al., 6 Jul 2026). A plausible implication is that 2DCS-based linewidth partitions are not merely better constrained statistically; they can also correspond to a different microscopic observable.

Recent work generalizes these analyses beyond Gaussian disorder. A bivariate spectral distribution function framework replaces the standard elliptical Gaussian assumption with an arbitrary correlated inhomogeneous distribution, while retaining a homogeneous response kernel derived from the optical Bloch equations (De et al., 11 Apr 2025). In that formulation the diagonal slice obeys

$S(\omega_t,\omega_\tau)=FFT[Z(t,\tau)]$1

so the inhomogeneous distribution $S(\omega_t,\omega_\tau)=FFT[Z(t,\tau)]$2 is convolved with a Lorentzian homogeneous kernel even when the disorder is non-Gaussian (De et al., 11 Apr 2025). The paper demonstrates the method on a GaAs quantum-well exciton with a clearly non-Gaussian diagonal slice and extracts

$S(\omega_t,\omega_\tau)=FFT[Z(t,\tau)]$3

from four repeated measurements (De et al., 11 Apr 2025). It further argues that in arbitrary inhomogeneity, cross-diagonal widths alone are not reliable homogeneous-linewidth estimators because local cross-diagonal shape depends on local oscillator density in the distribution (De et al., 11 Apr 2025). This sharply distinguishes 2DCS lineshape analysis from simple width-reading heuristics.

The broader implication is methodological. Claims about microscopic disorder or dissipation mechanisms inferred from spectral decomposition are not only questions of fitting function choice; they are questions of identifiability set by measurement geometry (Alfrey et al., 6 Jul 2026, De et al., 11 Apr 2025). In that sense, 2DCS converts what is a hidden convolution in one dimension into anisotropy and correlation structure in two dimensions (Alfrey et al., 6 Jul 2026).

4. Electronic, excitonic, and band-geometric applications

In excitonic and polaritonic systems, 2DCS is often most valuable when the linear spectrum mixes multiple quasiparticle branches or obscures interaction effects. A microscopic many-body calculation for charge-tunable TMD monolayers in microcavities predicts three kinds of off-diagonal cross peaks in the 2D spectrum of trion-polaritons and exciton-polaritons, corresponding to coherent coupling among upper, middle, and lower polaritonic branches (Hu et al., 2022). Because the theory is built from an extended Chevy ansatz for the attractive and repulsive polaron sectors, the cross peaks are tied directly to the excitonic residues $S(\omega_t,\omega_\tau)=FFT[Z(t,\tau)]$4 of the many-body eigenstates rather than to an effective few-level model (Hu et al., 2022). In a related one-dimensional exciton-polaron theory, the excited-state absorption pathway explicitly probes the two-impurity sector; in weak coupling ESA cancels the combined excited-state-emission and ground-state-bleaching contributions, whereas in strong coupling ESA and ESE+GSB remain separately visible, providing direct information about polaron-polaron interactions (Wang et al., 2023).

For ordered quantum matter, 2DCS can separate collective modes from single-particle backgrounds more cleanly than linear optics. In Ta$S(\omega_t,\omega_\tau)=FFT[Z(t,\tau)]$5NiSe$S(\omega_t,\omega_\tau)=FFT[Z(t,\tau)]$6, time-dependent Hartree-Fock calculations show that the third-order 2DCS signal in the excitonic regime is overwhelmingly controlled by the condensate amplitude mode, with a detectable massive relative phase mode analogous to a Leggett mode and negligible single-particle contribution (Chen et al., 22 Dec 2025). The dominant peaks appear at

$S(\omega_t,\omega_\tau)=FFT[Z(t,\tau)]$7

corresponding to nonrephasing, rephasing, and pump-probe sectors, respectively (Chen et al., 22 Dec 2025). Near the critical temperature, the integrated 2DCS peak intensities are reported to scale numerically as

$S(\omega_t,\omega_\tau)=FFT[Z(t,\tau)]$8

making the nonlinear response a sharp marker of the symmetry-broken state (Chen et al., 22 Dec 2025). The same framework shows that a large static order parameter does not guarantee a large 2DCS signal: when electron-phonon coupling drives the system into a phonon-dominated regime, the amplitude-mode contribution collapses even if the order parameter remains large (Chen et al., 22 Dec 2025).

A different condensed-matter direction recasts 2DCS as a direct probe of two-frequency nonlinear conductivity. In this formulation, two time-delayed pulses $S(\omega_t,\omega_\tau)=FFT[Z(t,\tau)]$9 and $_2$0 generate a second-order current $_2$1, and Fourier transformation yields the two-frequency tensor $_2$2 (Froese et al., 5 Jun 2025). The paper decomposes this conductivity into seven contributions,

$_2$3

and identifies $_2$4 as a quantum-connection term with no analogue in linear response (Froese et al., 5 Jun 2025). For diagonal tensor components $_2$5 in time-reversal-symmetric, inversion-broken systems, the diagonal slice of the 2D spectrum isolates the imaginary part of the quantum connection because the Drude-, anomalous-, doubly resonant-, higher-order-pole-, and injection-type diagonal terms vanish and the three-band term vanishes on the frequency diagonal (Froese et al., 5 Jun 2025). This shifts 2DCS from a spectroscopic classifier of excitations to a probe of band geometry itself.

Second-order 2DCS of a Kitaev magnet provides another example of the method’s reach. Electric-field-induced finite-temperature calculations show a strong antidiagonal feature in the $_2$6 plane, interpreted as a galvanoelectric effect of fractional fermions, while the temperature evolution is strongly reshaped by thermally excited visons (Brenig et al., 2024). The width perpendicular to the antidiagonal is controlled by phenomenological quasiparticle relaxation rates beyond the bare Kitaev model, suggesting that 2DCS can extract single-particle lifetime information from inside a multi-particle continuum (Brenig et al., 2024).

5. THz 2DCS, quantum magnets, and fractionalized excitations

THz-2DCS places 2DCS in the meV regime of collective modes and correlated matter. The general THz protocol uses two phase-locked THz pulses separated by $_2$7 and phase-resolved electro-optic sampling of the emitted field versus gate time $_2$8; the nonlinear signal is again defined by subtraction, $_2$9 (Huang et al., 2 Jul 2025). The review literature emphasizes that this makes it possible to study superconducting Higgs and Leggett modes, Josephson plasmons, magnons, phonons, Landau levels, polaritons, and other low-energy collective excitations on equal footing (Huang et al., 2 Jul 2025). A recurring motif is that 2DCS can reveal hidden excitation pathways, separate homogeneous from inhomogeneous broadening, and expose higher-order correlations that remain obscured in pump-probe traces or equilibrium spectra (Huang et al., 2 Jul 2025).

Quantum-magnet applications have used the one-dimensional TFIM as a benchmark for fractionalization. Exact-diagonalization calculations show that in the deconfined ferromagnetic regime a sharp anti-diagonal rephasing feature, the “spinon echo,” appears in the third-order 2D spectrum because a local probe creates opposite-momentum spinon pairs whose phases rephase during the second time interval (Watanabe et al., 2024). When a longitudinal field confines the spinons into bound states, the anti-diagonal continuum breaks into a grid of discrete peaks and cross peaks associated with the confinement ladder (Watanabe et al., 2024). A separate path-integral treatment extends this to nonintegrable settings by incorporating self-energy corrections into dressed propagators, and argues that 2DCS can extract momentum-dependent decay rates of fractionalized quasiparticles from the transverse broadening of the rephasing streak (Hart et al., 2022). The combination of these results makes a precise statement: 2DCS does not merely detect continua, but can distinguish a continuum of sharp deconfined quasiparticles from lifetime-broadened excitations and from confinement-induced discretization (Watanabe et al., 2024, Hart et al., 2022).

In realistic magnetic materials, the light-matter coupling itself becomes part of the spectroscopy problem. A general theory of nonlinear spectroscopy of quantum magnets shows that the detected THz electric field can contain both induced polarization and induced magnetization,

$_5$0

so interpreting 2DCS in terms of magnetization alone is generally incomplete (Srivastava et al., 24 Feb 2025). The same framework derives second- and third-order susceptibilities with electric, magnetic, and mixed magneto-electric vertices, and uses exchange-striction and spin-current polarization operators as explicit microscopic couplings (Srivastava et al., 24 Feb 2025). Reversing pulse propagation or equivalently rotating the sample by $_5$1 about the magnetic-field axis isolates different symmetry channels, separating purely electric-plus-purely-magnetic contributions from cross-coupled ones (Srivastava et al., 24 Feb 2025). This is an important correction to simplified THz-2DCS narratives: in magnets, the 2D map is often a coherent sum of $_5$2, $_5$3, and mixed terms (Srivastava et al., 24 Feb 2025).

Material-specific calculations sharpen these ideas. For CoNb$_5$4O$_5$5, a quasi-one-dimensional Ising magnet, four-spinon calculations predict that above the low-temperature ordered phase the 2D spectrum should display sharp anti-diagonal spinon-echo features signaling deconfined spinons, whereas adding the interchain confinement potential suppresses those echoes and replaces them with broad sign-alternating oscillations (Watanabe et al., 18 Dec 2025). The same work identifies a four-spinon bound state, a “tetraquark,” visible in 2DCS but absent in ordinary linear response (Watanabe et al., 18 Dec 2025). In field-induced chain realizations of Ce$_5$6Zr$_5$7O$_5$8 and Nd$_5$9Zr$$P^{(3)}(t)\sim \iiint dt_3dt_2dt_1\, R^{(3)}(t_3,t_2,t_1)\, E(t-t_3)E(t-t_3-t_2)E(t-t_3-t_2-t_1),$$0O$$P^{(3)}(t)\sim \iiint dt_3dt_2dt_1\, R^{(3)}(t_3,t_2,t_1)\, E(t-t_3)E(t-t_3-t_2)E(t-t_3-t_2-t_1),$$1, polarization dependence of the probe operator picks out different chain sectors: $$P^{(3)}(t)\sim \iiint dt_3dt_2dt_1\, R^{(3)}(t_3,t_2,t_1)\, E(t-t_3)E(t-t_3-t_2)E(t-t_3-t_2-t_1),$$2 isolates the $$P^{(3)}(t)\sim \iiint dt_3dt_2dt_1\, R^{(3)}(t_3,t_2,t_1)\, E(t-t_3)E(t-t_3-t_2)E(t-t_3-t_2-t_1),$$3-chain spinon continuum, $$P^{(3)}(t)\sim \iiint dt_3dt_2dt_1\, R^{(3)}(t_3,t_2,t_1)\, E(t-t_3)E(t-t_3-t_2)E(t-t_3-t_2-t_1),$$4 isolates the polarized $$P^{(3)}(t)\sim \iiint dt_3dt_2dt_1\, R^{(3)}(t_3,t_2,t_1)\, E(t-t_3)E(t-t_3-t_2)E(t-t_3-t_2-t_1),$$5-chain magnon sector, and $$P^{(3)}(t)\sim \iiint dt_3dt_2dt_1\, R^{(3)}(t_3,t_2,t_1)\, E(t-t_3)E(t-t_3-t_2)E(t-t_3-t_2-t_1),$$6 is particularly sensitive to the lower band edge of the spinon continuum in Ce$$P^{(3)}(t)\sim \iiint dt_3dt_2dt_1\, R^{(3)}(t_3,t_2,t_1)\, E(t-t_3)E(t-t_3-t_2)E(t-t_3-t_2-t_1),$$7Zr$$P^{(3)}(t)\sim \iiint dt_3dt_2dt_1\, R^{(3)}(t_3,t_2,t_1)\, E(t-t_3)E(t-t_3-t_2)E(t-t_3-t_2-t_1),$$8O$$P^{(3)}(t)\sim \iiint dt_3dt_2dt_1\, R^{(3)}(t_3,t_2,t_1)\, E(t-t_3)E(t-t_3-t_2)E(t-t_3-t_2-t_1),$$9, providing a measure of proximity to a quantum critical point (Potts et al., 2023). For Nd$\chi^{(2)}$0Zr$\chi^{(2)}$1O$\chi^{(2)}$2, the relative intensity of one- and two-magnon signals in the $\chi^{(2)}$3-chain response probes the dipolar-octupolar mixing angle $\chi^{(2)}$4 (Potts et al., 2023). These studies collectively establish 2DCS as a practical spectroscopic discriminator between fractionalized spinons, confined bound states, and conventional magnons (Potts et al., 2023, Watanabe et al., 18 Dec 2025).

6. Control, tailoring, and current methodological frontiers

Beyond passive diagnosis, 2DCS can be used to engineer and read out tailored nonlinear responses. One route is prepulse control of an inhomogeneous ensemble. In a rephasing transient four-wave-mixing geometry, a strong prepulse modifies the subsequent third-order signal of each frequency class through a factor

$\chi^{(2)}$5

where $\chi^{(2)}$6 is the excited-state population created by the prepulse and $\chi^{(2)}$7 its pulse area (Kumar et al., 9 Jan 2026). The simulations show central and side-peak restructuring of the 2D spectrum, with an ensemble-averaged Rabi splitting energy of about $\chi^{(2)}$8 meV at $\chi^{(2)}$9 and about $\tau$00 meV at $\tau$01 (Kumar et al., 9 Jan 2026). The limitation is explicit: the prepulse method works best when the prepulse spectral bandwidth is comparable to the ensemble full width at half maximum; increasing the prepulse bandwidth from $\tau$02 meV to $\tau$03 meV washes out the modulation (Kumar et al., 9 Jan 2026).

A more flexible route is perturbative double-pulse tailoring. Splitting the final excitation pulse into $\tau$04 and $\tau$05 with delay $\tau$06 and relative phase $\tau$07 produces two photon echoes whose interference generates a spectral phase

$\tau$08

(Kumar et al., 9 Jan 2026). Constructive and destructive conditions,

$\tau$09

allow selective enhancement or suppression of chosen frequency components, while the modulation period obeys the paper’s relation

$\tau$10

(Kumar et al., 9 Jan 2026). Because the control mechanism is interference rather than strong-field inversion, the double-pulse method avoids the prepulse bandwidth constraint and is described as the more versatile route for manipulating the coherent optical response of inhomogeneous ensembles (Kumar et al., 9 Jan 2026). This suggests a broader role for 2DCS as a coherent-control framework for optical switching and coherent storage, not only as a readout technique.

At the same time, recent theory warns that measured 2D maps need not coincide with intrinsic nonlinear kernels. In a many-body diagrammatic treatment of THz spectroscopy in electronic systems, the 2D signal is recast as the sum of an intrinsic third-order response problem and a propagation problem (Fiore et al., 29 Sep 2025). In the velocity gauge, the intrinsic current is expressed through a third-order kernel $\tau$11, with spot-like structures associated with fully paramagnetic pathways and stripe-like structures associated with fully diamagnetic pathways (Fiore et al., 29 Sep 2025). But in bulk dispersive media the measured outgoing field acquires additional factors from screening and wave mixing, so the experimental map may be dominated by linear filtering and propagation rather than by the detailed structure of $\tau$12 (Fiore et al., 29 Sep 2025). The Josephson-plasmon example is particularly stark: intrinsic instantaneous and two-plasmon kernels would differ qualitatively, yet propagation reshapes the measured spectrum into a narrowband-looking four-spot pattern that obscures that distinction (Fiore et al., 29 Sep 2025). This suggests that in THz condensed-matter 2DCS, inverse modeling of the measured map must include both many-body response and Maxwell propagation.

Current frontier directions combine these methodological threads. THz review work highlights magneto-THz 2DCS, pressure-compatible THz-2DCS in diamond anvil cells, and THz 2D coherent microscopy as emerging instrumental opportunities (Huang et al., 2 Jul 2025). Optical developments continue to push toward weaker and smaller samples, where rapid electronic phase cycling, fluorescence-detected collinear geometries, and statistically explicit lineshape analysis address sensitivity, scatter, and parameter covariance simultaneously (Munoz et al., 2020, Revesz et al., 2024, Alfrey et al., 6 Jul 2026). Taken together, these developments indicate that 2DCS is evolving from a specialized nonlinear spectroscopy into a general framework for resolving, controlling, and quantitatively modeling coherent many-body dynamics across optical and THz frequency ranges (Huang et al., 2 Jul 2025).