Room-Temperature Polariton Spectroscopy

• Room-temperature polariton spectroscopy is a technique that uses advanced microcavity and lattice architectures to probe hybrid exciton-photon states, enabling direct observation of condensation, lasing, and topologically protected modes.
• The methodology employs angle-resolved photoluminescence, reflectivity, and real-space interferometry to extract quantitative metrics such as Rabi splitting, mode linewidths, and topological gaps.
• Applications include on-chip bosonic simulation and quantum devices, illustrating the ambient-stability and scalability of engineered polaritonic platforms for many-body and topological photonic phenomena.

Room-temperature polariton spectroscopy is the experimental and analytic methodology for probing exciton-polariton quasiparticles—hybrid superpositions of cavity photons and matter excitons—at ambient conditions, typically using advanced microcavity and lattice architectures with large Rabi splittings. This field leverages materials with robust excited-state binding (e.g., organic dyes, fluorescent proteins, wide bandgap semiconductors) and high-Q optical resonators engineered for strong light–matter coupling, enabling direct observation of phenomena such as condensation, lasing, nonlinear interactions, and topological states at or near 300 K. The following sections present a comprehensive account of the principles, microcavity and lattice designs, spectroscopic protocols, key results, and analysis frameworks foundational to room-temperature polariton spectroscopy.

1. Fundamental Theory and Spectroscopic Signatures

The exciton-photon coupled-mode framework establishes the essential physics of polariton formation at room temperature. For a planar or structured microcavity with in-plane wavevector $k$ and a suitable active medium (Frenkel or Wannier-type exciton),

$$H = \sum_k \Big[ E_C(k) a_k^\dagger a_k + E_X b_k^\dagger b_k + g(a_k^\dagger b_k + b_k^\dagger a_k) \Big],$$

where $a_k^\dagger$ ($b_k^\dagger$) creates a photon (exciton) at $k$ and $g$ is the Rabi coupling. The bare photon dispersion is $E_C(k) = E_C(0) + \hbar^2 k^2/2m_{ph}$ (with $m_{ph}\sim10^{-5}~m_e$), while excitons possess a comparatively flat $E_X$; $g$ is typically extracted via angle-resolved reflectivity/PL from the anti-crossing at $E_C = E_X$, with observed Rabi splittings 2$\hbar\Omega_R$ ranging from tens to hundreds of meV in room-temperature platforms.

Diagonalization yields lower and upper polariton branches: $$E_\pm(k) = \frac{E_C(k) + E_X}{2} \pm \frac{1}{2} \sqrt{[E_C(k) - E_X]^2 + 4g^2}.$$

Polariton modes inherit properties from both constituents. At resonance, the excitonic fraction $|X|^2$ and photonic fraction $|C|^2$ (Hopfield coefficients) are $1/2$ each; the hybrid character is tunable via detuning ($\delta = E_C(0) - E_X$). These eigenstates display nontrivial dispersion in engineered lattices and form the basis of all spectroscopic analysis.

2. Spectroscopic Architectures and Methodologies

Contemporary room-temperature polariton spectroscopy deploys a spectrum of device architectures:

• Planar Dielectric Microcavities: E.g., DBR/DBR (Ta$_2$O$_5$/SiO$_2$ or SiO$_2$/TiO$_2$ stacks) with embedded organic layers or quantum wells, optimized for target stop-band wavelengths (Dusel et al., 2020, Gebhardt et al., 2018).
• Patterned and Lattice Microcavities: Focused-ion-beam (FIB) milled dimples/caps in DBRs define coupled resonator arrays (1D SSH chains, honeycomb “graphene” lattices, or higher-order topological configurations) supporting band structure analogs and defect-localized modes (Dusel et al., 2020, Betzold et al., 18 Jan 2024, Bennenhei et al., 11 Jan 2024).
• 0D/1D defects and tight-binding potentials: Intracavity traps, pillar arrays, or etched waveguides realize strong lateral confinement and custom coupling topologies for polariton localization, band engineering, and robust topological defect state occupation (Urbonas et al., 2019, Bennenhei et al., 11 Jan 2024).
• Excitation/Detection Protocols:
  • Angle-resolved Photoluminescence (PL) and reflectivity, collected in Fourier (back-focal-plane) geometry using high-NA objectives (NA = 0.42 typical), with energy and $k$ spectral resolutions down to 150–200 $\mu$eV.
  • CW and pulsed non-resonant optical pumping (e.g., 532 nm, 6–7 ns pulses, or fs excitation) to probe both linear and nonlinear (condensation/lasing) regimes.
  • Real-space tomography (motorized lens scanning) and Michelson interferometry for spatial coherence/phase information (Dusel et al., 2020, Bennenhei et al., 11 Jan 2024).

3. Room-Temperature Polariton Band Engineering and Topological Defect Lasing

In systems such as the organic SSH chain microcavity (Dusel et al., 2020), two alternating site-to-site spacings ($a_1$, $a_2$, with coupling rates $w > v$) imprint the canonical SSH Hamiltonian:

$$H_\text{SSH} = \sum_{m=1}^{N} \left( v A_m^\dagger B_m + w B_m^\dagger A_{m+1} + \text{h.c.} \right),$$

with topologically nontrivial band structures. Domain boundaries (“v–v” double weak bonds) produce mid-gap zero modes, observable as spectrally isolated lines in the photoluminescence map and exhibiting strong exponential localization.

Key results include:

• Measured topological gap: $\Delta E_\text{gap} \approx 4.9$ meV.
• Defect mode linewidths: $\gamma_\text{dom} \approx 385\ \mu$eV (linear regime), narrowing to the instrumental limit ($\sim$150 $\mu$eV) in the condensed state.
• Thresholds for condensation/lasing: $P_\text{th}^\text{dom} \sim 0.10$ nJ/pulse (6 ns pulse), with a $\times10^3$ nonlinearity in intensity and spectrally resolved linewidth collapse.

The flatness and robustness of defect modes are established spectroscopically—trackable in both $k$-space and real-space tomographies—and are confirmed to be protected by the large band gap compared to the mode linewidth, ensuring spectral isolation at 293 K.

4. Quantitative Metrics: Rabi Splitting, Linewidths, and Coherence

The following table consolidates key quantitative parameters for organic planar and SSH lattice microcavities (Dusel et al., 2020), giving indicative values at room temperature:

Parameter	Planar/SSH Cavity	Domain Defect Mode
Exciton Energy $E_X$	2.085 eV	2.085 eV
Cavity-Exciton Detuning	$\delta = -230$ meV	$\delta = -230$ meV
Rabi Splitting 2$\hbar\Omega_R$	215 meV	215 meV
LP/UP Linewidth (linear)	$\gamma_\text{LP} \sim 1$ meV	$\gamma_\text{dom} = 385\ \mu$eV
Topological Gap $\Delta E_\text{gap}$	--	4.9 meV
Lasing Threshold $P_\text{th}$	--	$0.10$–$0.25$ nJ/pulse
Condensed Linewidth	--	$< 150\ \mu$eV (spectrometer limit)

Above threshold, PL linewidths collapse to the $\sim$150 $\mu$eV instrumental limit, and output intensities increase nonlinearly, signifying high phase coherence and condensation. Real-space and Fourier-space coherence are routinely evaluated by spatial interferometry and $k$-space mapping, respectively, confirming macroscopic occupation and phase rigidity of the condensate.

5. Topological Analysis and Detection

The topological character of defect-localized modes is grounded in the winding number $W$ of the SSH Hamiltonian; in $k$-space,

$$H_\text{Bloch}(k) = (v + w e^{-ikd}) \sigma_+ + (v + w e^{+ikd}) \sigma_-,$$

$$W = \frac{1}{2\pi} \oint_\text{BZ} dk\, \partial_k \phi(k),\ \phi(k) = \arg[v + w e^{-ikd}],$$

with $W = 1$ (nontrivial) for $v < w$.

Defect modes are identified spectroscopically by:

• Flat lines in energy ($E_\text{dom}$, $E_\text{edge}$) within the topological gap in angle-resolved PL, absent under bulk excitation.
• Real-space exponential localization on alternating weak-bond sites.
• Spectral isolation and persistence of the mode under condensation (i.e., topological protection against hybridization and thermal broadening).

6. Ambient-Condition Stability and Applications

The architecture combines ultra-stable Frenkel excitons (e.g., from fluorescent proteins) with microcavity photon fields for persistently strong light–matter coupling at 300 K, with excitonic fractions $\ll 10\%$ at large negative detuning, yet sufficient Rabi splitting to preserve the spectral identity and coherence of polariton states.

Robust room-temperature operation has broad implications:

• Paradigm for on-chip Bosonic many-body physics at ambient conditions, providing new access to nonequilibrium phase transitions, quantum simulation, and dissipative topological lasing platforms.
• Contrasts with traditional III–V and II–VI quantum well microcavities, where operation is strictly limited to cryogenic temperatures due to melting of excitons.
• Scalability to complex potential landscapes (e.g., higher-order topology, driven–dissipative lattices) by arbitrary FIB patterning and flexible organic film encapsulation.
• Modes are robust against moderate disorder and temperature-induced broadening, as the topological gap far exceeds both condensed and linear-regime linewidths.

7. Generalization to Other Room-Temperature Polaritonic Platforms

The principles applied here—large vacuum Rabi splitting, engineered tight-binding lattices, real-space and momentum-resolved spectroscopy, and topological band engineering—are directly extensible to diverse architectures including:

• 2D honeycomb (“graphene”) and higher-order topological lattices (Betzold et al., 18 Jan 2024, Bennenhei et al., 11 Jan 2024);
• Zero-dimensional polariton “molecules” and tight-binding arrays (Urbonas et al., 2019);
• Wide-bandgap semiconductor and hybrid perovskite cavities for constructive comparisons of materials-dependent figures of merit (Guillet et al., 2016, Struve et al., 24 Aug 2024).

Room-temperature polariton spectroscopy thus establishes a framework for the direct, in situ investigation of many-body, nonlinear, and topological photonic states, enabling the fabrication and interrogation of practical polaritonic devices and simulators operable under ambient conditions (Dusel et al., 2020).