Cavity Polariton & Bipolariton States

• Cavity polariton and bipolariton states are hybrid quasiparticles formed by strong coupling between cavity photons and excitons.
• Resonant mechanisms like the Feshbach resonance enhance polariton–polariton interactions, enabling phenomena such as photon blockade.
• These states underpin applications in quantum nonlinear optics and solid-state devices, with spatial confinement refining their interaction dynamics.

Cavity polaritons and bipolaritons are hybrid quasiparticles arising from the strong coupling between electromagnetic cavity modes and matter excitations, most notably excitons. Their properties, interactions, and effective Hamiltonians underpin a range of nonlinear optical phenomena, quantum many-body effects, and device applications in both solid-state and atomic systems. Bipolaritons, typically associated with bound pairs of polaritons or resonantly accessed biexciton states, introduce a new layer of correlated dynamics that is central to quantum nonlinear optics and strongly correlated light–matter platforms.

1. Fundamental Principles of Cavity Polariton and Bipolariton States

Cavity polaritons result from the diagonalization of a Hamiltonian that couples a photonic field mode with a matter excitation (such as a quantum well exciton, atomic excitation, or a collective superconducting mode). The generic Hamiltonian for an exciton–photon system is given by

$$H = \sum_k \left[\omega_{\mathrm{ex}} b_k^\dagger b_k + \omega_{\mathrm{cav}} a_k^\dagger a_k + g\left(a_k^\dagger b_k + b_k^\dagger a_k\right)\right],$$

where $a_k$ and $b_k$ denote photon and matter excitation operators, and $g$ is the coupling rate. Diagonalization yields upper and lower polariton branches with anticrossing energy splitting proportional to $g$.

Bipolariton states arise under conditions where two-particle (pair or bound) interactions become resonant or long-lived due to the presence of additional bound states, such as biexcitons (bound states of two excitons). Inter-polariton interactions can be enhanced via mechanisms such as Feshbach resonance—where the energy of a two-polariton state is tuned into resonance with a biexciton (Carusotto et al., 2010).

2. Resonantly Enhanced Nonlinearity: The Polariton–Biexciton Feshbach Blockade

A pivotal regime for achieving strong polariton–polariton interactions is when the two-polariton state is tuned into resonance with a biexciton. The Hamiltonian includes terms allowing two lower-branch polaritons ($\Psi_{\mathrm{LP},\sigma}$) to convert into a biexciton ($\Psi_{B}$), with coupling strength set by the Rabi frequency, Hopfield coefficients, and the biexciton wavefunction overlap: $$H_{\mathrm{BXC}} = \frac{1}{2} \sum_{\sigma= \uparrow, \downarrow} \int d^2 r_1 d^2 r_2 \left[ \left( \frac{\hbar \Omega_R}{a_B}\right) u_{LP}^X u_{LP}^C h(r/a_B) \Psi_B^\dagger(R) \Psi_{LP,\sigma}(R-r/2) \Psi_{LP,-\sigma}(R+r/2) + \mathrm{h.c.} \right].$$ The effective two-polariton scattering is captured by a T-matrix of resonant form: $$T_{\uparrow \downarrow}(E) = \frac{|\tilde{g}|^2}{E - E_B^o + \Delta_\mathrm{rad}(E) + i \Gamma_{\mathrm{rad}}/2},$$ where the resonance denominator is minimized when $2E_{LP} \approx E_B$, dramatically enhancing interactions. This leads to a polariton blockade regime analogous to photon blockade in cavity QED: occupation of the first polariton mode shifts the energy ladder out of resonance for subsequent excitations, enabling antibunched photon (non-classical light) emission (Carusotto et al., 2010).

The presence of a Feshbach resonance is directly analogous to ultracold atom physics but realized in a solid-state context. Notably, the strength of the Kerr nonlinearity can exceed the polariton linewidth, making this regime highly viable for quantum nonlinear optics and single-photon devices.

3. Spatially Confined and Defect-Bound Polaritons

In planar microcavities, natural defects—such as point-like Ga droplet inclusions or misfit dislocations—create lateral modulation of the polariton potential landscape, with depth/height on the order of 10–15 meV (Zajac et al., 2011). Polaritons localized by these potential minima form discrete bound states with well-resolved s-, p-, d-like spatial modes, as verified via spectrally resolved transmission imaging in both real and reciprocal (k) space.

Key attributes:

• Defect-bound polaritons exhibit long lifetimes (~10 ps), attributed to the smoothness of the confining potential, which suppresses high-k scattering losses.
• Theoretical modeling reconstructs the effective potential via the local density of bound wavefunctions,

$$V_m(r) = - D_m(r)/D_{2D}, \quad D_{2D} = m/(2\pi \hbar^2),$$

where $D_m(r) = \sum_n |\Psi_n(r)|^2$.

• The analogy to Feshbach resonances extends: discrete states embedded in the continuum may participate in resonant scattering, offering a pathway to paper confined bipolariton formation and potential engineering for polaritonic device arrays.

4. Theoretical Descriptions and Effective Hamiltonians

The resonant enhancement of polariton–polariton interactions via biexcitons modifies the excitation ladder. In “polariton dots,” where photonic modes are zero-dimensional, the simplified effective Hamiltonian reduces to

$$H = E_{LP} a^\dagger a + E_B b^\dagger b + \frac{V}{2} a^\dagger a^\dagger a a + G (b^\dagger a a + a^\dagger a^\dagger b).$$

Here $G$ encodes the Feshbach-enhanced resonant nonlinearity, while $V$ is the background (non-resonant) interaction. The coupling $G$ splits the two-polariton state into doublets with splitting $\sim \sqrt{2}G$, yielding strong anharmonicity and enabling photon blockade.

Resonant T-matrix formalism captures the energy-dependent scattering processes: $$T_{\uparrow \downarrow}(E) = \frac{|\tilde{g}|^2}{E-E_B^o+ (M_{LP}|\tilde{g}|^2/(4\pi \hbar^2))\log(E_{\mathrm{max}}/E) + i (M_{LP}|\tilde{g}|^2/(4\hbar^2))}.$$

5. Experimental Realizations and Engineering Considerations

Experimental progress encompasses both large-area planar microcavities—where bound polariton states originate from natural defects—and nanostructured “polariton dots” that realize isolated mode ladders. Key factors include:

• Strong exciton–photon coupling (vacuum Rabi splitting greater than system losses) is essential.
• Sharp control over cavity length or photonic confinement tunes polariton energy and facilitates access to resonance with biexcitonic states.
• Spectroscopic signatures: nonlinear shifts of photoluminescence, splitting of resonance peaks at the two-polariton level, and photon antibunching statistics provide evidence of strong nonlinearities and polariton blockade (Carusotto et al., 2010).

These systems have implications for single-photon sources, deterministic quantum gates, and observation of non-classical light in semiconductor environments.

6. Broader Implications for Nonlinear Quantum Optics and Many-Body Physics

Resonant coupling to biexciton (bipolariton) states provides tunable, strong effective interactions between polaritons, opening up new regimes of quantum nonlinear optics unattainable in cavity QED with bare atoms or uncoupled excitonic states. The ability to transition between weakly and strongly interacting light–matter regimes by cavity tuning has ramifications for:

• Quantum simulation of strongly correlated photonic systems.
• Formation and control of many-body polariton states and their quantum statistics.
• Realization of robust non-classical light sources and the exploration of nonequilibrium many-body effects (blockade ladders, photon crystallization, etc.).
• Exploration of hybrid excitations where coupled confined polariton and biexciton states may provide longer coherence times (e.g., via defect-bound or spatially engineered potentials) or enhance nonlinearity.

Collectively, the Feshbach-resonance-based polariton–bipolariton coupling mechanism and its realization in confined and spatially modulated microcavities serve as building blocks for next-generation quantum optoelectronic platforms and deepen understanding of collective light–matter hybridization in the solid state.