Collective radiance in degenerate quantum matter: interplay of exchange statistics and spatial confinement

Abstract

Collective radiance in quantum degenerate systems is shaped by the interplay of spatial confinement and exchange statistics. We investigate this interplay using a purely dissipative field theoretic quartic Lindblad master equation, which captures the nonlinear dynamics of the combined motional and electronic manifolds. Our framework maps the crossover between the permutational symmetry of the trap and the exchange symmetry of the particles, quantifying how bosonic enhancement and Pauli blocking dictate superradiant and subradiant scaling. We identify two distinct routes to distinguishable dynamics: thermal dilution of the initial state at high temperatures and the dynamical breakdown of collective order via recoil induced transport in soft traps. This analysis provides a benchmark for collective emission in quantum-degenerate atomic systems with coupled motional and internal dynamics, such as optical lattice clocks and spinor gases, when dissipation is engineered to control recoil and motional heating.

Figures (8)

• Figure 1: Illustration of the model and symmetry competition in quantum gases: a) Dual species degenerate Bose and Fermi gases in a 1-dimensional harmonic trap. b) Illustration of the influence of particle statistics on the dissipation process. While for bosons the decay of an excited particle into a level already occupied by a ground particle is enhanced, it is forbidden for fermions by the Pauli-exclusion principle. c) Illustration of the non-Hermitian Hamiltonian, where an excited particle and a ground particle exchange a photon, resulting in a change in the electronic and motional degrees of freedom. d) Symmetry of particle exchange diminishes as temperature is increased (for simplicity, only illustrated for fermions). e) Permutational symmetry of the Lindbladian decreases as the trap width is increased.
• Figure 2: Thermal crossover from quantum-statistical to distinguishable radiance: (a--c) Instantaneous intensity $I(0)$ for $\mathcal{N}=12$ (Bosons: blue; Fermions: orange). At $T=0$ (a), bosons follow quadratic Dicke scaling while fermions exhibit subradiant suppression, with a larger slope after $\mathcal{N}^{(e)}/\mathcal{N}=1/2$. Increasing temperature (b--c) drives the system toward the linear distinguishable limit (black line) as motional level co-occupation is diluted. (d--f) Time evolution $I(t)$ for inversions $1/4$ ($\bigcirc$), $3/4$ ($\square$), and $1$ (origin=c]45$\square$). A superradiant burst requires $\mathcal{N}^{(e)} > \mathcal{N}/2$ (above the Bloch sphere equator), occurring here for $\mathcal{N}^{(e)}=3\mathcal{N}/4$. At full inversion ($\mathcal{N}^{(e)}=\mathcal{N}$), dynamics are initially independent of statistics.
• Figure 3: Mapping quantum statistics to collective spin shells. a) At full inversion ($\mathcal{N}^{(e)}=\mathcal{N}$), all particles occupy a unique non-degenerate state; dynamics are restricted to the fully symmetric Dicke subspace ($S=\mathcal{N}/2$) regardless of statistics or temperature. b) At $T=0$, bosons (blue) remain in the $S=\mathcal{N}/2$ shell. Fermions (orange) occupy a reduced spin shell $S=|\mathcal{N}^{(e)} - \mathcal{N}^{(g)}|/2$ because fully filled lower levels form spin-singlets. c) At finite temperature, a thermal state contains a mixture of population across multiple spin shells. In the high-temperature limit ($k_\textrm{B} T \gg \hbar\nu$), the spin-shell distributions for bosons and fermions converge as exchange symmetry becomes irrelevant.
• Figure 4: Thermal crossover of collective spin and radiance. (a) Collective spin length $\langle S^2 \rangle$ vs. temperature for $N=40$ (Bosons: blue; Fermions: orange). Statistical effects vanish at $k_B T \gg \hbar\nu$, where both species converge to the distinguishable limit (horizontal lines) obtained from Eqs. \ref{['eq:CGs_infty']},\ref{['eq:S^2_dist']}. Due to symmetry, results are invariant under $\mathcal{N}^{(e)} \leftrightarrow \mathcal{N}^{(g)}$. (b) Time-dependent intensity $I(t)$ for varying inversions and temperatures for bosons (top) and fermions (bottom). Dynamics converge to the distinguishable limit (black) from above (bosons) or below (fermions). (c--d) Residual excitations and peak intensity as a function of $T$ and $\mathcal{N}^{(e)}$. At high temperatures, observables become species-independent as level co-occupation is suppressed. Calculations use $10^5$ thermal state samples per point and $\mathcal{N} = 40$.
• Figure 5: Weakening of collective radiance in the Lamb-Dicke regime. a),b) Bosons at $T=0$: Increasing the trap width $\eta$ monotonically reduces the instantaneous intensity [Eq. \ref{['eq:inst_int_bose_lamb_dicke']}] and suppresses the superradiant burst. c),d) Fermions at $T=0$: The instantaneous intensity remains largely invariant with $\eta$, except near half-excitation (see inset), confirming Eq. \ref{['eq:int_inst_fermi_lamb_dicke']}. Below half-excitation ($\mathcal{N}^{(e)} < \mathcal{N}/2$), dynamics are frozen; at $\mathcal{N}^{(e)} = \mathcal{N}/2$, dynamics are highly subradiant but follow the analytical small-$\eta$ limit. Above half-excitation, the superradiant burst intensity diminishes with $\eta$. Inset d): Peak intensity vs. $\eta$ for full inversion, normalized to the $\eta=0$ limit. The numerical simulations in c),d) are performed for $\mathcal{N} = 8$ particles and include processes up to $\eta^6$. In e,f) we show how the scaling of the superradiant burst as a function of $\eta$ and for different particle numbers. While for bosons the peak intensity reduces as $\eta^2$, for fermions it reduces as $\mathcal{N}\eta^2$. The solid lines are the mean-field result from the main text. To isolate leading order effects, the simulations in e),f) only include processes up to $\eta^2$.