Deterministic single-photon source over the terahertz regime

TL;DR

This work proposes a deterministic terahertz (THz) single-photon source based on optically dressed polar quantum emitters coupled to a hybrid THz cavity, triggered by a pair of coherent optical pulses. The scheme leverages permanent dipole moments to enable THz transitions between laser-dressed states and employs Purcell enhancement to achieve on-demand emission with high brightness, purity, and indistinguishability, while providing tunability across the THz band. Analytical expressions for the maximum single-photon probability and its optimal pulse timing are derived as functions of the effective cooperativity $\tilde{C}$ and dressing ratio $h$, complemented by an efficient Liouvillian-spectral-decomposition framework for fast computation of time-integrated correlators and heralding efficiencies. The study also analyzes realistic pulse shapes, heralding strategies, and the impact of decoherence (thermal effects and pure dephasing), outlining practical operating regimes and highlighting the potential of THz quantum optics with dressed polar emitters for future quantum technologies.

Abstract

We propose a deterministic single-photon source in the terahertz (THz) regime, triggered by a sequence of coherent optical pulses. The scheme leverages the permanent dipole moment of a single-polar quantum emitter to induce THz transitions between optically dressed states, enhanced by a resonant coupling to a hybrid THz cavity. We present a cavity design that delivers high efficiency, purity, and indistinguishability while also enabling easy tunability of the emission frequency across the THz range. A key challenge in this new class of dressed-state sources is that, unlike standard solid-state single-photon sources, the dressed nature of the transitions can lead to undesired optical repumping during emission due to spontaneous photon emission in the visible range, which reduces the purity of the THz single-photon state. We show that this issue can be mitigated through optimized pulse areas and a sufficiently high Purcell rate, criteria that are met by our proposed cavity design. Finally, we demonstrate the significant purity enhancement of postselected THz photons by means of optical heralding, illustrating the new opportunities unlocked by the unique integration of terahertz and visible technologies with dressed polar quantum emitters.

Figures (12)

• Figure 1: (a) Electric field cross-section simulation and sketch (b) of a potential experimental implementation of a deterministic single photon THz source consisting of a quantum emitter held in a hybrid nanocavity made up by two GaP nanocones (length $11.07~\mu\text{m}$, tip radius $0.39~\mu\text{m}$, bottom radius $2.37~\mu\text{m}$) separated by 50nm, both embedded within a Fabry-Pérot resonator which is triggered by the initialization and activation pulse protocols in the visible (green and blue areas). (c) Spectral density simulations of three different frequency-detuned hybrid cavities with lengths $\{L_1,L_2,L_3\} = \{108.9~\mu\text{m}, 74.7~\mu\text{m}, 63.4~\mu\text{m}\}$. (d): Temporal evolution of the population of $|+\rangle$ during the first two pulses, including trajectory on the Bloch sphere. The first pulse (green section) populates $|+\rangle$ and the second enables the decay of the TLS from $|+\rangle$ to $|-\rangle$ by generating the THz splitting and enabling the transition (red section).
• Figure 2: $P_1(\tau)$ obtained numerically (solid red) and analytically (brown diamonds), and heralding efficiency $E(\tau)$ (blue circles) versus activation pulse time $\tau$. (a) Cavity design with $L_1 =108.9\,\mu\text{m}$: $\chi/2\pi = 4\,\text{GHz}$, $\kappa/2\pi = 3.5\,\text{GHz}$, $\omega_c/2\pi = \Omega_R/2\pi = 3078.6\,\text{THz}$, $\gamma/2\pi = 39.79\,\text{MHz}$, and $\Omega/2\pi = 0.2\,\text{THz}$, corresponding to $h= 0.0325$ and $\tilde{C} = 1.94$. (b) Cavity design with length $L_3 =63.4\,\mu\text{m}$: $\chi/2\pi = 12.5\,\text{GHz}$, $\kappa/2\pi = 0.974\,\text{GHz}$, $\omega_c/2\pi = \Omega_R/2\pi = 5.1169\,\text{THz}$, $\Omega/2\pi = 0.2\,\text{THz}$, corresponding to $h= 0.01955$ and $\tilde{C} = 24.65$. The maximum efficiency obtained are (a) $P_1(\tau_\text{max})=0.67$ and (b) $P_1(\tau_\text{max})=0.90$.
• Figure 3: Maximum single-photon detection probability $P_\text{max}$ (solid red), optimal activation pulse duration $\tau_\text{max}$ (dashed blue), and their corresponding analytical estimates (dashed black for $P_\text{max}$ and dash-dotted black for $\tau_\text{max}$), alonsgside the indistinguishability $I(\tau_\text{max})$ (black crosses), plotted as functions of: (a) cooperativity $C$, varied via $\chi=\sqrt{C\kappa\gamma/4}$; (b) Dressing ratio $h$, varied via the detuning $\Delta$. Both sweeps effectively modify $\tilde{C}$ (upper axes). The parameters correspond to cavity length $L_1$, i.e., $\kappa/2\pi = 3.5\,\text{GHz}$ and $\Omega_R/2\pi =3.078\,\text{THz}$. In (a), we set $\Omega/2\pi \approx 0.2\,\text{THz}$, corresponding to $h\approx 0.0325$. In (b), we set $\chi/2\pi = 4\, \text{GHz}$.
• Figure S1: Single-photon probability for a near-resonant drive $\Omega \sim \Omega_R$. The numerically computed single-photon probability $P_1(\tau)$ (solid red) is shown alongside the analytical prediction (dotted black) and the numerical probabilities of detecting zero photons $P_0(\tau)$ (dashed blue) and more than one photon $P_{>1}(\tau)$ (dash-dotted green), for the parameter set $\chi/2\pi = 12.5\,\text{GHz}$, $\kappa/2\pi = 0.974\,\text{GHz}$, $\gamma/2\pi = 39.78\,\text{GHz}$, $\Omega/2\pi = 4\,\text{THz}$, $\Delta/2\pi = 3.19\,\text{THz}$, and $\omega_c/2\pi = 5.116\,\text{THz}$.
• Figure S2: Single-photon probability for different initial states. Maximum single-photon detection probability $P_\text{max}$, obtained numerically (solid red) as a function of the detuning $\Delta$ for the parameter set $\{\chi,\kappa,\gamma,\Omega,\Omega_R\}/2\pi=\{4,3.5,39.78,0.2,3078\}$ GHz. The dashed blue line in the bottom plot represents the situation where the initial state is $|g\rangle$.