Efficient optical cat state generation using squeezed few-photon superposition states

Optical Schrödinger cat states are non-Gaussian states with applications in quantum technologies, such as for building error-correcting states in quantum computing. Yet the efficient generation of high-fidelity optical Schrödinger cat states is an outstanding problem in quantum optics. Here, we propose using squeezed superpositions of zero and two photons, $|θ\rangle = \cos{(θ/2)}|0\rangle + \sin{(θ/2)}|2\rangle$, as ingredients for protocols to efficiently generate high-fidelity cat states. We present a protocol using linear optics with success probability $P\gtrsim 50%$ that can generate cat states of size $|α|^2=5$ with fidelity $F>0.99$. The protocol relies only on detecting single photons and is remarkably tolerant of loss, with $2%$ detection loss still achieving $F>0.98$ for cats with $|α|^2=5$. We also show that squeezed $θ$ states are ideal candidates for nonlinear photon subtraction using a two-level system with near deterministic success probability and fidelity $F>0.98$ for cat states of size $|α|^2=5$. Schemes for generating $θ$ states using quantum emitters are also presented. Our protocols can be implemented with current state-of-the-art quantum optics experiments.

💡 Research Summary

The paper addresses the long‑standing challenge of generating high‑fidelity, large‑amplitude optical Schrödinger cat states, which are essential non‑Gaussian resources for photonic quantum computing and for preparing error‑correcting states such as the Gottesman‑Kitaev‑Preskill (GKP) code. Traditional approaches rely on photon subtraction from squeezed vacuum or on strong optical nonlinearities; both suffer from low heralding probabilities and extreme sensitivity to loss.

The authors propose a new class of resource states, the “θ‑states”, defined as a superposition of vacuum and a two‑photon Fock component, |θ⟩ = cos(θ/2)|0⟩ + sin(θ/2)|2⟩, which can be deterministically prepared using modern quantum emitters (quantum dots, atoms in cavities, NV centers, etc.). By applying moderate squeezing (up to ≈10 dB) to these states, they obtain squeezed θ‑states |r, θ⟩ = S(r)|θ⟩ that possess a higher stellar rank than squeezed two‑photon Fock inputs, giving them richer non‑Gaussian structure while preserving photon‑number parity.

Two distinct cat‑generation protocols are presented:

1. Linear photon‑subtraction scheme (Fig. 1a). Two squeezed θ‑states, characterized by parameters (r₁, θ₁) and (r₂, θ₂), are interfered on a beam‑splitter with transmissivity cos γ. A single‑photon detection in one output heralds a squeezed cat state in the other output, which can be unsqueezed if desired. Global optimization over r₁, r₂, θ₁, θ₂, γ and the final unsqueezing strength yields cat states with |α|² in the range 2–6, success probabilities P_suc≈0.43–0.53 and fidelities F≥0.99 for |α|²≤5.4. The scheme remains robust under realistic detector inefficiency (ε = 0.98, i.e., 2 % loss), still achieving F > 0.98 for |α|²≤4, a marked improvement over previous multi‑stage subtraction protocols.

2. Non‑linear photon‑subtraction scheme (Fig. 1b). A single squeezed θ‑state |r, θ_max⟩ is launched into a waveguide chirally coupled to a two‑level system (TLS). The TLS scatters the pulse, producing a dominant output mode (the prospective cat) and an orthogonal mode containing a single photon. Detection of that photon heralds the cat. The authors model the scattering using a Born‑Markov Hamiltonian and discretized input‑output theory, solving the dynamics with matrix‑product‑state (MPS) techniques. The optimal θ_max(r) = π − arctan