Spin-to-polarization mapping with a coherent quantum dot-cavity receiver

AI summary

Overview

Research area: Quantum photonics — coherent light-matter interfaces, specifically spin-photon interfaces using semiconductor quantum dots (QDs) embedded in micropillar cavities.

Technical level: Advanced. The paper assumes familiarity with quantum optics, Stokes vectors/Poincaré sphere formalism, cavity quantum electrodynamics, and time-correlated single-photon measurements.

Scope (1 sentence): This paper reports an experimental demonstration that the polarization of a single photon reflected from a charged quantum-dot–cavity device is bijectively linked to the resident electron spin state, achieving 95 ± 2 % spin projection fidelity with a single reflected photon detection.

What This Paper Is About

Coherent quantum receivers — devices that deterministically rotate a photon's quantum state depending on the state of a stationary qubit — are a building block for deterministic entangling gates and photon-photon gates. Such gates require a one-to-one (bijective) mapping between orthogonal photonic polarization states and orthogonal spin states. The authors use the spin-dependent Kerr rotation of a negatively charged InGaAs quantum dot in an AlGaAs micropillar cavity to experimentally evidence this mapping, projecting the electron spin into an eigenstate by detecting one reflected photon and then reading out the subsequent spin relaxation with a second reflected photon.

Key Contributions

1. Experimental signature of a bijective spin-to-polarization mapping. The authors show that detecting a single reflected photon in a chosen polarization basis projects the resident electron spin, with conditional probabilities P↑|φ↑ = 95 ± 2 % and P↓|φ↑ = 3 ± 2 % for the optimal basis.
2. A time-resolved, two-photon conditional tomography protocol. Using two polarimeters and time-correlated single-photon detection, they measure the conditional Stokes parameter s_φφ̄|φ(τ) as a function of the delay between two successive reflected photons, transferring spin relaxation dynamics onto the polarization of the second photon.
3. Identification of the timescales limiting the interface. They separate a transient regime governed by the trion radiative lifetime T1(rad) = 200 ± 20 ps from spin relaxation (T1(spin) = 1.9 ± 0.2 ns) and charge co-tunneling (τ_esc = 4.1 ± 0.2 ns), showing that spin projection features are read for τ ≳ 1 ns.
4. Device characterization and modeling. They report cavity quality factors Q_H = 7400 and Q_V = 6900, cooperativities C_H = 1.4 ± 0.2 and C_V = 1.3 ± 0.2, and support all data with numerical simulations including optical pure dephasing, electron hyperfine interaction, and charge co-tunneling, plus an analytical semiclassical description.

Main Findings

• Spin projection fidelity: A single reflected photon detection projects the electron spin with 95 ± 2 % fidelity onto one eigenstate (P↑|φ↑ = 95 ± 2 %, P↓|φ↑ = 3 ± 2 %), corresponding to a simulated spin population imbalance ⟨σ̂_z⟩|φ↑(0) = 0.94 ± 0.02 and a conditional charge occupation P_charge|φ↑ = 98 ± 2 %.
• Measurement-dependent response: For a basis rotated by 87° from optimal (φ = φ↑ − 87° = −15°), the spin remains nearly mixed, with P↑|φ = 51 ± 2 % and P↓|φ = 47 ± 2 %, demonstrating that the effect is genuinely measurement-induced rather than a device artifact.
• Conditional Stokes parameter reaches ≈ 0.7: After the transient regime, s_φφ̄|φ ≈ 0.7 for φ = φ↑, whereas it remains ≈ 0 for φ = φ↑ − 87°, directly evidencing efficient spin projection.
• Transient regime: The coherent optical response requires a build-up time governed by T1(rad) = 200 ± 20 ps after a photon detection abruptly modifies the density matrix; a fully coherent response requires the dipoles of both optical transitions to oscillate at the laser frequency under monochromatic CW excitation.
• Spin relaxation timescale: s_φφ̄|φ decays to zero and partially recovers, consistent with spin relaxation via the Overhauser field with T1(spin) = 1.9 ± 0.2 ns, before fully decaying at τ ∼ 10 ns due to charge co-tunneling with escape time τ_esc = 4.1 ± 0.2 ns.
• Optimal operating point: The optimal positive detuning used is Δω_opt/2π = 0.14 GHz, where the average Stokes parameter s_HV(avg) = 0 and the spin-dependent polarization states are predicted to be orthogonal; it is chosen over the negative-detuning solution because it is closer to resonance with the H cavity mode and gives higher count rates.
• Two orthogonal conditional polarization states: For delays τ ≳ 1 ns, conditional Stokes parameters s_DA|φ1 and s_RL|φ1 for the two heralding bases (φ1 = 56°, φ̄1 = 236°) are almost opposed, the signature of spin-dependent polarization rotation — the spin-to-polarization mapping. (The provided text is truncated mid-sentence at this point, so the quantitative purity and relative-angle values of Fig. 4c are not reported in the available content.)
• Residual imperfections: The residual probability of the wrong spin state is attributed to incoherent processes (pure dephasing and electron hyperfine interaction) that broaden the optical transition and average the S↑ and S↓ Stokes vectors, so that the ideal condition S↑ = −S↓ with |S↑| = |S↓| = 1 is not perfectly met.
• Charge occupation: Charge co-tunneling yields a non-unity stationary charge occupation P_charge = 0.96 ± 0.02 (96 ± 2 %).

Methodology in Plain English

The team uses a single negatively charged InGaAs quantum dot, emitting at 925 nm, grown inside an AlGaAs micropillar cavity that supports two slightly birefringent, orthogonally polarized modes (H and V). Because the cavity's birefringence is small, polarization qubits can be used directly without extra correction.

An H-polarized continuous-wave laser, tuned in the low-power regime and detuned from the dot's resonance, is focused onto the device inside a cryostat at 4 K. The light reflected from the micropillar is a superposition of light bouncing directly off the top mirror and light that interacted with the dot. Which superposition you get depends on the electron spin state — this is the spin-dependent Kerr rotation.

To prove the mapping, the reflected beam is split between two polarimeters. The first one detects a photon in a chosen polarization basis; that detection "heralds" (projects) the spin. The second polarimeter then performs full polarization tomography (in the H/V, D/A, and R/L bases) on a later photon, delayed by a controlled time τ. Correlation electronics record coincidences, allowing the conditional probabilities P_φ|φ(τ) and P_φ̄|φ(τ), and hence the conditional Stokes parameter s_φφ̄|φ(τ), to be extracted. Data are compared against numerical simulations that include optical pure dephasing, hyperfine interaction, and charge co-tunneling, using a single parameter set.

Why This Matters

Impact on research: The work provides the first direct experimental evidence of a one-to-one spin-to-polarization mapping in a solid-state cavity device, a prerequisite for deterministic photon-photon gates. It also establishes time-resolved conditional tomography as a tool for diagnosing spin-photon interfaces, and it identifies the specific competing timescales (radiative lifetime vs. spin relaxation vs. charge co-tunneling) that currently limit performance with electron spins.

Real-world applications (bullets):

• Deterministic entangling and photon-photon gates for gate-based photonic quantum computing.
• Deterministic generation of entangled resource states for measurement-based quantum computing.
• Quantum memories and remote spin-photon entanglement for quantum repeaters and networks.
• Spin-photon gates and small-scale quantum processors built from scalable solid-state spin-photon interfaces.

Industry relevance: The author list includes an affiliation with Quandela (Massy, France), a photonic quantum computing company, indicating direct industrial interest in deterministic spin-photon gates and scalable semiconductor-based photonic hardware. The device platform — deterministically fabricated QD-micropillar cavities — is compatible with semiconductor manufacturing, and the finding that hole spins could relax more slowly offers a concrete engineering route to higher-performance receivers.

Future Directions

• Switch to hole spins: The authors explicitly propose using hole spins, which display increased relaxation times, to relieve the competition between electron spin relaxation and the trion radiative lifetime that currently limits the results.
• Push toward true orthogonality: Improve the device (for instance via higher cooperativity or reduced dephasing) so that S↑ = −S↓ with unit-length Stokes vectors, maximizing the purity of the conditional polarization states.
• Reduce charge co-tunneling and dephasing: Charge co-tunneling (τ_esc = 4.1 ± 0.2 ns) and the resulting non-unity charge occupation (96 ± 2 %) truncate the useful time window; improving charge stability would extend it.
• Demonstrate deterministic logic gates: The stated goal is to exploit this one-to-one mapping to implement deterministic spin-photon and multi-photon gates, which remains to be shown experimentally.

Target Audience

Researchers and graduate students in quantum photonics, cavity QED, and semiconductor quantum-dot physics; engineers developing spin-photon interfaces for quantum computing and quantum networking; and technical readers interested in the practical limits (radiative lifetime, hyperfine-induced spin relaxation, charge co-tunneling) on solid-state coherent quantum receivers.

Authors’ abstract

Coherent light-matter interfaces controllably modifying the state of a photon upon interaction with a stationary qubit are a key resource for implementing deterministic entangling gates for optical quantum technologies. This requires a one-to-one mapping between the state of the scattered photon and that of the embedded qubit. Here, we present an experimental signature of such a bijection by leveraging the spin-induced Kerr rotation present in a low-noise charged quantum dot-micropillar cavity device. Through time-resolved polarization measurements, we project the electron spin to one of its eigenstates with $95\pm2\%$ fidelity with a single reflected photon detection, and follow the subsequent spin relaxation through the detection of a second reflected photon. We demonstrate that, after a transient regime governed by the trion radiative lifetime, two orthogonal polarization states can be produced, each associated to a given spin eigenstate. While the current results are limited by a timescale competition between electron spin relaxation and trion radiative lifetime, they could be improved using hole spins displaying increased relaxation times. Our work paves the way towards deterministic logic gates exploiting this one-to-one mapping between a spin and the polarization of a scattered photon.