Single-qubit detection by collective phase imprinting

AI summary

Overview

Research area: Experimental neutral-atom quantum physics — Rydberg atoms, optical tweezers/optical lattices, and quantum measurement.

Technical level: Advanced. The paper assumes familiarity with Rydberg dressing, AC-Stark shifts, Ramsey interferometry, and hyperfine state encoding.

Scope in one sentence: The paper demonstrates that a single Rydberg-encoded control qubit can imprint a controllable collective phase on up to eight surrounding ground-state atoms in an optical lattice, and uses this effect to detect the control qubit's Rydberg state non-destructively with a state-assignment fidelity of ℱ = 99.81^{+0.17}_{-1.47} %.

What This Paper Is About

Reading out a single qubit is hard because the information is carried by one atom, so any measurement signal is tiny. The authors solve this by coupling one control atom (encoded in the ground-to-Rydberg transition of ⁸⁷Rb) to a small ensemble of neighbouring atoms that has been "Rydberg-dressed" — weakly admixed with a Rydberg state — so that the control atom's state switches the phase evolution of every ensemble atom at once. The ensemble's collective response then amplifies a single-qubit signal while remaining insensitive to how many ensemble atoms are actually present.

Key Contributions

1. A new coupling platform. A single control qubit (ground state |g⟩ ↔ Rydberg state |S⟩ = |36S₁/₂, m_J = −1/2⟩) is coupled to a Rydberg-dressed target ensemble in a 3 × 3 array of ⁸⁷Rb atoms with lattice spacing a_lat = 752 nm, without requiring programmable gates or native long-range interactions between separate species.
2. A qubit-controlled collective phase shift. The control atom's state switches the target atoms' AC-Stark shift from δ_g = 2π × 578(4) kHz (control in |g⟩) down to δ_S ≈ 2π × 9.8 kHz (control in |S⟩), producing a sharp change in Ramsey fringe contrast that encodes the control state.
3. Intrinsic robustness to atom number and atom loss. Because the per-target phase shift is independent of ensemble size, the dynamics are equivalent for N = 8 and N = 4 target spins: fitted precession rates of 2π × 564(4) kHz and 2π × 569(6) kHz agree within uncertainties.
4. Non-destructive single-Rydberg-excitation detection. Using a modified Ramsey sequence with a final phase of π (θ_R = 3π/2) and a detection threshold of ≥ 3 target spins, the authors report a background-free Rydberg-state assignment fidelity of ℱ = 99.81^{+0.17}_{-1.47} %.

Main Findings

• Measured controlled phase: The AC-Stark shift with the control in |g⟩ was measured as δ_g = 2π × 578(4) kHz, in reasonable agreement with the theoretical value δ_g^theory = 2π × 670 kHz.
• Strong suppression with the control excited: With the control in |S⟩, the shift collapses to δ_S ≈ 2π × 9.8 kHz, so the target phase remains negligible for probe times below 3 µs.
• Distance dependence follows Rydberg pair potentials: Fixing the Ramsey phase at φ = π, the target population in |0⟩ rises monotonically with control–target separation, consistent with the ∝ 1/r³ scaling of the |S⟩–|P⟩ interaction; beyond approximately four lattice sites the interaction is negligible relative to the dressing detuning.
• Number-insensitive phase imprinting: Fitted precession rates of 2π × 564(4) kHz (N = 8) and 2π × 569(6) kHz (N = 4, with the four diagonal target spins removed) agree within fit uncertainties, confirming negligible interactions among target spins.
• Higher-order effects are small: Fourth-order corrections to the AC-Stark shift amount to only ∼2 % of the total phase shift, and the spatial variation of δ_g across individual target spins is approximately 3 % for both the 8- and 4-spin configurations.
• Coherent transfer verified: Rabi oscillations of the control spin measured by Rydberg-induced atom loss give Ω_S = 2π × 4.45(6) MHz; the target ensemble's collective response oscillates at 2π × 4.48(5) MHz, tracking the control drive.
• Two detection modes compared: With only a θ_R = π/2 final pulse, overlapping histograms (peaks at 6–8 spins for |g⟩_C, 0–1 spins for |S⟩_C) give an upper bound of ℱ ≲ 93 %. The inverted logic (θ_R = 3π/2) confines signal and preparation error to 0–1 spins and enables the 99.81 % figure.
• Atom loss is characterised: Off-resonant coupling to 36P₁/₂ causes loss of 0.03(2) atoms/µs with the control in |g⟩ and 0.07(1) atoms/µs with the control in |S⟩, the increase attributed to additional decay channels opened by |S⟩–|P⟩ interactions.
• Entanglement verification is not performed: The authors note that confirming the GHZ-like state 1/√2(|g⟩_C|0⟩_T^⊗N + |S⟩_C|1⟩_T^⊗N) is beyond the present work, because the spin-selective push-out readout precludes simultaneous detection of both subsystems.

Methodology in Plain English

The team starts with a near unity-filled two-dimensional array of about 100 ⁸⁷Rb atoms held in the motional ground state of a three-dimensional optical lattice. Using single-site addressing, they carve out a 3 × 3 block of nine atoms, with the central atom as the control and the eight surrounding atoms as targets. A magnetic field of B = 30.32 G sets the quantization axis; the control is prepared in |g⟩ = |F = 2, m_F = −2⟩ and the targets in |0⟩ = |F = 1, m_F = −1⟩.

The targets are then weakly coupled to Rydberg P states with laser light far from resonance (detunings Δ₋ = 2π × 40 MHz and Δ₊ = 2π × 11.88 MHz, Rabi frequencies Ω_P₋ = 2π × 7.11(1) MHz and Ω_P₊ = Ω_P₋/√3). This "dressing" shifts the energy of state |0⟩ but not |1⟩, so the shift appears as a phase in a Ramsey sequence driven by a Raman transition (Ω_R = 2π × 1.26(1) MHz). Crucially, if the control atom is instead excited to the Rydberg state |S⟩, the strong |S⟩–|P⟩ interaction pushes the dressing transition far off resonance, and the phase imprinted on the targets largely disappears. Reading out the remaining population in |0⟩ by spin-selective push-out of |1⟩ therefore reveals whether the control atom was in |g⟩ or |S⟩.

Two design choices make the scheme work. First, the per-atom phase shift depends only on the control atom's state and the local interaction, not on how many targets are present, so missing atoms do not corrupt the signal. Second, keeping the Rydberg admixture β = Ω_P/2Δ small suppresses the residual fourth-order intra-ensemble interaction (∼β⁴Δ), so the targets behave as independent spectators. The collective signal-to-noise ratio then grows as √N.

Why This Matters

Impact on research: Mid-circuit readout of Rydberg states is a long-standing obstacle for neutral-atom quantum processors and simulators, since conventional Rydberg detection destroys the state and removes the atom. This work shows that a single Rydberg excitation can be converted into a collective, non-destructive signal on neighbouring ground-state atoms using only global dressing beams — with a fidelity of 99.81 %, competitive with existing approaches — while sidestepping the dephasing in dense ensembles and the large atom numbers that limit transmission/absorption-based schemes.

Potential applications (as framed by the authors):

• Non-destructive mid-circuit readout of Rydberg states in neutral-atom quantum simulators and processors.
• Efficient interfaces between single qubits and photonic modes, with faster Rydberg detection through increased photon collection from the target ensemble.
• Building blocks for scalable multi-qubit phase gates, including the C_kNOT gate, in dual-qubit architectures using ⁸⁷Rb clock states (|F = 1, m_F = 0⟩ and |F = 2, m_F = 0⟩).
• Cavity-enhanced readout of the collective target ensemble, and control of the quantum-optical response of sub-wavelength target arrays.

Industry relevance: The work targets the measurement bottleneck of neutral-atom quantum computing hardware, where atom loss and readout fidelity directly limit error-correction overhead. The demonstrated loss tolerance to atom-number fluctuations is relevant to any architecture that must tolerate imperfect tweezer loading.

Future Directions

• Verify entanglement. Directly measuring correlations and coherence between control and target spins would confirm preparation of the GHZ-like state; the authors suggest selecting different hyperfine m_F levels, using non-destructive spin-resolved detection, or applying a final π-rotation on the control before the global push-out.
• Scale up the target ensemble. Because the per-atom performance is number-insensitive, larger ensembles should yield a corresponding √N improvement in distinguishing the two histograms.
• Remove addressing crosstalk. The single-species implementation is limited by the shared spin basis of control and target; encoding targets in the ⁸⁷Rb clock states would enable a dual-qubit architecture with independent control.
• Integrate with cavities and quantum optics. Coupling the collective ensemble to an optical cavity, or exploiting sub-wavelength array geometry, is proposed as a route to faster and more efficient readout.

Target Audience

Experimentalists and theorists working on neutral-atom quantum computing, quantum simulation, and Rydberg physics; atomic-physics groups building mid-circuit measurement and feedback capabilities; and quantum-optics researchers interested in collective spin–light interfaces and single-excitation amplification. Readers without a background in AMO physics will find the qualitative idea accessible, but the quantitative results require familiarity with Rydberg dressing and Ramsey interferometry.

Authors’ abstract

The amplification of quantum information carried by a single quantum excitation is a recurring challenge across diverse quantum platforms. The coupling between a single qubit and a mesoscopic ensemble of spins, for example, can be leveraged to realize non-destructive detection of the qubit state. However, realizing robust couplings between such systems is experimentally challenging and typically requires programmable quantum gates or native long-range interactions. Here, we introduce a platform that couples a single qubit, encoded in the ground-to-Rydberg transition of a control atom, to a Rydberg-dressed target ensemble of ground-state atoms trapped in an optical lattice. We show that the state of the control qubit can be coherently mapped onto the ensemble via a qubit-controlled collective phase shift. By Rydberg-dressing the ensemble, the controlled phase shift per target atom becomes independent of the number of target atoms, making the protocol intrinsically insensitive to atom-number fluctuations and atom loss, which are the dominant experimental imperfections in our system. Exploiting the collective response of up to eight target spins, we demonstrate the efficacy of the scheme by realizing non-destructive detection of a single Rydberg excitation with a state-assignment fidelity of $\mathcal{F} = 99.81^{+0.17}_{-1.47}\,\%$. Our approach demonstrates the key ingredients for high-fidelity transfer of quantum information from a single qubit to a mesoscopic ensemble, opening a route to non-destructive mid-circuit readout of Rydberg states and to efficient interfaces between single qubits and photonic modes.