Realization of a Quantum Topological Photon Pump

AI summary

Overview

Research area: Superconducting circuit quantum electrodynamics (circuit QED), specifically topological band theory applied to driven qubit–cavity systems (Floquet engineering / quantum topological pumping).

Technical level: Advanced. The paper relies on Floquet quasi-energy spectra, spectral flow, winding numbers and Chern numbers; the summary below translates these into plain language.

Scope: This paper reports the first direct experimental realization of a topological photon pump, in which a transmon qubit coupled to a microwave cavity transfers photons into the cavity at a quantized rate of one photon per drive cycle, starting from vacuum, reaching approximately 7 photons and producing sub-Poissonian states for the first few cycles.

What This Paper Is About

Topological pumps move charge or energy at a rate fixed by the topology of the system's band structure rather than by the precise details of the control fields, so they should keep working even when the controls are imperfect. Photon versions of such pumps had been proposed as a way to reliably build up non-classical states of a microwave cavity, but had never been directly observed. The authors build one using a superconducting qubit coupled to a microwave cavity and demonstrate that photons are pumped in at the quantized rate of one photon per cycle.

Key Contributions

1. First experimental observation of a topological photon pump. The pump is operated in the quantum regime, initialized from the cavity vacuum, and pumps the cavity up to a mean photon number of approximately 7.
2. Experimental mapping of the pump phase diagram. The authors derive analytic boundaries for where pumping occurs, including the conditions B > B_min(Δ) = (Δ² − g²)/Δ and Δ < Δ_max(B) = (B + √(B² + 4g²))/2, and identify sharp resonances at Δ_ℓ = (B + √(B² + 4g²ℓ))/(2ℓ) for ℓ = 1, 2, 3, … where the maximum pumped photon number n_max drops to zero. Predictions and measurements agree, including the locations of sharp dips in the final photon number.
3. Demonstration of a quantized and robust pump rate. The measured pump rate P matches the ideal quantized rate P_q = 1/T across a range of drive amplitudes B and detunings Δ = 80, 90 and 101 MHz, and vanishes in the trivial regime.
4. Generation of non-classical cavity states from vacuum. Photon-number-resolved spectroscopy shows the pumped states have strong overlap with the 1-, 2- and 3-photon Fock states, with measurably sub-Poissonian statistics up to ⟨n⟩ = 3 — unlike a conventional displacement operation, which would produce Poissonian coherent states.

Main Findings

• Quantized pumping from vacuum: Starting from |0, g⟩, the pump adds one photon per drive cycle, with a mean photon number reaching approximately 7 at B = 120 MHz, Δ = 7.7g = 101 MHz and ω = 5 MHz.
• Two loss-limited operating regimes: In one configuration (Δ = 3.8g = 50 MHz) the maximum photon number is capped by the theoretical bound n_max; in the other (Δ = 7.7g = 101 MHz) it is capped by cavity decay κ, saturating at a value well below n_max = 14.
• Phase diagram with resonance structure: The analytic phase diagram (computed for g = 13 MHz, neglecting cavity loss) predicts maximum photon numbers as large as n_max ≈ 20 at large B and Δ, interrupted by resonances where n_max = 0. The largest predicted n_max values fall in the range Δ₂ < Δ < Δ₁.
• Large-detuning operation is the good regime: The pump works best for large cavity detuning, which the authors emphasize is physically distinct from the small-detuning pump discussed in previous proposals. At small detuning (measured at Δ = 0.5g = 6 MHz), qubit back-action causes large cycle-to-cycle variations in photon number that disrupt pumping, and the data show exactly this predicted behavior.
• Robust quantization: Measured P ≈ 0 in the trivial regime B < B_min(Δ), non-quantized behavior when B − B_min ≲ ω = 5 MHz (where instantaneous gaps vanish), and P/P_q ≈ 1 deep in the topological regime, i.e. for B > B_min(Δ) + 10 MHz, independent of B and Δ.
• Agreement with loss-inclusive simulation: Over 11 cycles at B = 120 MHz, the measured final photon number versus detuning agrees well with a numerical simulation including cavity decay; the curves deviate only for Δ ≲ g.
• Sub-Poissonian states: Strong overlap with 1-, 2- and 3-photon Fock states is observed, with appreciable sub-Poissonian character up to ⟨n⟩ = 3. Cavity decay limits fidelity in the present device, and nonlinearities in the photon-number-resolved qubit spectrum limit the highest detectable Fock state.
• Bidirectional operation: Supplemental data at B = 120 MHz, Δ = 20 MHz and ω = 5 MHz show that reversing the drive direction reverses the photon current — pumping for three cycles to n ≈ 3, then depumping back toward |0, g⟩ over three further cycles — a zig-zag pumping–depumping–pumping sequence.
• Restricted robustness class: Spectral winding relies on exact level crossings protected by polariton-number conservation along the vertical stroke of the protocol, so the pump tolerates arbitrary deformations of the semicircular segment but not transverse fields applied during the vertical stroke. The rotating-frame implementation suppresses ambient transverse-field noise.

Methodology in Plain English

The hardware is a tunable-frequency transmon qubit coupled to a coplanar waveguide cavity, with cavity frequency ω_c = 2π × 5.04 GHz, coupling g = 2π × 13 MHz, cavity decay time 2 μs = 1/κ = 1/(2π × 84 kHz), and effective fields up to B = 2π × 125 MHz.

The pump Hamiltonian combines a cavity detuning term, a qubit–cavity exchange term, and a time-dependent effective magnetic field acting on the qubit. That field traces a semicircular arc in the (B_x, B_z) plane for the first half of each period and then moves vertically for the second half. In the first half, the qubit state flips while the photon number stays put; in the second half, the excitation is handed to the cavity and the qubit returns to its ground state. The net effect, if the system follows the instantaneous eigenstates closely enough, is exactly one photon added per period. This requires the hierarchy κ ≪ ω < g ≪ Δ, B.

Experimentally, the effective field is synthesized by amplitude-modulating a Rabi drive together with flux modulation of the qubit frequency, following earlier proposals. Photon number is not measured directly: it is inferred from qubit spectroscopy of the cavity-photon-induced AC Stark shift after the m-th cycle, χ(mT) = n(mT)·χ₁, where χ₁ is the one-photon shift. After the desired number of cycles the control fields are switched off adiabatically and the qubit is moved to a reference detuning 140 MHz below the cavity for the readout pulse. For Fock-state resolution, a closer reference detuning of 40 MHz is used to enhance the photon-number-dependent splitting. The pump rate is extracted by fitting the observed n(mT) over the first 5 cycles to n(mT) ≈ (P/κ)(1 − e^(−κmT)).

The theoretical side pairs an analytic treatment of the driven system — including a semiclassical model and Floquet quasi-energies — with numerical simulation including cavity loss, and the two are compared against measured phase diagrams and pump rates.

Why This Matters

Impact on research: This is the first direct observation of a topological photon pump, closing a gap between theory and experiment that followed several theoretical proposals and a few proof-of-principle efforts. It also shows that the useful operating regime is the large-detuning one, not the small-detuning regime previously emphasized, and it connects the pumping to a Chern-number description of the driven qubit states.

Real-world applications (as framed by the authors):

• Robust generation of non-classical cavity states such as high-photon-number Fock states and Schrödinger cat states, useful as sensitive sensors and for encoding quantum information.
• Heisenberg-limited quantum sensing and bosonic error-correcting codes, using superpositions of pumping and depumping qubit states to create superpositions of Fock states with very different photon numbers.
• On-demand cavity reset: running the pump in reverse could rapidly reset high-Q bosonic modes to vacuum regardless of their initial state.
• Adapting the protocol to optical cavities coupled to atomic or Rydberg ensembles to generate on-demand large-N photonic Fock states of optical photons, a long-standing goal in cavity QED.

Industry relevance: Quantized, control-insensitive state preparation is directly relevant to superconducting quantum computing hardware, where robust Fock-state and cat-state sources and fast cavity reset are practical needs, and where tolerance to control imperfections matters for scaling.

Future Directions

• Reduce cavity loss. The authors note that superconducting microwave cavities with photon lifetimes exceeding a millisecond have already been demonstrated in planar and 3D geometries, so the present fidelity limits are not fundamental and substantially larger Fock states should be accessible.
• Suppress non-adiabatic processes. They propose adding a lossy mode that selectively removes population from the depumping photon ladder, enabling faster and higher-fidelity pumping.
• Reach larger and better Fock states, and cat states. Combining improved loss and reduced non-adiabaticity with qubit superposition protocols could produce higher-quality Fock states and cat states.
• Extend beyond microwaves. Adapting the protocol to optical cavities coupled to atomic or Rydberg ensembles could yield on-demand large-N optical Fock states, and reversed pumping could serve as a general reset for high-Q bosonic modes.

Target Audience

This paper is best suited to researchers and graduate students in superconducting circuit QED, Floquet/topological band engineering, and quantum control of bosonic modes, as well as to quantum-computing hardware groups interested in robust state preparation and cavity reset. Readers without background in topology or driven quantum systems will find the experimental narrative accessible but should expect the theoretical framing to require prior familiarity.

Authors’ abstract

Topological pumps transfer charge or energy at quantized rates determined solely by band topology, independent of the details of the control fields. Photon pumps operating on this principle could enable the robust preparation of non-classical states in a quantum cavity, even in the presence of control imperfections, but have not been directly observed. We present the first experimental observation of a topological photon pump, using a transmon qubit coupled to a microwave cavity. The pump operates in the quantum regime, pumping up from the vacuum state up to $\approx 7$ photons, and produces demonstrably non-classical cavity states for the first few cycles.