Quantum dynamics of microwave photons in synthetic frequency dimension

TL;DR

This work addresses extending synthetic frequency dimensions into the quantum regime by implementing single-photon dynamics in a frequency lattice built from a 16 m superconducting cable coupled to a transmon qubit. The authors employ a tunable SQUID-based modulator to synthesize inter-mode couplings and gauge fields, enabling controllable hopping and effective fluxes with mode frequencies $\omega_m=\omega_0+m\,\Omega_{\mathrm{fsr}}$ and a drive detuning $\Delta$, yielding Bloch oscillations with period $T_B=2\pi/|\Delta|$ and accessible band spectroscopy. They demonstrate single-photon quantum random walks, Bloch oscillations, nonadiabatic unidirectional frequency conversion, and wave-packet dynamics, including a multimode Jaynes-Cummings regime with a Lorentzian width of $\approx31\,\mathrm{MHz}$, and map the band structure via qubit-assisted measurements. The platform provides programmable Hamiltonians and synthetic gauge fields in a scalable superconducting circuit, with clear potential to realize higher-dimensional or topological synthetic lattices by adding more drive tones or coupling multiple cables. Overall, the work establishes a versatile, low-loss quantum platform for synthetic dimensions and quantum simulations at the single-photon level, with implications for quantum information processing and photonic quantum simulations.

Abstract

Synthetic frequency dimension offers a powerful approach to simulate lattice models and control photon dynamics. However, extending this concept into the quantum regime, particularly at the single-photon level, has remained challenging in photonic platforms. Here, we demonstrate quantum-state initialization and detection of single-photon evolutions within a synthetic frequency lattice by integrating a superconducting qubit with a 16-meter aluminum coaxial cable. A tunable superconducting quantum interference device (SQUID)-based modulator is employed to synthesize lattice couplings and artificial gauge fields. We observe single-photon quantum random walks and Bloch oscillations, as well as nonadiabatic, unidirectional frequency conversion under rapid temporal modulation of the lattice Hamiltonian, together with band-structure measurements. The lattice connectivity can be readily reconfigured to construct higher-dimensional lattices using multiple drive tones. Our results establish superconducting quantum circuits as a versatile platform for programmable Hamiltonians and extensible synthetic lattices with flexible single-photon control.

Figures (4)

• Figure 1: Experimental setup. (a) Schematic of the setup. A flux-tunable qubit (blue) is connected to a 16-meter low-loss superconducting cable via a gmon tunable coupler (green). The opposite end of the cable is connected to a modulator (red) before terminated to ground. (b) Optical micrograph of the modulator. The cable extends to the chip and is connected via direct wirebonds. Zoom in reveals the detailed structure the modulator SQUID. The open-end port on the right is short compared to the mode wavelengths and can be neglected. (c) Exciteted state population of qubit in the single-photon vacuum-Rabi oscillations with the cable modes. The JC coupling $\kappa/2\pi=0.36$ MHz is kept weak for individually addressing the modes. The black dashed line indicates the full swap time.
• Figure 2: Dynamics of single-site excitations in the frequency dimension. (a),(b) Schematic of the pulse sequence, showing the steps for initial state preparation, modulation application, residual photon resetting, and final state measurement. (c),(d) Time evolution for the on-resonance modulation case with drive frequencies of $\Omega/2\pi = 7.33$ MHz and $14.66$ MHz, respectively. (e),(f) Time evolution for the off-resonance modulation case with drive frequencies of $\Omega/2\pi = 7.13$ MHz and $14.46$ MHz, respectively. (g),(h) Energy band structures for a 1D tight-binding model with nearest- and next-nearest-neighbor coupling at $\phi=\pi$.
• Figure 3: Wave-packet excitation propagation. (a) Initial distribution of the photon wave packet, achieved by tuning the gmon coupler to a strong-coupling regime. The red dotted line represents the fitted Lorentzian envelope. (b) Schematic of the pulse sequence. (c),(d) Evolution of the wave packet under single-tone driving with $\Omega/2\pi = 7.13$ MHz and $7.53$ MHz, corresponding to detunings $\Delta/2\pi=-0.2$ MHz and $\Delta/2\pi=0.2$ MHz. (e),(f) Schematic of modulation with a periodically changing frequency and the corresponding pulse sequence. (g),(h) Evolution of the wave packet under periodic detuning reversal, starting at $\Omega/2\pi = 7.13$ MHz and $7.53$ MHz, where the sign of $\Delta$ is reversed every half-cycle (2.5 $\mathrm{\mu s}$).
• Figure 4: Single-photon dynamics with a synthetic gauge field. (a) The equivalent lattice is a triangular chain, with each plaquette characterized by a phase $\Phi$. (b),(c) Energy bands for double driving with phases $\phi_1 = \pi$, $\phi_2 = \pi$ and $0.5\pi$. (d),(e) Time evolution of a single-site excitation under simultaneous driving at $7.13$ MHz and $14.26$ MHz, with phases $\phi_1 = \pi$, $\phi_2 = \pi$ and $0.5\pi$. (f),(g) Time evolution of a wave-packet state under the same driving conditions as (d) and (e).