Temporal-Mode Engineering for Multiplexed Microwave Photons and Mode-Selective Quantum State Transfer

Abstract

Quantum communication between distant superconducting qubits on separate chips using itinerant microwave photons has been studied to realize distributed quantum information processing. To enhance information capacity and fault tolerance in quantum networks, it is beneficial to encode a large quantity of quantum information using auxiliary degrees of freedom of these photons. In this work, we experimentally investigate the use of temporal modes of photon wave packets. Through the photon-shaping technique with a fixed-frequency transmon qubit, we generate single microwave photons in four orthogonal temporal modes propagating along a waveguide. We demonstrate mode-selective absorption across orthogonal modes via the time-reversed process of emission, achieving absorption efficiencies exceeding 0.89 for mode-matched cases, while remaining below 0.13 for orthogonal modes. Photons rejected by a given receiver mode can remain mutually orthogonal, enabling selective absorption at subsequent receivers in future multi-node architectures. These results highlight the feasibility of temporal-mode engineering for constructing a higher-dimensional orthogonal basis for multiplexed quantum networks.

Figures (11)

• Figure 1: Basic concepts of temporal-mode multiplexing and selective absorption of microwave photons using a superconducting qubit. (a) Temporal-mode engineering via a resonator-assisted Raman process. The photon mode $m$ with the waveform $\xi_m(t)$, is engineered through the effective decay rate $\Gamma_m(t)$, controlled by the sender's drive $\zeta^\text{S}_m(t)$. (b) Mode-matched photon absorption. A photon in mode $0$ with the waveform $\xi_0(t)e^{-i\omega_\text{ph}t}$, generated by the sender under the drive $\zeta^\text{S}_0(t)$, is perfectly absorbed by the receiver with the drive $\zeta^{\text{R}}_0(-t+\Delta t)$. (c) Orthogonal-mode photon rejection. A photon in mode $1$ with the mode function $\xi_1(t)e^{-i\omega_\text{ph}t}$ generated by the sender under the drive $\zeta^\text{S}_1(t)$, is perfectly rejected by the receiver with the drive $\zeta^{\text{R}}_0(-t+\Delta t)$.
• Figure 2: Photon generation in orthogonal temporal modes $m=0,\,\ldots,\,3$. (a) Measured demodulated photon modes in the time domain. Light blue solid lines show the averaged photon waveforms emitted from the sender. Dark blue lines show the real (solid) and imaginary (dashed) parts of the modes $\xi_m^\text{S}(t)$. Coral solid lines represent the real parts of the target modes. (b) Measured demodulated photon modes in the frequency domain. Dark blue lines show the real (solid) and imaginary (dashed) parts of the Fourier amplitude of the modes $\xi_m^\text{S}(\omega)$. Coral solid lines indicate the target spectra: the real part for even modes ($m=0$ and 2) and the imaginary part for odd modes ($m=1$ and 3). (c) Squared-overlap matrix $\{|I_{mm'}|^2\}$ obtained from the experimentally generated waveforms.
• Figure 3: Mode-selective absorption. (a) Pulse sequence for the absorption process. The initial sender state $\ket{\psi}_\pm^\text{S}=(\ket{g}\pm\ket{e})/\sqrt{2}$ is prepared by a $\pm(\pi/2)_\text{ge}$ pulse. Then, a $\pi_\text{ef}$ pulse followed by the sender's drive $\zeta^\text{S}(t)$ induces the $|f,0\rangle$--$|g,1\rangle$ transition. After a time delay $\tau$, a time-reversed receiver's drive $\zeta^{\text{R}}(-t+\Delta t)$ and a $\pi_\text{ef}$ pulse are applied to the receiver. (b) Mode-matched photon absorption as a function of the delay $\tau$. (c) Mode-selective absorption. In (b) and (c), dots shows the absorption efficiency $R_{mn}$ as a function of the delay $\tau$ of the drive pulse. Dashed lines show the squared-overlap of the emitted and absorbed photon modes, $|I'_{mn}|^2$. (d) Summary of the mode-selective absorption efficiencies $R_{mn}$ with the optimal delay time $\tau^\mathrm{opt}$ [vertical dashed lines in (b) and (c)].
• Figure 4: Rejected photons during mode-selective absorption when the receiver mode does not match the incoming photon mode ($m\neq n$). (a) Rejected photon waveforms for $(m,n)=(3,0)$. (b--d) Rejected photon waveform for receiver drive fixed at $n=3$ and incoming photon modes $m=0,\,1,$ and 2. In (a--d), the amplitude of the rejected photon waveforms $\xi_{mn}^\mathrm{S,res}(t)$ is shown by solid lines, with corresponding simulated results shown by dashed lines. Black dotted lines indicate the incoming photon waveforms $\xi_{m}^\mathrm{S}(t)$. (e) Squared-overlap matrix calculated from the experimentally measured rejected waveforms $\xi_{m3}^\mathrm{S,res}(t)$ for $m=0,\,1,$ and 2.
• Figure 5: Sech-based orthogonal waveform engineering. Here, the pulse-width parameter $\kappa_\text{ph}/2\pi$ is set to $5$ MHz. (a) Analytically constructed orthogonal photon waveforms $\xi_m(t)$ based on the hyperbolic secant function for $m=0, \ldots,7$. (b) Numerically obtained decay rates $\Gamma_m(t)$ corresponding to $m = 0,\ldots,7$. (c) Infidelity of photon waveforms depending on the vertical resolution of the DAC.