Temporal magnon-qubit Mach-Zehnder interferometer

Abstract

A temporal magnon-qubit Mach-Zehnder (MZ) interferometer is proposed. The interferometer is based on controllable entanglement of a microwave qubit and a magnonic state, achieved by application of a pulsed magnetic field playing the role of a magnon-qubit temporal "beam splitter". Analogous to a typical MZ interferometer, the generated interference pattern of the final qubit population carries information about the magnon dynamics. One important application of the proposed scheme is the study of single magnon decoherence. Interestingly, this scheme allows one to independently determine rates of two possible decoherence channels. This may help enable single magnon state applications and answer fundamental questions of quasi-particle decoherence at single quantum levels.

Figures (4)

• Figure 1: Temporal magnon-qubit MZI measurement scheme and protocol. (a) Schematic diagram of a hybrid quantum system consisting of coupled magnon mode ($m$) and qubit ($q$). (b) Dynamic control of the magnon frequency $\omega_\mathrm{m}(t)$ by pulsed magnetic field $B(t)$. (c) Temporal MZI: two magnetic pulses $\mathrm{TBS}_1$ and $\mathrm{TBS}_2$ (shaded areas) serve as temporal “beam splitters” that couple magnon and qubit modes. In between the pulses, the two subsystems evolve independently. The interference result is measured as the final qubit state.
• Figure 2: Operation of the magnon–qubit temporal beam splitter (TBS). Rows correspond to different detunings: (a, b, c) $|\Delta\omega| = 0$, (d, e, f) $|\Delta\omega| = g$, (g, h, i) $|\Delta\omega| = g$ (with finite rise/fall time of 2.5 ns). Columns correspond to different operating regimes: (a, d, g) coherent magnon–qubit dynamics during the coupling pulse, (b, e, h) "entangling" operation for a balanced TBS pulse, (c, f, i) corresponding "unentangling" operation. Balanced TBS pulse durations: (b, c) $\tau \approx 6.25$ ns, (e, f) $\tau \approx 6.49$ ns, (h, i) $\tau \approx 6.58$ ns. Magnon-qubit coupling rate $g = 2\pi \times 20 \mathrm{MHz}$.
• Figure 3: Influence of the residual off-resonance coupling on temporal magnon-qubit MZI measurement scheme. (a) Cartoon diagram of magnon-qubit frequency gap $\Delta\omega(t)$ during MZI operation. (b) Numerical simulation of the magnon (green) and qubit (blue) populations during MZI operation. Fast small-amplitude oscillations during “free” evolution are due to the residual coupling. (c) Interference pattern for fixed-frequency-gap mode (fixed $\Omega$ and varying $T$). (d) Interference pattern for fixed-evolution-time mode (fixed $T$ and varying $\Omega$). (e) Dependence of the periodicity of the interference pattern on the frequency gap $\Omega$; gray highlight indicates periodicity $\geq$90%. (f) Dependence of the visibility on the frequency gap $\Omega$; gray highlight indicates visibility $\geq$90%, dashed and solid red lines denote TBS pulse detunings of $g$ and $2g$, respectively. Simulation parameters: $g = 2\pi \times 20$ MHz, $|\Delta\omega| = 2\pi \times 20$ MHz, $\tau \approx 6.49$ ns, (b) $\Omega = 2\pi \times 400$ MHz, $T \approx 79.3$ ns, (c) $\Omega = 2\pi \times 40$ MHz, (d) $T \approx 39.8$ ns.
• Figure 4: Interference patterns for measurement of single magnon decoherence. (a–c) Fixed-frequency-gap interference pattern, (d) fixed-evolution-time interference pattern. (a) Amplitude noise, (b) phase noise, (c, d) mixture of amplitude and phase noise. Dashed black and gray lines in (a–d) indicate the envelope (i.e., the maxima $P_\mathrm{max}$ and minima $P_\mathrm{min}$) and average $P_\mathrm{avg}$ of the final qubit population (solid blue lines), respectively. Simulation parameters: (a–d) $g = 2\pi \times 20$ MHz, $\Delta\omega = 0$, $\tau \approx 6.25$ ns, (a–c) $\Omega = 2\pi \times 100$ MHz, (d) $T \approx 9.95$ ns, (a, c, d) $\Gamma_\mathrm{amplitude} \approx 37.7~\mu\mathrm{s}^{-1}$, (b–d) $\Gamma_\mathrm{phase} \approx 50.3~\mu\mathrm{s}^{-1}$.