Slowing and Storing Microwaves in a Single Superconducting Fluxonium Artificial Atom

Abstract

Three-level Lambda systems provide a versatile platform for quantum optical phenomena such as Electromagnetically Induced Transparency (EIT), slow light, and quantum memory. Such Lambda systems have been realized in several quantum hardware platforms including atomic systems, superconducting artificial atoms, and meta-structures. Previous experiments involving superconducting artificial atoms incorporated coupling to additional degrees of freedom, such as resonators or other superconducting atoms. In this work, we performed an EIT experiment in microwave frequency range utilizing a single Fluxonium qubit within a microwave waveguide. The Lambda system is consisted of two plasmon transitions in combination with one metastable state originating from the fluxon transition. In this configuration, the controlling and probing transitions are strongly coupled to the transmission line, safeguarding the transition between 0 and 1 states, and ensuring the Fluxonium qubit is close to the sweet spot. Our observations include the manifestation of EIT, a slowdown of light with a delay time of 217 ns, and photon storage. These results highlight the potential as a phase shifter or quantum memory for quantum communication in superconducting circuits.

Figures (4)

• Figure 1: Light matter interaction of the Fluxonium qubit implemented in a effective one-dimensional waveguide. (a) Experimental arrangement showing the fluxonium qubit inside the copper three-dimensional (3D) waveguide. The 3D waveguide has the cut-off frequency at $6.5 \,\,\rm{GHz}$, shown in (c). We send in the input field, $V_{\rm{in}}$, and control field, $V_{\rm{c}}$, through one of the port, and measure the $V_{\rm{out}}$. (b) Schematic diagram of a single Fluxonium qubit interacting with the electromagnetic field. The microwave field is confined as $TE_{10}$ mode of the waveguide and the electric field is polarized in one direction. (c) Transition frequencies and corresponding $\langle i|\varphi_{ij}|j\rangle$ of the Cooper pair number operator $-i\partial_{\phi}$ (stars), and we bias at $\phi_{ext}/\phi_0$=0.53. The solid blue curve shows microwave transmission measured with a two-port configuration at room temperature. (d) The schematic diagram of the lowest three energy levels of the fluxonium qubit. The three-level system is driven by a control field (purple) and a weak probe field (red), where the $\Omega_{p} \ll \Gamma_{02}/2 + \gamma_{22}$. The probe field with frequency $\omega_{\rm{p}}$ has a detuning $\Delta_{\rm{p}}$ with the transition between $|0\rangle$and $|2\rangle$ and the control field with frequency $\omega_{\rm{c}}$ has a detuning $\Delta_{\rm{c}}$ with the transition between $|1\rangle$ and $|2\rangle$. The corresponding driving strengths are $\Omega_{\rm{p}}$ and $\Omega_{\rm{c}}$.(e) Optical microscope images of the measured device. The bowtie antenna connects to the weak junction and junction arrays of the fluxonium. The holes of the antenna are dug to avoid the formation of mobile vortex causing the frequency fluctuation of the qubit. The red and blue arrows indicate the polarization direction of the electric and magnetic field respectively. The SEM images show the details of the weak junction and the part of the junction array as a superinductance.
• Figure 2: Spectroscopy of EIT. (a) Transmission coefficient $|t|$ as a function of power of control tone field $P_{\mathrm{c}}$ and $\Delta_{\mathrm{p}}$ for both experimental data and fitting results obtained using Eq. \ref{['mseq']}. (b) Linecuts of the experimental data and corresponding fits from (a), the correspoding power is indicated by the arrows in (a), illustrating the crossover from EIT to ATS for different control field strengths: $P_{\mathrm{c}}=-142\,\mathrm{dBm}$ (blue),$-157\,\,\mathrm{dBm}$ (red), and$-172\,\,\mathrm{dBm}$ (green). (c) Effective $\Omega_{\mathrm{c}}$ as a function of control voltage, extracted by fitting the measured transmission coefficient $|t|$. The linear fit demonstrates $\Omega_{\mathrm{c}}\propto\sqrt{P_{\mathrm{c}}}$. The black dashed line represents the threshold for $\Omega_{\mathrm{EIT}}$.
• Figure 3: Demonstration of slow and fast light. (a) Linecuts of $\mathrm{Arg(t)}$ as a function of $\Delta_{\mathrm{p}}$ from Fig. \ref{['EIT']} (b) and (c) Delay time $\tau_{\mathrm{d}}$ as a function of $\Omega_{\mathrm{c}}$ and $\Delta_{\mathrm{p}}$, respectively. The experimentally extracted delay time $\tau_{\mathrm{d}}$ from pulsed measurements (red triangles), using the reference pulse for comparison, and spectroscopic measurements based on Eq. \ref{['delay']}, are shown for d $\Delta_{\mathrm{p}}/2\pi\approx 0~\mathrm{MHz}$ and (d) $\Omega_{\mathrm{c}}/2\pi=2.6~\mathrm{MHz}$. Experimental data (blue circles) and theoretical results (blue dashed curve) are compared. The red and green arrows indicate slow light and absorption cases, respectively, while the purple arrow indicates the fast light case in (d). (d) Envelopes of the probe Gaussian pulse measured under two different $\Omega_{\mathrm{c}}$ and $\Delta_{\mathrm{p}}$. The slow light (red) and fast light (purple) cases are shown, in comparison with the reference pulse (orange), measured under far-detuned conditions, and the weak $\omega_{\rm{c}}$ case (green). The black solid lines are fits obtained by solving the master equation [Eq. \ref{['mseq']}]. (b) (a), corresponding to the two different $\Omega_{\mathrm{c}}$ values indicated by the arrows of the same color in Fig. \ref{['EIT']}(a). The solid curves show theoretical simulations.
• Figure 4: EIT-based microwave photon storage and retrieval (a)Storge pulse with the single atom. The reference pulse (blue) and the slow light (red). The dynamical control pulse is shown as grey dashed curve. The green trace shows the stored-and-retrieval after $\tau_{\rm{s}}=0.5\,\, \mu s$. The black solid curve is the fitting result. (b) Storage efficiency $\eta$ as function of $\tau_{\rm{s}}$. The blue dashed line is the fitting of the experimental data.