Engineering a multi-level bath for transmons with three-wave mixing and parametric drives

Abstract

A quantum system with a tunable bath temperature provides an additional degree of freedom for quantum simulators. Such a system can be realized by parametrically modulating the coupling between the system and the bath. Here, by coupling a transmon qubit to a lossy Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) mode, we experimentally create a tunable bath for the qubit mode. The effective temperature of this bath can be precisely controlled, ranging from negative to positive values. We show that the qubit can be thermalized to equilibrium with different population distributions under different parametric pumping conditions. We further extend our method to the third level of the transmon, demonstrating its potential utility beyond the two-level case. Our results provide a useful tool that can be readily integrated with quantum simulators that would benefit from a nontrivial photon population distribution.

Figures (10)

• Figure 1: Experiment concept and schematic. (a) Experiment setup. The qubit and SNAIL are fabricated on the same sapphire chip, which is housed in a two-part enclosure comprising the aluminum cavity and a copper tunnel (see Fig. \ref{['fig:devicephoto']} for a photograph of the device). By applying external pump signals, different parametric interactions with rates $g_{\delta}$ and $g_{\Sigma}$ can be established between the qubit and SNAIL (see text for details). (b), (c) Level diagram of the system. (b) Heating process with the $\Sigma$ drive. The system starts in its joint ground state and is brought to $\ket{1, e}$ with the $\Sigma$ pump. It will quickly falls into the $\ket{0, e}$ state due to the lossy nature of the SNAIL, which results in an effective "heating" process with rate $\Gamma_{ge}^p$. (c) Cooling process with the $\delta$ drive. The qubit is prepared in $\ket{e}$ and the $\delta_{s, ge}$ drive converts the excitation to the SNAIL, which quickly decays. This process creates an effective parametric cooling rate $\Gamma_{eg}^p$ to empty the qubit. (d) Tuning the artificial temperature with parametric processes. Positive temperature (top left) is achieved by setting $\Gamma_{eg} > \Gamma_{ge}$ while negative temperature (top right) is achieved with $\Gamma_{eg} < \Gamma_{ge}$. When the two rates are balanced, the system thermalizes to an infinite artificial temperature (bottom left). 'Non-thermal' states where the transmon relaxes away from $\ket{e}$ without preference between $\ket{g}$ and $\ket{f}$ (bottom right).
• Figure 2: Result of heating and cooling processes. (a) Pulse sequence of the experiment: The qubit is initialized in the ground/excited state for the "heating"/"cooling" experiment, respectively. Next, we apply the corresponding pumps with varying amplitude and duration. The qubit is measured at the end of the pump. (b) Qubit state populations (blue $\ket{g}$, green $\ket{e}$ and red $\ket{f^+}$) as a function of pump duration in the heating process with increasing pump strength $g_{\Sigma_{s, ge}}$, from left to right. (c) Qubit state populations as a function of pump duration in the cooling process with increasing pump strength $g_{\delta_{s, ge}}$. All experiment data are fitted to a semi-classical model (solid line, see Appendix \ref{['parametricbathengineering']}) to extract the effective state transition rates.
• Figure 3: Heating and cooling balance. (a) Schematic of the process. Both $\Sigma_{s, ge}$ and $\delta_{s, ge}$ pumps are applied to the system simultaneously to reach a $50\% \ket{g}$ - $50\% \ket{e}$ mixed state by balancing both state transition rates. (b) Pulse sequence of the experiment: The qubit is initialized in the ground state, followed by the $\Sigma_{s, ge}$ and $\delta_{s, ge}$ pumps with varying durations. The qubit is measured at the end of the pumps. (c) Qubit state populations as a function of time for two different pump settings. Under different pump conditions, the qubit thermalizes to the same nearly-equal thermal mixture of $\ket{g}$ and $\ket{e}$ states with different rates.
• Figure 4: Bath engineering for a three-level qubit. (a) Schematic of the process. Both $\delta_{s, ge}$ and $\Sigma_{s, ef}$ pumps are simultaneously applied with matched rates away from $\ket{e}$ to achieve a mixed state with $50\% \ket{g}$ - $50\% \ket{f^+}$. (b) Pulse sequence of the experiment: The qubit is initialized in the ground state, followed by the $\Sigma_{s, ef}$ and $\delta_{s, ge}$ pumps with varying durations. The qubit is measured at the end of the pumps. (c) Qubit state populations as a function of time under both pumps with the qubit initially prepared in $\ket{g}$. The $\ket{e}$ population is non-zero due to qubit decay from $\ket{f^+}$ and thermal excitations from $\ket{g}$.
• Figure 5: Transmon natural decay measurement. The transmon is prepared in different initial states ($\ket{g}$, $\ket{e}$, and $\ket{f}$, shown from left to right) and allowed to thermalize to its natural steady state with no external pumps applied. The state populations are shown as a function of time, and the qubit's natural decay and heating rate can be obtained by fitting it to a semi-classical three-level model.