In this experiment, we couple a superconducting transmon qubit to a high-impedance $645\phantom{\rule{0.28em}{0ex}}\mathrm{\ensuremath{\Omega}}$ microwave resonator. Doing so leads to a large qubit-resonator coupling rate $g$, measured through a large vacuum Rabi splitting of $2g\ensuremath{\simeq}910$ MHz. The coupling is a significant fraction of the qubit and resonator oscillation frequencies $\ensuremath{\omega}$, placing our system close to the ultrastrong coupling regime ($\overline{g}=g/\ensuremath{\omega}=0.071$ on resonance). Combining this setup with a vacuum-gap transmon architecture shows the potential of reaching deep into the ultrastrong coupling $\overline{g}\ensuremath{\sim}0.45$ with transmon qubits.
In this experiment, we couple a superconducting transmon qubit to a high-impedance 645\ensuremathΩ microwave resonator. Doing so leads to a large qubit-resonator coupling rate g, measured through a large vacuum Rabi splitting of 2g\ensuremath≃910 MHz. The coupling is a significant fraction of the qubit and resonator oscillation frequencies \ensuremathω, placing our system close to the ultrastrong coupling regime (g=g/\ensuremathω=0.071 on resonance). Combining this setup with a vacuum-gap transmon architecture shows the potential of reaching deep into the ultrastrong coupling g\ensuremath∼0.45 with transmon qubits.
We study the feasibility of reaching the ultrastrong (USC) and deep-strong coupling (DSC) regimes of light-matter interaction, in particular at resonance condition, with a superconducting charge qubit, also known as Cooper-Pair box (CPB). We show that by shunting the charge qubit with a high-impedance LC-circuit, one can maximally reach both USC and DSC regimes exceeding the classical upper bound ∣g∣≤ωqωr/2 between two harmonic systems with frequencies ωq and ωr. In our case, the fundamental model corresponds to an enhanced quantum Rabi model, which contains a displacement field operator that breaks its internal parity symmetry. Furthermore, we consider a multipartite device consisting of two CPBs ultrastrongly coupled to an oscillator as a mediator and study a quantum state transfer protocol between a pair of transmon qubits, all of them subjected to local incoherent noise channels with realistic parameters. This work opens the door for studying light-matter interactions beyond the quantum Rabi model at extreme coupling strengths, providing a new building block for applications within quantum computation and quantum information processing.
The interaction of light and matter is often described by the exchange of single excitations. When the coupling strength is a significant fraction of the system frequencies, the number of excitations are no longer preserved and that simple picture breaks down. This regime is known as the ultrastrong coupling regime and is characterized by non-trivial light–matter eigenstates and by complex dynamics. In this work, we propose to use an array Josephson junctions to increase the impedance of the light mode enabling ultrastrong coupling to a transmon qubit. We show that the resulting dynamics can be generated and probed by taking advantage of the multi-mode structure of the junction array. This proposal relies on the frequency tunability of the transmon and, crucially, on the use of a low frequency mode of the array, which allows for non-adiabatic changes of the ground state.
In the circuit quantum electrodynamics architecture, both the resonance frequency and the coupling of superconducting qubits to microwave field modes can be controlled via external electric and magnetic fields to explore qubit-photon dynamics in a wide parameter range. Here, we experimentally demonstrate and analyze a scheme for tuning the coupling between a transmon qubit and a microwave resonator using a single coherent drive tone. We treat the transmon as a three-level system, with the qubit subspace defined by the ground and the second excited states. If the drive frequency matches the difference between the resonator and the qubit frequencies, a Jaynes-Cummings-type interaction is induced, which is tunable in both amplitude and phase. We show that coupling strengths of about 10 MHz can be achieved in our setup, limited only by the anharmonicity of the transmon qubit. This scheme has been successfully used to generate microwave photons with a controlled temporal shape [M. Pechal et al., Phys. Rev. X 4, 041010 (2014)] and can be directly implemented with superconducting quantum devices featuring larger anharmonicity for higher coupling strengths.
We study a circuit QED setup where multiple superconducting qubits are ultrastrongly coupled to a single radio-frequency resonator. In this extreme parameter regime of cavity QED the dynamics of the electromagnetic mode is very slow compared to all other relevant timescales and can be described as an effective particle moving in an adiabatic energy landscape defined by the qubits. The focus of this paper is placed on settings with two or multiple qubits, where different types of symmetry-breaking transitions in the ground- and excited-state potentials can occur. Specifically, we show how the change in the level structure and the wave-packet dynamics associated with these transition points can be probed via conventional excitation spectra and Ramsey measurements performed at GHz frequencies. More generally, this analysis demonstrates that state-of-the-art circuit QED systems can be used to access a whole range of particlelike quantum-mechanical phenomena beyond the usual paradigm of coupled qubits and oscillators.
I discuss the design, fabrication and measurement at millikelvin-temperatures of Al/AlOx/Al Josephson junction-based transmon qubits coupled to superconducting thin-film lumped element microwave resonators made of aluminum on sapphire. The resonators had a center frequency of around 6GHz, and a total quality factor ranging from 15,000 to 70,000 for the various devices. The area of the transmon junctions was about 150nm×150nm and with Josephson energy EJ such that 10GHz≤EJ/h≤30GHz. The charging energy of the transmons arising mostly from the large interdigital shunt capacitance, was Ec/h≈300MHz. I present microwave spectroscopy of the devices in the strongly dispersive regime of circuit quantum electrodynamics. In this limit the ac Stark shift due to a single photon in the resonator is greater than the linewidth of the qubit transition. When the resonator is driven coherently using a coupler tone, the transmon spectrum reveals individual ``photon number'' peaks, each corresponding to a single additional photon in the resonator. Using a weighted average of the peak heights in the qubit spectrum, I calculated the average number of photons nˉ in the resonator. I also observed a nonlinear variation of nˉ with the applied power of the coupler tone Prf. I studied this nonlinearity using numerical simulations and found good qualitative agreement with data. In the absence of a coherent drive on the resonator, a thermal population of 5.474GHz photons in the resonator, at an effective temperature of 120mK resulted in a weak n=1 thermal photon peak in the qubit spectrum. In the presence of independent coupler and probe tones, the n=1 thermal photon peak revealed an Autler-Townes splitting. The observed effect was explained accurately using the four lowest levels of the dispersively dressed Jaynes-Cummings transmon-resonator system, and numerical simulations of the steady-state master equation for the coupled system. I also present time-domain measurements on transmons coupled to lumped-element resonators. From T1 and Rabi oscillation measurements, I found that my early transmon devices (called design LEv5) had lifetimes (T1∼1μs) limited by strong coupling to the 50Ω transmission line. This coupling was characterized by the the rate of change of the Rabi oscillation frequency with the change in the drive voltage (dfRabi/dV) -- also termed the Rabi coupling to the drive. I studied the design of the transmon-resonator system using circuit analysis and microwave simulations with the aim being to reduce the Rabi coupling to the drive. By increasing the resonance frequency of the resonator ωr/2π from 5.4GHz to 7.2GHz, lowering the coupling of the resonator to the transmission line and thereby increasing the external quality factor Qe from 20,000 to 70,000, and reducing the transmon-resonator coupling g/2π from 70MHz to 40MHz, I reduced the Rabi coupling to the drive by an order of magnitude (∼ factor of 20). The T1∼4μs of devices in the new design (LEv6) was longer than that of the early devices, but still much shorter than the lifetimes predicted from Rabi coupling, suggesting the presence of alternative sources of noise causing qubit relaxation. Microwave simulations and circuit analysis in the presence of a dielectric loss tangent tanδ≃5×10−6 agree reasonably well with the measured T1 values, suggesting that surface dielectric loss may be causing relaxation of transmons in the new designs.
A transmon qubit in the 3-dimensional microwave cavity is a versatile system for various circuit QED experiments. We have performed numerical calculations of the vacuum Rabi coupling g in 3D transmon circuit QED system, and compared the values with the experimental measurements. We used COMSOL Multiphysics RF package with an appropriate model to efficiently calculate the coupling strength. The calculation agrees with the measurement within a few percents in simple cases. Depending on the position of the qubit in the cavity, we calculated the coupling strengths to different eigenmodes. We compared our result for the fundamental mode (TE101) and a higher mode (TE201) with the experiment by changing the qubit position, as shown in Fig. 2. This simulation and characterization enable efficient design methods for future 3D circuit QED experiments. We confirm that we can design and predict the qubit coupling to the cavity modes with enough accuracy in 3D circuit QED system.